Black Hole Masses in Active Galactic Nucleidenney/DenneyFinOSUDiss.pdfbased Mass for the Central Black Hole in NGC 4151”, ApJ, 651, 775, (2006). 5. K. D. Denney, et al. (17 coauthors),

Black Hole Masses in Active Galactic Nuclei

Dissertation

Presented in Partial Fulfillment of the Requirements for the Degree Doctor ofPhilosophy in the Graduate School of The Ohio State University

By

Kelly D. Denney

Graduate Program in Astronomy

The Ohio State University

2010

Dissertation Committee:

Professor Bradley M. Peterson, Advisor

Professor Richard W. Pogge

Professor B. Scott Gaudi

Copyright by

Kelly D. Denney

2010

ABSTRACT

We present the complete results from two, high sampling-rate, multi-month,

spectrophotometric reverberation mapping campaigns undertaken to obtain either

new or improved Hβ reverberation lag measurements for several relatively low-

luminosity active galactic nuclei (AGNs). We have reliably measured the time delay

between variations in the continuum and Hβ emission line in seven local Seyfert 1

galaxies. These measurements are used to calculate the mass of the supermassive

black hole at the center of each of these AGNs. We place our results in context to

the most current calibration of the broad-line region (BLR) RBLR–L relationship,

where our results remove many outliers and significantly reduce the scatter at the

low-luminosity end of this relationship.

A detailed analysis of the data from our high sampling rate, multi-month

reverberation mapping campaign in 2007 reveals that the Hβ emission region

within the BLRs of several nearby AGNs exhibit a variety of kinematic behaviors.

Through a velocity-resolved reverberation analysis of the broad Hβ emission-line

flux variations in our sample, we reconstruct velocity-resolved kinematic signals for

ii

our entire sample and clearly see evidence for outflowing, infalling, and virialized

BLR gas motions in NGC3227, NGC3516, and NGC5548, respectively.

Finally, we explore the nature of systematic errors that can arise in

measurements of black hole masses from single-epoch spectra of AGNs by utilizing

the many epochs available for NGC 5548 and PG1229+204 from reverberation

mapping databases. In particular, we examine systematics due to AGN variability,

contamination due to constant spectral components (i.e., narrow lines and host

galaxy flux), data quality (i.e., signal-to-noise ratio, S/N), and blending of spectral

features. We investigate the effect that each of these systematics has on the

precision and accuracy of single-epoch masses calculated from two commonly-used

line-width measures by comparing these results to recent reverberation mapping

studies. We then present an error budget which summarizes the minimum observable

uncertainties as well as the amount of additional scatter and/or systematic offset

that can be expected from the individual sources of error investigated.

iii

Dedicated to my loving and supportive husband and parents...

iv

ACKNOWLEDGMENTS

I first wish to thank my husband for his continued support throughout the

years. He has followed me around the country and through the highs and lows of my

educational, professional, and personal pursuits, and I could not have come this far

without his love and devotion.

Next, I must acknowledge the unending encouragement and assistance of my

family, particularly my parents and grandparents. They have been a sustained

source of support and inspiration to me throughout these years. They have helped

me in unfathomable ways, including but not limited to climbing mountaintops and

crossing oceans to be there when I needed them the most. I am truly thankful for

being blessed with such a loving, supportive, and dependable family.

I also wish to gratefully acknowledge my advisor, Brad Peterson. It is hard for

me to even describe how invaluable his advice and seemingly limitless support have

been in the past six years. I have likely tested and/or surprised him multiple times

with various endeavors ranging from my insistence to do outreach to my multiple

pregnancies, but he has backed me on whatever I have set my heart and mind to,

while somehow seamlessly keeping me on track professionally. His encouragement of

v

my success in whatever I choose to do means so much to me. He has easily made

the largest contribution to making my time at OSU an exceptional one, and I thank

him from the bottom of my heart.

Furthermore, my friends and office mates throughout the years have significantly

contributed to me keeping my sanity through this extended and sometimes frustrating

process of earning a PhD. They have been there to listen to me vent, give me hugs,

answer just one more question about Fortran or Supermongo, and put things in

perspective with fun and laughter when I needed it the most. I cherish the cheerful

companionship and support that my friends have given me.

Finally, I would like to acknowledge all of my collaborators, particularly my

OSU collaborators, including Rick Pogge. This dissertation is largely based on data

obtained through international collaborations of astronomers, telescopes, and other

observing resources and could not have been completed without the support of this

group of exceptional individuals who provided me with data, advice, help observing

during my extended campaigns, and protection from illegal aliens...

vi

VITA

September 9, 1981 . . . . . . . . . . . . . Born – Wichita, Kansas, USA

2004 . . . . . . . . . . . . . . . . . . . . . . . . . . . B.A. Astronomy and Physics (Summa Cum Laude),Boston University

2004 – 2005 . . . . . . . . . . . . . . . . . . . . Graduate Teaching Associate,The Ohio State University

2005 – 2006 . . . . . . . . . . . . . . . . . . . . National Science Foundation GK-12 Fellow,The Ohio State University

2006 . . . . . . . . . . . . . . . . . . . . . . . . . . . M.S. Astronomy,The Ohio State University

2006 – 2009 . . . . . . . . . . . . . . . . . . . . Graduate Research Associate,The Ohio State University

2009 – 2010 . . . . . . . . . . . . . . . . . . . . . Presidential Fellow,The Ohio State University

PUBLICATIONS

Research Publications

1. L. P. Dyrud, K. D. Denney, S. Close, M. Oppenheim, J. Chau, L. Ray,“Meteor Velocity Determination with Plasma Physics”, Atmospheric Chemistry andPhysics Discussions, Vol. 4, (2004).

2. L. P. Dyrud, L. Ray, M. Oppenheim, S. Close, K. D. Denney, “Modellinghigh-power large-aperture radar meteor trails”, Journal of Atmospheric andSolar-Terrestrial Physics, V67, 1171D, (2005).

vii

3. L. P. Dyrud, K. D. Denney, J. Urbina, D. Janches, E. Kudeki, S. Franke,“THE METEOR FLUX: It Depends How You Look”, Earth, Moon, and Planets,p.1–12, (2005).

4. M. C. Bentz, K. D. Denney, et al. (16 coauthors), “A Reverberation-based Mass for the Central Black Hole in NGC 4151”, ApJ, 651, 775, (2006).

5. K. D. Denney, et al. (17 coauthors), “The Mass of the Black Hole in theSeyfert 1 Galaxy NGC 4593 from Reverberation Mapping”, ApJ, 653, 152, (2006).

6. M. C. Bentz, K. D. Denney, et al. (16 coauthors), “NGC 5548 in a Low-Luminosity State: Implications for the Broad-Line Region”, ApJ, 662, 205, (2007).

7. K. D. Denney, M. C. Bentz, B. M. Peterson, R. W. Pogge, “The Mass ofthe Black Hole in NGC 4593 Using Reverberation Mapping”, The Central Engine ofActive Galactic Nuclei, ASPCS, 373, 23, (2007).

8. M. C. Bentz, K. D. Denney, B. M. Peterson, R. W. Pogge, “Refining theRadius-Luminosity Relationship for Active Galactic Nuclei”, The Central Engine ofActive Galactic Nuclei, ASPCS, 373, 380, (2007).

9. C. J. Grier, et al. (13 coauthors, incl. K. D. Denney), “The Mass of theBlack Hole in the Quasar PG 2130+099”, ApJ, 688, 837, (2008).

10. K. D. Denney, B. M. Peterson, M. Dietrich, M. Vestergaard, M. C.Bentz, “Systematic Errors in Black Hole Masses Determined with Single EpochSpectra”, ApJ, 692, 246, (2009).

11. K. D. Denney, et al. (32 coauthors), “A Revised Broad-Line Region Ra-dius and Black Hole Mass for the Narrow-Line Seyfert 1 NGC 4051”, ApJ, 702,1353, (2009).

12. K. D. Denney, et al. (8 coauthors), “Reverberation Mapping Resultsfrom MDM Observatory”, Co-Evolution of Central Black Holes and Galaxies, IAUSymposium 267, (2009).

13. K. D. Denney, et al. (42 coauthors), “Diverse Kinematic SignaturesFrom Reverberation Mapping of the Broad-Line Regions in Active Galactic Nuclei”,ApJL, 704, L80, (2009).

14. K. D. Denney, et al. (42 coauthors), “Reverberation Mapping Measure-

viii

ments of Black Hole Masses in Six Local Seyfert Galaxies”, ApJ, submitted,(2010).

FIELDS OF STUDY

Major Field: Astronomy

ix

Table of Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Vita . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 The Central Engine of Active Galactic Nuclei . . . . . . . . . . . . . 1

1.2 Measuring Black Hole Masses with Reverberation Mapping . . . . . . 4

1.3 Velocity Resolved Reverberation Mapping . . . . . . . . . . . . . . . 8

1.4 Measuring Black Hole Masses from Single Epoch Spectra . . . . . . . 11

Chapter 2 The Mass of the Black Hole in the Seyfert 1 Galaxy

NGC 4593 from Reverberation Mapping . . . . . . . . . . . . . . . . 15

2.1 Observations and Data Analysis . . . . . . . . . . . . . . . . . . . . . 16

2.1.1 Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.1.2 Photometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.1.3 Light Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2 Time Series Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.3 Black Hole Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

x

2.4 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 28

Chapter 3 A Revised Broad-Line Region Radius and Black Hole Mass

for the Narrow-Line Seyfert 1 NGC 4051 . . . . . . . . . . . . . . . 40


3.1.1 Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.1.2 Photometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.1.3 Light Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.1.4 Time Series Analysis . . . . . . . . . . . . . . . . . . . . . . . 51

3.2 Comparison with Previous Results . . . . . . . . . . . . . . . . . . . 52

3.3 Black Hole Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.4 Velocity-Resolved Investigation . . . . . . . . . . . . . . . . . . . . . 62

3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Chapter 4 Reverberation Mapping Measurements of Black Hole

Masses in Six Local Seyfert Galaxies . . . . . . . . . . . . . . . . . . 83


4.1.1 Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.1.2 Photometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.1.3 Light Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4.1.4 Time-Series Analysis . . . . . . . . . . . . . . . . . . . . . . . 94

4.2 Black Hole Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

4.3 Velocity-Resolved Reverberation Lags . . . . . . . . . . . . . . . . . . 99

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

4.4.1 Comparison with Previous Results . . . . . . . . . . . . . . . 100

4.4.2 The BLR Radius Luminosity Relationship . . . . . . . . . . . 106

xi

4.4.3 Velocity-Resolved Results . . . . . . . . . . . . . . . . . . . . 109

4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Chapter 5 Diverse Kinematic Signatures From Reverberation

Mapping of the Broad-Line Region in Active Galactic Nuclei . . . 148


5.2 Velocity-Resolved Time Series Analysis . . . . . . . . . . . . . . . . . 151

5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

Chapter 6 Systematic Uncertainties in Black Hole Masses Determined

from Single Epoch Spectra . . . . . . . . . . . . . . . . . . . . . . . . 163

6.1 Data and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

6.1.1 NGC 5548 Spectra . . . . . . . . . . . . . . . . . . . . . . . . 169

6.1.2 PG1229+204 Spectra . . . . . . . . . . . . . . . . . . . . . . . 171

6.1.3 Methodology for Measuring Virial Masses . . . . . . . . . . . 172

6.1.4 Evaluation of Constant Components . . . . . . . . . . . . . . 177

6.1.5 Spectral Decomposition: Deblending the Spectral Features . . 178

6.2 Analysis and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

6.2.1 Effects of Variability . . . . . . . . . . . . . . . . . . . . . . . 185

6.2.2 Accounting for Constant Components . . . . . . . . . . . . . . 188

6.2.3 Systematic Effects due to S/N . . . . . . . . . . . . . . . . . . 195

6.2.4 Systematic Effects Due to Blending . . . . . . . . . . . . . . . 201

6.3 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 210

Chapter 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

7.1 Summary of Completed Work . . . . . . . . . . . . . . . . . . . . . . 243

xii

7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

xiii

List of Tables

2.1 Continuum and Hβ Fluxes for NGC 4593 . . . . . . . . . . . . . . . . 36

2.1 Continuum and Hβ Fluxes for NGC 4593 . . . . . . . . . . . . . . . . 37

2.2 Light Curve Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.3 Reverberation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.1 V -band, Continuum, and Hβ Fluxes for NGC 4051 . . . . . . . . . . 74









3.3 Reverberation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.1 Object List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

4.2 Spectroscopic Observations . . . . . . . . . . . . . . . . . . . . . . . . 125

4.3 Photometric Observations . . . . . . . . . . . . . . . . . . . . . . . . 126

4.4 Constant Spectral Properties . . . . . . . . . . . . . . . . . . . . . . . 127

4.5 V -band and Continuum Fluxes . . . . . . . . . . . . . . . . . . . . . 128

xiv












4.6 Hβ Fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

4.6 Hβ Fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

4.6 Hβ Fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

4.6 Hβ Fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

4.6 Hβ Fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

4.6 Hβ Fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145


4.8 Rest Frame Lags, Line Widths, Black Hole Masses, and Luminosities 147

5.1 Light Curve Statistics and Mean Hβ Lags . . . . . . . . . . . . . . . 162

6.1 Systematic Effects due to Variability . . . . . . . . . . . . . . . . . . 238

6.2 Systematic Effects due to Constant Components . . . . . . . . . . . . 239

6.3 Systematic Effects due to Signal-to-Noise Ratio . . . . . . . . . . . . 240

6.4 Systematic Effects due to Blending . . . . . . . . . . . . . . . . . . . 241

xv

6.5 Individual Error Sources for SE Mass Measurements . . . . . . . . . . 242

xvi

List of Figures

1.1 Unified model of AGNs. . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.1 Mean and RMS spectrum of NGC 4593 from MDM observations. . . 31

2.2 Light curve showing complete data sets from all three sources. . . . . 32

2.3 Light curve showing subset of data constrained to the time frame ofthe MDM observations and used for time series analysis. . . . . . . . 33

2.4 NGC4593 cross correlation function, discrete correlation function, andauto correlation function. . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.5 Cross correlation functions (CCF) from time series analysis of the redand blue sides of line profile. . . . . . . . . . . . . . . . . . . . . . . . 35

3.1 Mean and rms spectra of NGC 4051 from MDM observations. . . . . 67

3.2 Light curves showing complete set of observations from all four sources. 68

3.3 Merged and binned light curves of NGC4051. . . . . . . . . . . . . . 69

3.4 Cross correlation function from NGC4051 time series analysis. . . . . 70

3.5 Optical continuum and Hβ light curves reproduced from P00. . . . . 71

3.6 Velocity-resolved Hβ rms spectral profile and time-delay measurementsfor NGC4051. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

3.7 Most recently calibrated RBLR–L relation with new measurement. . . 73

4.1 Mean and rms (variable emission) spectra from MDM observations. . 116

4.2 Light curves for complete data set (1 of 2). . . . . . . . . . . . . . . . 117

4.3 Light curves showing complete set of observations from all sources forall objects (2 of 2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

xvii

4.4 Merged and detrended light curves for time series analysis and crosscorrelation functions for full sample (1 of 2). . . . . . . . . . . . . . . 119

4.5 Merged and detrended light curves for time series analysis and crosscorrelation functions for full sample (2 of 2). . . . . . . . . . . . . . . 120

4.6 Velocity-divided line profiles and velocity-resolved time-delaymeasurements of complete sample. . . . . . . . . . . . . . . . . . . . 121

4.7 Most recently calibrated RBLR–L relation with new measurementsdisplayed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

4.8 Mrk 817 light curves from four equal flux bins and associated crosscorrelation functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

5.1 Mean and rms spectra of NGC3227, NGC3516, and NGC5548 fromMDM observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

5.2 Light curves of NGC3227, NGC3516, and NGC5548. . . . . . . . . . 158

5.3 Velocity-divided line profiles and velocity-resolved time-delaymeasurements of NGC3227. . . . . . . . . . . . . . . . . . . . . . . . 159



6.1 Luminosity and line width measurements from NGC5548 spectra. . . 218

6.2 The multi-component fit to a typical spectrum of NGC 5548 fordecomposition method A. . . . . . . . . . . . . . . . . . . . . . . . . 219

6.3 The multi-component fit to a typical spectrum of NGC 5548 fordecomposition method B. . . . . . . . . . . . . . . . . . . . . . . . . 220

6.4 Virial mass distributions for the full NGC 5548 (a) and PG1229 (b)data sets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

6.5 Broad line region radius-luminosity relationship for PG1229 NGC5548. 222

6.6 Differences between each SE mass in a given observing year and thereverberation virial mass from that same year. . . . . . . . . . . . . . 223

xviii

6.7 Virial mass distributions for NGC 5548 and PG1229 without removinghost contribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

6.8 Mean spectra of NGC 5548 and PG1229. . . . . . . . . . . . . . . . . 225

6.9 Virial mass distributions for NGC 5548 and PG1229 without removingnarrow-line contributions. . . . . . . . . . . . . . . . . . . . . . . . . 226

6.10 Virial mass distributions for NGC 5548 and PG1229 without removinghost or narrow-line contributions. . . . . . . . . . . . . . . . . . . . . 227

6.11 Example original and three S/N degraded spectra of NGC 5548. . . . 228

6.12 Virial masses for original and S/N degraded NGC 5548 spectra, usingline widths measured from the data. . . . . . . . . . . . . . . . . . . . 229

6.13 Virial masses for original and S/N degraded NGC 5548 spectra, usingline widths measured from Gauss-Hermite fits. . . . . . . . . . . . . . 230

6.14 Cumulative distribution functions of NGC 5548 SE virial masses fordecomposition data sets. . . . . . . . . . . . . . . . . . . . . . . . . . 231

6.15 Comparison of the Hβ line dispersion measurements from differenttechniques of continuum subtraction. . . . . . . . . . . . . . . . . . . 232

6.16 Mean spectra of NGC 5548 created using three different techniques tofit the continuum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

6.17 Mean spectra of NGC 5548 both before and after subtracting theHe iiλ4686 emission line. . . . . . . . . . . . . . . . . . . . . . . . . . 234

6.18 Comparison of the Hβ line dispersion measurements from differentcontinuum subtraction methods after removing He iiλ4686 emission. . 235

6.19 Comparison of the Hβ FWHM measurements from different techniquesof continuum subtraction. . . . . . . . . . . . . . . . . . . . . . . . . 236

6.20 FWHM measurements of the Hβ line for JD2452030 using each of thethree spectral analysis methods. . . . . . . . . . . . . . . . . . . . . . 237

xix

Chapter 1

Introduction

1.1. The Central Engine of Active Galactic Nuclei

Strong emission lines and stellar-like cores were the first observed properties

of a distinct class of galaxies found in the local universe, eventually termed Seyfert

galaxies (Seyfert 1943), and radio observations later connected these objects to a

similar class of distant radio sources known as quasars. Certain properties were

soon observed to be characteristic, but not necessarily ubiquitous, of both local and

distant sources that we now refer to collectively as active galaxies, or active galactic

nuclei (AGNs): star-like objects/cores that may (or may not) have associated radio

emission, time-variable continuum flux, large ultraviolet (UV) flux, broad emission

lines, large redshifts (in the case of quasars), and variable X-ray flux (Schmidt 1969;

Elvis et al. 1978). Because the central cores of these galaxies are so luminous that

they are capable of outshining the rest of the stars in their host galaxy, astronomers

had to derive a new interpretation for how such large amounts of radiation could be

generated in a such a small volume (e.g., much less than a cubic parsec). The black

hole mass paradigm for the central engines of AGNs, whereby the large amount

1

of radiation is generated by gravitational infall of material from a hot accretion

disk onto a supermassive black hole (SMBH), was therefore invoked to explain the

incredibly large luminosities (e.g., 108 – 1012 L⊙) observed from the central cores of

these galaxies (Lynden-Bell 1969).

As sample sizes increased, clear differences emerged in the observed spectra

that led astronomers to separate AGNs into various subclasses. Two such subclasses

arose based on differences between the widths of the emission lines in the optical and

UV regions of the spectra: Type 1, or broad-line, and Type 2, or narrow-line AGNs

(Khachikian & Weedman 1974). Type 1 AGNs have broad emission lines arising

from permitted atomic transitions with widths up to ∼ 104 km s−1 that originate

from a high-density region in the nucleus, deemed the broad line region (BLR).

These broad lines are superposed on top of narrower emission lines with widths

hundreds of kilometers per second (still broader than typical stellar features) that

originate from a low-density, extended region called the narrow line region. Type 2

AGNs were only observed to have the narrow lines in their spectra, until Antonucci

& Miller (1985) discovered broad emission lines in the spectrum of the Type 2

Seyfert galaxy NGC1068 from observations of the polarized light coming from the

nucleus. This discovery suggested that the differences between Type 1 and Type 2

AGNs may simply be an inclination effect, and the unified model of AGNs emerged

(Antonucci 1993). Figure 1.1 shows a schematic diagram of an AGN as defined

by this unified model, where the BH, hot accretion disk, and broad line region are

2

surrounded by a dusty torus, such that emission from the broad line region can only

be seen directly in objects (Type 1 AGNs) with low enough inclination (i.e., closer

to face-on than edge-on). Type 2 AGNs are then objects at high inclination in which

the BLR is blocked by the obscuring torus and visible only in reflected (polarized)

light scattered by particles above the torus opening.

In Type 1 AGNs, our ability to observe the broad line region allows us to greatly

expand our understanding of the central engine because (1) the broad emission lines

vary in response to continuum variations, suggesting that the BLR gas is reprocessing

the photons emitted by the ionizing continuum, which presumably comes from the

hot accretion disk and cannot be observed directly, and thus, the BLR provides

indirect information about this region, and (2) the proximity of the broad line region

to the presumed SMBH means that bulk motions within the BLR are dominated by

gravity, and the emission lines are assumed to be Doppler-broadened as a result of

these motions, so that observations of the broad-line emission can be directly related

to the mass of the black hole. The work I have done for my dissertation will exploit

these two characteristic properties of the BLR emission in AGNs to explore black

hole masses in active galaxies.

3

1.2. Measuring Black Hole Masses with Reverberation

Mapping

Recent theoretical and observational studies have provided strong evidence

suggesting that all massive galaxies (not only AGNs) contain a SMBH at their

center and that there is a connection between SMBH growth and galaxy evolution

(e.g., Silk & Rees 1998; Kormendy & Gebhardt 2001; Haring & Rix 2004; Di Matteo

et al. 2005; Bennert et al. 2008; Somerville et al. 2008; Hopkins & Hernquist 2009;

Shankar et al. 2009). Empirical relationships have been discovered for both quiescent

and active galaxies that show similar correlations between the central SMBH

and properties of the stars within the bulge of the host galaxy (well outside the

gravitational sphere of influence of the black hole). Examples include correlations

between the SMBH mass and total luminosity of stars in the galactic bulge —

the MBH–Lbulge relationship (Kormendy & Richstone 1995; Magorrian et al. 1998;

Wandel 2002; Graham 2007; Bentz et al. 2009a) — and between SMBH mass and

the bulge stellar velocity dispersion — the MBH–σ⋆ relationship (Ferrarese & Merritt

2000; Gebhardt et al. 2000a,b; Ferrarese et al. 2001; Tremaine et al. 2002; Onken

et al. 2004; Nelson et al. 2004).

The current thrust to better understand this SMBH-galaxy connection relies

on mass measurements of large samples of black holes in both the local and distant

Universe. The masses of SMBHs in distant galaxies can only be measured indirectly

4

using the scaling relationships mentioned above, as well as the AGN RBLR–L

relationship (Kaspi et al. 2000, 2005; Bentz et al. 2006a, 2009b), which provides the

capability to estimate SMBH masses from a single spectrum of an AGN (Wandel

et al. 1999). In order to understand the evolution of SMBH and galaxy growth over

cosmological times, it is useful to compare the location of distant galaxies on these

relationships with local samples. This can only be done by calibrating the local

relations with direct SMBH mass measurements.

Local masses are measured directly in quiescent galaxies using dynamical

methods (see Kormendy & Richstone 1995; Ferrarese & Ford 2005, for reviews)

that rely on resolving the motions of gas and stars within the sphere of influence

of the central SMBH and are thus very resolution intensive and only applicable in

the nearby Universe. Direct measurements can also be made from observations of

megamasers sometimes seen in Type 2 AGNs, but making these observations relies

on a particular viewing angle into the nuclear region of these galaxies and is thus

not applicable to large numbers of objects. Direct mass measurements can also

be made in Type 1 (i.e., broad line) AGNs using a technique called reverberation

mapping (Blandford & McKee 1982; Peterson 1993), which is a method that relies

on time resolution to trace a light-travel-time delay between continuum and broad

emission-line flux variations with spectroscopic monitoring campaigns to measure

the characteristic size of the broad line region (BLR). This technique has been used

to directly measure black hole masses in relatively local broad-line (Type 1) AGNs

5

for over two decades (see compilation by Peterson et al. 2004). Because the BLR

gas is well within the sphere of influence of the black hole and studies have provided

evidence for virialized motions within this region (e.g., Peterson et al. 2004, and

references therein), the size of the BLR, RBLR = cτ , can be related to the mass of

the SMBH through the velocity dispersion of the BLR gas:

MBH =fcτ(∆V )2

G, (1.1)

where τ is the measured emission-line time delay, c is the speed of light, and ∆V is the

velocity dispersion of the gas, determined from the Doppler-broadened emission-line

width. The dimensionless factor f depends on the structure, kinematics, and

inclination of the BLR and is of order unity. Although reverberation mapping is

technically applicable at all redshifts, the reverberation time-delay scales with the

AGN luminosity (i.e., the RBLR–L relationship), and this coupled with time dilation

effects make it difficult and particularly time-consuming to make such measurements

out to high redshift (see Kaspi et al. 2007).

The constraints for making direct SMBH mass measurements at large distances

make the use of the RBLR–L relationship particularly attractive for obtaining even

indirect mass estimates at all redshifts for which a broad-line AGN spectrum can be

obtained. In addition, masses can be estimated for large samples of objects (e.g.,

Kollmeier et al. 2006; Shen et al. 2008b; Vestergaard et al. 2008), facilitating studies

of the BH-galaxy connection and its evolution across cosmic time (e.g., Vestergaard

6

& Osmer 2009). However, in order to reliably apply these relationships to high

redshift objects and determine any evolution in the relationships themselves, local

versions of the relationships need to be well-populated with high-quality data, so

that calibration of these local relationships is secure (i.e., observational scatter

minimized) and any intrinsic scatter is well characterized (see, e.g., Bentz et al.

2006a, 2009a,b; Graham 2007; Gultekin et al. 2009; Woo et al. 2010, for recent efforts

to improve scaling relation calibration and characterization of intrinsic scatter).

Furthermore, systematic uncertainties also need to be understood and minimized so

that the local relations, on which all other related studies are based, are as robust as

possible. For instance, systematic uncertainties are present in the direct, dynamical

mass measurements of the SMBHs in quiescent galaxies due to model-dependencies

of the mass derivation (e.g., Gebhardt & Thomas 2009 find more than a factor

of two difference in the measured SMBH mass in M87 when they include a dark

matter halo in their model; see also Shen & Gebhardt 2010 and van den Bosch

& de Zeeuw 2010 for more recent model-dependent changes made to previously

measured quiescent black hole masses that change the masses by similar amounts,

i.e., factors of ∼2). On the other hand, reverberation-based masses as I present them

in this dissertation (measuring simply the mean BLR radius from the reverberation

time-delay) do not rely on any physical models; instead, the largest systematic

uncertainty comes from the additional zero-point calibration of the mass scale (Woo

et al. 2010). This calibration is needed due to a number of uncertainties, such as the

7

relationship between the line-of-sight (LOS) velocity dispersion measured from the

broad-line width and the actual velocity dispersion of the BLR, systematic effects in

determining the effective radius, and the role of non-gravitational forces. Therefore,

establishing a secure calibration across a wide dynamic range in parameter space

and better understanding any intrinsic scatter in these relations is essential. To

accomplish this, we must continue to make new direct measurements as well as to

check previous results that are, for one reason or another, suspect.

Chapters 2, 3, and 4 of this dissertation present new reverberation mapping

results in which I measure BLR radii and black hole masses in several Type 1

AGNs. Specifically, in Chapters 2 and 3, I present new data and reverberation

BLR radii and black hole mass measurements for NGC4593 and NGC4051,

respectively. Both objects had previous reverberation mapping results that were

highly uncertain, mostly due to undersampled, spectroscopic monitoring data, so we

revisit these objects in an effort to improve upon past results. In Chapter 4, I present

additional reverberation mapping results for a sample of local Seyfert Galaxies from

a multi-month campaign undertaken in 2007.

1.3. Velocity Resolved Reverberation Mapping

Although reverberation mapping has become extremely useful and quite

successful in its application of directly measuring BLR radii and black hole masses

8

(MBH), the fundamental objective of reverberation mapping, as its name implies,

is to reconstruct or map the emissivity and velocity distribution of the BLR

line-emitting gas as a function of position as it ‘reverberates’ in response to the

flux variations of the ionizing continuum. Because the position of the gas can

be inferred through the emission-line time delay, τ (RBLR = cτ), the resulting

reconstruction is called a velocity–delay map (see Horne et al. 2004) and is the best

means, with current technology, to obtain direct knowledge about the geometry and

kinematics of the BLR. Further understanding the detailed structure and kinematics

of the BLR is crucial for reducing systematic uncertainties in reverberation-based

MBH measurements. These uncertainties are folded into the mass calculation (i.e.,

Equation 1.1) in the form of the scale factor, f , which is currently the largest source

of systematic uncertainty in reverberation-based mass measurements (see e.g., Collin

et al. 2006; Woo et al. 2010).

Past attempts at producing velocity–delay maps (e.g., Done & Krolik 1996;

Ulrich & Horne 1996; Kollatschny 2003) have not yielded completely satisfactory

results, primarily on account of limitations in temporal sampling, with inadequate

time resolution or campaign duration or both. Even given these limitations, previous

studies have successfully measured time delays and black hole masses in over 40

type 1 AGNs (see e.g., Peterson et al. 2004; Bentz et al. 2009c). In addition, basic

investigations into time delay differences between multiple emission lines have shown

that the BLR is virialized across broad line-emitting regions of different species

9

(e.g., Peterson et al. 2004, and references therein). Other studies of the velocity

dependence of the lag across a single emission line region have shown suggestive

evidence that the BLR commonly contains a radial inflow component in addition

to circular motions (e.g., Gaskell 1988; Crenshaw & Blackwell 1990; Koratkar &

Gaskell 1991; Done & Krolik 1996).

The experiences from earlier reverberation programs have led to more recent

campaigns that address the main observational obstacles encountered in the past —

relative sampling rate, campaign duration, and data quality. Consequently, there has

been consistent success in measuring BLR radii in new targets and remeasuring radii

that now supersede previous, lower-precision or ambiguous measurements due to

inadequate time-sampling (e.g., Denney et al. 2006; Bentz et al. 2006b; Grier et al.

2008; Denney et al. 2009b, see Chapters 2 and 3). Furthermore, these campaigns

enable statistically significant detections of reverberation signals at higher velocity

resolutions than have previously been found due mainly to the data restrictions

discussed above. For example, Bentz et al. (2008) found a clear signal of radial

inflow within the Hβ emission region of the BLR in Arp 151, and Bentz et al. (2009c)

show further evidence for distinct kinematic behavior in at least one other AGN

from the same program (the Lick AGN Monitoring Project). In Chapter 5, I present

a detailed velocity-resolved reverberation mapping study of three of the targets we

observed during our 2007 reverberation mapping campaign (the main results of

10

which are presented in Chapter 4) that serves as a preliminary investigation into our

potential to recover velocity-delay maps from this data set.

1.4. Measuring Black Hole Masses from Single Epoch

Spectra

Because understanding the demographics of SMBHs is imperative to expanding

our understanding of the present state as well as the cosmic evolution of galaxies,

in particular, the links between SMBHs and properties of host galaxies that point

to coevolution (Kormendy & Richstone 1995; Ferrarese & Merritt 2000; Gebhardt

et al. 2000a), we must trace the cosmic evolution of SMBHs by determining SMBH

masses as a function of cosmic time. This requires the measurement of SMBH

masses at large distances. As mentioned previously the direct methods (e.g. stellar

and gas dynamics, megamasers) that have succeeded for ∼ 30 − 40 comparatively

local, mostly quiescent galaxies (see review by Ferrarese & Ford 2005) fail at large

distances because they require high angular resolution to resolve motions within

the radius of influence of the SMBH. A solution to this distance problem is to use

AGNs as tracers of the SMBH population at redshifts beyond the reach of the

above mentioned methods. AGNs are luminous and easier to observe than quiescent

galaxies at large distances. Most importantly, their masses can be determined by

reverberation mapping, which does not depend on angular resolution.

11

The masses that have been measured for ∼ 45 active galaxies with reverberation

mapping (RM) methods (see the recent compilation by Peterson et al. 2004; Bentz

et al. 2009c) have led to the identification of certain scaling relationships for AGNs,

specifically. The correlation between SMBH mass and bulge/spheroid stellar velocity

dispersion, i.e. the MBH − σ⋆ relation, for AGNs (Gebhardt et al. 2000b; Ferrarese

et al. 2001; Onken et al. 2004; Nelson et al. 2004) is consistent with that discovered

for quiescent galaxies (Ferrarese & Merritt 2000; Gebhardt et al. 2000a; Tremaine

et al. 2002). In addition, and more relevant for this study, is the correlation between

the BLR radius and the luminosity of the AGN, i.e. the RBLR–L relation (Kaspi

et al. 2000, 2005; Bentz et al. 2006a, 2008), which allows estimates of SMBH

masses from single-epoch (SE) spectra. By combining a single measurement of

the monochromatic luminosity to use as a proxy for the BLR radius (through the

RBLR–L relation) with a broad-line width measured from the same spectrum, an SE

mass estimate can be made by using Equation 1.1. Calculating masses in this way

affords great economy of observing resources, allowing masses to be calculated for

the large number of AGNs/quasars with SE spectra obtained from surveys such as

the SDSS and AGES (e.g., Vestergaard 2002; Corbett et al. 2003; Vestergaard 2004;

Kollmeier et al. 2006; Vestergaard et al. 2008; Shen et al. 2008a,b; Fine et al. 2008).

These masses can subsequently be used to infer evolutionary properties of galaxies

(e.g., Vestergaard & Osmer 2009).

12

One difficulty in using this method, however, is that there are many systematic

uncertainties associated with these SE mass estimates that are dependent both

on properties of the AGNs and properties of the data. Therefore, in Chapter 6, I

investigate the presence and magnitude of several of these systematic uncertainties

by comparing SE mass estimates made for two individual objects for which we

have large databases of spectra derived from reverberation mapping studies. The

results of this investigation then allow me to discuss methods for minimizing these

systematic uncertainties in future studies.

13

Fig. 1.1.— Schematic diagram of an AGN based on the unified model of AGNs. Thisgeometrical interpretation was created to explain the observed differences betweenType 1 and Type 2 AGN spectra. Adapted from Urry & Padovani (1995); copieddirectly from http://www.mpe.mpg.de/ir/Research/AGN/index.php.

14

Chapter 2

The Mass of the Black Hole in the Seyfert 1

Galaxy NGC 4593 from Reverberation Mapping

The mass of the black hole in NGC 4593 was previously measured by

reverberation mapping (Dietrich et al. 1994; Onken et al. 2003), but the Hβ lag

determination of τcent = 3.1 days was unfortunately much smaller than the average

interval between observations of 15.8 days. This resulted in uncertainties (+7.1,−5.1

days) much larger than the time delay itself, and as such, were consistent with no lag

at all. Therefore, we have completed a ∼40 night spectroscopic monitoring campaign

during which we obtained nearly nightly observations of NGC4593. By revisiting

this object with our program, we were able to achieve the sampling necessary to

drive down the previous high uncertainties in the time lag and black hole mass.

Here, we present new lag and MBH determinations from reverberation mapping of

15

NGC 4593. The observational uncertainties from this campaign represent a factor of

several improvement over previous results.

2.1. Observations and Data Analysis

Observations of NGC 4593 were obtained as part of a large reverberation

mapping campaign undertaken in early 2005 on the 1.3m McGraw-Hill telescope of

the MDM Observatory on Kitt Peak in Arizona. Details beyond the descriptions

below, for our spectral and photometric observations and data reduction, are given

by Bentz et al. (2006b). NGC 4593 is one of three AGNs from which we were able

to observe sufficient variability within the time frame of our program to warrant a

reverberation analysis. It was first recognized as a host to a type 1 AGN by Lewis

et al. (1978) as part of the Michigan-Tololo Curtis Schmidt survey for extragalactic

emission-line objects (see MacAlpine et al. 1979). NGC 4593 is a type (R)SB(rs)b

spiral galaxy at a redshift of z = 0.0090.

2.1.1. Spectroscopy

MDM Observations: We obtained spectra of the central region of NGC 4593

at 24 epochs between 2005 February and April with the Boller and Chivens CCD

spectrograph on the 1.3-meter telescope at MDM Observatory, at a spatial scale

of 0.′′75 per pixel. For our campaign, we used a grating of 350 grooves/mm,

16

corresponding to a dispersion of 1.33 A/pixel. The spectral coverage was from

∼ 4300 − 5700 A, centered on Hβ λ4861 and the [O iii]λλ4959, 5007 lines, resulting

in a spectral resolution of 7.6 A across this range. The slit width was set to 5.′′0

projected on the sky, with a position angle of 90. Figure 2.1 shows the mean and

rms spectrum of NGC 4593, made from the complete set of MDM observations.

CrAO Observations: We also acquired spectra of the nuclear region of

NGC 4593 from the Nasmith spectrograph with the Astro-550 580 × 520 pixel CCD

(Berezin et al. 1991) on the 2.6-m Shajn telescope of the Crimean Astrophysical

Observatory (CrAO). For these observations a 3.′′0 slit was utilized, with a 90

position angle. Spectral wavelength coverage for this data set was from ∼ 4300−5600

A, with a dispersion of 2.0 A/pix and a spectral resolution of 8.2 A.

2.1.2. Photometry

MAGNUM Observations: In addition to spectral observations, we also

obtained V -band photometry from the 2.0-m Multicolor Active Galactic NUclei

Monitoring (MAGNUM) telescope at the Haleakala Observatories in Hawaii,

imaged with the multicolor imaging photometer (MIP) as described by Kobayashi

et al. (1998a,b), Yoshii (2002), and Yoshii et al. (2003). Photometric reduction of

NGC 4593 was similar to that described for other sources by Minezaki et al. (2004)

and Suganuma et al. (2006), except the host-galaxy contribution to the flux within

17

the aperture was not subtracted and the filter color term was not corrected because

these photometric data were later scaled to the MDM and CrAO continuum light

curve (as described below). Also, minor corrections (of order 0.01 mag or less) due

to the seeing dependence of the host-galaxy flux were ignored.

2.1.3. Light Curves

Following reduction of the data, light curves were created for the subsequent

cross-correlation analysis. The spectral fluxes of the MDM observations were

calibrated based on the [O iii]λ5007 line flux between observed frame wavelengths of

5022−5062 A in the mean spectrum. Individual spectra were scaled to this reference

spectrum using software that employs a χ2 goodness of fit estimator (van Groningen

& Wanders 1992). Because few MDM observations were taken under photometric

conditions, our absolute [O iii]λ5007 flux calibrations are not reliable. Therefore,

the final light curves are calibrated to the [O iii]λ5007 flux given by Dietrich et al.

(1994). Light curves from the CrAO spectra were made following a similar method,

only the final light curve flux measurements were not calibrated to the Dietrich et al.

(1994) value because this data set was later scaled to the MDM data set, as described

below. Continuum and line flux measurements were obtained by first fitting the

continuum on either side of the Hβ line, between wavelength ranges 4795 − 4815 A

and 5120− 5170 A in the observed frame. The Hβ flux was calculated by integrating

above the continuum over the wavelength range 4825 − 4963 A. The continuum flux

18

density was then taken to be the average over 5120− 5170 A. Although at least some

contamination from Fe ii emission is unavoidable when measuring the continuum in

the optical, we chose this continuum region because it is the cleanest window, with

respect to this contamination, within the spectral coverage of our observations. In

addition, Vestergaard & Peterson (2005) demonstrate that although Fe ii emission

is variable, the amplitude of variability is generally low. We do not expect Fe ii

contamination to significantly affect our measurements.

In order to intercalibrate the data from various sources (i.e. place them

on a consistent flux scale), corrections to the measured line and continuum flux

values are necessary because of systematic differences, mostly attributable to

seeing and aperture effects (see Peterson et al. 1991). Given data sets from

two sources, flux differences were determined by comparing all possible pairs of

simultaneous observations between the two data sets. Here, we relaxed the meaning

of ‘simultaneous’ to include pairs separated by at most 2.0 days so as to increase the

number of pairs contributing to each comparison. However, this relaxed assumption

does not produce significantly larger (i.e. less than 1.0%) uncertainties, implying that

there is no evidence for intrinsic variability on such short timescales. Based on the

average difference in flux between these closely spaced pairs, a single multiplicative

point-source correction factor, ϕCrAO = 0.89, was applied to all points in both the

emission-line and continuum light curves of the secondary data set (CrAO) to scale

it to the primary set (MDM), following the methods of Peterson et al. (1991).

19

Physically, this scaling factor accounts for differences in the amount of [O iii]λ5007

flux measured due to different aperture geometries and seeing between the two

data sets. Seeing can also effect the internal calibrations of the continuum and Hβ

emission-line flux measurements, based on F ([O iii]λ5007), which is assumed to be

constant. However, given the large slit widths used in the current MDM and CrAO

observations (5.′′0 and 3.′′0, respectively) as well as the compact (no larger than 1.′′7)

emission region of [O iii] in NGC 4593 (Schmitt et al. 2003), seeing is an insignificant

effect in our internal calibrations. Further tests of the effect of seeing on our internal

flux calibrations will be addressed in §3.

In addition to this multiplicative correction, an additive correction factor,

GCrAO = −1.60 × 10−15 erg s−1 cm−2 A−1, was also made to the continuum flux,

accounting for the starlight contribution in the different apertures of the various

data sets. These correction methods were employed to scale both the continuum

and Hβ light curves from the CrAO observations to the MDM data, since the MDM

data formed the largest, individual set, and thus served as the base onto which to

tie the others. For the same reason, the photometric, V -band observations from

the MAGNUM data were then scaled to the newly combined MDM and CrAO

continuum light curve, with additive correction factor GMAGNUM = 0.65 × 10−15

erg s−1 cm−2 A−1. The continuum light curve was finally corrected for host

galaxy starlight, where, for this slit geometry, the contribution is measured to be

Fgal(5100A)= (1.11+0.10−0.11) × 10−14 erg s−1 cm−2 A−1 from a recent Hubble Space

20

Telescope image taken with the Advanced Camera for Surveys High Resolution

Camera. The methods by which this flux contribution was determined are described

by Bentz et al. (2006a), and the complete results specific to this object will appear

in a future paper. The full set of observations used in constructing these light curves

can be found in Table 2.1, and Figure 2.2 shows the corresponding light curves.

2.2. Time Series Analysis

For the time series analysis, the light curves from Figure 2.2 were modified by

first merging the three sets of observations by binning data points more closely spaced

than 0.5 day through the use of a variance-weighted average. Cross-correlation

analysis was restricted to the subset of the light curves where both continuum

and emission-line measurements are available, i.e. JD2453430 – JD2453472. In

addition, two observations from the CrAO data set, JD2453463.4 and JD2453465.9,

show anomalously high continuum flux for reasons that could not be determined.

Conducting the cross-correlation analysis including these points resulted in lag

determinations consistent with removing the points, although the uncertainties in

the lags were higher. Since this time period was otherwise well sampled, none of the

other observations show a similar peak in continuum flux, and because the results

from exclusion are consistent with inclusion, we omit these two continuum points

from the final light curve.

21

Figure 2.3 shows the modified light curves that were used for the cross

correlation analysis. The statistical parameters describing these final light curves

are shown in Table 2.2. Column (1) gives the spectral feature, and Column (2)

shows the number of data points in each light curve. Columns (3) and (4) are mean

and median sampling intervals, respectively, between data points. The mean flux

with standard deviation is given in column (5), while column (6) shows the mean

fractional error, based on comparison between closely spaced observations. Column

(7) gives the excess variance, calculated as

Fvar =

√σ2 − δ2

〈f〉 (2.1)

where σ2 is the variance of the observed fluxes, δ2 is their mean square uncertainty,

and 〈f〉 is the mean of the observed fluxes. Finally, column (8) is the ratio of the

maximum to minimum flux in the light curves.

We conducted the time-series analysis by cross correlating the continuum light

curve with the Hβ light curve using two methods designed for unevenly spaced

observations. The primary method uses an interpolation scheme that averages two

results: first, cross correlating an interpolated continuum light curve with the original

emission-line light curve, and second, cross correlating the original continuum with

an interpolated emission-line light curve (Gaskell & Peterson 1987). We employed

an interpolation interval of 0.5 day (equal to half of the median time span between

observations), chosen to create equal spacing on a scale smaller than that of the

22

actual data, yet large enough to prevent the introduction of artifacts due to the

correlation of adjacent interpolated flux values. The correlation coefficient, r, is

computed from pairs of points from each light curve matched based on different lags

being imposed upon the trailing curve. For a given time lag realization, unpaired

points at the beginning or end of the time series are excluded from the correlation

analysis. By calculating r for multiple potential lag times, a cross-correlation

function (CCF) is constructed, shown in Figure 2.4, which gives the correlation

coefficient at each of these different lag times, τ . From the CCF, we can characterize

the time delay through two parameters. The peak lag, τpeak, is simply taken as the

lag time which produces the highest correlation coefficient, rmax, whereas the centroid

lag, τcent, is the centroid of the CCF, computed from values with r ≥ 0.8rmax.

The uncertainties in the time lag measurements were computed via model-

independent Monte-Carlo simulations and based on the bootstrap method referred to

as FR/RSS (for flux redistribution/random subset selection), described by Peterson

et al. (1998) and which utilized the modifications of Peterson et al. (2004). A large

number of realizations of this method (e.g. 10,000 in this study) are employed

to build up two distributions of CCFs: the cross correlation centroid distribution

(CCCD) and the cross correlation peak distribution (CCPD). The values τcent and

τpeak are the means of these respective distributions. The uncertainties are calculated

such that 15.87% of the realizations yield values larger than the mean plus the upper

error, and 15.87% yield values smaller than the mean minus the lower error; these

23

would correspond to the 1σ errors in the case of a Gaussian distribution. Table 2.3

gives the calculated values of τcent and τpeak for NGC 4593, after being corrected for

time dilation.

The second cross correlation method we employ creates a discrete correlation

function (DCF), described by Edelson & Krolik (1988), including modifications by

White & Peterson (1994). Shown in Figure 2.4, the DCF is created by determining

correlations at different lag times between the Hβ and continuum light curves,

just as in the interpolation method, but through time binning of data rather than

interpolation. Under-sampled data or data with large time gaps could lead to

spurious lag determinations through the interpolation method, in which case there

are advantages to using the DCF method. For example, only the actual data are

used in the analysis and due to the binning, statistical uncertainties can be assigned

to the correlation coefficient for each bin (see White & Peterson 1994). For this

analysis, a time bin of 2.0 days was adopted. One can see from Figure 2.4 that

the DCF agrees well with the CCF from the interpolation method showing that

interpolation is not introducing artifacts. Figure 2.4 also shows the auto-correlation

function (ACF), which is computed by cross correlating the continuum with itself.

The ACF is interesting because the CCF is the convolution of this distribution

(ACF) and the transfer function, which describes the emission-line response to the

continuum variations and is the quantity reverberation mapping is fundamentally

attempting to recover (see Peterson 1993).

24

The cross-correlation functions in Figure 2.4 also demonstrate that our

continuum and Hβ emission-line internal flux calibration to the [O iii]λ5007 emission

line are not adversely affected by nightly changes in seeing. Because calibration

errors due to seeing would result in correlated errors, with both the continuum and

the line flux affected in the same direction, if variable seeing is a significant effect, it

would lead to a spike in the cross-correlation function at a lag of zero days. Figure 2.4

clearly shows no such feature in either the CCF or DCF for NGC 4593. Bentz et al.

(2006b) report on results for NGC 4151 from this same observing campaign and

do not see any evidence for this zero lag spike either. The only object from this

campaign in which a zero-lag spike is detected in the cross-correlation function is

NGC 5548 (Bentz et al. 2007), which was in a very low-flux state at the time. In this

case, the amplitude of variability was so low that the weak correlated-error signature

was above the detection threshold.

To investigate the possibility of detecting bulk motions within the BLR, we

then broke the Hβ broad emission-line into velocity bins and performed the cross

correlation anaylsis between these individual bins. First, the Hβ line was divided

in half based on the peak in the mean spectrum (see Fig. 2.1), with the blue side

defined by wavelengths 4825 – 4903 A, and the red side defined by wavelengths

4903 – 4963 A. The flux was determined by integrating the line flux above the same

continuum fit as described above. The lags determined through this cross correlation

analysis are τcent = 0.5 ± 1.0 day and τpeak = 0.7+1.0−1.5 day, with variations in the blue

25

side slightly lagging behind those in the red side. Second, the line was broken into a

‘core’ and ‘wings’ such that the integrated flux in the core was equal to the summed

flux in both red and blue wings. These regions were defined from the mean spectrum

such that the blue wing constituted the integrated flux between wavelengths 4825 –

4881.8 A, the core between 4881.8 – 4924.2, and the red wing between 4924.2 – 4963

A. The lags determined for this scenario are τcent = 0.5±0.7 day and τpeak = 0.1±1.0

day, with variations in the wings leading the core as would be expected. The CCFs

from both of these analyses are shown in Figure 2.5. Unfortunately, any signature

of inflow/outflow or bulk Keplarian motions was too weak to be detected with

confidence through this investigation, as the lags measured for both scenarios were

consistent with zero.

2.3. Black Hole Mass

Assuming that the motions within the line-emitting region are gravitationally

dominated so that the virial theorem can be utilized, the mass of the black hole can

be defined such that

MBH =fcτ(∆V )2

G, (2.2)

where τ is the measured emission-line time delay and ∆V is the emission-line width,

which can be characterized by either the full width at half maximum (FWHM) of

26

the broad emission-line or by the emission-line dispersion, σline. The dimensionless

factor f depends on the structure, kinematics, and inclination of the BLR and is

of order unity. By normalizing the reverberation-based black hole masses to the

MBH − σ⋆ relationship of quiescent galaxies, Onken et al. (2004) have shown that f

has an average value of 5.5, when the emission-line dispersion, or second moment of

the profile, is used (as opposed to the FWHM1) for ∆V .

After first removing the narrow line component of the Hβ emission line, the

FWHM and the line dispersion were measured from both the mean and the rms

spectra of NGC 4593. Peterson et al. (2004) describe in detail the bootstrap method

used to determine these quantities and their respective uncertainties. The measured

values for the FWHM and σline are given in Table 2.3.

To calculate the black hole mass for NGC 4593, we use the centroid lag, τcent,

for the time delay, τ , and the line dispersion, σline, of the Hβ emission line, measured

from the rms spectrum, for the emission-line width, ∆V . Peterson et al. (2004)

argue that this combination of parameters gives the most reliable black hole mass

determinations, based on virial arguments and fits between all possible combinations

of parameters. The black hole mass calculated for NGC 4593 from this work is

MBH = (9.8 ± 2.1) × 106M⊙, where the uncertainties quoted include statistical and

1See Collin et al. (2006) for a discussion of systematic differences between the use of the FWHM

and the line dispersion in calculating the virial product, and thus MBH.

27

observational considerations but not an intrinsic uncerainty in the method, no larger

than a factor of 2-3, that accounts for unknowns such as inclination.

Our result is consistent with the mass estimate based on a previous reverberation

program. Onken et al. (2003) reanalyzed observations of NGC 4593 by the “Lovers

of Active Galaxies (LAG)” consortium (Dietrich et al. 1994) and determined a black

hole mass based on Hβ to be MBH = (5.4+9.4−7.0) × 106M⊙, where we have used the

Onken et al. (2004) calibration (Peterson et al. 2004). The improved time sampling

of the new reverberation mapping observations has significantly decreased the

uncertainties in the black hole mass estimate for this object.

2.4. Discussion and Conclusion

Results presented here for the emission-line lag and black hole mass of

NGC 4593 of τcent = 3.73 ± 0.75 days and MBH = (9.8 ± 2.1) × 106M⊙, for

these respective quantities, represent a factor of several improvement over past

measurements. Previous measurements for this object from LAG data exhibited

much larger uncertainties due in part to the average sampling interval, which

due mostly to bad weather, was much larger (by about a factor of 4) than the

emission-line lag of this object. In addition, for rather short observing campaigns,

some of the success of reverberation mapping comes from serendipitously observing

a large variability event during the campaign. The best results come from observing

28

a large increase and then decrease (or vice versa) in the flux, which we observed in

this campaign but was unfortunately not seen to the same degree in the previous

campaign of NGC 4593. This represents yet another example exhibiting the need for

longer observing campaigns.

The results reported here were obtained as part of a larger spectroscopic

monitoring campaign whose primary goal was to improve the emission-line lag

and black hole mass measurements for some of the nearest, apparently brightest

AGNs. The proximity of these AGNs makes them especially important not only as

calibrators of the AGN MBH–σ∗ and BLR radius–luminosity relationships (Bentz

et al. 2006a), but also as candidates for measurement of their black hole masses

through other means that depend on high angular resolution. Key elements of

this program were (1) scheduled daily observations of each of these relatively

low-luminosity AGNs, (2) supporting observations at multiple sites to mitigate

the effects of gaps in the time series caused by weather, and (3) high-quality

homogeneous data that permitted relative spectrophotometric flux calibration at

better than the 2% level. Our 42-night program yielded improved Hβ lags and black

hole masses with a factor of several improvement in precision relative to previous

campaigns for three of the six AGNs in our sample, NGC 4151 (Bentz et al. 2006b),

NGC 5548, which was observed in the lowest-luminosity state yet recorded (Bentz

et al. 2007), and NGC 4593, as described here. Three other AGNs in our program,

NGC 3227, NGC 3516, and NGC 4051 were insufficiently variable during this

29

relatively brief campaign, underscoring the point that longer duration programs are

necessary for detection of variability signatures that are favorable for reverberation

analysis.

30

Fig. 2.1.— Mean and RMS spectrum of NGC 4593 from MDM observations. Thesolid line shows the spectrum with the narrow-line components of Hβ, [O iii]λ4959,and [O iii]λ5007 removed. The dotted line shows where these narrow-line componentscontributed to the spectrum before they were removed. The large increase in rms fluxshortward of 4800 A is due to variations in the broad He iiλ4686 emission line.

31

Fig. 2.2.— Light curve showing complete data sets from all three sources. The toppanel shows the 5100 A continuum flux in units of 10−15 erg s−1 cm−2 A−1, while thebottom is the Hβ λ4861 line flux in units of 10−13 erg s−1 cm−2. The crosses show thetwo continuum points that were later omitted from the final light curve (see §2.2).

32

Fig. 2.3.— Light curve showing subset of data constrained to the time frame of theMDM observations that was used for time series analysis. Observations within 0.5day of each other have been averaged together. The top panel shows the 5100 Acontinuum in units of 10−15 erg s−1 cm−2 A−1, while the bottom is the Hβ λ 4861line flux in units of 10−13 erg s−1 cm−2.

33

Fig. 2.4.— Cross correlation function (CCF), discrete correlation function (DCF),and auto correlation function (ACF) from time series analysis of the continuum andHβ light curves of NGC 4593.

34

Fig. 2.5.— Cross correlation functions (CCF) from time series analysis of the red andblue sides of the broad Hβ emission line (solid line) and of the wings and the core ofthe Hβ emission line (dashed line) of NGC 4593.

35

JD Fλ (5100 A) Hβ λ4861 Data Set

(-2450000) (10−15 erg s−1 cm−2 A−1) (10−13 erg s−1 cm−2)

3391.986 10.69 ± 0.10 · · · MAGNUM

3411.926 9.23 ± 0.10 · · · MAGNUM

3419.121 9.86 ± 0.05 · · · MAGNUM

3430.844 8.94 ± 0.18 4.59 ± 0.09 MDM

3430.962 9.78 ± 0.08 · · · MAGNUM

3431.832 8.75 ± 0.18 4.52 ± 0.09 MDM

3433.816 8.52 ± 0.17 4.61 ± 0.09 MDM

3437.499 9.68 ± 0.32 4.67 ± 0.10 CrAO

3437.926 9.39 ± 0.19 4.77 ± 0.10 MDM

3438.073 10.37 ± 0.04 · · · MAGNUM

3438.805 9.81 ± 0.20 5.03 ± 0.10 MDM

3439.789 9.60 ± 0.19 5.00 ± 0.10 MDM

3440.824 9.51 ± 0.19 5.08 ± 0.10 MDM

3441.848 9.24 ± 0.19 5.12 ± 0.10 MDM

3442.820 8.92 ± 0.18 5.34 ± 0.11 MDM

3443.820 9.05 ± 0.18 5.23 ± 0.11 MDM

3444.450 8.75 ± 0.29 5.08 ± 0.11 CrAO

3445.456 7.99 ± 0.26 5.07 ± 0.11 CrAO

3445.832 8.80 ± 0.18 5.01 ± 0.10 MDM

3446.448 8.64 ± 0.29 4.91 ± 0.10 CrAO

3446.816 8.63 ± 0.17 4.97 ± 0.10 MDM

3450.832 8.19 ± 0.16 4.53 ± 0.09 MDM

3451.840 8.38 ± 0.17 4.36 ± 0.09 MDM

3452.793 8.66 ± 0.17 4.27 ± 0.09 MDM

3459.848 8.99 ± 0.18 4.56 ± 0.09 MDM

3460.809 8.71 ± 0.17 4.58 ± 0.09 MDM

3461.812 9.00 ± 0.18 4.56 ± 0.09 MDM

3462.848 9.00 ± 0.18 4.63 ± 0.09 MDM

(cont’d)

Table 2.1. Continuum and Hβ Fluxes for NGC 4593

36

Table 2.1—Continued

JD Fλ (5100 A) Hβ λ4861 Data Set

(-2450000) (10−15 erg s−1 cm−2 A−1) (10−13 erg s−1 cm−2)

3463.425 10.23 ± 0.34 4.78 ± 0.10 CrAOa

3464.426 9.58 ± 0.32 4.76 ± 0.10 CrAOa

3465.746 9.19 ± 0.18 4.80 ± 0.10 MDM

3465.890 9.93 ± 0.15 · · · MAGNUM

3467.844 9.19 ± 0.18 4.70 ± 0.09 MDM

3469.355 9.33 ± 0.31 4.87 ± 0.10 CrAO

3469.785 9.41 ± 0.19 4.80 ± 0.10 MDM

3470.364 9.34 ± 0.31 5.05 ± 0.11 CrAO

3470.852 9.54 ± 0.19 5.00 ± 0.10 MDM

3471.848 9.29 ± 0.19 4.90 ± 0.10 MDM

3478.823 9.60 ± 0.07 · · · MAGNUM

3485.007 9.70 ± 0.07 · · · MAGNUM

3508.910 9.91 ± 0.05 · · · MAGNUM

3527.847 9.99 ± 0.03 · · · MAGNUM

3539.818 10.61 ± 0.12 · · · MAGNUM

3556.769 10.46 ± 0.06 · · · MAGNUM

3572.766 8.44 ± 0.12 · · · MAGNUM

3579.766 9.35 ± 0.25 · · · MAGNUM

aContinuum point omitted from final light curve. See §2.2.

37

Sampling Mean

Time Interval(days) Mean Fractional

Series N 〈T 〉 Tmedian Fluxa Error Fvar Rmax

(1) (2) (3) (4) (5) (6) (7) (8)

5100 A 25 1.7 1.0 4.8 ± 0.7 0.06 0.14 1.87 ± 0.19

Hβ 27 1.6 1.0 8.4 ± 0.5 0.02 0.05 1.25 ± 0.04

aSame flux units as Table 2.1 for 5100 A continuum and Hβ, respectively.

Table 2.2. Light Curve Statistics

38

Parameter Value

(1) (2)

τcent 3.73 ± 0.75 days

τpeak 3.4+0.5−1.0 days

σline(mean) 1790 ± 3 km s−1

FWHM (mean) 5143 ± 16 km s−1

σline(rms) 1561 ± 55 km s−1

FWHM (rms) 4141 ± 416 km s−1

MBH (9.8 ± 2.1) × 106M⊙

Table 2.3. Reverberation Results

39

Chapter 3

A Revised Broad-Line Region Radius and Black

Hole Mass for the Narrow-Line Seyfert 1

NGC 4051

We present the first results from a high sampling rate, multi-month reverberation

mapping campaign undertaken primarily at MDM Observatory with supporting

observations from telescopes around the world. The primary goal of this campaign

was to obtain either new or improved Hβ reverberation lag measurements for several

relatively low luminosity AGNs. We feature results for NGC 4051, an SAB(rs)bc

galaxy with a narrow-line Seyfert 1 (NLS1) nucleus at redshift z = 0.00234, here

because, until now, this object has been a significant outlier from AGN scaling

relationships, e.g., it was previously a ∼2–3σ outlier on the relationship between the

broad-line region (BLR) radius and the optical continuum luminosity — the RBLR–L

relationship. (Peterson et al. 2000, 2004) place it above the RBLR–L relation, i.e.,

the BLR radius is too large for its luminosity (cf. Figure 2 of Kaspi et al. 2005).

It also appears to be accreting mass at a lower Eddington rate than other NLS1s

(cf. Figure 16 of Peterson et al. 2004). These two anomalies together suggest that

perhaps the BLR radius has been overestimated by Peterson et al. (2000, 2004);

40

indeed an independent reverberation measurement of the BLR radius in NGC

4051 by Shemmer et al. (2003, hereafter S03) is about half the value measured by

Peterson et al. (2000, hereafter P00). Furthermore, neither the P00 nor S03 data

sets are particularly well sampled on short time scales, so neither set is suitable

for detection of smaller time lags (e.g., ∼<2–3 days). In addition, Russell (2003)

reports a Tully-Fisher distance to NGC 4051 that is ∼50% larger than that inferred

from its redshift (i.e., 15.2 Mpc versus 10.0 Mpc, respectively). This suggests that

the luminosity derived in past studies from the redshift could be an underestimate

and might also be a contributing factor to the placement of NGC 4051 above the

RBLR–L relation. Our campaign significantly improves on the sampling rates of

these previous studies by spanning more than 4 months, during which time we

consistently obtained multiple photometric observations per night and spectroscopic

observations nearly every night from a combination of five different observatories

around the globe.


Most data acquisition and analysis practices employed here follow closely those

described by Denney et al. (2006, i.e., see Chapter 2) and laid out by Peterson et al.

(2004). The reader is referred to these works for additional details and discussions.

Throughout this work, we assume the following cosmological parameters: Ωm = 0.3,

ΩΛ = 0.70, and H0 = 70 km sec−1 Mpc−1.

41

3.1.1. Spectroscopy

Spectra of the nuclear region of NGC 4051 were obtained from both the

1.3-meter telescope at MDM Observatory and the 2.6-meter Shajn telescope of the

Crimean Astrophysical Observatory (CrAO). The MDM observations utilized the

Boller and Chivens CCD spectrograph, where 86 observations were taken over the

course of 89 nights between JD2454184 and JD2454269, targeting the Hβ λ4861 and

[O iii]λλ4959, 5007 emission line region of the optical spectrum. The position angle

was set to 0, with a slit width of 5.′′0 projected on the sky, resulting in a spectral

resolution of 7.6 A across this emission-line region. Figure 3.1 shows the mean

and rms spectra of NGC 4051 based on the MDM observations. We acquired 22

CrAO spectra over 34 nights between JD2454266 and JD2454300 with the Nasmith

spectrograph and SPEC-10 1340 × 100 pixel CCD. For these observations a 3.′′0 slit

was utilized, with a 90 position angle. Spectral wavelength coverage for this data

set was from ∼3800–6000 A, with a dispersion of 1.8 A/pix and a spectral resolution

of 7.5 A. Note that (1) the dispersion varies with wavelength: the value 1.8 A/pix is

given for 5100A, and (2) the real wavelength coverage is slightly greater than given

but the red and blue edges of the CCD frame are unusable (too low S/N ratio)

because of vignetting.

A relative flux calibration of each set of spectra was performed based on the

constancy of the narrow [O iii]λ5007 line flux. Because this line emission originates

42

in the extended, low-density narrow line region, it can be assumed constant over

the timescale of this campaign and therefore serves as the basis for a reliable

relative flux calibration. However, the data quality is not identical from night to

night due to, e.g., seeing, weather conditions, atmospheric transparency, etc. This

affects not only the integrated line flux in each observation, but also properties of

the spectrum such as S/N and resolution. Consequently, we employ the spectral

scaling algorithm of van Groningen & Wanders (1992) for the [O iii]λ5007 flux

calibration. This algorithm determines the best scaling through χ2 minimization

of residuals rather than simply calculating a simple multiplicative scale factor to

scale the spectral fluxes. Following this method, we created a reference spectrum by

averaging all spectra from a given data set. We then formed a difference spectrum by

subtracting the reference spectrum from each individual spectrum. The algorithm

uses a least squares method to minimize the residuals of the [O iii]λ5007 line flux

in each difference spectrum by making small zero-point wavelength calibration

adjustments, correcting for resolution differences, and applying a multiplicative

scale factor to the [O iii]λ5007 line flux of the individual spectrum. Because this

method is based on minimizing residuals between each individual spectrum and

the reference spectrum, there is a small residual dispersion in the line fluxes after

calibration. This dispersion is related to the data quality and the ability of the

scaling algorithm to mitigate night to night differences between individual spectra,

related largely to seeing and S/N. Tests of the original algorithm by van Groningen

43

& Wanders (1992) estimated errors in the scaled fluxes of better than 5%, however,

past studies employing somewhat improved versions of this same scaling algorithm

typically achieved dispersions across a data set of ∼2% (e.g., Peterson et al. 1995).

We measure a dispersion of ∼1.5%, demonstrating the high level of homogeneity

that we have been able to achieve in the current data set.

3.1.2. Photometry

In addition to spectral observations, we obtained supplemental V -band

photometry from the 2.0-m Multicolor Active Galactic NUclei Monitoring

(MAGNUM) telescope at the Haleakala Observatories in Hawaii, the 70-cm telescope

of the CrAO, and the 0.4-m telescope of the University of Nebraska.

The MAGNUM observations were imaged with the multicolor imaging

photometer (MIP) as described by Kobayashi et al. (1998a,b), Yoshii (2002), and

Yoshii et al. (2003). Photometric fluxes measured from 23 observations between

JD2454182 and JD2454311 within an aperture of 8.′′3. Photometric reduction of

NGC 4051 was similar to that described for other sources by Minezaki et al. (2004)

and Suganuma et al. (2006), except the host-galaxy contribution to the flux within

the aperture was not subtracted and the filter color term was not corrected because

these photometric data were later scaled to the MDM continuum light curve (as

44

described below). Also, minor corrections (of order 0.01 mag or less) due to the

seeing dependence of the host-galaxy flux were ignored.

The 76 CrAO photometric observations were collected between J245D4180 and

JD2454299 with the AP7p CCD mounted at the prime focus of the 70-cm telescope

(f = 282 cm). In this setup, the 512 × 512 pixels of the CCD field covers a 15.′

× 15.′ field of view. Photometric fluxes were measured within an aperture of 15.′′0.

For further details of the CrAO V -band observations and reduction, see the similar

analysis described by Sergeev et al. (2005).

The University of Nebraska observations were conducted by taking and

separately measuring a large number of one-minute images (∼20) each of 28

nights between JD2454195 and JD2454290. Details of the observing and reduction

procedure are as described by Klimek et al. (2004). Comparison star magnitudes

were calibrated following Doroshenko et al. (2005a,b) and Chonis & Gaskell (2008).

To minimize the effects of variations in the image quality, fluxes were measured

through an aperture of radius 8 arcseconds. The errors given for each night are the

errors in the means.

3.1.3. Light Curves

Light curves of the Hβ flux were made based on integrated fluxes measured in

the MDM and CrAO spectra between 4815–4920 A and over a linearly interpolated

45

continuum defined between the average flux density in each of the following regions

blueward and redward of Hβ, respectively: 4770–4780 A and 5090–5130 A. The

CrAO Hβ light curve was then scaled to the MDM light curve with a multiplicative

constant based on the average flux ratio between the four pairs of closely spaced

points in the MDM and CrAO Hβ light curves separated by no more than 0.5 day.

This scaling is necessary to account for differences in the amount of [O iii]λ5007

emission line flux that enters the slit in the different data sets due to seeing and

aperture affects. The lower panel of Figure 3.2 shows the Hβ light curve derived

from both data sets after scaling the CrAO fluxes to those measured from MDM

spectra.

A continuum light curve was created with observations from each V -band

photometric data set and the average continuum flux density measured over

5090–5130 A (i.e., rest frame ∼5100 A) in each spectrum of the spectroscopic data

sets. First, the multiplicative scale factor determined above to scale the CrAO Hβ

fluxes to the MDM light curve was also applied to the CrAO continuum fluxes, since

the calibration of these fluxes is also susceptible to the same seeing and aperture

affects as the Hβ flux calibration. Next, this light curve as well as the individual

photometric light curves (see Fig. 3.2, upper panel) were scaled, one by one, to

the same flux scale as the MDM light curve by making an additive, relative flux

adjustment to each. This additive correction is necessary for both spectroscopic

and photometric data because of differences in host galaxy starlight that enters the

46

different aperture sizes of the various data sets. For the photometric observations,

there is an additional component (also additive) due to the larger width of the

filter bandpass. Each light curve was merged with the parent light curve to which

it was scaled before the next light curve was scaled, thus building up a larger,

more well-sampled light curve in the following order: MDM, MAGNUM, CrAO

photometry, University of Nebraska, and CrAO spectroscopy. This was done so

that the smaller, and in some cases shorter, light curves could be scaled to a longer

and more densely sampled parent light curve. The scale factor applied to each

secondary light curve to scale it to its parent light curve was calculated based on the

difference between a linear least squares fit to this light curve and to the parent light

curve before it, starting with the MDM light curve as the initial parent light curve.

The fits to each light curve, both parent and secondary were limited to using only

observations within the same overall temporal range, so that, when necessary, the

beginning and/or ends of the light curves were truncated during the fitting process.

Assignment of uncertainties to the photometric fluxes is described above in the

text or in references describing the photometric data sets. However, we calculated

the uncertainties in the MDM and CrAO spectroscopic fluxes after creating the

light curves for these data sets but before intercalibration. Typically, we determine

uncertainties in our light curve flux measurements by applying a mean fractional

error to all points. This fractional error is determined by comparing the average

flux difference between closely spaced pairs of observations, assuming that flux

47

differences across these short times scales are due to noise rather than genuine

variability. Because real variability has been confirmed by Klimek et al. (2004) to

occur in NGC 4051 on time scales shorter than 2 days, and our sampling rate is ∼1

day, on average, we could not use this method to determine the relative errors on

our spectroscopic flux measurements for this object. Instead, we took advantage of

the observations of other higher-luminosity AGNs that we monitored as part of this

larger campaign (i.e., same telescopes, instrumental setup, and observing conditions;

see Chapter 4). Unlike NGC 4051, these objects neither exhibit variability on such

short time scales nor have such short measured lags. Therefore, the uncertainties

assigned to the NGC 4051 spectroscopic observations seen in Figure 3.2 are an

average of the uncertainties in the flux measurements calculated as described above

from closely spaced observations (separations of ∼<2.0 days) of these other objects

(e.g., typical fractional errors in the range ∼ 0.12 − 0.21 and ∼ 0.14 − 0.27 for the

continuum and line fluxes, respectively).

The merged continuum and Hβ light curves shown in Figure 3.3 are used for the

subsequent time series analysis. These differ from simply combining the individual

light curves, shown in Figure 3.2, in the following ways:

• First, we applied an absolute flux calibration to both light curves by

applying a single multiplicative scale factor determined from the ratio of

the [O iii]λ5007 emission line flux determined by P00 to that measured in

48

the reference spectrum used above for the relative flux calibration. Unlike

the emission line flux in our reference spectrum, the P00 flux measurement

of F ([O iii]λ5007) = (3.91 ± 0.12) × 10−13 erg s−1 cm−2 was taken from

observations obtained under photometric conditions and, consequently, ∼8%

larger than our measured value. Additionally, the P00 measurement was

made employing observing strategies and measurement practices similar to

what we present here, thus validating this direct comparison. This additional

flux calibration does not affect the reverberation results but is necessary for

accurately measuring the 5100A continuum luminosity.

• Second, we subtracted the host galaxy starlight contribution to the

continuum flux, determined using the methods of Bentz et al. (2009a) to be

Fgal(5100A)= (9.18 ± 0.85) × 10−15 erg s−1 cm−2 A−1.

• Third, we binned closely spaced observations as a weighted average and applied

this to continuum flux measurements separated by ≤0.25 days and Hβ flux

measurements separated by ≤0.5 days.

Fluxes for individual observations (i.e., before time binning) from all sources

are listed in Table 3.1. Values listed represent the flux of each observation

after completing all flux calibrations described above (i.e., relative calibration to

intercalibrate all data sets onto the MDM flux scale, followed by absolute calibration

based on the P00 [O iii]λ5007 line flux and removal of host starlight contamination).

49

Column 1 gives the Julian Date of each observation. The 5100 A continuum or

V -band flux and integrated Hβ flux are given in columns (2) and (3), respectively,

and column (4) lists the source of each measurement. Photometric and spectroscopic

observations from CrAO can be differentiated by noting that no Hβ flux values are

present for photometric observations.

Table 3.2 displays statistical parameters describing the final light curves shown

in Figure 3.3. Column (1) gives the spectral feature represented by each light curve,

and the number of data points in each light curve is shown in column (2). Columns

(3) and (4) are mean and median sampling intervals, respectively, between data

points. The mean flux with standard deviation is given in column (5), while column

(6) shows the mean fractional error in these fluxes. Column (7) gives the excess

variance, calculated as

Fvar =

√σ2 − δ2

〈f〉 (3.1)


and 〈f〉 is the mean of the observed fluxes (Rodriguez-Pascual et al. 1997; Edelson

et al. 2002). Finally, column (8) is the ratio of the maximum to minimum flux in the

light curves.

50

3.1.4. Time Series Analysis

A times series analysis of the continuum and Hβ light curves was performed

to determine the mean light travel time lag between continuum and emission line

variations. We used two cross correlation schemes designed for data sets with uneven

time sampling:

1. An interpolation scheme (Gaskell & Sparke 1986; Gaskell & Peterson 1987;

White & Peterson 1994) with an interval of 0.2 day. A cross-correlation function

(CCF) is constructed from the mean value of the correlation coefficient, r,

computed from cross correlating both the interpolated line light curve with the

original continuum light curve and then the interpolated continuum light curve

with the original line light curve, a process during which a range of possible

lags, τ , are imposed on the Hβ light curve.

2. A time binning scheme (Edelson & Krolik 1988; White & Peterson 1994)

with a bin size of 1.0 day. Here, a discrete correlation function (DCF) is

produced, which determines r as a function of lag, similar to the CCF. In this

scheme, however, only the actual data are cross correlated, and the resulting

values of r for all discretely correlated pairs are binned as a function of

lag. The DCF that results gives the mean value of r in each bin, where the

corresponding uncertainty is assigned in a statistical manner (see White &

Peterson 1994). This method prevents possible spurious lag determinations

51

that could potentially arise in the interpolation method due to under-sampling

or large gaps in the data.

The resulting CCF and DCF are shown in Figure 3.4, along with the auto-

correlation function (ACF) computed by cross correlating the continuum with itself.

We characterize the time delay between the continuum and emission line variations

using two parameters derived from the CCF; τpeak is the lag that corresponds to

the largest correlation coefficient, rmax, and τcent is the centroid of the CCF based

on all points with r ≥ 0.8rmax. Time dilation corrected values of τpeak and τcent

determined from the CCF in Figure 3.4 are given in Table 3.3. Uncertainties in

both lag parameters are computed via model-independent Monte-Carlo simulations

that employ the bootstrap method of Peterson et al. (1998), with the additional

modifications of Peterson et al. (2004).

3.2. Comparison with Previous Results

Our measured Hβ lag of τcent = 1.87+0.54−0.50 days from this work is consistent,

within the errors, to the most recent results for this object by S03, who measured

a lag of τcent = 3.1 ± 1.6 days. It is not clear how meaningful a direct comparison

might be, however, because S03 measured the time delay between variations in the

∼6800A continuum flux density and the integrated Hα flux rather than between

the ∼5100A continuum and Hβ. We also note that the median sampling rate of

52

S03 was larger than our measured lag, suggesting to us that the S03 light curves are

undersampled. Furthermore, S03 only perform a cross correlation analysis based on

the DCF method, which sacrifices time resolution.

Our new time delay measurements are inconsistent, however, with the previous

measurement of τcent = 5.8+2.6−1.8 days by Peterson et al. (2004) using data from

P00. These differences are unlikely a luminosity effect, since the average luminosity

states of NGC 4051 were similar during this and the P00 campaigns (logλL5100 =

41.82 and logλL5100 = 41.87, respectively)1. Therefore, we carefully re-examined

the light curves used by P00 to better understand possible causes for the observed

inconsistency.

Netzer & Maoz (1990) suggested that the cause for a similar inconsistency

between lag measurements from two reverberation mapping campaigns of NGC 5548

(Netzer et al. 1990; Peterson et al. 1991) was due to different continuum variability

timescales observed in the separate campaigns: longer continuum variability

timescales lead to larger lag measurements. However, this explanation is unlikely to

be the cause for the current inconsistency between our measured lag and that of P00

because the prominent variability timescales observed in both the P00 and current

continuum light curves are similar (∼40–50 days). Instead, the simplest explanation

for the inconsistency between our measured lag and that of P00 is random error.

1The average observed flux of the S03 campaign was within ∼ 10% that of the Peterson et al.

campaign as well.

53

We investigated this possibility by performing Monte Carlo simulations using the

“Subset 1” Hβ and 5100A continuum flux light curves from P00 with the goal of

estimating the likelihood that a lag of τcent = 5.8 days would be measured, even

if the actual BLR radius of the Hβ emission was 2.7 light days, as expected from

the Bentz et al. (2009a) RBLR–L relation for the average luminosity of NGC 4051

during this time period. In each simulation we created a simulated Hβ light curve by

convolving a modified continuum light curve with a transfer function that assumed a

BLR with a thin spherical shell geometry of radius 2.7 light days. The sampling was

increased in the modified continuum light curve over that of the original Subset 1

continuum light curve by interpolating between the actual points on a 0.5 day scale.

Noise was added to the flux of each interpolated point using a random Gaussian

deviate. The size of each deviate was based on the average uncertainty in flux of the

closest ‘real’ continuum point on each side of the interpolated point. The simulated

emission-line light curve was then sampled identically to the original Subset 1 Hβ

light curve. We cross correlated this new emission-line light curve with the original

Subset 1 continuum light curve to determine a reverberation lag. The simulation

was repeated 10,000 times, and lags were measured similarly for each iteration. We

found that the average lag recovered was 2.7 days (reassuring, since this was our

input radius). However, we were unable to reproduce even a single lag of 5.8 days. In

fact, the largest lag our simulations recovered was 4.0 days. A couple of possibilites

suggest themselves:

54

• The BLR has physically changed in the 11-year interval between the time

of P00’s Subset 1 and the time of our recent campaign. This is a physical

possibility since the dynamical timescale of the BLR in NGC 4051 is <∼ 5

years.

• The P00 data are undersampled and there are really unresolved variations

occurring on timescales shorter than the typical sampling interval of 2.2 days

in Subset 1, the best-sampled part of the P00 light curve.

We have no particular reason to believe the former possibility. However, the

latter is suggested by how P00 established the relative uncertainties of their fluxes,

namely by assuming that there are no true variations on time scales shorter that

the typical sampling time scales and that any differences between closely spaced

measurements reflect random errors only, not true variability. The estimates of the

relative flux errors in the P00 Subset 1 based on comparing measurements separated

by 2 days or less are about 3.2% for both the contiuum and the line. In our new

data set, obtained with the same instrument, we find relative errors of about 1.4%

and 2.1% in the continuum and the line, respectively, using the method described

in Section 3.1.3. We conclude that the flux uncertainties of the P00 data were

overestimated due to short timescale variability.

Proceeding with the assumption that the P00 light curves are undersampled,

we isolated the portion of the light curves that has the highest sampling across the

55

sharpest features. We made this selection in an attempt to avoid occurrences of

undersampling more complex variability. From the initial light curve, reproduced

in Figure 3.5, we removed the first 10 observations that exhibit a broad inflection

in the flux with a poorly defined peak. We perform a cross correlation analysis on

these shortened light curves and determine a shorter lag, τcent = 3.5+3.7−1.9 days. This

lag determination is consistent with both the expected radius of 2.7 light days from

the RBLR–L relation, the current results, and the results of S03.

If we continue with the assumption that the light curves of P00 are

undersampled, and the P00 flux uncertainties are overestimated, their assigned

uncertainties would act to decrease the significance of short timescale variability,

likely attributing it to noise instead. If we impose the average continuum flux

uncertainty measured from our current data set (given above) on the shortened

P00 continuum light curve, we can further improve the precision of this revised lag

measurement to τcent = 3.5+3.2−1.5 days.

We then conducted another simulation in which we applied the sampling rate

from the P00 light curves to the light curves from this work. By undersampling our

current light curves, we can determine the probability that undersampling could lead

to an overestimated lag similar to that measured by P00. This type of simulation

can provide further evidence that the lag measured by P00 was an overestimate

and a consequence of undersampling. At the same time, it could diminish the

possibility that the discrepancy in lag measurements is due to a difference in the

56

physical conditions or structure of the BLR during the P00 campaign compared to

the present. Using the continuum and Hβ light curves shown in Figure 3.3 as the

starting point, we modified them similarly to the continuum light curve described

for our first set of simulations (i.e., increasing the sampling by interpolating between

data points and adding noise to these points with a Gaussian deviate), but this time

we interpolated both the continuum and emission line light curves from this work on

a 0.1 day interval. We then drew sample light curves from this parent light curve

with the same length and sampling pattern as the full P00 light curve shown in

Figure 3.5. We applied the same cross-correlation analysis (as described in Section

3.1.4) to measure lags from these sample light curves. The parent light curves cover

a longer time span than the sample light curves and therefore allow for multiple

iterations of sample light curves to be chosen from different subsets of the parent

light curves. The first iteration of sample light curves are created from the subset of

the parent light curves where the beginning points match up, but the ends of the

parent light curves are discarded. We then build up multiple iterations by shifting

the starting point of the sample light curve in time by one time step, i.e., 0.1 day,

across the parent light curves. In this way, we were able to build up 330 sample light

curves, where in the last iteration, the sample light curves begin in the middle of the

parent light curves, but both sets of light curves end at the same time. Based on

the cross correlation analysis from these 330 sample light curves, the probability of

measuring τcent ≥5.0 days is 0.6% (2 out of 330), and the probability of measuring

57

τcent ≥3.5 days (i.e, the lag we calculated above from only a portion of the P00

light curve) is ∼8% (25 out of 330). We conclude that undersampling is at least a

plausible explanation for the difference between the P00 results and those reported

here.

3.3. Black Hole Mass

Applying virial assumptions to the reverberating gas in the BLR, the mass of

the black hole can be defined by

MBH =fcτ(∆V )2

G, (3.2)

where τ is the measured emission-line time delay, so that cτ represents the BLR

radius, and ∆V is the BLR velocity dispersion (Peterson et al. 2004). The

dimensionless factor f depends on the structure, kinematics, and inclination of the

BLR and is of order unity.

We estimate the BLR velocity dispersion from the line width of Hβ emission

line. The line width can be characterized by either the FWHM or the line dispersion,

i.e., the second moment of the line profile. The FWHM and the line dispersion,

σline, were measured from both the mean and the rms spectra of NGC 4051 shown

in Figure 3.1. Here, we have measured both quantities and their uncertainties

employing methods described in detail by Peterson et al. (2004). All measured

58

values of the Hβ line width are listed in Table 3.3. Typically, the narrow-line

emission component of the line should be removed before measuring the line width

(see Denney et al. 2009a, Chapter 6 of this dissertation); however, this component

could not be reliably isolated from the rest of the line profile in this object. As a

result the line widths measured in the mean spectrum, particularly the FWHM, are

less reliable for these purposes than the widths measured from the rms spectrum2.

We calculate the black hole mass for NGC 4051 using τcent, for the time

delay, τ , and the line dispersion, σline, measured from the Hβ emission line in

the rms spectrum, for the emission-line width, ∆V . We utilize the calibration

of the reverberation mass scale of Onken et al. (2004) for this choice of lag

and line width parameters and therefore adopt a scale factor value of f=5.5.

We then use equation 3.2 to estimate the black hole mass of NGC 4051 to be

MBH = (1.73+0.55−0.52) × 106M⊙. Here, statistical and observational uncertainties have

been included, but intrinsic uncertainties from sources such as unknown BLR

inclination cannot be accurately ascertained.

Marconi et al. (2008) have considered the effect of radiation pressure on SMBH

mass estimates and provide a new prescription for calculating the SMBH mass that

includes a correction factor to account for radiation pressure. Radiation pressure

2Since only BLR emission varies in response to the ionizing continuum on reverberation

timescales, flux contributions from the narrow-line component will not contaminate the line width

measurement in the rms spectrum.

59

acts to partially counteract the force of gravity on the BLR gas, since the outward

radiation force has the same radial dependence (r−2) as the inward gravitational

force. As a result the BLR gas motions are effectively under the influence of an

apparently smaller SMBH mass, which leads to an underestimate of the true SMBH

mass. Marconi et al. (2008) determine that although taking radiation pressure

into account is most important for black holes radiating near the Eddington limit,

it should be considered even for systems with L < LEdd. On the other hand,

in a comparison study of Type 1 versus Type 2 black hole masses determined

with independent methods, Netzer (2009) sees better agreement between the mass

and L/LEdd distributions of these two populations if radiation pressure forces are

neglected. Netzer concludes that either the effects of radiation pressure on the BLR

gas in these objects is negligible or that BLR column densities must be significantly

larger, i.e., NH ∼> 1024cm−2, than assumed by Marconi et al. (2008; NH = 1023cm−2).

In a more recent paper, Marconi et al. (2009) reinvestigate the results of Netzer

(2009) and support their findings on the dependence of the effect of radiation

pressure on column density but conclude that, until it is possible to determine the

nature of the apparent dependence of NH on source properties (e.g., L/LEdd), one

should always consider the possibility that radiation forces are important, and black

hole masses should consequently be determined using the correction of Marconi et al.

(2008).

60

The importance of radiation pressure forces on black hole mass determinations

is still under debate. Therefore, in addition to our virial mass estimate for

NGC 4051 given above, we also estimate the SMBH mass in NGC 4051 taking

radiation pressure into consideration (cf. equation 6 of Marconi et al. 2008), with

f = 3.1 ± 1.4 and log g = 7.6 ± 0.3, which are derived by Marconi et al. from fits

to SMBH masses from reverberation mapping studies. With these scale factors

and the same line width and BLR radius measurements used above, we calculate

a mass of MBH−rad = (1.24+0.57−0.56) × 106M⊙. Contrary to the expectations from the

physical arguments, we calculate a mass smaller than that determined in the case

where we did not consider the effect of radiation pressure. Because NGC 4051 is a

low-luminosity AGN radiating well below the Eddington limit (L/LEdd = 0.030),

the correction to the mass due to radiation pressure is small (smaller even than

the formal observational uncertainties on the mass), adding only 0.26 × 106M⊙

to the mass. However, this radiation-corrected mass estimate is smaller than our

original estimate because the value of f derived by Marconi et al. is a factor of 1.8

smaller than the Onken et al. (2004) value we adopted above. Because this scale

factor was derived in a statistical sense by both Onken et al. and Marconi et al.,

the difference in f values between these two studies has the potential to affect the

mass of an individual object more than would be expected for a statistical sample,

particularly for the low accretion-rate objects that need only a small radiation

pressure correction.

61

3.4. Velocity-Resolved Investigation

The lag measurements between the continuum and Hβ emission in Table 3.3

represent the average time delay across the BLR. Because the BLR is an extended

region and the velocity of the gas is most likely a function of position, gas in different

locations of the BLR should respond to variations in the ionizing continuum flux

on slightly different time scales. The observable result should be a difference in the

reverberation lag measurement in different parts of the line profile (i.e., separated in

velocity space). Velocity-resolved reverberation mapping thus gives us information

about the kinematics of gas in the BLR. Previous studies of time delay differences

between multiple emission lines and the velocity dependence of the lag within a

single emission line have shown that the BLR is virialized and commonly contains an

additional inflow component (e.g., Gaskell 1988; Koratkar & Gaskell 1991; Korista

et al. 1995; Done & Krolik 1996; Welsh et al. 2007; Bentz et al. 2008); however,

the creation of full velocity–delay maps (see Horne et al. 2004) is an aspect of the

reverberation mapping technique that has not yet been fully realized (though see

Horne et al. 1991, Done & Krolik 1996, Ulrich & Horne 1996, and Kollatschny 2003

for previous attempts). By resolving the velocity-dependent reverberation response

of the BLR better than has been done in the past, we can reconstruct and analyze

the velocity–delay map to gain further insights into the geometry and kinematics of

the BLR.

62

We searched for a velocity-dependent reverberation signal by dividing the Hβ

emission line flux into 8 velocity-space bins. The blue and red sides of the line

were separately divided into 4 bins of equal velocity width, covering only the most

variable portions of the line profile, i.e., the outer-most wavelength boundaries were

reduced from those considered for the analysis of the full profile to only include

flux within the range 4840–4900A (roughly ±2,000 km s−1). Light curves were

created from measurements of the integrated Hβ flux in each bin and then cross

correlated with the continuum light curve following the same procedures described

above. The top panel of Figure 3.6 shows the division of the Hβ line profile from

the rms spectrum into the eight velocity bins, and the bottom panel shows the lag

measurements for each of these bins. Error bars in the velocity direction represent

the bin width. The evidence for a velocity-stratified BLR response to continuum

variations is present, but marginal. In particular, the lags measured for bins 1-2

and 7-8 are consistent with zero and might simply reflect correlated errors due to

continuum contamination. Although the shape of the velocity-resolved signal in

Figure 3.6 supports our virial assumptions, since the higher velocity gas varies on

shorter time scales than the low velocity gas, there are no strong indications for

either outflow or inflow. Outflow could be suggested by the larger lag measured

in bin 5 (red side of the line) compared to bin 4 (blue side of the line), but the

difference is very marginal. Even with the high sampling rate and spectral resolution

we achieved during this campaign, observing a velocity-resolved signal for NGC 4051

63

as clearly as that detected for Arp 151 by Bentz et al. (2008) would have been rather

surprising for the following reasons. First, the precision with which we can measure

a lag is somewhat dependent on the median observational sampling interval, which,

for NGC 4051, was still not much shorter than the measured lag. This indicates

that in order to better resolve a velocity-dependent signal, we need even higher time

resolution for this object. Second, because the Hβ line is particularly narrow in this

object, there are only a few velocity resolution elements across the line.

3.5. Discussion

Based on our simulations, reanalysis of the light curves from P00, and the

additional arguments we presented above, we conclude that the inconsistency

between the past measurements of the Hβ reverberation lag in NGC 4051 and

our present measurements most likely results from an overestimation of the lag

by P00. Therefore, we adopt the results from the current reverberation campaign

over previous campaign results measuring this lag in NGC 4051. Using the lag

measurement of τcent = 1.87+0.54−0.50 days presented here and the Tully-Fisher distance of

Russell (2003), NGC 4051 is no longer an outlier on the RBLR–L relationship. Figure

3.7 replicates the most recent version of this relationship by Bentz et al. (2009a) with

both the previous and current lag values of NGC 4051 marked. Secure placement of

low-luminosity objects such as NGC 4051 on the RBLR–L relationship is important

64

for supporting the extrapolation of this relationship to the even lower-luminosity

regime potentially populated by intermediate-mass black holes. Additional results

from the present campaign Denney et al. (2010, see also Chapter 4, this dissertation),

as well as results from a recent monitoring campaign at the Lick Observatory (e.g.,

Bentz et al. 2009c), aim to further populate this low-luminosity end of the RBLR–L

relationship, thus solidifying the calibration in a relatively under-sampled region of

the relation. A reliable calibration of this relationship is imperative for large studies

of black hole masses and galaxy evolution, since it allows for the calculation of black

hole masses from single-epoch spectra and provides luminosity and radius estimates

that help constrain parameter space in the search for intermediate-mass black holes.

Our new results provide a measure of the BLR radius of NGC 4051 that

is closer to the value naively expected from its luminosity. However, these new

results do not resolve the unexpected location of this object on the MBH–L relation:

NLS1s tend to lie on a locus of this relation with relatively high Eddington ratios

(L/LEdd ∼> 0.1; see Figure 16 of Peterson et al. 2004). However, based on the black

hole mass of MBH = (1.73+0.55−0.52) × 106M⊙ that we have calculated, the Eddington

ratio of NGC 4051 is still only L/LEdd = 0.030. It seems unlikely that we have

overestimated the mass of the black hole (and thus underestimated L/LEdd), since

our mass measurement is already a factor of a few lower than predicted by the

MBH–σ⋆ relationship (Nelson & Whittle 1995; Ferrarese et al. 2001). In this case,

the narrowness of the Balmer lines in the spectrum of NGC 4051 might be due at

65

least in part to the inclination of the BLR relative to our line of sight — indeed,

inclination has been invoked as one possible way to explain the NLS1 phenomenon

since the early days of research on these sources (e.g., Osterbrock & Pogge 1985;

Boller et al. 1996). From observations of the narrow-line region in NGC 4051,

Christopoulou et al. (1997) estimate that the inclination of this source is ∼ 50, near

the maximum expected for a Type 1 active nucleus in unified models. It is entirely

reasonable to suppose that the BLR and accretion disk are at the same inclination as

the narrow-line region. Even so, accounting for this high inclination would increase

the line width by only about a factor of 2, still within the NLS1 regime. Clearly

further investigation is required to understand the low value of L/LEdd in NGC 4051

compared to other NLS1s.

66

Fig. 3.1.— Mean and rms spectra of NGC 4051 from MDM observations. Therms spectrum was formed after removing the [O iii]λ4959 and [O iii]λ5007 narrowemission lines. The variability signature of Hβ is clearly visible in the rms spectrum,and the large increase in rms flux shortward of 4800 A is due to variations in thebroad He iiλ4686 emission line.

67

Fig. 3.2.— Light curves showing complete set of observations from all four sources.The top panel shows the 5100 A continuum flux in units of 10−15 erg s−1 cm−2 A−1,while the bottom is the Hβ λ4861 line flux in units of 10−13 erg s−1 cm−2. The opentriangles (CrAOsp) correspond to spectroscopic observations taken at CrAO, whilethe closed triangles (CrAOph) represent photometric observations from CrAO.

68

Fig. 3.3.— Same as Fig. 3.2 except data from all sources have been merged and closelyspaced observations binned such that weighted averages were calculated for continuumobservations separated by less than 0.25 day and Hβ observations separated by lessthan 0.5 day.

69

Fig. 3.4.— Cross correlation function (CCF; solid line), discrete correlation function(DCF; filled circles), and auto correlation function (ACF; dotted line) from time seriesanalysis of the continuum and Hβ light curves of NGC 4051 shown in Fig. 3.3.

70

Fig. 3.5.— Optical continuum and Hβ light curves reproduced from P00. Points withX’s represent those that were excluded from the new time series analysis of this lightcurve described in Section 3.2. Units are the same as in Fig. 3.2.

71

Fig. 3.6.— Velocity-resolved Hβ rms spectrum profile (top) and time-delaymeasurements (bottom) for NGC 4051. Vertical dashed lines plotted on the lineprofile (top) and error bars on the lag measurements in the velocity direction (bottom)show the bin size, with each bin labeled by number in the top panel. Error bars onthe lag measurements are determined similarly to those for the mean BLR lag. Thehorizontal solid and dotted lines in the bottom panel show the mean BLR centroid lagand associated errors, calculated in Section 3.1.4, while the horizontal dotted-dashedline in the top panel represents the linearly-fit continuum level. Flux units are thesame as in Fig. 3.1.

72

Fig. 3.7.— Most recently calibrated RBLR–L relation (Bentz et al. 2009a, solid line).The filled square shows the location of NGC 4051 based on results from Peterson et al.(2004) and used by Bentz et al. The filled circle shows the new lag measurement of1.87 days presented in this work at the luminosity calculated using the Tully-Fisherdistance to NGC 4051 of Russell (2003): the error bar in luminosity reflects both therange of flux variations, as for all of the other data points, plus the uncertainty dueto the distance, added in quadrature. The error bar is asymmetric, as we favor thelarger distance. Open squares represent other objects from Bentz et al. (2009a).

73

JD Fλ (5100 A)a Hβ λ4861 Observatory

(−2450000) (10−15 erg s−1 cm−2 A−1) (10−13 erg s−1 cm−2)

4180.30 5.03 ± 0.18 · · · CrAO

4181.37 5.66 ± 0.16 · · · CrAO

4182.02 5.47 ± 0.09 · · · MAGNUM

4182.41 5.07 ± 0.22 · · · CrAO

4184.79 5.41 ± 0.20 5.22 ± 0.11 MDM

4185.71 4.51 ± 0.19 4.96 ± 0.10 MDM

4186.49 4.51 ± 0.22 · · · CrAO

4186.71 4.89 ± 0.20 4.15 ± 0.09 MDM

4187.38 4.82 ± 0.22 · · · CrAO

4187.85 5.27 ± 0.20 4.95 ± 0.10 MDM

4188.37 4.32 ± 0.25 · · · CrAO

4188.71 4.81 ± 0.20 4.90 ± 0.10 MDM

4189.39 4.75 ± 0.26 · · · CrAO

4189.61 4.78 ± 0.19 4.62 ± 0.10 MDM

4189.96 5.53 ± 0.21 4.88 ± 0.10 MDM

4189.96 4.94 ± 0.05 · · · MAGNUM

4190.41 4.82 ± 0.23 · · · CrAO

4190.72 4.82 ± 0.20 4.73 ± 0.10 MDM

4191.38 4.59 ± 0.32 · · · CrAO

4191.62 4.91 ± 0.20 4.51 ± 0.09 MDM

4191.91 5.27 ± 0.20 4.77 ± 0.10 MDM

4192.43 4.84 ± 0.32 · · · CrAO

4192.75 4.02 ± 0.19 4.44 ± 0.09 MDM

4193.61 4.86 ± 0.20 4.34 ± 0.09 MDM

4193.92 4.41 ± 0.19 4.57 ± 0.10 MDM

4194.73 4.62 ± 0.19 4.60 ± 0.10 MDM

4195.45 4.49 ± 0.16 · · · UNebr.

4195.63 4.30 ± 0.19 4.06 ± 0.09 MDM

4196.62 4.59 ± 0.19 4.22 ± 0.09 MDM

4197.78 4.22 ± 0.19 4.43 ± 0.09 MDM

4198.44 4.34 ± 0.14 · · · UNebr.

4198.78 4.51 ± 0.19 4.80 ± 0.10 MDM

(cont’d)

Table 3.1. V -band, Continuum, and Hβ Fluxes for NGC 4051

74



(−2450000) (10−15 erg s−1 cm−2 A−1) (10−13 erg s−1 cm−2)

4198.93 4.46 ± 0.06 · · · MAGNUM

4199.36 4.68 ± 0.17 · · · CrAO

4199.40 4.78 ± 0.15 · · · UNebr.

4199.86 4.55 ± 0.19 4.37 ± 0.09 MDM

4200.40 4.52 ± 0.15 · · · CrAO

4200.72 4.19 ± 0.19 4.29 ± 0.09 MDM

4201.31 4.84 ± 0.23 · · · CrAO

4201.73 4.59 ± 0.19 4.49 ± 0.09 MDM

4202.37 4.56 ± 0.18 · · · CrAO

4202.95 4.93 ± 0.08 · · · MAGNUM

4204.40 4.53 ± 0.17 · · · CrAO

4204.73 4.35 ± 0.19 4.58 ± 0.10 MDM

4205.34 4.34 ± 0.16 · · · CrAO

4205.62 3.97 ± 0.18 4.37 ± 0.09 MDM

4205.83 4.32 ± 0.03 · · · MAGNUM

4205.91 4.28 ± 0.19 4.54 ± 0.10 MDM

4206.36 4.19 ± 0.18 · · · CrAO

4206.40 4.23 ± 0.23 · · · UNebr.

4206.62 4.31 ± 0.19 4.46 ± 0.09 MDM

4207.40 4.30 ± 0.15 · · · UNebr.

4207.82 4.40 ± 0.19 4.60 ± 0.10 MDM

4208.34 4.42 ± 0.15 · · · CrAO

4208.40 4.26 ± 0.17 · · · UNebr.

4208.62 4.24 ± 0.19 4.58 ± 0.10 MDM

4208.88 4.25 ± 0.03 · · · MAGNUM

4209.40 4.46 ± 0.15 · · · CrAO

4209.78 4.81 ± 0.20 4.81 ± 0.10 MDM

4210.62 5.01 ± 0.20 4.99 ± 0.10 MDM

4211.41 4.70 ± 0.31 · · · CrAO

4212.34 4.64 ± 0.15 · · · CrAO

4212.72 5.11 ± 0.20 5.01 ± 0.11 MDM

4212.75 4.78 ± 0.03 · · · MAGNUM

(cont’d)

75



(−2450000) (10−15 erg s−1 cm−2 A−1) (10−13 erg s−1 cm−2)

4213.34 5.11 ± 0.19 · · · CrAO

4213.74 4.90 ± 0.20 4.50 ± 0.09 MDM

4214.34 4.65 ± 0.20 · · · CrAO

4214.73 4.92 ± 0.20 5.15 ± 0.11 MDM

4215.40 4.72 ± 0.21 · · · CrAO

4215.74 4.84 ± 0.20 4.84 ± 0.10 MDM

4216.32 5.15 ± 0.21 · · · CrAO

4216.73 4.73 ± 0.19 5.09 ± 0.11 MDM

4217.35 4.49 ± 0.23 · · · CrAO

4217.73 4.73 ± 0.19 5.22 ± 0.11 MDM

4218.31 4.58 ± 0.19 · · · CrAO

4218.80 4.31 ± 0.19 4.74 ± 0.10 MDM

4218.91 4.70 ± 0.04 · · · MAGNUM

4219.32 4.73 ± 0.21 · · · CrAO

4219.40 4.71 ± 0.16 · · · UNebr.

4219.83 5.06 ± 0.20 4.70 ± 0.10 MDM

4220.31 4.78 ± 0.25 · · · CrAO

4220.40 5.05 ± 0.16 · · · UNebr.

4220.74 5.18 ± 0.20 4.89 ± 0.10 MDM

4221.35 5.23 ± 0.38 · · · CrAO

4221.74 4.91 ± 0.20 4.75 ± 0.10 MDM

4221.99 4.78 ± 0.08 · · · MAGNUM

4222.40 5.08 ± 0.26 · · · CrAO

4222.74 4.91 ± 0.20 4.83 ± 0.10 MDM

4223.38 4.47 ± 0.25 · · · CrAO

4223.74 4.73 ± 0.19 5.22 ± 0.11 MDM

4224.37 5.12 ± 0.19 · · · CrAO

4224.73 4.81 ± 0.20 5.41 ± 0.11 MDM

4225.35 4.46 ± 0.16 · · · CrAO

4225.80 4.30 ± 0.19 4.56 ± 0.10 MDM

4225.88 4.43 ± 0.03 · · · MAGNUM

4226.29 4.46 ± 0.20 · · · CrAO

(cont’d)

76



(−2450000) (10−15 erg s−1 cm−2 A−1) (10−13 erg s−1 cm−2)

4226.75 3.88 ± 0.18 4.55 ± 0.10 MDM

4227.43 4.28 ± 0.23 · · · CrAO

4227.74 4.12 ± 0.19 4.58 ± 0.10 MDM

4228.80 3.81 ± 0.18 4.54 ± 0.10 MDM

4229.37 3.91 ± 0.15 · · · CrAO

4229.78 3.91 ± 0.18 4.31 ± 0.09 MDM

4230.73 4.38 ± 0.19 4.36 ± 0.09 MDM

4231.36 4.07 ± 0.16 · · · CrAO

4231.59 4.58 ± 0.28 · · · UNebr.

4231.75 4.81 ± 0.20 4.61 ± 0.10 MDM

4232.28 4.47 ± 0.16 · · · CrAO

4232.38 4.59 ± 0.22 · · · UNebr.

4232.73 4.22 ± 0.19 4.53 ± 0.09 MDM

4233.32 4.51 ± 0.15 · · · CrAO

4233.44 4.88 ± 0.18 · · · UNebr.

4233.73 4.64 ± 0.19 4.72 ± 0.10 MDM

4234.32 4.17 ± 0.16 · · · CrAO

4234.73 4.51 ± 0.19 4.69 ± 0.10 MDM

4234.85 4.29 ± 0.03 · · · MAGNUM

4235.31 4.35 ± 0.14 · · · CrAO

4235.46 4.80 ± 0.36 · · · UNebr.

4235.73 4.43 ± 0.19 4.56 ± 0.10 MDM

4236.31 4.53 ± 0.15 · · · CrAO

4236.73 3.96 ± 0.18 4.54 ± 0.09 MDM

4237.31 4.17 ± 0.14 · · · CrAO

4237.52 4.13 ± 0.28 · · · UNebr.

4237.73 3.94 ± 0.18 4.28 ± 0.09 MDM

4238.49 4.38 ± 0.17 · · · UNebr.

4238.73 4.16 ± 0.19 4.42 ± 0.09 MDM

4238.93 4.05 ± 0.06 · · · MAGNUM

4239.35 4.19 ± 0.17 · · · CrAO

4239.43 4.34 ± 0.18 · · · UNebr.

(cont’d)

77



(−2450000) (10−15 erg s−1 cm−2 A−1) (10−13 erg s−1 cm−2)

4239.75 3.81 ± 0.18 4.40 ± 0.09 MDM

4240.29 3.69 ± 0.14 · · · CrAO

4240.47 3.69 ± 0.18 · · · UNebr.

4240.72 3.97 ± 0.18 4.37 ± 0.09 MDM

4241.31 3.74 ± 0.16 · · · CrAO

4241.38 3.92 ± 0.24 · · · UNebr.

4241.73 3.75 ± 0.18 4.30 ± 0.09 MDM

4242.29 3.75 ± 0.14 · · · CrAO

4242.75 3.56 ± 0.18 3.91 ± 0.08 MDM

4243.29 3.35 ± 0.19 · · · CrAO

4243.74 3.39 ± 0.18 4.05 ± 0.09 MDM

4244.78 3.68 ± 0.18 3.90 ± 0.08 MDM

4245.35 4.38 ± 0.25 · · · CrAO

4245.75 4.36 ± 0.19 4.03 ± 0.09 MDM

4245.77 4.21 ± 0.06 · · · MAGNUM

4246.34 4.95 ± 0.18 · · · CrAO

4246.40 4.49 ± 0.17 · · · UNebr.

4246.74 4.06 ± 0.19 4.12 ± 0.09 MDM

4247.74 4.57 ± 0.19 4.20 ± 0.09 MDM

4248.33 4.50 ± 0.21 · · · CrAO

4248.73 4.50 ± 0.19 4.48 ± 0.09 MDM

4249.45 4.36 ± 0.22 · · · CrAO

4249.74 4.40 ± 0.19 4.52 ± 0.09 MDM

4250.41 3.56 ± 0.33 · · · CrAO

4250.74 4.07 ± 0.19 4.44 ± 0.09 MDM

4251.32 3.74 ± 0.30 · · · CrAO

4251.74 4.02 ± 0.19 4.39 ± 0.09 MDM

4252.39 4.47 ± 0.27 · · · CrAO

4252.73 4.15 ± 0.19 4.22 ± 0.09 MDM

4252.88 4.17 ± 0.05 · · · MAGNUM

4253.73 4.44 ± 0.19 4.19 ± 0.09 MDM

4254.35 4.62 ± 0.16 · · · CrAO

(cont’d)

78



(−2450000) (10−15 erg s−1 cm−2 A−1) (10−13 erg s−1 cm−2)

4254.39 4.52 ± 0.17 · · · UNebr.

4255.38 4.73 ± 0.24 · · · CrAO

4255.76 4.40 ± 0.19 4.50 ± 0.09 MDM

4256.35 5.02 ± 0.14 · · · CrAO

4256.71 4.75 ± 0.19 4.56 ± 0.10 MDM

4257.40 4.80 ± 0.17 · · · CrAO

4257.74 4.64 ± 0.19 4.47 ± 0.09 MDM

4258.35 4.52 ± 0.16 · · · CrAO

4258.50 5.06 ± 0.32 · · · UNebr.

4258.76 4.83 ± 0.20 4.91 ± 0.10 MDM

4259.34 5.15 ± 0.17 · · · CrAO

4259.75 4.92 ± 0.20 4.97 ± 0.10 MDM

4259.84 4.81 ± 0.13 · · · MAGNUM

4260.30 4.96 ± 0.17 · · · CrAO

4260.75 4.36 ± 0.19 4.70 ± 0.10 MDM

4261.31 5.08 ± 0.16 · · · CrAO

4261.42 5.15 ± 0.14 · · · UNebr.

4261.74 4.82 ± 0.20 5.16 ± 0.11 MDM

4262.30 4.78 ± 0.16 · · · CrAO

4262.74 4.39 ± 0.19 4.72 ± 0.10 MDM

4263.35 4.68 ± 0.17 · · · CrAO

4263.39 4.47 ± 0.22 · · · UNebr.

4263.72 4.52 ± 0.19 5.01 ± 0.11 MDM

4263.88 4.61 ± 0.11 · · · MAGNUM

4264.76 4.73 ± 0.19 5.12 ± 0.11 MDM

4265.76 5.43 ± 0.20 5.15 ± 0.11 MDM

4266.34 4.84 ± 0.27 5.18 ± 0.23 CrAO

4266.76 5.55 ± 0.21 5.29 ± 0.11 MDM

4267.30 4.43 ± 0.26 5.43 ± 0.24 CrAO

4267.75 4.55 ± 0.19 5.24 ± 0.11 MDM

4268.29 4.33 ± 0.26 5.34 ± 0.23 CrAO

4268.75 4.38 ± 0.19 5.17 ± 0.11 MDM

(cont’d)

79



(−2450000) (10−15 erg s−1 cm−2 A−1) (10−13 erg s−1 cm−2)

4269.32 4.57 ± 0.26 5.16 ± 0.23 CrAO

4269.75 4.56 ± 0.19 5.39 ± 0.11 MDM

4269.84 4.37 ± 0.06 · · · MAGNUM

4270.36 5.09 ± 0.27 5.12 ± 0.23 CrAO

4270.37 4.37 ± 0.20 · · · UNebr.

4271.31 4.52 ± 0.26 5.38 ± 0.24 CrAO

4272.85 4.54 ± 0.04 · · · MAGNUM

4274.31 4.78 ± 0.26 5.16 ± 0.23 CrAO

4275.81 4.31 ± 0.03 · · · MAGNUM

4276.41 4.80 ± 0.20 · · · UNebr.

4277.29 4.42 ± 0.26 4.79 ± 0.21 CrAO

4278.29 4.01 ± 0.25 4.99 ± 0.22 CrAO

4278.48 3.66 ± 0.37 · · · UNebr.

4278.84 4.14 ± 0.06 · · · MAGNUM

4279.31 4.33 ± 0.26 4.74 ± 0.21 CrAO

4279.32 4.22 ± 0.21 · · · CrAO

4280.32 4.61 ± 0.26 4.87 ± 0.21 CrAO

4280.34 4.38 ± 0.43 · · · CrAO

4281.32 4.34 ± 0.24 · · · CrAO

4281.32 4.38 ± 0.26 4.88 ± 0.22 CrAO

4282.33 3.96 ± 0.24 · · · CrAO

4282.35 4.22 ± 0.25 4.47 ± 0.20 CrAO

4283.31 3.78 ± 0.25 4.63 ± 0.20 CrAO

4283.33 3.75 ± 0.24 · · · CrAO

4283.42 3.56 ± 0.20 · · · UNebr.

4284.30 3.64 ± 0.24 4.50 ± 0.20 CrAO

4284.31 3.87 ± 0.18 · · · CrAO

4285.77 3.70 ± 0.09 · · · MAGNUM

4289.29 4.20 ± 0.25 4.22 ± 0.19 CrAO

4289.45 3.65 ± 0.25 · · · UNebr.

4290.30 3.85 ± 0.25 4.41 ± 0.19 CrAO

4290.40 4.27 ± 0.22 · · · UNebr.

(cont’d)

80



(−2450000) (10−15 erg s−1 cm−2 A−1) (10−13 erg s−1 cm−2)

4291.30 3.53 ± 0.24 4.34 ± 0.19 CrAO

4294.29 4.63 ± 0.18 · · · CrAO

4295.32 4.51 ± 0.34 · · · CrAO

4296.29 4.35 ± 0.26 4.67 ± 0.21 CrAO

4296.30 4.57 ± 0.17 · · · CrAO

4298.32 4.78 ± 0.26 4.38 ± 0.19 CrAO

4299.28 4.29 ± 0.26 4.65 ± 0.20 CrAO

4299.31 4.87 ± 0.16 · · · CrAO

4300.28 4.14 ± 0.25 4.68 ± 0.21 CrAO

4304.79 4.66 ± 0.11 · · · MAGNUM

4311.76 4.79 ± 0.09 · · · MAGNUM

aThis column contains the average continuum flux density measured at rest-frame

∼5100A from spectroscopic observations as well as the V -band flux from photometric

observations. Spectroscopic and photometric fluxes were intercalibrated and merged

to create a single continuum light curve (see Section 3.1.3).

Sampling Mean

Time Interval(days) Mean Fractional

Series N 〈T 〉 Tmedian Fluxa Error Fvar Rmax

(1) (2) (3) (4) (5) (6) (7) (8)

5100 A 186 0.71 0.56 4.5 ± 0.4 0.04 0.09 1.69 ± 0.11

Hβ 100 1.17 1.00 4.7 ± 0.3 0.02 0.07 1.39 ± 0.04

aSame flux units as Table 3.1 for 5100 A continuum and Hβ, respectively.


81

Parameter Value

(1) (2)

τcent 1.87+0.54−0.50 days

τpeak 2.60+0.79−1.40 days

σline(mean) 1045 ± 4 km s−1

FWHM (mean) 799 ± 2 km s−1

σline(rms) 927 ± 64 km s−1

FWHM (rms) 1034 ± 41 km s−1

MBHa (1.73+0.55

−0.52) × 106M⊙

MBH−radb (1.24+0.57

−0.56) × 106M⊙

aUsing Onken et al. (2004) calibration.

bUsing Marconi et al. (2008) calibration.

Table 3.3. Reverberation Results

82

Chapter 4

Reverberation Mapping Measurements of Black

Hole Masses in Six Local Seyfert Galaxies

In this work, we present new reverberation-mapping measurements of the BLR

radius and black hole mass for several nearby Seyfert galaxies from an intensive

spectroscopic and photometric monitoring program (the first results of which

were presented in Chapter 3). The goals of this program are (1) to improve the

calibration of local scaling relationships by populating them with not only additional

high-quality measurements, but also replace previous measurements of either poor

quality or that were suspect for one reason or another, and (2) to take the method

of reverberation mapping one step past its currently successful application of

measuring BLR radii and BH masses to uncover velocity-resolved structure in the

reverberation delays from the Hβ emission line. This velocity-resolved analysis

serves as a preliminary assessment to judge the likelihood of recovering Hβ transfer

functions, or “velocity–delay maps”, which describe the response of the emission-line

to an outburst from the ionizing continuum as a function of LOS velocity and

light-travel time-delay (for a tutorial, see Peterson 2001; Horne et al. 2004). Creation

of velocity–delay maps will provide unique knowledge of the structure, inclination,

83

and kinematics of the BLR, which in turn will reduce systematic uncertainties in

reverberation-based black hole mass measurements.

Our monitoring program spanned more than four months, over which primary

spectroscopic observations were obtained nightly (weather permitting) for the first

three months at MDM Observatory. Supplementary observations were gathered from

other observatories around the world. Objects in our sample were targeted because

(a) they had short enough expected lags (i.e., low enough luminosity) that we were

likely to see sufficient variability over the course of our ∼3–4 month campaign

to securely measure a reverberation time delay, (b) they appeared as outliers on

AGN scaling relationships and/or had large uncertainties associated with previous

results due to suspected undersampling or other complications, and (c) previous

observations demonstrated the potential for our high sampling-rate observations to

uncover a velocity-resolved line response to the continuum variations. We also note

that some of the AGNs observed in this program are among the closest AGNs and

are therefore the best candidates for measuring the central black hole masses by

other direct methods such as modeling of stellar or gas dynamics, which will allow

a direct comparison of mass measurements from multiple independent techniques.

This paper is arranged such that we present our observations and analysis in

Section 4.1, the black hole mass measurements are described in Section 4.2, any

84

velocity-resolved structures that we uncovered are presented in Section 4.3, and our

results are discussed in Section 4.4.


Except where noted, data acquisition and analysis practices employed here

follow closely those laid out by Denney et al. (2009b, see Chapter 3, this dissertation)

for the first results from this campaign on NGC4051. The reader is also referred to

similar previous works, such as Denney et al. (2006, Chapter 2, this dissertation)

and Peterson et al. (2004), for additional details and discussions on these practices.

Throughout this work, we assume the following cosmology: Ωm = 0.3, ΩΛ = 0.70,

and H0 = 70 km sec−1 Mpc−1.

4.1.1. Spectroscopy

Spectra of the nuclear region of our complete1 sample (see Table 4.1) were

obtained daily (weather permitting) over 89 consecutive nights in Spring 2007

with the 1.3 m McGraw–Hill telescope at MDM Observatory, and supplemental

spectroscopic observations of most targets were obtained with the 2.6 m Shajn

telescope of the Crimean Astrophysical Observatory (CrAO) and/or the Plaskett

1We also monitored MCG 08-23-067, but because this object did not vary sufficiently during our

campaign, we did not complete a full reduction and analysis of the data and do not include it as

part of our final, complete sample.

85

1.8 m telescope at Dominion Astrophysical Observatory (DAO) to extend the

total campaign duration to ∼120 nights. We used the Boller and Chivens CCD

spectrograph at MDM with the 350 grooves/mm grating (i.e., a dispersion of

1.33 A/pix) to target the Hβ λ4861 and [O iii]λλ4959, 5007 emission line region

of the optical spectrum. The position angle was set to 0, with a slit width of

5.′′0 projected on the sky, resulting in a spectral resolution of 7.6 A across this

spectral region. We acquired the CrAO spectra with the Nasmith spectrograph

and SPEC-10 1340 × 100 pixel CCD. For these observations a 3.′′0 slit was utilized,

with a 90 position angle. Spectral wavelength coverage for this data set was from

∼3800–6000 A, with a dispersion of 1.8 A/pix and a spectral resolution of 7.5 A

near 5100 A. The actual wavelength coverage is slightly greater than this, but the

red and blue edges of the CCD frame are unusable due to vignetting. The DAO

observations of the Hβ region were obtained with the Cassegrain spectrograph and

SITe-5 CCD, where the 400 grooves/mm grating results in a dispersion of 1.1 A/pix.

The slit width was set to 3.′′0 with a fixed 90 position angle. This setup resulted

in a resolution of 7.9 A around the Hβ spectral region. Figure 4.1 shows the mean

and rms spectra of our sample based on the MDM observations. Table 4.2 gives

more detailed statistics of the spectroscopic observations obtained for each target,

including number of observations, time span of observations, spectral resolution, and

spectral extraction window.

86

A relative flux calibration of each set of spectra was performed using the χ2

goodness of fit estimator algorithm of van Groningen & Wanders (1992) to scale

relative fluxes to the [O iii]λ5007 constant narrow-line flux. This algorithm not only

makes a multiplicative scaling to account for the night-to-night differences in flux in

this line caused primarily by aperture affects, but it also makes slight wavelength

shifts to correct for zero-point differences in the wavelength calibration and small

resolution corrections to account for small variations in the line width caused by

variable seeing. The best-fit calibration is found by minimizing residuals in the

difference spectrum formed between each individual spectrum and the reference

spectrum, which was taken to be the average of the best spectra of each object (i.e.,

those obtained under photometric or near-photometric conditions). Because of this

multiple-component calibration method, the final, scaled [O iii]λ5007 line flux in

each spectrum is not exactly the same as the reference spectrum. Instead, there is

a small standard deviation in the mean line flux due to differences in data quality

that averages ∼1.2% across our sample.

4.1.2. Photometry


photometry from the 2.0 m Multicolor Active Galactic NUclei Monitoring

(MAGNUM) telescope at the Haleakala Observatories in Hawaii, the 70 cm telescope

of the CrAO, and the 0.4 m telescope of the University of Nebraska. The number of

87

observations obtained from each telescope and the time span over which observations

were made of each target are given in Table 4.3.

The MAGNUM observations were made with the multicolor imaging photometer

(MIP) as described by Kobayashi et al. (1998a,b), Yoshii (2002), and Kobayashi

et al. (2004). Photometric fluxes were measured within an aperture with radius

8.′′3. Reduction of these observations was similar to that described for other sources

by Minezaki et al. (2004) and Suganuma et al. (2006), except the host-galaxy

contribution to the flux within the aperture was not subtracted and the filter color

term was not corrected because these photometric data were later scaled to the

MDM continuum light curves (as described below). Also, minor corrections (of order

0.01 mag or less) due to the seeing dependence of the host-galaxy flux were ignored.

The CrAO photometric observations were collected with the AP7p CCD

mounted at the prime focus of the 70 cm telescope (f = 282 cm). In this setup, the

512 × 512 pixels of the CCD field projects to a 15.′ × 15.′ field of view. Photometric

fluxes were measured within an aperture diameter of 15.′′0. For further details of

the CrAO V -band observations and reduction, see the similar analysis described by

Sergeev et al. (2005).

The University of Nebraska observations were conducted by taking and

separately measuring a large number of one-minute images (∼20). Details of

the observing and reduction procedure are as described by Klimek et al. (2004).

88

Comparison star magnitudes were calibrated following Doroshenko et al. (2005a,b)

and Chonis & Gaskell (2008). To minimize the effects of variations in the image

quality, fluxes were measured through an aperture of radius 8.′′0. The errors given

for each night are the errors in the means.

4.1.3. Light Curves

Except where noted below for individual objects, continuum and Hβ light

curves were created as followed. Continuum light curves for each object were made

with the V -band photometric observations and the average continuum flux density

measured from spectroscopic observations over the spectral ranges listed in Table

4.2 (i.e., rest frame ∼5100 A). Continuum light curves from each source were scaled

to the same flux scale following the procedure described by Denney et al. (2009b,

Chapter 3, this dissertation). Figure 4.2 (top panels) shows these merged light

curves, where measurements from each different observatory are shown by the

different symbols described in the figure caption.

Light curves of the Hβ flux were made by integrating the line flux above

a linearly interpolated continuum, locally defined by regions just blueward and

redward of the Hβ emission line. The Hβ emission line was defined between the

observed frame wavelength ranges given for each object in Table 4.2. The Hβ light

curves formed from each separate spectroscopic data set (i.e., MDM, CrAO, and

89

DAO) were placed on the same flux scale (i.e., that of the MDM observations) by

again following the scaling procedures described by Denney et al. (2009b, Chapter

3, this dissertation). An additional flux calibration step was used for NGC3516,

however, because it has a particularly extended [O iii] narrow-line emission region.

In an attempt to decrease the uncertainties in our relative flux calibration from slit

losses of this extended emission, we made an additional correction to each MDM Hβ

flux measurement to account for possible differences in the observed [O iii]λ5007

flux due to seeing effects. To measure the expected differences in [O iii]λ5007 flux

entering the slit as a result of changes in the nightly seeing, we followed the procedure

of Wanders et al. (1992), using their artificially seeing-degraded narrow-band image

of the [O iii]λ5007 emission from the nuclear region of NGC3516 (details regarding

the narrow-band data are described by Wanders et al.). Using the differences in

measured flux, we scaled our MDM flux measurements accordingly. We could only

do this for the MDM measurements, since we do not have accurate seeing estimates

for the CrAO and DAO data sets. Because of our deliberately large aperture (see

Table 4.2, Column 8), the effect was not appreciable for most observations, and there

is no indication that our inability to complete the same analysis for the CrAO and

DAO data had any measurable effect on the subsequent time-series analysis. The

lower panels of Figure 4.2 show the Hβ light curves for each object after merging the

separate data sets into a single Hβ light curve.

90

Before completing the time-series analysis, the light curves shown in Figure 4.2

were modified in the following ways:

1. An absolute flux calibration was applied to both continuum and Hβ light

curves by scaling to the absolute flux of the [O iii]λ5007 emission line given

for each object in Column 3 of Table 4.4. For objects in which there was not a

previously reported absolute flux, we calculated one from the average line flux

measured from only photometric observations obtained at MDM.

2. The host galaxy starlight contribution to the continuum flux was subtracted.

This contribution, listed for each target in Column 5 of Table 4.4, was

determined using the methods of Bentz et al. (2009b) for all objects except

Mrk 290, which had not been targeted for reverberation mapping prior to our

observing campaign2. For Mrk 290, we use an estimate made from the spectral

decomposition of a spectrum covering optical wavelengths from 3500–7150 A,

following decomposition method “B” described by Denney et al. (2009a, see

also Chapter 6, this dissertation). This value is only a lower limit, however,

because the slit width through which this broad optical wavelength-coverage

observation was obtained was smaller than that of our campaign observations

(1.′′5 versus 5.′′0).

2The 2008 LAMP campaign (Bentz et al. 2009c) subsequently monitored Mrk 290, and it is

currently being targeted for HST observations (GO 11662, PI Bentz) to measure its host starlight

contribution, but the observations have not yet been completed.

91

3. We “detrended” any light curves in which we detected long-term secular

variability over the duration of the campaign that is not associated with

reverberation variations (Welsh 1999; see also Sergeev et al. 2007, who show

that there is little correlation between long-term continuum variability and

Hβ line properties, demonstrating the independence of this variability on

reverberation processes). Detrending is important because if the time series

contains long-term trends (i.e., compared to reverberation timescales), the flux

measurements are not randomly distributed about the mean and are, thus,

highly correlated on these long timescales. These long time scale correlations

then dominate the results of the cross correlation analysis that determines the

time delay, biasing the desired correlation due to reverberation. Welsh (1999)

strongly recommends removing these low-frequency trends with low order

polynomials (a linear fit at the very least) to improve the reliability of cross

correlation lag determinations. We took a conservative approach and only

linearly detrended light curves in which clear secular variability was detected:

both light curves from Mrk 290, the Hβ light curve from Mrk 817, and the

continuum light curve from NGC3227. These fits are shown in Figure 4.2 for

each of these respective light curves. It was unnecessary to detrend all light

curves, as no improvement in the cross correlation analysis would result from

detrending light curves that already have a relatively flat mean flux. Also,

it is not surprising for associated continuum and line light curves to exhibit

92

different long-term secular trends, since the relationship between the measured

continuum and the ionizing continuum responsible for producing the emission

lines may not be a linear one (Peterson et al. 2002), and the exact response of

the line depends on the detailed structure and dynamics of the BLR.

4. We excluded the points from the Mrk 817 lightcurve with JD<2454200 because

(1) there is a large gap in the data between these points and the rest of the

light curve, and (2) there is little to no coherent variability pattern seen

here (i.e., the continuum is relatively flat and noisy, and the Hβ fluxes are

particularly noisy and essentially useless anyway, given there are no continuum

points at earlier times).

Tabulated continuum and Hβ fluxes for all objects, except for NGC4051 which

were previously reported by Denney et al. (2009b, Chapter 3, this dissertation),

are given in Tables 4.5 and 4.6, respectively. Values listed represent the flux of

each observation after completing all flux calibrations described above, but before

detrending, since this results in an arbitrary flux scale normalized to 1.0. The final

calibrated light curves used for the subsequent time-series analysis are shown for

each object in the left panels of Figure 4.4. Statistical parameters describing these

light curves are given in Table 4.7, where Column (1) lists each object. Columns (2)

and (3) are mean and median sampling intervals, respectively, between data points

93

in the continuum light curves. The mean continuum flux is shown in column (4),

while column (5) gives the excess variance, calculated as

Fvar =

√σ2 − δ2

〈f〉 (4.1)


and 〈f〉 is the mean of the observed fluxes. Column (6) is the ratio of the maximum

to minimum flux in the continuum light curves. Columns (7–11) display the same

quantities as Columns (2–6) but for the Hβ light curves.

4.1.4. Time-Series Analysis

We performed a cross correlation analysis to evaluate the mean light-travel

time delay, or lag, between the continuum and Hβ emission line flux variations.

We primarily employed an interpolation scheme (Gaskell & Sparke 1986; Gaskell

& Peterson 1987, with the modifications of White & Peterson 1994) in which we

alternate interpolating (with an interval equal to roughly half the median data

spacing, i.e., ∼0.5 day) between points in the line (continuum) light curve before

cross correlating it with the original continuum (line) light curve. We then average

the two determinations of the cross correlation coefficient, r, from each interpolation

process, for every possible value of the lag. We checked these results with the discrete

correlation method of Edelson & Krolik (1988), also employing the modifications

of White & Peterson (1994), but we do not show these results here, since they are

94

consistent with our primary cross correlation method, and provide no additional

information.

The right panels of Figure 4.4 show the results of the cross correlation analysis

for each object. Here, the auto-correlation function (ACF), computed by cross

correlating the continuum with itself, is shown in the top right panel for each object,

and the cross correlation function (CCF), computed by cross correlating the Hβ light

curve with that of the continuum, is shown in the bottom right. Because the CCF is

a convolution of the transfer function with the ACF, it is instructive to compare the

two distributions, as the lag measured through this type of cross correlation analysis

will depend not only on the delay map, but also on characteristic time scales of the

continuum variations (see, e.g., Netzer & Maoz 1990). We characterize the time

delay between the continuum and emission-line variations by the parameter τcent,

the centroid of the CCF based on all points with r ≥ 0.8rmax, as well at the lag

corresponding to the peak in the CCF at r = rmax, τpeak. Time dilation-corrected

values of τcent and τpeak determined for each object, using the redshifts listed in Table

4.1, are given in Table 4.8. Uncertainties in both lag determinations are computed

via model-independent Monte-Carlo simulations that employ the bootstrap method

of Peterson et al. (1998), with the additional modifications of Peterson et al. (2004).

95

4.2. Black Hole Masses

We assume that the motions of the BLR are dominated by the gravity of the

central black hole so that the mass of the black hole can be defined by

MBH =fcτ(∆V )2

G. (4.2)

Here, τ is the measured emission-line time delay, so that cτ represents the BLR

radius, and ∆V is the BLR velocity dispersion. The dimensionless factor f depends

on the structure, kinematics, and inclination of the BLR, and we adopt the value

of Onken et al. (2004), f = 5.5 ± 1.4, determined empirically by adjusting the

zero-point of the reverberation-based masses to scale the AGN MBH–σ⋆ relationship

to that of quiescent galaxies.

An estimate of the BLR velocity dispersion is made from the width of the

Doppler-broadened Hβ emission line. This line width is commonly characterized by

either the FWHM or the line dispersion, i.e., the second moment of the line profile.

Table 4.8 gives both FWHM and line dispersion, σline, measurements from the rms

spectra of all objects except Mrk 817, in which the rms profile was not well defined

(see Figure 4.1), and thus we measured the width from the mean spectrum. All

widths and their uncertainties were measured employing methods described in detail

by Peterson et al. (2004). We removed the narrow-line [O iii]λλ4959, 5007 emission

and the narrow-line component of Hβ from all objects before these line widths

96

were measured (except for NGC4051, where this component could not be reliably

isolated due to the line profile shape and, in any case, does not affect our rms line

width measurements; see Denney et al. 2009b, or Chapter 3, this dissertation). Flux

contributions from the narrow-line component will not contaminate the line widths

measured in the rms spectrum (i.e., the narrow-line component does not vary in

response to the ionizing continuum on reverberation timescales), so removal of this

component was generally unnecessary here, except for Mrk 817, as removal of this

component is particularly important when line widths are measured from the mean

spectrum (as was done in Mrk 817) and from any single-epoch spectrum (see Denney

et al. 2009a, or Chapter 6, this dissertation). However, for consistency and to check

the accuracy of our Hβ to O iiiλ5007 line ratio determinations (i.e., we compare

the rms spectra before and after narrow-line removal in Figure 4.1 to look for any

residual narrow-line components), we still remove these components from all objects.

For the width measurements in two cases, Mrk 290 and NGC3227, we narrowed the

line boundaries to 4935–5064 A and 4810–4942 A, respectively, compared to what

was used for the flux measurements, since the rms line profiles of these objects were

clearly narrower than their mean profiles (the rms profile is often narrower than the

mean profile, which is not surprising, given that likely not all flux seen in the mean

spectrum varies in response to the continuum; see, e.g., Korista & Goad 2004).

Black hole masses for all objects, calculated from equation (4.2), are listed in

Table 4.8 and were calculated using τcent, for the time delay, τ , and the quoted line

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dispersion, σline, for the emission-line width, ∆V . This combination of measurements

for the line width and reverberation lag is not only appropriate because it is the

combination used by Onken et al. (2004) to determine the value of the scale factor,

f , that we adopt here, but also because Peterson et al. (2004) show that this

combination also results in the strongest virial relation between line width and

BLR radius, i.e., R ∼ ∆V −0.5. The exception to this prescription for the black

hole mass calculation is Mrk 817, which has a poorly defined, triple-peaked rms line

profile. Because the rms profile is weak and poorly-defined, we measure the line

widths from the mean spectrum and use the Collin et al. (2006) calibration of the

scale factor determined for the line dispersion measured from the mean spectrum,

f = 3.85. Statistical and observational uncertainties have been included in these

mass measurements, but intrinsic uncertainties from sources such as unknown BLR

inclination cannot be accurately ascertained. We also note here that there has been

some debate in the literature as to the importance of radiation pressure on black hole

masses calculated using virial assumptions, since the outward radiation force has the

same radial dependence as gravity (see Marconi et al. 2008; Netzer 2009; Marconi

et al. 2009). As there is not yet conclusive evidence suggesting a radiation-pressure

correction is important for the relatively low Eddington ratio objects we present

here, we do not make this correction, but a radiation-pressure corrected mass can

be computed from the observables given in Table 4.8 and the formulae provided by

Marconi et al. (2008).

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4.3. Velocity-Resolved Reverberation Lags

The primary cross correlation analysis presented above was intended to measure

the average time delay across the full extent of the BLR from which to ascertain

the mean, or “characteristic,” radius of the Hβ-emitting region of the BLR to use

for calculating black hole masses. For this reason, we utilized the full line flux

from which to measure the reverberation signal. However, the BLR is an extended

region, and therefore, the light-travel time for the ionizing continuum to reach

different volume elements within the BLR will vary across the extent of the emitting

region. The expectation is then that the responding BLR gas variations will lag the

continuum variations on slightly different time scales as a function of the line of

sight velocity. Measuring and mapping these slight differences in the BLR response

time across velocity space recovers the transfer function, which is easily visualized

as a velocity–delay map (see Horne et al. 2004). Recovering an unambiguous

velocity–delay map is a continuing goal of reverberation mapping analyses, as the

construction and analysis of such a map is our best hope, with current technology,

of gaining insight into the geometry and kinematics of the BLR.

The construction and analysis of full two-dimensional velocity–delay maps is

beyond the scope of this work and remains the focus of future research. However,

we do present a more simple reconstruction of the velocity-dependent reverberation

signal, observed across the Hβ emission line region when we divide the line flux

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into eight velocity-space bins of equal flux. These results for NGC4051, NGC3516,

NGC3227, and NGC5548 have been previously published (Denney et al. 2009b,c,

Chapters 3 and 5, this dissertation) but are included again here for completeness.

Line boundaries are the same as those used in the full line analysis, except where

noted in Table 4.2. In these cases the narrowed boundaries given above for Mrk 290

were used, and a discussion of the difference in boundary choices for the other

objects are discussed by Denney et al. (2009c, Chapter 5, this dissertation). Light

curves were created from measurements of the integrated Hβ flux in each bin and

then cross correlated with the continuum light curve following the same procedures

described above. Figure 4.6 shows the results of this analysis for all objects, where

the top panel shows the division of each rms Hβ line profile into the eight velocity

bins, and the bottom panels shows the lag measurements and uncertainties for each

of these bins. Error bars in the velocity direction represent the bin width. We see a

variety of velocity-resolved responses that we discuss in further detail below.

4.4. Discussion

4.4.1. Comparison with Previous Results

Some of the objects in this campaign were targeted, at least in part, because

they have previously appeared as outliers on AGN scaling relationships, in

particular, the RBLR–L relationship. As such, all objects except Mrk 290 have

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previous reverberation results, several of which, as evidenced by goals of this

campaign, were suspect for one reason or another and warranted re-observation.

Based on the outcomes of the current analysis, we will group our results into

three categories: (1) new measurements for an object never before targeted, i.e.,

Mrk 290, (2) replacement measurements for objects that had uncertain results

(typically due to undersampling) and for which our results completely replace any

previous measurements of the Hβ reverberation lag, i.e., NGC3227, NGC3516, and

NGC4051, and (3) additional measurements of objects for which we already trust

the previous lag measurements, i.e., NGC5548 and Mrk 817. In this context, we can

compare our new results to previously published results.

New Measurements

At the time of our campaign (first half of 2007), reverberation mapping had

never before targeted Mrk 290. However, in 2008 LAMP also monitored Mrk 290

for a reverberation analysis (see Bentz et al. 2009c), although they were unable to

recover an unambiguous reverberation lag measurement from their data because

Mrk 290 exhibited little variability during their campaign. Therefore, the results we

present here are the only reverberation measurements of this object.

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Replacement Measurements

Our current measurements of NGC3227, NGC3516, and NGC4051 should

completely supercede previous results measuring a reverberation radius based on Hβ

and the black hole mass. A thorough comparison between our new measurement

of the BLR radius of NGC4051 and that from past studies is discussed by Denney

et al. (2009b, Chapter 3, this dissertation), and the reader is referred to this work

for details. However, the main conclusion of that comparison is that the light

curves from which previous measurements of the lag were made (e.g., Peterson et al.

2000) were undersampled, leading to an overestimate of the lag. Our current study

remedied this problem with a much higher sampling rate, routinely obtaining more

than one observation per day.

Previous reverberation lag measurements of the Hβ-emitting region in NGC3227

(Salamanca et al. 1994; Winge et al. 1995; Onken et al. 2003) were reanalyzed by

Peterson et al. (2004). The Hβ light curves of Salamanca et al. (1994) from a Lovers

of Active Galaxies (LAG) campaign were undersampled, and they do not even

attempt to measure a time delay from them. Winge et al. (1995) report an Hβ lag of

18 ± 5 days from observations taken during a period in which the optical luminosity

was only ∼0.3 dex larger than our current observations (i.e., a change in radius of

∼40% is expected from such a change in luminosity, based on a RBLR–L relationship

slope of ∼0.5). However, their average and median sampling intervals were ∼6 and

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four days, respectively, which is marginally sampled compared to what is needed

for this low luminosity source. These were among the very earliest reverberation

campaigns, and therefore, simply did not have the benefit of the predictive power

that we currently have with the RBLR–L relationship to use for planning campaign

observations; i.e., these campaigns were fundamentally exploratory. A reanalysis of

the LAG consortium data presented by Salamanca et al. (1994) was conducted by

Onken et al. (2003) using the van Groningen & Wanders (1992) algorithm to reduce

uncertainties in the relative flux calibration of the spectra. Onken et al. found an

Hβ lag of τcent = 12.0+26.7−9.1 days, consistent with the results of Winge et al. (1995).

Later, Peterson et al. (2004) also re-analyzed the CTIO data presented by Winge

et al. (1995) with the van Groningen & Wanders (1992) algorithm and further

re-examined the LAG data rescaled by Onken et al. (2003). This reanalysis resulted

in some improvement in the Hβ lag determinations and uncertainties, i.e., smaller

overall lags, however, the reanalyzed values still had large uncertainties, resulting in

a measurement consistent with zero lag: τcent = 8.2+5.1−8.4 days and τcent = 5.4+14.1

−8.7 days

for the CTIO and LAG data sets, respectively (Peterson et al. 2004). It is clear that

our new measurement of the Hβ lag in NGC3227 of τcent = 3.75+0.76−0.82 days should

supersede these past results.

Likewise, the previous reverberation data for NGC3516 also came from a LAG

consortium campaign, also with a sampling interval of ∼4 days (Wanders et al.

1993). Since the lag for this object was at least larger than the sampling rate, the

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undersampling was not as severe a handicap as for other objects in our sample, such

as NGC4051 and NGC3227. Thus, reanalysis of the LAG data first by Onken et al.

(2003) and then by Peterson et al. (2004) measure lags of τcent = 7.3+5.4−2.5 days and

τcent = 6.7+6.8−3.8 days, respectively, that are consistent with the original analysis by

Wanders et al., who measure the peak Hβ lag to be 7 ± 3 days, with the centroid of

the CCF yielding a radius of 11 light days. All of these values are consistent with our

new measurement of τcent = 11.68+1.02−1.53 days. Also, the LAG spectra were obtained

through a narrow (2.′′0) slit; as the narrow-line region in this object is partially

resolved, it was necessary to make seeing-dependent corrections to the continuum

and emission-line measurements (Wanders et al. 1992) that are both large and

uncertain. For our new measurements, the aperture corrections are small and have

a negligible effect on the final results; the seeing-corrected and uncorrected fluxes

differ by, on average, 0.09 ± 0.05%, which is smaller than the standard deviation of

our relative flux scaling of 1.6% for NGC3516. Clearly, our new observations with

an approximately daily sampling rate show great improvement over past campaigns,

for these objects, and the results presented here should supersede past values of the

Hβ lag measured for NGC3227, NGC3516, and NGC4051.

Additional Measurements

The goals of this campaign were not only to re-observe outliers or objects with

highly uncertain lag measurements but also to explore the possibility of uncovering

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velocity-resolved kinematic signatures and eventually reconstruct velocity–delay

maps. Therefore, we also monitored two objects, NGC5548 and Mrk 817, for

which previous reverberation mapping results are solid, and lags measured from

this campaign are simply to be considered additional measurements of the BLR

radius. Reasons for making repeat reverberation measurements of AGNs include

(1) exploring the radius-luminosity relationship in a single source, (2) checking

the repeatability of the mass measurements for AGNs at different times, in

different luminosity states, and with different line profiles, and (3) testing different

characterizations of the line width (i.e., determining what line width measure leads

to the most repeatable mass value). The mean lag and black hole mass results

presented here for NGC5548 are consistent with past results, taking into account the

luminosity state of NGC5548 during our campaign compared with other campaigns

(i.e., NGC5548 has been in a low luminosity state for the past several years, but the

measured lags have been consistently smaller, as expected for this low state; also see

Bentz et al. 2007, 2009c).

We also monitored Mrk 817, which is the highest luminosity object in our

present sample. Previous measurements of the Hβ radius were made by Peterson

et al. (1998) from an eight-year campaign to monitor nine Seyfert 1 galaxies.

From this campaign, they separately measured the lag from three different

observing seasons. The reanalysis of this data by Peterson et al. (2004) resulted in

rest-frame τcent measurements of 19.0+3.9−3.7, 15.3+3.7

−3.5, and 33.6+6.5−7.6 days. Bentz et al.

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(2009b) calculate a weighted average of log τcent from these three measurements of

(converted back to linear space) 〈τcent〉wt = 21.8+2.4−3.0 days at an average luminosity

of 〈log L5100〉wt = 43.64 ± 0.03 to use in calibrating the RBLR–L relationship. The

luminosity of Mrk 817 during our campaign was only about 0.1 dex higher than

the weighted average luminosity quoted by Bentz et al., and our measured lag of

τcent = 14.04+3.41−3.47 days is highly consistent with the shortest lag of Peterson et al. and

marginally consistent with the 19.0 day lag and the weighted average. Furthermore,

the virial mass that we measure (see Column 8 of Table 4.8) is also consistent with

those given by Peterson et al. (2004). Unfortunately, we were not able to improve

on the uncertainties associated with these measurements, as our Hβ light curve for

this object was rather noisy (see Figures 4.2 and 4.4), which decreases the certainty

with which we are able to trace the reverberated continuum variations in the line

light curve. Since there was neither an improvement over nor a discrepancy with

past measurements, this new result is simply added to past results as an additional

measurement of the Hβ-based BLR radius and MBH in Mrk 817.

4.4.2. The BLR Radius Luminosity Relationship

To investigate the outcome of our goal to improve the calibration of scaling

relations by re-examining objects that had large measurements uncertainties

and/or that appeared as outliers on these scaling relationships, we place our new

measurements in context to the RBLR–L relationship most recently calibrated by

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Bentz et al. (2009b). Luminosities were measured from the average, host-corrected

continuum flux density measured within the 5100 A rest-frame continuum windows

listed for each object in Table 4.2. For most objects, we simply corrected for Galactic

reddening along the line of sight (Schlegel et al. 1998); however, NGC3227 and

NGC3516 show evidence of internal reddening that must be taken into account in

determining the luminosity. Gaskell et al. (2004) argue that the UV-optical continua

of AGNs are all very similar, so that the reddening can be estimated by dividing

the spectrum of a reddened AGN by the spectrum of an unreddened AGN. In the

case of NGC3227, we use the value of AB determined by Crenshaw et al. (2001) by

comparing the UV-optical spectrum of NGC3227 to the unreddened spectrum of

NGC4151. For NGC3516, we consider two methods for estimating the reddening,

which result in consistent estimates of AB: (1) we follow the Crenshaw et al. method,

comparing the spectrum of NGC3516 again to that of NGC4151, which results

in AB = 1.72, and (2) we use the Balmer decrement measured from the broad

components of the Hα and Hβ emission lines to estimate a reddening of AB = 1.68.

These two values are highly consistent, and we adopt the average between the two

methods of AB = 1.70. Our measured luminosities are given in Column 9 of Table

4.8, where the uncertainties in the luminosities are the standard deviation in the

continuum flux over the course of the campaign, except for NGC4051, where the

uncertainty in the distance is added in quadrature to this (see Denney et al. 2009b,

Chapter 3, this dissertation).

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The top panel of Figure 4.7 shows the Bentz et al. (2009b) RBLR–L relationship,

reproduced from the bottom panel of their Figure 5. Here, we have differentiated the

objects targeted for our present campaign with solid squares, while all other objects

presented by Bentz et al. are open squares. The bottom panel of Figure 4.7 shows

our current results, where the objects for which our new measurements are either

truly new (i.e., Mrk 290) or have become replacements for old values are shown by

the solid stars, and we no longer plot the old values. Our additional measurements

for NGC5548 and Mrk 817 are shown with the open stars, and the previous weighted

average lags and luminosities for these objects as reported by Bentz et al. are still

present in this bottom panel. The reader should immediately notice the increased

precision and accuracy of our new and replacement measurements, where it is

important to note that we have not determined a new fit to the data3. Clearly,

these better measurements emphasize the small intrinsic scatter in this relationship,

reinforcing the apparently homologous nature of AGNs, even over many orders of

magnitude in luminosity. The results from this campaign also support the conclusion

of Peterson (2010) that improving this relationship further will not come from simply

obtaining more BLR radii measurements to “beat down” the noise, but rather, from

more reliable, higher-precision measurements.

3Re-evaluating the fit to and scatter in this relationship is outside the scope of this paper but is

planned for future work that will include all new, relevant data (see, e.g., Bentz et al. 2009c).

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4.4.3. Velocity-Resolved Results

The cleanest cases of a velocity-resolved reverberation response are for

NGC3516, NGC3227, and NGC5548, where we see kinematic signatures indicating

apparent infall, outflow, and non-radial, or “virialized,” motions, respectively.

Denney et al. (2009c, Chapter 5, this dissertation) discuss the velocity-resolved

results for these three objects and the implications of these different kinematic

signatures in the context of our overall understanding of the BLR and the use of

BLR radii measurements for determining black hole masses. In addition, Denney

et al. (2009b, Chapter 3, this dissertation) present and discuss the marginally

velocity-resolved lags shown here for NGC4051, and so those results are not

discussed further here.

The objects not discussed in previous publications are Mrk 290 and Mrk 817.

Figure 4.6 shows that there is very little variation in the reverberation lag across

the full width of the Mrk 290 line profile, indicating that any differences in the

reverberation lag across the extent of the Hβ-emitting region in this object were

unresolvable with the sampling rate of our campaign. An additional possibility

for the uniform response we observed (i.e., small range in lags and no short lags

observed) could be that the highest velocity gas seen in the wings of the mean

spectrum is optically thin, and therefore does not respond to the continuum

variations. This is supported by the narrowness of the Hβ profile in the rms

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spectrum compared to that observed in the mean spectrum. On the other hand,

based on the relative emission-line strengths of the high-velocity wings in several

AGNs, Snedden & Gaskell (2007) argue against this interpretation.

At first glance, Mrk 817 appears to show an outflow signature similar to that

of NGC3227, however, cross correlation between the continuum light curve and

those derived from the line flux in the first four velocity bins actually results in

lag determinations that are, though negative, largely consistent with zero lag.

Ignoring these first bins gives results similar to Mrk 290, where no velocity-dependent

differences in the lags are resolved. Taken at face value, this result is curious. We

present binned light curves of the Mrk 817 line profile in Figure 4.8, where to increase

the clarity of the discrepancy between the red and blue sides of the line for this

discussion, we have combined sets of two bins to make a total of 4 bins instead of

eight, i.e., we plot the flux from bin 1 added to that of bin 2, bin 3 added to bin

4, etc. For completeness we also recompute the CCFs (also shown in Fig. 4.8) and

velocity-resolved lag measurements for these four combined bins and find results

consistent with simply taking the average of the lags of each set of two bins that we

combined, though the uncertainties in the newly measured lags are generally smaller,

particularly for the bluest and reddest bins. Upon inspection of the individual light

curves for these bins, it becomes apparent that the cross correlation analysis for these

bins essentially failed, not finding a strong correlation between the continuum flux

variability and that seen in the light curves of Bin 1 and Bin 2. The light curves show

110

a lack of variability in the flux in these bins during the first half of the campaign,

and then a fairly monotonic rise in flux during the second half, so the peak in the

continuum flux seen near ∼JD2454230 is not seen in the light curves of Bins 1 and

2, and instead, the feature the cross correlation analysis picks up is the trough near

∼JD2454282, apparently seen in the Bins 1 and 2 light curves ∼8–10 days earlier.

This combination causes the cross correlation analysis to give unreliable results.

Furthermore, no real indication of the expected positive lag can been seen by eye, as

can with the other bins (and other objects, for that matter). The observations could

be explained by some gas having an unresolved velocity structure near the mean

radius measured for this object and there also being an outflowing component in the

BLR of this object, so that the blue-shifted gas is primarily along line of sight and

a resulting zero day lag is measured. However, given that (1) the overall variability

observed in this object was small during this campaign, and (2) the Hβ profile is

very broad, leading to a small variability signal spread over a large wavelength range,

we cannot make any strong conclusions at this time. Future efforts will be made

both to glean further information from the velocity–delay map reconstructed from

our current data as well as to re-analyze the previous monitoring data on this object

in an attempt to search for any other indications of velocity-resolved signatures.

Despite the differences we see in the velocity-resolved kinematics across our

sample of objects, we do not see anything obvious that causes concern for the

masses derived from the mean BLR radii measured from these reverberation lags.

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Observing unresolved, virial, or infalling gas motions certainly do not question

the validity of our assumptions of the gravitational dominance of the BH over the

BLR gas. Although the indications of outflow may be somewhat problematic, we

note that even given these signatures, the mean lag we measure is still consistent

with lags derived from the majority of the emission-line gas. Besides, it is only

gas outflowing at velocities larger than the escape velocity that would break the

validity of our assumptions, and this does not seem to be the case. Likely, there

are multiple components within the BLR, and the disk-wind model of Murray et al.

(1995), for example, is still able to justify the constraint of the black hole mass by

the reverberation mapping radii measurements, even with the presence of a wind

(see Chiang & Murray 1996).

From velocity-resolved studies such as the one discussed here and in our

previous publications on this data set (Denney et al. 2009b,c, Chapters 3 and 5,

this dissertation), it is clear that high-cadence reverberation mapping studies are

beginning to push the envelope with respect to the amount of information we are

able to glean from data of high quality and homogeneity. The next goal is to attempt

a reconstruction of the velocity-resolved transfer function through the production of

velocity–delay maps, with priority placed on the objects shown here and discussed

by Denney et al. (2009c, Chapter 5, this dissertation) that exhibit statistically

significant kinematic signatures of infall, outflow, and virialized motions (NGC3516,

NGC3227, and NGC5548, respectively). Preliminary results from this analysis show

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the potential to reveal the types of structured maps that will hopefully provide

additional constraints on future models of the BLR and more clearly reveal distinct

kinematic structures responsible for the velocity-resolved signatures we presented

here.

4.5. Conclusion

We have reported the results for our complete sample of six local Seyfert 1

galaxies that were monitored in a reverberation mapping campaign that aimed to

remeasure the BLR radius from Hβ emission in objects that previously had poor

measurements (large measurement uncertainties and/or undersampled light curves)

or that were targeted with the aim of recovery of velocity-resolved reverberation

lag signals and/or transfer functions. Based on the measured luminosities of our

sample over the course of our ∼4 month campaign, we measure Hβ lags that are

in excellent agreement with the expectations of the most recent calibration of the

RBLR–L relationship of Bentz et al. (2009b).

Combining these lag measurements with velocity dispersion measurements

estimated from the width of the broad Hβ emission line, we make direct black hole

mass measurements for our entire sample. Based on a comparison of our results with

previous measurements (where available), most of our sample constitutes results

that are either entirely new (Mrk 290) or supercede past measurements (NGC3227,

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NGC3516, and NGC4051). However, for NGC5548 and Mrk 817, we compared our

current mass measurements with past results and find them consistent within the

measurements uncertainties, and therefore, place these results under the category of

“additional measurements” for these objects.

An additional goal of this campaign was to determine velocity-resolved

reverberation lags across the extent of the Hβ-emitting region of the BLR for use

in future efforts to recover velocity–delay maps to help constrain the geometry and

kinematics of the BLR. Though the velocity structure in some of our targets remained

unresolved on sampling-rate-limited time scales, we still found some statistically

significant and kinematically diverse velocity-resolved signatures, even within this

small sample. We see indications of apparent infall, outflow, and virialized motions,

which, if taken at face value, would indicate that the BLR is a complicated region

that differs from object to object. However, given the small scatter in the RBLR–L

relation and the consistency with which we are able to measure the BLR radius and

black hole mass in multiple objects across dynamical time scales (e.g., NGC5548 and

Mrk 817), it is unlikely that the steady-state dynamics within this region are truly

this diverse. The BLR could be made up of multiple kinematic components with

possible transient features such as winds and/or warped disks that travel through

the line of sight to the observer over dynamical timescales. In such a scenario,

evidence for different types of kinematic signatures would arise depending on the

observer’s line of sight through this region at a given time. In order to quantify such

114

possibilities and fit models to the velocity-resolved data, it is necessary to collect

more velocity-resolved reverberation mapping results for these objects, as well as

others. This remains a goal for future observing programs, and efforts are focused

on recovering velocity–delay maps for the current sample. Similar efforts are being

made by the LAMP consortium (M. Bentz, priv. comm.) with the sample presented

by Bentz et al. (2009c), increasing our probability of success for this elusive goal of

reverberation mapping.

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Fig. 4.1.— Mean and rms (variable emission) spectra from MDM observations. Thesolid lines show the narrow-line subtracted spectra, while the dotted lines show thenarrow-line component of Hβ and the [O iii]λλ4959, 5007 narrow emission lines andrms residuals.

116

Fig. 4.2.— Light curves for complete data set. Top: The 5100 A continuum flux inunits of 10−15 ergs s−1 cm−2 A−1. Bottom: Hβ λ4861 line flux in units of 10−13 ergss−1 cm−2. Observations from different sources are as follows: CrAO photometry —solid triangles, MAGNUM photometry — solid circles, UNebr. photometry — solidsquares, MDM spectroscopy — open circles, CrAO spectroscopy — open triangles,and DAO spectroscopy — asterisks. Solid lines show detrending fits to light curves.

117

Fig. 4.3.— Light curves showing complete set of observations from all sources for allobjects (continued). See Figure 4.2 for details.

118

Fig. 4.4.— Left panels: Merged and detrended (where applicable) continuum (top)and Hβ (bottom) light curves used for cross correlation analysis. Units are the sameas Tables 4.5 and 4.6, but the flux scale of each detrended light curve is arbitrary.Right panels: Cross-correlation functions for the light curves. Each top panel showsthe autocorrelation function of each continuum light curve, and the bottom panelsshow the cross-correlation function of Hβ with the continuum.

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Fig. 4.5.— Merged and detrended light curves for time series analysis and crosscorrelation functions for full sample (continued). See Figure 4.4 for details.

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Fig. 4.6.— Top panels: Hβ rms profile of each object broken into bins of equalflux (numbered and separated by dashed lines) with the linearly-fit continuum levelshown (dotted-dashed line). Flux units are the same as in Fig. 4.1. Bottom panels:

Velocity-resolved time-delay measurements. Measurements and errors are determinedsimilarly to those for the mean BLR lag, and error bars in the velocity direction showthe bin size. The horizontal lines show the mean BLR centroid lag and errors.

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Fig. 4.7.— Top: Most recently calibrated RBLR–L relation (Bentz et al. 2009b, solidline). The closed points show the location of our targets, and open points show allother objects used by Bentz et al. Bottom: Same as top but with our new resultsdisplayed. Solid stars show new objects or improvements upon past results whichreplace solid points of NGC4051, NGC3227, NGC3516, and Mrk 290 in top panel,and open points show results for NGC5548 and Mrk 817, which serve as additionalmeasurements for these objects but do not replace previous measurements. Note thatwe keep the same calibration of the relationship as determined by Bentz. et al.; nonew fit has been calculated with our new results.

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Fig. 4.8.— Left panels: Continuum (top) and linearly detrended Hβ light curves ofMrk 817 from four equal flux bins. Units are the same as Tables 4.5 and 4.6. Right

panels: Cross-correlation functions for the light curves. The top panel shows theautocorrelation function of the continuum light curve, and the lower panels show thecross-correlation function of each Hβ bin with the continuum.

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Objects z α2000 δ2000 Host AB

(hr min sec) ( ′ ′′) Classification (mag)

(1) (2) (3) (4) (5) (6)

Mrk 290 0.02958 15 35 52.3 +57 54 09 E1 0.065

Mrk 817 0.03145 14 36 22.1 +58 47 39 SBc 0.029

NGC3227 0.00386 10 23 30.6 +19 51 54 SAB(s) pec 0.76a

NGC3516 0.00884 11 06 47.5 +72 34 07 (R)SB(s) 1.70a

NGC4051 0.00234 12 03 09.6 +44 31 53 SAB(rs)bc 0.056

NGC5548 0.01717 14 17 59.5 +25 08 12 (R’)SA(s)0/a 0.088

aValues have been adjusted to account for additional internal reddening as described

in section 4.4.2.

Table 4.1. Object List

124

Julian Dates Res 5100A Cont. Hβ Line Extraction

Objects Observ. Nobs (-2450000) (A) Window (A) Limits (A) Window (′′)

(1) (2) (3) (4) (5) (6) (7) (8)

Mrk 290 MDM 71 4184–4268 7.6 5235–5265 4915–5086a,b 5.0×12.75

CrAO 18 4266–4301 7.5 5235–5265 4915–5086 3.0×11.0

DAO 11 4262–4290 7.9 5235–5265 4915–5086 3.0×6.28

Mrk 817 MDM 65 4185–4269 7.6 5245–5275 4900–5099 5.0×12.75

CrAO 23 4265–4301 7.5 5245–5275 4900–5099 3.0×11.0

NGC3227 MDM 75 4184–4268 7.6 5105–5135 4795–4942a,b 5.0×8.25

NGC3516 MDM 74 4184–4269 7.6 5130–5160 4845–4965b 5.0×12.75

CrAO 19 4266–4300 7.5 5130–5160 4845–4965b 3.0×11.0

NGC4051 MDM 86 4184–4269 7.6 5090–5130 4815–4920 5.0×12.75

CrAO 22 4266–4300 7.5 5090–5130 4815–4920 3.0×11.0

NGC5548 MDM 77 4184–4267 7.6 5170–5200 4845–5004b 5.0×12.75

CrAO 20 4265–4301 7.5 5170–5200 4845–5004b 3.0×11.0

DAO 11 4276–4293 7.9 5170–5200 4845–5000b 3.0×6.28

aHβ line limits were narrowed for the measurement of the line width in the rms

spectrum. See Section 4.2 for details.

bHβ line limits were changed for the velocity-resolved lag investigation. See Section

4.3 for details.

Table 4.2. Spectroscopic Observations

125

Julian Dates

Objects Observatory Nobs (-2450000)

(1) (2) (3) (4)

Mrk 290 MAGNUM 17 4200–4321

CrAO 61 4180–4298

UNebr 6 4199–4252

Mrk 817 MAGNUM 24 4185–4330

CrAO 69 4180–4299

NGC3227 MAGNUM 19 4181–4282

CrAO 58 4180–4263

UNebr 19 4195–4276

NGC3516 MAGNUM 10 4190–4277

CrAO 73 4181–4299

UNebr 22 4195–4258

NGC4051 MAGNUM 23 4182–4311

CrAO 76 4180–4299

UNebr 28 4195–4290

NGC5548 MAGNUM 48 4182–4332

CrAO 71 4180–4299

UNebr 13 4198–4289

Table 4.3. Photometric Observations

126

FWHM([O iii]λ5007)a F ([O iii]λ5007)b Hβnar FHostc

Objects rest frame (km s−1) Line Strength

(1) (2) (3) (4) (5)

Mrk 290 380 1.91 ± 0.12 0.08 1.79

Mrk 817 330 1.32 ± 0.07 0.08 1.84 ± 0.17

NGC3227 485 6.81 ± 0.54 0.088d 7.30 ± 0.67

NGC3516 250 3.35 ± 0.42 0.07 16.1 ± 1.5

NGC4051 190 3.91 ± 0.12d · · · 9.18 ± 0.85

NGC5548 410 5.58 ± 0.27e 0.11f 4.48 ± 0.41

aFrom Whittle (1992).

bUnits of 10−13 ergs s−1 cm−2

cUnits of 10−15 ergs s−1 cm−2 A−1

dFrom Peterson et al. (2000).

eFrom Peterson et al. (1991).

fFrom Peterson et al. (2004).

Table 4.4. Constant Spectral Properties

127

Mrk290 Mrk 817 NGC3227 NGC3516 NGC5548

JDa Fcontb JDa Fcont

b JDa Fcontb JDa Fcont

b JDa Fcontb

4180.47p 1.083±0.015 4180.44p 4.621±0.038 4180.28p 3.959±0.064 4181.33p 6.433±0.104 4180.41p 2.800±0.055

4181.54p 1.070±0.015 4181.52p 4.622±0.036 4181.32p 3.971±0.057 4182.39p 6.135±0.126 4181.50p 2.878±0.058

4184.97m 1.102±0.047 4185.02g 4.654±0.048 4181.90g 3.250±0.052 4184.74m 5.574±0.364 4182.06g 3.128±0.032

4185.96m 1.109±0.047 4185.92m 4.602±0.078 4182.36p 3.836±0.059 4185.66m 5.897±0.369 4184.92m 2.912±0.118

4186.61p 1.102±0.033 4186.60p 4.744±0.060 4184.68m 3.363±0.149 4186.47p 5.753±0.162 4185.86m 2.643±0.114

4186.94m 1.194±0.048 4186.87m 4.552±0.077 4185.61m 3.623±0.153 4187.36p 5.823±0.139 4186.58p 2.709±0.062

4187.48p 1.184±0.021 4187.46p 4.834±0.052 4186.45p 3.857±0.058 4188.35p 5.579±0.185 4186.83m 2.624±0.113

4187.96m 1.242±0.049 4188.49p 4.778±0.046 4187.35p 3.915±0.079 4188.66m 6.065±0.373 4188.47p 2.627±0.060

4188.52p 1.194±0.018 4188.91m 4.561±0.077 4187.61m 3.502±0.151 4189.36p 5.607±0.134 4188.86m 2.852±0.117

4188.95m 1.188±0.048 4189.52p 4.830±0.055 4188.34p 4.044±0.076 4189.71m 6.641±0.379 4189.50p 2.608±0.068

4189.54p 1.201±0.023 4189.86m 4.602±0.078 4188.61m 4.003±0.159 4190.39p 5.620±0.113 4189.81m 2.556±0.113

4189.90m 1.229±0.049 4190.55p 4.720±0.082 4190.61m 3.994±0.158 4190.66m 5.847±0.371 4189.88g 2.569±0.038

4190.56p 1.167±0.025 4191.13g 4.835±0.136 4191.36p 3.961±0.104 4190.78g 5.424±0.108 4190.53p 2.676±0.081

4190.93m 1.274±0.050 4191.53p 4.746±0.072 4191.66m 4.012±0.159 4191.31p 5.722±0.137 4190.88m 2.413±0.111

4191.55p 1.225±0.033 4191.86m 4.796±0.080 4192.42p 4.053±0.096 4191.71m 5.205±0.359 4191.50p 2.487±0.112

4191.95m 1.205±0.048 4192.56p 4.756±0.059 4192.61m 4.495±0.165 4192.40p 5.691±0.179 4191.81m 2.771±0.116

4192.58p 1.187±0.026 4192.90m 4.734±0.079 4193.66m 4.096±0.160 4192.66m 4.738±0.351 4191.86g 2.437±0.036

4192.94m 1.270±0.050 4194.92m 4.772±0.080 4193.80g 3.737±0.031 4193.75m 4.686±0.351 4192.54p 2.414±0.125

4194.96m 1.249±0.049 4200.55p 4.786±0.042 4194.62m 3.892±0.157 4194.68m 4.744±0.352 4192.85m 2.660±0.114

4197.97m 1.149±0.047 4201.12g 4.822±0.222 4195.37n 4.332±0.053 4195.43n 5.188±0.160 4193.71m 2.778±0.116

(cont’d)

Table 4.5. V -band and Continuum Fluxes

128


Mrk 290 Mrk 817 NGC3227 NGC3516 NGC5548



b JDa Fcontb

4199.40n 1.181±0.043 4201.43p 4.776±0.052 4195.69m 4.430±0.164 4196.67m 4.784±0.352 4194.10g 2.203±0.078

4199.98m 1.219±0.049 4201.90m 4.803±0.080 4196.38p 3.843±0.225 4197.70m 5.188±0.355 4194.87m 2.582±0.113

4200.36g 1.185±0.026 4202.52p 4.821±0.049 4196.81m 3.910±0.157 4198.44n 5.196±0.150 4197.81g 2.355±0.051

4200.57p 1.128±0.016 4204.51p 4.958±0.110 4197.64m 3.836±0.156 4198.69m 5.952±0.373 4197.92m 2.417±0.111

4201.46p 1.140±0.017 4204.85m 4.791±0.080 4197.96g 3.897±0.036 4198.90g 5.927±0.083 4198.60n 2.491±0.130

4201.95m 1.217±0.049 4205.46p 4.936±0.039 4198.40n 3.911±0.072 4199.34p 5.886±0.096 4198.84m 2.338±0.109

4202.54p 1.153±0.019 4205.86m 5.002±0.082 4198.64m 4.087±0.160 4199.40n 5.751±0.110 4199.06g 2.353±0.043

4204.50p 1.110±0.017 4206.50p 4.874±0.058 4199.32p 4.201±0.057 4200.37p 5.766±0.125 4199.51p 2.337±0.068

4204.90m 1.063±0.046 4207.11g 5.174±0.214 4199.39n 4.151±0.072 4200.67m 5.386±0.362 4199.93m 2.326±0.109

4205.49p 1.090±0.019 4207.92m 5.046±0.082 4199.63m 4.235±0.161 4201.29p 5.964±0.134 4200.53p 2.367±0.056

4205.96m 1.059±0.046 4208.48p 5.043±0.053 4200.36p 4.278±0.059 4201.67m 6.523±0.382 4200.83m 2.461±0.111

4206.40n 1.071±0.064 4208.88m 4.983±0.081 4200.62m 4.597±0.166 4202.35p 5.754±0.121 4201.05g 2.368±0.029

4207.97m 1.013±0.045 4209.53p 5.164±0.048 4200.84g 4.483±0.045 4204.69m 5.953±0.372 4201.41p 2.341±0.055

4208.44p 1.043±0.015 4209.89m 5.050±0.082 4201.28p 4.451±0.071 4205.31p 6.019±0.138 4201.85m 2.303±0.108

4208.92m 0.978±0.044 4210.89m 5.012±0.082 4201.62m 4.606±0.167 4205.71m 6.267±0.374 4202.49p 2.370±0.055

4209.55p 1.024±0.017 4212.51p 5.130±0.045 4202.34p 4.482±0.061 4205.90g 5.780±0.239 4203.02g 2.363±0.029

4209.94m 0.975±0.044 4212.88m 5.108±0.083 4203.84g 4.433±0.025 4206.34p 5.895±0.138 4204.47p 2.418±0.065

4210.96m 1.030±0.045 4213.48p 5.177±0.039 4204.31p 4.489±0.057 4206.40n 5.780±0.181 4204.79m 2.362±0.109

4212.52p 1.064±0.024 4213.89m 5.110±0.083 4204.64m 4.402±0.164 4206.73m 5.645±0.363 4205.54p 2.237±0.052

4212.58g 1.085±0.007 4214.48p 5.208±0.050 4205.27p 4.381±0.055 4207.40n 6.215±0.140 4205.82m 2.255±0.108

(cont’d)

129





b JDa Fcontb

4212.95m 1.065±0.046 4214.88m 5.178±0.084 4205.67m 4.532±0.166 4208.39p 6.112±0.155 4206.45p 2.305±0.051

4213.50p 1.037±0.015 4215.89m 5.231±0.085 4206.32p 4.265±0.062 4208.40n 6.277±0.181 4206.60n 2.064±0.156

4213.96m 1.041±0.045 4216.49p 5.147±0.042 4206.39n 4.271±0.086 4208.72m 5.656±0.369 4206.82m 2.212±0.107

4214.43p 1.070±0.017 4216.88m 5.210±0.084 4206.67m 4.198±0.161 4209.38p 6.189±0.127 4207.87m 2.279±0.108

4214.95m 1.078±0.046 4217.48p 5.059±0.066 4207.39n 4.128±0.072 4209.73m 5.659±0.367 4208.37p 2.437±0.053

4215.96m 1.034±0.045 4217.89m 5.013±0.082 4207.77m 4.346±0.163 4210.40n 6.825±0.150 4208.83m 2.219±0.107

4216.54p 1.076±0.014 4218.51p 5.172±0.043 4207.82g 4.009±0.056 4210.72m 6.637±0.385 4208.99g 2.114±0.069

4216.95m 1.098±0.046 4218.90m 5.106±0.083 4208.32p 4.301±0.059 4211.38p 5.942±0.098 4209.50p 2.259±0.051

4217.50p 1.108±0.018 4219.03g 5.208±0.026 4208.36n 4.203±0.119 4212.32p 5.904±0.096 4209.84m 2.160±0.107

4217.93m 1.102±0.047 4219.52p 5.280±0.047 4208.67m 4.077±0.160 4212.67m 6.556±0.383 4210.08g 2.208±0.049

4218.53p 1.112±0.017 4220.45p 5.117±0.059 4209.37p 4.204±0.058 4213.28p 5.921±0.111 4210.84m 2.214±0.107

4218.95m 1.094±0.046 4220.91m 5.079±0.083 4209.65m 4.114±0.160 4213.69m 5.446±0.365 4211.53p 2.284±0.060

4220.40n 1.067±0.043 4221.48p 5.192±0.073 4210.30n 4.332±0.072 4213.77g 6.283±0.114 4212.83m 2.203±0.107

4220.48p 1.084±0.024 4222.90m 5.200±0.084 4210.67m 4.291±0.162 4214.31p 5.884±0.128 4212.89g 2.257±0.035

4220.96m 1.139±0.047 4223.50p 5.316±0.065 4210.90g 4.044±0.091 4214.68m 5.957±0.371 4213.45p 2.238±0.053

4221.57g 1.073±0.050 4223.90m 5.421±0.087 4211.34p 4.150±0.055 4215.69m 5.740±0.368 4213.85m 2.075±0.105

4221.98m 1.131±0.047 4224.48p 5.407±0.071 4212.30p 3.963±0.055 4216.31p 5.694±0.129 4214.40p 2.250±0.056

4222.53p 1.067±0.025 4224.90m 5.287±0.085 4212.62m 3.892±0.157 4216.68m 6.342±0.377 4214.84m 2.121±0.105

4222.95m 1.137±0.047 4225.49p 5.408±0.058 4213.33p 3.924±0.059 4217.37p 6.017±0.137 4215.45p 2.155±0.095

4223.53p 1.098±0.024 4226.06g 5.511±0.081 4214.29p 3.868±0.067 4217.68m 5.616±0.368 4215.85m 2.081±0.105

(cont’d)

130





b JDa Fcontb

4223.94m 1.119±0.047 4226.44p 5.447±0.064 4214.63m 3.920±0.157 4218.44p 5.687±0.107 4216.46p 2.089±0.057

4224.45p 1.094±0.024 4226.89m 5.569±0.089 4215.37p 4.130±0.066 4218.75m 4.792±0.353 4216.84m 2.020±0.104

4224.94m 1.195±0.048 4227.53p 5.447±0.085 4215.64m 4.049±0.159 4219.28p 5.851±0.110 4217.44p 2.041±0.061

4225.52p 1.035±0.026 4227.90m 5.542±0.089 4216.63m 3.901±0.157 4219.40n 6.157±0.201 4217.84m 2.115±0.105

4225.92m 1.134±0.047 4228.91m 5.718±0.091 4217.31p 4.427±0.071 4219.79m 5.235±0.360 4218.47p 1.984±0.060

4226.42p 1.055±0.019 4229.53p 5.500±0.066 4217.63m 4.866±0.171 4220.27p 5.506±0.130 4218.77g 2.045±0.069

4226.94m 1.020±0.045 4229.88m 5.545±0.089 4218.29p 4.269±0.058 4220.40n 5.919±0.160 4218.86m 2.066±0.105

4227.95m 0.988±0.044 4230.91m 5.524±0.088 4218.30n 4.417±0.086 4220.69m 5.547±0.367 4219.50p 1.830±0.066

4228.94m 0.965±0.044 4231.45p 5.385±0.063 4218.70m 4.337±0.163 4221.33p 6.051±0.199 4219.88m 2.136±0.105

4229.45p 0.953±0.014 4231.91m 5.317±0.086 4219.30p 4.419±0.106 4221.69m 5.436±0.365 4220.41p 2.017±0.095

4229.93m 0.941±0.043 4232.02g 5.494±0.210 4219.30n 4.239±0.068 4221.84g 6.462±0.146 4220.60n 1.968±0.143

4230.95m 0.896±0.043 4232.43p 5.275±0.039 4219.74m 4.606±0.167 4222.38p 5.601±0.149 4220.86m 1.885±0.101

4231.43p 0.927±0.017 4232.90m 5.449±0.087 4219.93g 4.066±0.051 4222.69m 5.916±0.371 4221.07g 2.063±0.034

4231.50g 0.880±0.035 4233.44p 5.275±0.052 4220.29p 4.232±0.075 4223.34p 5.867±0.168 4221.46p 1.997±0.090

4231.95m 0.882±0.043 4233.89m 5.407±0.087 4220.31n 4.500±0.099 4223.69m 5.786±0.371 4221.84m 2.055±0.104

4232.38p 0.860±0.014 4234.43p 5.215±0.040 4220.64m 4.411±0.164 4224.35p 5.725±0.149 4222.51p 1.890±0.095

4232.94m 0.832±0.042 4234.89m 5.316±0.086 4221.32p 4.320±0.080 4224.69m 5.706±0.370 4222.85m 2.042±0.104

4233.47p 0.863±0.014 4235.44p 5.270±0.046 4221.35n 4.351±0.073 4226.39p 5.709±0.155 4223.05g 1.942±0.094

4233.94m 0.816±0.042 4235.90m 5.358±0.086 4221.64m 4.254±0.161 4226.71m 5.376±0.362 4223.48p 2.029±0.073

4234.46p 0.824±0.014 4236.45p 5.199±0.045 4222.37p 4.345±0.073 4227.41p 5.486±0.134 4223.85m 1.877±0.101

(cont’d)

131





b JDa Fcontb

4234.94m 0.904±0.043 4236.90m 5.345±0.086 4222.63m 4.532±0.166 4227.69m 5.385±0.364 4224.41p 2.033±0.064

4235.46p 0.843±0.013 4237.44p 5.154±0.055 4223.36p 4.358±0.068 4229.42p 5.783±0.150 4224.85m 2.062±0.105

4235.94m 0.818±0.042 4237.90m 5.451±0.087 4223.64m 4.439±0.164 4229.73m 5.490±0.363 4225.06g 1.971±0.034

4236.95m 0.851±0.043 4239.90m 5.491±0.088 4223.83g 4.410±0.055 4230.27p 5.382±0.125 4225.46p 2.000±0.111

4237.42p 0.823±0.013 4239.93g 5.346±0.040 4224.33p 4.365±0.061 4230.69m 5.340±0.362 4225.89m 1.908±0.103

4237.95m 0.784±0.042 4240.48p 5.342±0.050 4224.63m 4.476±0.165 4231.41p 5.622±0.131 4226.37p 2.049±0.057

4238.49g 0.844±0.015 4240.89m 5.226±0.085 4225.33p 4.396±0.064 4231.70m 6.147±0.374 4226.83m 1.943±0.103

4239.57n 0.804±0.043 4241.44p 5.240±0.041 4226.26p 4.346±0.071 4232.35p 5.773±0.115 4227.50p 1.859±0.116

4239.94m 0.818±0.042 4241.89m 5.309±0.086 4226.64m 4.346±0.163 4232.68m 5.780±0.370 4227.86m 2.054±0.104

4240.44p 0.873±0.024 4242.49p 5.213±0.050 4226.81g 4.447±0.045 4233.42n 5.834±0.231 4228.86m 1.932±0.103

4240.93m 0.858±0.043 4243.51p 5.262±0.051 4227.64m 4.207±0.161 4233.68m 6.766±0.382 4229.40p 2.046±0.049

4241.47p 0.864±0.015 4243.90m 5.303±0.086 4228.75m 4.653±0.167 4234.30p 5.854±0.120 4229.84m 2.078±0.105

4241.93m 0.876±0.043 4244.90m 5.202±0.084 4229.34p 4.257±0.061 4234.68m 6.876±0.388 4230.86m 1.954±0.103

4242.45p 0.871±0.018 4245.45p 5.194±0.041 4229.68m 4.384±0.163 4235.29p 5.756±0.118 4231.38p 1.977±0.052

4242.94m 0.899±0.043 4245.90m 5.220±0.085 4230.64m 4.560±0.166 4235.44n 6.320±0.301 4231.84g 1.873±0.079

4243.46p 0.922±0.014 4246.51p 5.196±0.044 4231.32p 4.375±0.057 4235.68m 6.184±0.377 4231.86m 1.887±0.101

4243.95m 0.966±0.044 4246.89m 5.096±0.083 4231.65m 4.346±0.163 4236.27p 6.186±0.118 4232.33p 2.058±0.047

4244.94m 0.944±0.044 4247.84g 5.206±0.020 4232.27p 4.303±0.058 4236.68m 6.785±0.386 4232.85m 1.985±0.104

4245.48p 0.934±0.016 4247.88m 5.158±0.084 4232.63m 4.272±0.162 4237.38p 5.884±0.101 4233.43p 2.024±0.048

4245.95m 0.889±0.043 4248.89m 5.120±0.083 4233.30p 4.390±0.057 4237.50n 6.235±0.251 4233.85m 2.002±0.104

(cont’d)

132





b JDa Fcontb

4246.49p 0.915±0.014 4249.51p 5.127±0.047 4233.38n 4.650±0.133 4237.69m 6.212±0.378 4234.41p 1.902±0.048

4246.50n 0.994±0.043 4249.89m 5.028±0.082 4233.63m 4.727±0.168 4238.46n 5.375±0.271 4234.85m 2.067±0.105

4246.94m 0.889±0.043 4250.89m 5.049±0.082 4234.29p 4.474±0.058 4238.68m 5.997±0.373 4234.93g 2.041±0.027

4247.93m 0.918±0.043 4251.48p 5.135±0.064 4234.64m 4.523±0.165 4239.48p 5.676±0.154 4235.41p 1.997±0.049

4248.94m 0.914±0.043 4251.89m 4.822±0.080 4234.81g 4.764±0.035 4239.70m 5.400±0.363 4235.85m 2.003±0.104

4249.53p 0.875±0.019 4252.54p 5.036±0.111 4235.27p 4.543±0.057 4240.33p 5.426±0.119 4236.41p 2.115±0.047

4250.94m 0.829±0.042 4252.88m 5.082±0.083 4235.46n 4.874±0.113 4240.52n 5.741±0.261 4236.85m 2.020±0.104

4251.44p 0.791±0.026 4253.01g 5.119±0.058 4235.64m 4.476±0.165 4240.68m 6.180±0.376 4237.35p 1.955±0.047

4252.49g 0.770±0.015 4253.89m 4.987±0.082 4236.29p 4.520±0.055 4241.27p 5.557±0.120 4237.60n 1.960±0.195

4252.49p 0.763±0.022 4254.85m 4.924±0.081 4236.63m 4.569±0.166 4241.45n 5.615±0.281 4237.85m 1.942±0.103

4252.57n 0.716±0.085 4255.48p 4.958±0.057 4237.26p 4.501±0.058 4241.68m 6.231±0.377 4237.92g 2.047±0.027

4252.93m 0.795±0.042 4255.86m 4.780±0.080 4237.64m 4.467±0.165 4242.35p 5.518±0.106 4238.57n 2.167±0.182

4253.94m 0.764±0.041 4256.50p 5.061±0.052 4238.63m 4.467±0.165 4242.40n 5.558±0.311 4239.45p 2.062±0.057

4254.90m 0.734±0.041 4256.87m 4.868±0.080 4238.79g 4.764±0.024 4242.70m 5.973±0.372 4239.85m 1.990±0.104

4255.51p 0.723±0.020 4257.49p 4.951±0.044 4239.30p 4.374±0.061 4243.35p 5.110±0.136 4239.96g 2.041±0.027

4255.91m 0.584±0.038 4258.51p 5.007±0.062 4239.33n 4.204±0.120 4243.69m 5.861±0.371 4240.40p 2.032±0.053

4256.47p 0.715±0.017 4258.88m 5.094±0.083 4239.66m 4.616±0.167 4244.75m 5.083±0.357 4240.84m 1.912±0.103

4256.91m 0.628±0.039 4259.42p 4.951±0.039 4240.31p 4.542±0.059 4245.30p 4.978±0.136 4241.38p 2.016±0.068

4257.46p 0.725±0.015 4259.89m 5.012±0.082 4240.63m 4.783±0.169 4245.69m 4.521±0.349 4241.50n 2.176±0.195

4257.94m 0.610±0.038 4259.99g 4.935±0.094 4241.29p 4.641±0.058 4246.36n 4.467±0.171 4241.84m 2.236±0.108

(cont’d)

133





b JDa Fcontb

4258.48p 0.724±0.015 4260.49p 4.959±0.043 4241.63m 4.912±0.171 4246.37p 5.193±0.117 4241.97g 2.043±0.053

4258.93m 0.665±0.039 4260.89m 4.788±0.080 4242.33p 4.903±0.061 4246.69m 4.262±0.343 4242.38p 2.078±0.049

4259.45p 0.696±0.014 4261.41p 4.924±0.038 4242.64m 4.829±0.170 4247.69m 4.152±0.342 4242.92m 1.960±0.103

4259.47g 0.636±0.014 4261.89m 4.820±0.080 4243.31p 4.726±0.069 4247.86g 5.191±0.127 4243.38p 2.063±0.049

4259.94m 0.689±0.040 4262.42p 4.952±0.038 4243.64m 5.024±0.173 4248.36p 4.939±0.134 4243.85m 1.971±0.103

4260.44p 0.689±0.012 4263.44p 4.978±0.041 4244.68m 5.191±0.174 4248.69m 4.731±0.353 4244.85m 2.033±0.104

4260.94m 0.612±0.038 4263.86m 4.840±0.080 4245.33p 4.901±0.122 4249.30p 4.879±0.129 4245.43p 2.076±0.065

4261.44p 0.665±0.012 4264.86m 5.005±0.082 4245.65m 5.126±0.174 4249.69m 5.083±0.359 4245.85m 2.133±0.105

4261.93m 0.594±0.038 4264.92g 4.875±0.037 4246.34n 4.992±0.080 4250.28p 5.302±0.199 4245.89g 2.007±0.066

4262.45p 0.625±0.014 4265.44c 4.870±0.094 4246.64m 5.033±0.173 4250.69m 4.822±0.354 4246.40p 2.172±0.057

4262.45g 0.667±0.014 4265.88m 4.967±0.081 4246.76g 4.919±0.057 4251.34p 5.179±0.156 4246.85m 2.023±0.104

4262.84d 0.603±0.057 4266.44c 5.125±0.097 4247.65m 4.820±0.170 4251.69m 4.258±0.345 4247.84m 2.042±0.104

4263.50p 0.679±0.014 4266.86m 5.041±0.082 4248.30p 4.608±0.084 4252.37p 4.897±0.145 4248.41p 2.194±0.164

4263.91m 0.636±0.039 4267.42c 4.985±0.095 4248.64m 4.718±0.168 4252.49n 4.360±0.160 4248.85m 2.140±0.105

4264.92m 0.645±0.039 4267.86m 4.985±0.082 4249.32p 4.522±0.086 4252.69m 4.536±0.347 4249.48p 1.985±0.074

4265.93m 0.681±0.040 4268.48c 5.206±0.098 4249.64m 4.643±0.167 4253.68m 5.022±0.353 4249.85m 2.241±0.108

4266.48c 0.728±0.057 4268.85m 4.899±0.080 4249.80g 4.749±0.066 4253.81g 5.044±0.064 4249.94g 2.153±0.034

4266.91m 0.703±0.040 4269.85m 4.852±0.080 4250.31p 4.513±0.122 4254.42n 4.558±0.211 4250.84m 2.188±0.107

4267.44c 0.704±0.056 4269.88g 4.922±0.025 4250.64m 4.374±0.163 4255.43p 4.199±0.120 4251.38p 2.212±0.079

4267.91d 0.771±0.041 4270.47c 4.909±0.095 4251.64m 4.254±0.161 4255.51n 4.368±0.291 4251.84m 2.110±0.105

(cont’d)

134





b JDa Fcontb

4267.91m 0.713±0.060 4271.42c 4.800±0.093 4252.34p 4.219±0.072 4255.71m 4.081±0.341 4252.43p 2.116±0.088

4268.90m 0.762±0.041 4272.45c 4.846±0.094 4252.40n 4.214±0.067 4256.33p 4.295±0.116 4252.51n 1.967±0.156

4269.46c 0.755±0.058 4272.93g 4.849±0.055 4252.64m 4.096±0.160 4256.44n 4.633±0.251 4252.84m 2.258±0.108

4269.87d 0.798±0.062 4273.42c 4.956±0.095 4253.65m 3.873±0.157 4257.37p 4.542±0.087 4252.96g 2.221±0.048

4270.85d 0.841±0.063 4274.48c 4.870±0.094 4254.40n 3.844±0.080 4257.69m 3.544±0.333 4253.84m 2.077±0.105

4273.45c 0.996±0.063 4275.93g 4.900±0.031 4254.76g 4.596±0.050 4258.29p 4.365±0.143 4254.81m 2.093±0.105

4274.44c 0.946±0.062 4276.40c 4.941±0.095 4255.32p 4.603±0.058 4258.40n 4.378±0.181 4254.96g 2.249±0.042

4274.47g 0.847±0.020 4277.39c 4.902±0.095 4255.67m 4.402±0.164 4258.71m 4.111±0.341 4255.41p 2.215±0.062

4276.43g 0.863±0.012 4278.41p 4.891±0.056 4256.30p 4.598±0.058 4259.32p 4.073±0.099 4255.53n 2.159±0.182

4277.43c 0.936±0.062 4278.42c 4.919±0.095 4256.66m 4.179±0.161 4259.70m 4.091±0.336 4255.82m 2.305±0.109

4277.89d 0.891±0.064 4278.87g 4.809±0.037 4257.64m 3.994±0.158 4260.33p 4.104±0.098 4256.39p 2.388±0.056

4278.45p 0.880±0.018 4280.45p 4.734±0.097 4258.31p 4.362±0.084 4260.71m 3.871±0.334 4256.41n 2.392±0.130

4278.46c 0.879±0.061 4281.43p 4.802±0.059 4259.30p 4.203±0.054 4261.28p 4.108±0.121 4256.82m 2.492±0.112

4281.47p 0.912±0.024 4281.48c 4.510±0.089 4259.65m 3.650±0.153 4261.69m 3.127±0.323 4257.32p 2.427±0.047

4282.37g 0.892±0.014 4282.39p 4.738±0.054 4259.76g 3.848±0.111 4262.33p 3.566±0.116 4257.81m 2.654±0.114

4282.42p 0.885±0.027 4282.50c 4.535±0.089 4260.31p 4.116±0.060 4262.69m 3.147±0.321 4258.39n 2.389±0.182

4282.46c 0.881±0.061 4282.94g 4.596±0.053 4260.66m 4.152±0.161 4263.33p 3.638±0.098 4258.44p 2.431±0.056

4282.81d 0.996±0.067 4283.39c 4.694±0.092 4261.65m 3.836±0.156 4263.68m 3.264±0.323 4258.83m 2.557±0.113

4283.42c 0.848±0.060 4283.44p 4.701±0.041 4262.28p 3.965±0.061 4264.70m 2.746±0.319 4259.40p 2.459±0.052

4283.47p 0.941±0.026 4284.38c 4.582±0.090 4262.65m 3.613±0.153 4265.72m 1.946±0.301 4259.84m 2.523±0.112

(cont’d)

135





b JDa Fcontb

4284.41c 0.837±0.060 4284.40p 4.788±0.044 4263.30p 4.018±0.056 4266.36c 2.037±0.345 4259.88g 2.550±0.021

4284.42p 0.895±0.024 4285.92g 4.574±0.100 4263.37n 3.963±0.060 4266.69m 2.377±0.310 4260.36p 2.550±0.049

4285.86d 0.816±0.062 4290.41c 4.925±0.095 4263.76g 3.831±0.089 4267.69m 1.946±0.303 4260.84m 2.363±0.109

4286.86d 0.822±0.062 4291.38c 4.805±0.093 4264.65m 3.752±0.155 4268.34c 1.732±0.339 4261.39p 2.543±0.049

4287.86d 0.835±0.063 4293.39p 5.078±0.038 4265.67m 4.161±0.161 4268.69m 1.604±0.296 4261.53n 2.866±0.195

4288.44g 0.807±0.015 4294.42p 5.005±0.046 4266.65m 4.430±0.164 4269.29c 2.226±0.348 4261.84m 2.774±0.116

4288.86d 0.686±0.060 4295.40p 5.046±0.057 4267.64m 4.968±0.172 4269.69m 1.165±0.288 4261.93g 2.488±0.056

4289.42c 0.870±0.061 4296.41p 5.089±0.041 4268.64m 4.950±0.172 4271.37c 1.918±0.342 4262.40p 2.430±0.095

4290.44c 0.813±0.059 4297.43c 5.190±0.098 4268.78g 4.645±0.105 4271.79g 1.964±0.297 4262.80m 2.495±0.112

4290.85d 0.800±0.062 4298.34p 5.194±0.034 4270.35n 4.901±0.100 4272.37c 1.700±0.338 4263.41p 2.418±0.051

4291.41c 0.826±0.059 4298.45c 5.219±0.099 4273.77g 4.896±0.048 4273.36c 1.744±0.339 4263.81m 2.609±0.113

4293.43p 0.826±0.014 4299.38c 5.070±0.096 4274.33c 2.763±0.358 4263.94g 2.462±0.042

4296.42c 0.846±0.060 4299.46p 5.218±0.074 4274.80g 2.895±0.084 4264.82m 2.284±0.108

4296.43p 0.860±0.017 4300.36c 5.175±0.098 4277.33c 3.374±0.370 4265.81m 2.333±0.109

4297.48c 0.983±0.063 4300.85g 5.266±0.059 4277.77g 2.843±0.141 4266.82m 2.177±0.107

4298.42c 1.034±0.064 4301.43c 5.217±0.099 4278.32c 3.672±0.376 4267.81m 2.169±0.107

4298.43p 0.905±0.016 4305.84g 5.270±0.117 4279.29c 3.371±0.370 4268.86g 2.199±0.040

4300.38g 0.920±0.033 4311.83g 5.655±0.027 4279.29p 3.253±0.187 4270.43n 2.309±0.182

4300.40c 0.994±0.063 4314.83g 5.656±0.041 4280.29c 2.974±0.362 4270.90g 2.332±0.021

4301.46c 1.021±0.064 4319.83g 5.416±0.053 4280.41p 3.117±0.199 4272.89g 2.307±0.027

(cont’d)

136





b JDa Fcontb

4306.36g 0.975±0.046 4330.77g 5.578±0.048 4281.30p 2.860±0.132 4274.87g 2.335±0.021

4310.33g 1.049±0.022 4281.42c 2.761±0.358 4276.84d 2.089±0.118

4318.33g 1.126±0.015 4282.31p 2.816±0.130 4276.87g 2.379±0.027

4321.33g 1.079±0.013 4283.29c 2.665±0.356 4277.80d 2.276±0.122

4283.31p 3.087±0.112 4278.35p 2.318±0.104

4284.29p 2.822±0.109 4278.83d 2.596±0.127

4284.33c 2.548±0.354 4279.36p 2.348±0.082

4290.28c 2.676±0.357 4281.37p 2.207±0.111

4291.32c 2.386±0.351 4282.37p 2.337±0.086

4293.29p 3.044±0.099 4282.76d 2.592±0.127

4294.34p 2.712±0.092 4282.85g 2.474±0.027

4295.35p 2.708±0.099 4283.41p 2.276±0.084

4296.29p 2.561±0.102 4284.33p 2.221±0.066

4296.31c 2.512±0.354 4284.90g 2.419±0.027

4298.31p 2.797±0.087 4285.77d 2.311±0.122

4299.33c 2.761±0.358 4286.76d 2.238±0.121

4299.34p 2.986±0.097 4287.76d 2.341±0.122

4300.30c 3.347±0.369 4288.76d 2.387±0.123

4288.85g 2.541±0.021

4289.39n 2.363±0.117

(cont’d)

137





b JDa Fcontb

4290.75d 2.716±0.130

4290.85g 2.662±0.035

4292.84d 2.617±0.127

4293.36p 2.588±0.056

4293.77d 2.686±0.129

4294.82g 2.758±0.036

4296.38p 2.539±0.056

4298.38p 2.513±0.058

4299.38p 2.652±0.053

4299.83g 2.666±0.035

4304.81g 2.940±0.051

4307.84g 3.094±0.068

4309.80g 3.012±0.036

4311.81g 2.940±0.036

4313.81g 2.726±0.070

4318.81g 2.684±0.042

4319.81g 2.515±0.048

4320.80g 2.554±0.042

(cont’d)

138





b JDa Fcontb

4330.75g 2.414±0.034

4332.77g 2.348±0.060

aJulian Dates are −2450000 and include the following observatory code to indicate the origin of the observation: MDM

— m, MAGNUM — g, CrAO spectroscopy — c, CrAO photometry — p, UNebr. — n, and DAO — d.

bContinuum fluxes are in units of 10−15 ergs s−1 cm−2 A−1 and represent the average continuum flux density measured

∼5100 A, rest-frame, from spectroscopic observations or the photometric V -band flux. Spectroscopic and photometric

fluxes were scaled to a uniform scale as described in Section 4.1.3.

139

Mrk290 Mrk 817 NGC3227 NGC3516 NGC5548

JDa FHβb JDa FHβ

b JDa FHβb JDa FHβ

b JDa FHβb

4184.97m 2.203±0.049 4185.92m 2.491±0.082 4184.68m 3.559±0.103 4184.74m 5.833±0.185 4184.92m 2.285±0.212

4185.96m 2.253±0.050 4186.87m 2.515±0.083 4185.61m 3.576±0.104 4185.66m 6.170±0.195 4185.86m 2.298±0.213

4186.94m 2.230±0.049 4188.91m 2.340±0.077 4187.61m 3.506±0.102 4188.66m 6.150±0.195 4186.83m 2.227±0.207

4187.96m 2.196±0.048 4189.86m 2.169±0.071 4188.61m 4.066±0.118 4189.71m 6.130±0.193 4188.86m 2.184±0.203

4188.95m 2.183±0.048 4191.86m 2.518±0.083 4190.61m 3.690±0.107 4190.66m 5.782±0.184 4189.81m 1.941±0.181

4189.90m 2.158±0.047 4192.90m 2.450±0.080 4191.66m 3.853±0.111 4191.71m 5.633±0.179 4190.88m 1.830±0.170

4190.93m 2.251±0.050 4194.92m 2.261±0.075 4192.61m 3.774±0.110 4192.66m 5.495±0.175 4191.81m 1.730±0.161

4191.95m 2.285±0.051 4201.90m 2.416±0.080 4193.66m 3.945±0.114 4193.75m 5.534±0.176 4192.85m 1.517±0.142

4192.94m 2.217±0.049 4204.85m 2.389±0.079 4194.62m 4.015±0.116 4194.68m 5.674±0.181 4193.71m 1.572±0.146

4194.96m 2.221±0.049 4205.86m 2.537±0.083 4195.69m 3.840±0.111 4196.67m 5.466±0.174 4194.87m 1.764±0.164

4197.97m 2.261±0.050 4207.92m 2.351±0.078 4196.81m 4.010±0.116 4197.70m 5.664±0.178 4197.92m 1.659±0.155

4199.98m 2.323±0.051 4208.88m 2.390±0.079 4197.64m 4.052±0.118 4198.69m 6.280±0.200 4198.84m 1.353±0.126

4201.95m 2.315±0.051 4209.89m 2.380±0.079 4198.64m 4.319±0.125 4200.67m 5.621±0.179 4199.93m 1.672±0.156

4204.90m 2.233±0.049 4210.89m 2.312±0.077 4199.63m 3.940±0.114 4201.67m 5.840±0.186 4200.83m 1.730±0.161

4205.96m 2.274±0.050 4212.88m 2.314±0.077 4200.62m 4.138±0.120 4204.69m 5.804±0.185 4201.85m 1.587±0.148

4207.97m 2.240±0.049 4213.89m 2.535±0.083 4201.62m 4.138±0.120 4205.71m 5.899±0.186 4204.79m 1.513±0.140

4208.92m 2.281±0.050 4214.88m 2.436±0.080 4204.64m 4.481±0.130 4206.73m 5.455±0.172 4205.82m 1.427±0.133

4209.94m 2.198±0.048 4215.89m 2.531±0.083 4205.67m 4.416±0.128 4208.72m 5.886±0.188 4206.82m 1.392±0.130

4210.96m 2.169±0.048 4216.88m 2.367±0.078 4206.67m 4.539±0.132 4209.73m 6.035±0.192 4207.87m 1.456±0.135

4212.95m 2.169±0.048 4217.89m 2.293±0.076 4207.77m 4.573±0.133 4210.72m 6.305±0.201 4208.83m 1.581±0.147

(cont’d)

Table 4.6. Hβ Fluxes

140



JDa FHβb JDa FHβ


b JDa FHβb

4213.96m 2.220±0.049 4218.90m 2.536±0.083 4208.67m 4.636±0.135 4212.67m 6.385±0.204 4209.84m 1.522±0.142

4214.95m 2.214±0.049 4220.91m 2.538±0.083 4209.65m 4.672±0.135 4213.69m 5.732±0.183 4210.84m 1.629±0.152

4215.96m 2.214±0.049 4222.90m 2.375±0.079 4210.67m 4.708±0.136 4214.68m 6.438±0.204 4212.83m 1.414±0.131

4216.95m 2.129±0.047 4223.90m 2.486±0.082 4212.62m 4.658±0.135 4215.69m 5.980±0.190 4213.85m 1.297±0.121

4217.93m 2.149±0.047 4224.90m 2.369±0.079 4214.63m 4.249±0.123 4216.68m 6.325±0.200 4214.84m 1.500±0.139

4218.95m 2.253±0.050 4226.89m 2.566±0.084 4215.64m 4.041±0.117 4217.68m 6.218±0.199 4215.85m 1.309±0.122

4220.96m 2.265±0.050 4227.90m 2.395±0.079 4216.63m 4.169±0.121 4218.75m 5.753±0.184 4216.84m 1.348±0.125

4221.98m 2.331±0.052 4228.91m 2.519±0.083 4217.63m 4.128±0.120 4219.79m 5.699±0.181 4217.84m 1.305±0.121

4222.95m 2.251±0.050 4229.88m 2.618±0.086 4218.70m 4.037±0.117 4220.69m 5.870±0.188 4218.86m 1.126±0.105

4223.94m 2.234±0.049 4230.91m 2.639±0.087 4219.74m 3.914±0.113 4221.69m 5.930±0.189 4219.88m 0.881±0.082

4224.94m 2.212±0.049 4231.91m 2.538±0.083 4220.64m 3.961±0.115 4222.69m 6.144±0.196 4220.86m 0.987±0.092

4225.92m 2.246±0.050 4232.90m 2.512±0.083 4221.64m 3.899±0.113 4223.69m 6.466±0.207 4221.84m 0.845±0.078

4226.94m 2.314±0.051 4233.89m 2.516±0.083 4222.63m 4.025±0.117 4224.69m 6.518±0.209 4222.85m 0.957±0.088

4227.95m 2.303±0.051 4234.89m 2.386±0.079 4223.64m 4.311±0.125 4226.71m 6.145±0.195 4223.85m 1.087±0.101

4228.94m 2.256±0.050 4235.90m 2.610±0.086 4224.63m 4.467±0.130 4227.69m 6.234±0.199 4224.85m 0.976±0.091

4229.93m 2.291±0.051 4236.90m 2.655±0.088 4226.64m 4.022±0.117 4229.73m 6.050±0.192 4225.89m 1.084±0.101

4230.95m 2.313±0.051 4237.90m 2.517±0.083 4227.64m 4.001±0.116 4230.69m 6.079±0.194 4226.83m 1.122±0.104

4231.95m 2.108±0.046 4239.90m 2.627±0.087 4228.75m 4.069±0.118 4231.70m 6.181±0.196 4227.86m 1.160±0.108

4232.94m 2.214±0.049 4240.89m 2.547±0.084 4229.68m 3.858±0.112 4232.68m 6.254±0.200 4228.86m 1.010±0.094

4233.94m 2.169±0.048 4241.89m 2.561±0.084 4230.64m 3.888±0.113 4233.68m 6.371±0.201 4229.84m 1.027±0.095

(cont’d)

141



JDa FHβb JDa FHβ


b JDa FHβb

4234.94m 2.074±0.045 4243.90m 2.561±0.084 4231.65m 3.847±0.111 4234.68m 6.398±0.204 4230.86m 1.192±0.111

4235.94m 2.164±0.048 4244.90m 2.584±0.085 4232.63m 3.912±0.113 4235.68m 6.395±0.204 4231.86m 1.009±0.094

4236.95m 2.234±0.049 4245.90m 2.527±0.083 4233.63m 3.889±0.113 4236.68m 6.522±0.208 4232.85m 0.890±0.083

4237.95m 2.176±0.048 4246.89m 2.565±0.084 4234.64m 3.855±0.111 4237.69m 6.256±0.200 4233.85m 1.070±0.100

4239.94m 2.164±0.048 4247.88m 2.609±0.086 4235.64m 3.856±0.111 4238.68m 6.196±0.197 4234.85m 0.997±0.092

4240.93m 2.143±0.047 4248.89m 2.615±0.086 4236.63m 3.830±0.111 4239.70m 6.131±0.195 4235.85m 1.010±0.094

4241.93m 2.115±0.046 4249.89m 2.421±0.080 4237.64m 3.718±0.108 4240.68m 6.304±0.201 4236.85m 0.875±0.082

4242.94m 2.074±0.045 4250.89m 2.571±0.085 4238.63m 3.756±0.109 4241.68m 6.493±0.207 4237.85m 0.953±0.088

4243.95m 2.114±0.046 4251.89m 2.521±0.083 4239.66m 3.991±0.116 4242.70m 6.323±0.201 4239.85m 0.905±0.084

4244.94m 2.078±0.046 4252.88m 2.551±0.084 4240.63m 3.930±0.114 4243.69m 6.662±0.213 4240.84m 0.952±0.088

4245.95m 2.073±0.045 4253.89m 2.480±0.081 4241.63m 4.028±0.117 4244.75m 6.223±0.198 4241.84m 0.981±0.091

4246.94m 2.141±0.047 4254.85m 2.405±0.080 4242.64m 3.816±0.110 4245.69m 6.208±0.198 4242.92m 0.950±0.088

4247.93m 2.043±0.045 4255.86m 2.670±0.088 4243.64m 4.363±0.126 4246.69m 6.139±0.195 4243.85m 1.037±0.096

4248.94m 2.114±0.046 4256.87m 2.566±0.084 4244.68m 4.049±0.118 4247.69m 5.749±0.183 4244.85m 0.984±0.091

4250.94m 2.167±0.048 4258.88m 2.600±0.086 4245.65m 4.207±0.122 4248.69m 6.103±0.195 4245.85m 0.992±0.092

4252.93m 2.181±0.048 4259.89m 2.434±0.080 4246.64m 4.218±0.122 4249.69m 6.168±0.197 4246.85m 0.741±0.069

4253.94m 2.157±0.047 4260.89m 2.544±0.084 4247.65m 4.220±0.122 4250.69m 5.914±0.189 4247.84m 0.958±0.090

4254.90m 2.055±0.045 4261.89m 2.503±0.082 4248.64m 4.260±0.123 4251.69m 5.698±0.182 4248.85m 0.740±0.069

4255.91m 2.027±0.044 4263.86m 2.319±0.077 4249.64m 4.273±0.124 4252.69m 5.805±0.184 4249.85m 0.846±0.079

4256.91m 2.148±0.047 4264.86m 2.335±0.077 4250.64m 4.139±0.120 4253.68m 5.898±0.186 4250.84m 0.659±0.061

4257.94m 2.002±0.044 4265.44c 2.157±0.080 4251.64m 4.268±0.123 4255.71m 5.973±0.190 4251.84m 0.615±0.057

(cont’d)

142



JDa FHβb JDa FHβ


b JDa FHβb

4258.93m 2.005±0.044 4265.88m 2.346±0.078 4252.64m 4.034±0.117 4257.69m 5.576±0.178 4252.84m 0.801±0.074

4259.94m 1.928±0.043 4266.44c 2.326±0.086 4253.65m 3.873±0.112 4258.71m 6.062±0.193 4253.84m 0.827±0.077

4260.94m 2.033±0.044 4266.86m 2.341±0.078 4255.67m 3.695±0.107 4259.70m 5.887±0.185 4254.81m 0.870±0.081

4261.93m 1.908±0.042 4267.42c 2.392±0.089 4256.66m 3.857±0.112 4260.71m 5.631±0.178 4255.82m 1.070±0.100

4262.84d 1.915±0.060 4267.86m 2.360±0.078 4257.64m 3.473±0.101 4261.69m 5.493±0.174 4256.82m 0.988±0.092

4263.91m 1.920±0.043 4268.48c 2.435±0.090 4259.65m 3.872±0.112 4262.69m 5.194±0.163 4257.81m 1.093±0.101

4264.92m 1.856±0.041 4268.85m 2.447±0.080 4260.66m 3.476±0.101 4263.68m 5.431±0.171 4258.83m 1.028±0.096

4265.93m 1.818±0.040 4269.85m 2.338±0.077 4261.65m 3.537±0.103 4264.70m 5.417±0.173 4259.84m 1.174±0.109

4266.48c 1.820±0.061 4270.47c 2.234±0.082 4262.65m 3.183±0.092 4265.72m 5.004±0.156 4260.84m 0.984±0.091

4266.91m 1.845±0.041 4271.42c 2.105±0.078 4264.65m 3.394±0.098 4266.36c 5.213±0.369 4261.84m 1.306±0.121

4267.44c 1.887±0.062 4272.45c 2.254±0.083 4265.67m 3.471±0.100 4266.69m 5.238±0.165 4262.80m 1.200±0.112

4267.91d 1.894±0.042 4273.42c 2.166±0.080 4266.65m 3.519±0.102 4267.69m 5.161±0.163 4263.81m 1.121±0.104

4267.91m 1.770±0.055 4274.48c 2.170±0.080 4267.64m 3.661±0.106 4268.34c 4.934±0.349 4264.82m 1.089±0.101

4268.90m 1.876±0.042 4276.40c 2.082±0.077 4268.64m 3.892±0.113 4268.69m 5.101±0.160 4265.38c 1.253±0.120

4269.46c 1.866±0.062 4277.39c 2.067±0.077 4269.29c 5.047±0.357 4265.81m 1.114±0.104

4269.87d 1.894±0.060 4278.42c 2.182±0.080 4269.69m 4.768±0.149 4266.41c 0.987±0.094

4270.85d 1.805±0.057 4281.48c 2.148±0.080 4271.37c 4.018±0.284 4266.82m 1.095±0.101

4273.45c 1.865±0.062 4282.50c 2.185±0.080 4272.38c 3.586±0.254 4267.39c 1.275±0.121

4274.44c 1.859±0.062 4283.39c 2.387±0.088 4273.36c 3.521±0.249 4267.81m 1.277±0.118

4277.43c 1.982±0.066 4284.38c 2.288±0.084 4274.33c 3.911±0.277 4268.36c 1.248±0.118

4277.89d 1.942±0.061 4290.41c 2.211±0.081 4277.34c 3.974±0.281 4269.40c 1.088±0.104

(cont’d)

143



JDa FHβb JDa FHβ


b JDa FHβb

4278.46c 1.893±0.062 4291.38c 2.159±0.080 4278.32c 4.500±0.319 4271.39c 1.067±0.101

4282.46c 1.872±0.062 4297.43c 2.180±0.080 4279.29c 3.776±0.267 4272.41c 1.006±0.096

4282.81d 2.008±0.063 4298.45c 2.324±0.086 4280.29c 3.619±0.256 4273.38c 1.039±0.099

4283.42c 1.943±0.064 4299.38c 2.219±0.082 4281.42c 3.889±0.275 4274.35c 1.072±0.101

4284.41c 1.974±0.065 4300.36c 2.266±0.084 4283.29c 3.902±0.276 4276.84d 1.059±0.082

4285.86d 1.950±0.062 4301.43c 2.256±0.083 4284.33c 4.070±0.288 4277.36c 1.147±0.109

4286.86d 2.093±0.066 4290.28c 4.150±0.294 4277.80d 1.040±0.081

4287.86d 2.041±0.064 4291.32c 3.658±0.259 4278.39c 1.031±0.098

4288.86d 2.061±0.065 4296.31c 3.823±0.271 4278.83d 1.078±0.083

4289.42c 2.071±0.069 4299.33c 3.655±0.259 4282.76d 1.161±0.090

4290.44c 1.935±0.064 4300.30c 3.441±0.244 4283.35c 1.223±0.116

4290.85d 2.134±0.067 4284.35c 0.933±0.088

4291.41c 2.092±0.070 4285.77d 1.109±0.086

4296.42c 1.977±0.066 4286.76d 0.919±0.070

4297.48c 1.985±0.066 4287.76d 0.926±0.071

4298.42c 1.868±0.062 4288.76d 1.017±0.078

4300.40c 1.977±0.065 4289.34c 1.058±0.100

4301.46c 2.001±0.066 4290.38c 1.085±0.103

4290.75d 1.153±0.088

4291.35c 1.118±0.107

4292.84d 1.101±0.084

(cont’d)

144



JDa FHβb JDa FHβ


b JDa FHβb

4293.77d 1.143±0.088

4296.33c 1.215±0.116

4299.35c 1.286±0.122

4300.32c 1.251±0.118

4301.38c 1.277±0.121

aJulian Dates are −2450000 and include the same observatory codes as Table 4.5.

bHβ flux is in units of 10−13 ergs s−1 cm−2.

145

Continuum Statistics Hβ Line Statistics

Sampling(days) Mean Sampling(days) Mean

Objects 〈T 〉 Tmedian Fluxa Fvar Rmax 〈T 〉 Tmedian Fluxb Fvar Rmax

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)

Mrk 290 0.77 0.52 0.94 0.18 2.18 ± 0.17 1.18 1.00 2.09 0.07 1.32 ± 0.05

Mrk 817 0.84 0.56 5.06 0.05 1.27 ± 0.03 1.33 1.00 2.41 0.05 1.29 ± 0.06

NGC3227 0.55 0.45 3.27 0.10 1.88 ± 0.09 1.13 1.00 3.99 0.08 1.48 ± 0.06

NGC3516 0.60 0.54 4.86 0.28 5.90 ± 1.50 1.26 1.00 5.54 0.15 1.94 ± 0.15

NGC4051 0.56 0.45 4.49 0.09 1.69 ± 0.11 1.08 1.00 4.67 0.07 1.39 ± 0.07

NGC5548 0.70 0.48 2.29 0.11 1.71 ± 0.06 1.09 1.00 1.20 0.26 3.74 ± 0.49

aFluxes are the same units as Table 4.5.

bFluxes are the same units as Table 4.6.


146

τcent τpeak σline FWHM Mvir MBHa logL5100

Objects rmax (days) (days) (km/s) (km/s) (×106M⊙) (×106M⊙) (ergs s−1)

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Mrk 290 0.632 8.72+1.21−1.02 9.2+1.5

−1.4 1609 ± 47 4270 ± 157 4.42+0.67−0.67 24.3+3.7

−3.7 43.00+0.08−0.08

Mrk817b 0.614 14.04+3.41−3.47 16.0+3.9

−5.3 2025 ± 5 5627 ± 30 11.3+2.7−2.8 43.3+10.5

−10.7 43.78+0.02−0.02

NGC3227 0.547 3.75+0.76−0.82 2.99+2.00

−1.00 1376 ± 44 3578 ± 83 1.39+0.29−0.31 7.63+1.62

−1.72 42.11+0.04−0.04

NGC3516 0.894 11.68+1.02−1.53 7.43+1.99

−0.99 1591 ± 10 5175 ± 96 5.76+0.51−0.76 31.7+2.8

−4.2 43.17+0.15−0.15

NGC4051 0.583 1.87+0.54−0.50 2.60+0.79

−1.40 927 ± 64 1034 ± 41 0.31+0.10−0.09 1.73+0.55

−0.52 41.82+0.10−0.36

NGC5548 0.708 12.40+2.74−3.85 6.1+9.4

−2.8 1822 ± 35 4849 ± 112 8.04+1.80−2.51 44.2+9.9

−13.8 42.91+0.05−0.05

aUsing Onken et al. (2004) calibration (except Mrk 817, see below).

bThe weak and poorly defined, triple-peaked profile of the Hβ emission in the rms spectrum necessitated the use of

the line width measured from the mean spectrum for Mrk 817 (Columns 5 and 6) and a black hole mass (Column 8)

calculated with the scale factor determined by Collin et al. (2006) for the use of this line width measurement, f = 3.85,

instead of the standard Onken et al. (2004) value of f = 5.5 that was used for all other objects.

Table 4.8. Rest Frame Lags, Line Widths, Black Hole Masses, and Luminosities

147

Chapter 5

Diverse Kinematic Signatures From

Reverberation Mapping of the Broad-Line

Region in Active Galactic Nuclei

Here we report further on results of our recent high time-resolution monitoring

program undertaken at five observatories. The first results of this program have

already been published (Denney et al. 2009a, hereafter D09a, see Chapter 3),

and main results for the full sample are discussed in Chapter 4 (Denney et al.

2010, hereafter D10). In this Letter, we present the most clear velocity-resolved

reverberation signals recovered from this campaign. Our results highlight three

distinctly different BLR kinematic signatures — inflow, outflow, and virialized

motions — for three separate targets — NGC3227, NGC3516, and NGC5548,

respectively. These results reveal kinematic diversity in reverberation signals and

underscore the importance of higher time resolution spectral monitoring. This

represents an important step between measuring average BLR response times and

148

black hole masses to realizing the full potential of this technique through the recovery

of a velocity–delay map.


Spectra of the nuclear regions of NGC3227, NGC3516, and NGC5548 were

obtained from a combination of the 1.3 m telescope at MDM Observatory, the 2.6 m

Shajn telescope of the Crimean Astrophysical Observatory (CrAO), and the Plaskett

1.8 m telescope at Dominion Astrophysical Observatory (DAO). Spectroscopic

observations targeted the Hβ λ4861 and [O iii]λλ4959, 5007 emission line region of

the optical spectrum. The top panels of Figure 5.1 show the mean spectrum of

each of the three targets based on the MDM observations, and the bottom panels

show only the variable emission in the form of an rms spectrum for each object,

respectively. Emission line light curves were made from the integrated Hβ flux

measured above a linearly interpolated continuum fit to the MDM, CrAO, and DAO

spectra.


photometry from the 2.0-m Multicolor Active Galactic NUclei Monitoring

(MAGNUM) telescope at the Haleakala Observatories in Hawaii (Yoshii 2002;

Yoshii et al. 2003), the 70-cm telescope of the CrAO, and the 0.4-m telescope of

the University of Nebraska (UNebr.). Continuum light curves were created with

observations from each V -band photometric data set and the average continuum

149

flux density near rest frame ∼5100 A in each spectrum of the spectroscopic data

sets. The reader is referred to D09a and D10 (Chapters 3 and 4 of this dissertation,

respectively) for details describing campaign observing setups and data reduction,

flux calibration of the spectra, and intercalibration of the data sets to form the single

set of optical continuum and Hβ emission line light curves shown for each object in

Figure 5.2.

Table 5.1 displays basic statistical parameters describing the final light curves

shown in Figure 5.2. Column 1 gives the object, and Column 2 lists the spectral

feature represented by each light curve. The number of data points in each light

curve is shown in Column 3, with the median sampling interval between these data

points given in Column 4. Column 5 shows the mean fractional error in the fluxes of

each time series. Column 6 gives the excess variance, calculated as

Fvar =

√σ2 − δ2

〈f〉 (5.1)


and 〈f〉 is the mean of the observed fluxes (Rodriguez-Pascual et al. 1997). Column

7 is the ratio of the maximum to minimum flux in the light curves, and Column

8 gives the adopted mean Hβ time lag and uncertainties determined through the

primary time series analysis which utilized the full Hβ line profile and is described

in detail for each object by D10 (see Chapter 4, this dissertation).

150

5.2. Velocity-Resolved Time Series Analysis

The lag measurements between the continuum and Hβ emission listed in Table

5.1 represent the average time delay across the BLR, measured from the centroid

of the cross correlation function (see Peterson et al. 1998, and references therein)

produced during the time series analysis of the continuum and full Hβ line profile

light curves shown in Figure 5.2 (see D09a or Chapter 3 of this dissertation for

details). Here, we focus on the velocity-resolved time series analysis we performed

on each target to investigate the potential for recovering velocity-dependent time

delays across the Hβ emission line in order to infer the kinematic structure of the

line emitting gas.

We divided the Hβ emission line into eight velocity-space bins, whose boundaries

were determined by the division of the rms spectrum of each object into eight bins

of equal flux, as depicted in the top panels of Figures 5.3 – 5.5. Compared to the

line boundaries used for the full profile analysis leading to the light curves shown

in Figure 5.2, those used for this analysis were slightly narrowed in the cases of

NGC3516 and NGC3227 in order to include only the most variable portions of the

line profile, and boundaries were broadened for NGC5548 because the rms spectrum

shows variability in the red Hβ wing that extends beneath the [O iii]λ4959 narrow

emission line.

151

Light curves were created from measurements of the integrated Hβ flux in each

bin and then cross correlated with the continuum light curves shown in Figure 5.2.

The bottom panels of Figures 5.3 – 5.5 show the lag measurements for each of these

bins. Error bars in the velocity direction represent the bin width. The evidence for

a velocity-stratified BLR response to continuum variations is clear in all three cases.

Interestingly, each case demonstrates a different kinematic signature: (1) outflow is

indicated in NGC3227, given the generally longer lags from red-shifted BLR gas

compared to the gas on the blue-shifted side of the line, (2) NGC3516 shows the

opposite signature, with the blue side of the line lagging the red side — an indication

that there is an infall component to the gas in this region, similar to that observed in

Arp 151 by Bentz et al. (2008), and (3) NGC5548 shows no radial gas motions, with

relatively symmetric lags measurements extending to equally large velocities on both

the red and blue sides of line — a clear indication of virialized gas motions, with the

high-velocity line wings arising in gas closest to the central source (see Robinson &

Perez 1990; Welsh & Horne 1991; Perez et al. 1992; Bentz et al. 2009c for examples

of how velocity resolved responses can be related to different BLR geometries; see

Peterson (2001) for a related tutorial).

152

5.3. Discussion

The velocity-resolved reverberation signals exhibited by the Hβ-emitting gas

in the BLR of these three sources show striking differences in kinematic behavior.

This is of particular interest because black hole masses derived from reverberation

mapping are only valid under the assumption of gravitational domination of

the BLR gas dynamics by the black hole. The influence of gravity on the BLR

in NGC3516 and NGC5548 is evidenced by the signatures of an infalling gas

component in the former and a lack of significant radial motions of any kind in

the latter (see Figs. 5.4 and 5.5). The apparent evidence for outflow in the case

of NGC3227 is a first for reverberation mapping. In some sense, this should be no

surprise given the overwhelming evidence for large-scale mass loss from the inner

regions of AGNs (Crenshaw, Kraemer, & George 2003). On the other hand, this

does call into question the assumptions that allow us to estimate the mass of the

central object, though we do hasten to point out that an outflow at escape velocity

would still allow us to measure the black hole mass with the levels of accuracy

currently claimed. Furthermore, the black hole mass we calculate for NGC3227 of

MBH = (7.6+1.6−1.7) × 106M⊙, based on the lag in Table 5.1 and the line dispersion

of the broad Hβ line measured from the rms spectrum (see D10, Chapter 4, this

dissertation), is consistent within the statistical and systematic uncertainties in this

method to independent measurements using galactic stellar (Davies et al. 2006) and

gas (Hicks & Malkan 2008) dynamics. We also note that while the Hβ emission line

153

is blueward asymmetric, the Hβ profiles of NGC3516 and NGC5548 are even more

so, so we ascribe little importance to this. It strikes us as likely that we are observing

a complex system such as a two-component BLR, in which there is an outflowing

wind, in addition to a virialized, disk component (Murray & Chiang 1997; Eracleous

& Halpern 2003). In this case, the mean lag that we measure, which is tracing the

position of the majority of the line-emitting gas, arises from the disk component

and is therefore under the gravitational influence of the black hole. Meanwhile,

the high-velocity, blueshifted emission with very short lags arises from a wind at

the inner BLR. Additional support for this scenario comes from the double-peaked

profile shape of the rms spectrum, suggesting a disk-like origin (e.g., Eracleous &

Halpern 1994). A further test for the virial nature of the BLR in NGC3227 is to

search for reverberation signals from multiple emission lines in this object. Data

from this same campaign suggest that the He iiλ4686 emission-line flux also varied

significantly over the course of the campaign, and future work is planned to search

for a reverberation signal from this variable line emission.

The observations of virial motions in NGC5548 and the outflow in NGC3227,

in particular, are of further interest in the context of comparisons with previous

velocity-resolved studies of a similar nature (e.g., Sergeev et al. 1999; Doroshenko

et al. 2008). These are largely focused on NGC5548 (the object for which we have

the most reverberation mapping data), and a comprehensive summary of many

of these past studies is given by Gaskell & Goosmann (2008), who discuss the

154

support for infalling BLR gas as implied by these various results, particularly for

low-ionization lines like Hβ. This is in contrast to what we clearly see in NGC5548

and NGC3227. It is entirely possible that the velocity fields in these regions could

change as a function of accretion rate, luminosity state, or over dynamical timescales.

Interpretation of these new results is problematic and probably will remain so with

only a handful of examples at single epochs. At this point, generalizing from these

few sources is premature.

5.4. Summary

In this work, we have presented three clear cases of differing velocity signatures

of Hβ-emitting gas from the BLR of three nearby AGNs, demonstrating the diversity

and probable complexity of the kinematics in this region. Our ability with this work

and that of Bentz et al. (2009c, see also Bentz et al. 2008) to recover statistically

significant velocity-resolved reverberation responses for multiple objects is principally

due to successful completion of campaigns in which high quality, homogeneous

observations were obtained over long durations (i.e., multiples of the reverberation

lags) with a sampling rate that was high compared to the relevant timescales being

investigated. Velocity-resolved reverberation mapping studies such as described here

are the next step toward producing a velocity–delay map, which will reconstruct the

two-dimensional kinematic structure of the BLR. This, in turn, will allow further

155

insight into the geometry and dynamics of the BLR, potentially leading to estimates

of its inclination and ultimately reducing the systematic uncertainties in MBH

determinations. In particular, placing direct observational constraints on the value

of the reverberation mapping mass scale factor, f (see Onken et al. 2004), even

in individual objects, could reduce the scatter in the MBH–σ⋆ relation for AGNs

(Gebhardt et al. 2000b; Ferrarese et al. 2001; Onken et al. 2004; Nelson et al. 2004).

Despite the diversity in BLR kinematic signatures seen here, we do not see any

systematic trends in the location of these objects on the MBH–σ⋆ relation, suggesting

that any effects the different velocity fields of these objects have on their black hole

mass estimates are within the current scatter in this relationship. More detailed

information about the velocity fields of these objects is needed to say anything

further on the effect these kinematic differences have on their black hole mass

measurements. Future work will focus on revealing more structure in BLR velocity

fields as we work to create velocity–delay maps of the Hβ emission in NGC3227,

NGC3516, and NGC5548 from the data presented here.

156

Fig. 5.1.— Mean and rms spectra of NGC3227 (left), NGC3516 (middle), andNGC5548 (right) from MDM observations. The solid line shows the mean and rmsspectrum formed after removal of the [O iii]λλ4959, 5007 narrow emission lines, andthe dotted lines represent the spectra prior to this subtraction (note the small residualsin the rms spectra).

157

Fig. 5.2.— Final light curves, after merging all data sets, of the 5100A continuum (toppanels) and broad Hβ emission line flux (bottom panels) in units of 10−15 erg s−1 cm−2

A−1 and 10−13 erg s−1 cm−2, respectively, for NGC3227 (top), NGC3516(middle),and NGC5548 (bottom). Except for the continuum flux scale of NGC3227, which isarbitrary because a linear fit to long-term secular trends has been divided out, theflux scales reflect all relative and absolute flux calibrations described by D10.

158

Fig. 5.3.— Top panels: Hβ rms profile of NGC3227 broken into bins of equal flux(numbered and separated by dashed lines) with the linearly-fit continuum level shown(dotted-dashed line). Flux units are the same as in Fig. 5.1. Bottom panels: Velocity-resolved time-delay measurements. Measurements and errors are determined similarlyto those for the mean BLR lag, and error bars in the velocity direction show the binsize. The horizontal solide and dotted lines show the mean BLR centroid lag anderrors, respectively.

159

Fig. 5.4.— Velocity-divided line profiles and velocity-resolved time-delaymeasurements of NGC3516. Same as Figure 5.3 but for NGC3516.

160

Fig. 5.5.— Velocity-divided line profiles and velocity-resolved time-delaymeasurements of NGC5548. Same as Figure 5.3 but for NGC5548.

161

Time Tmedian Mean

Object Series N (days) Frac. Err Fvar Rmax τcent (days)

(1) (2) (3) (4) (5) (6) (7) (8)

NGC3227 5100 A 171 0.45 0.03 0.10 1.9 ± 0.1 · · ·Hβ 75 1.00 0.03 0.08 1.5 ± 0.1 3.8 ± 0.8

NGC3516 5100 A 198 0.54 0.06 0.28 5.9 ± 1.5 · · ·Hβ 93 1.00 0.04 0.15 1.9 ± 0.2 11.7+1.0

−1.5

NGC5548 5100 A 182 0.56 0.03 0.11 1.7 ± 0.1 · · ·Hβ 108 1.00 0.09 0.26 3.7 ± 0.5 12.4+2.7

−3.9

Table 5.1. Light Curve Statistics and Mean Hβ Lags

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Chapter 6

Systematic Uncertainties in Black Hole Masses

Determined from Single Epoch Spectra

Using the AGN RBLR–L scaling relation (Kaspi et al. 2000, 2005; Bentz et al.

2006a, 2009a) and a measurement of the broad line region (BLR) gas velocity from

Doppler-broadened emission-line widths to measure supermassive black hole (BH)

masses from single-epoch (SE) spectra presents itself as a remarkably powerful tool

for determining black hole masses at all redshifts for potentially all spectroscopically

observed quasars. However, many effects limit the precision of these measurements,

the most important being how well the emission-line widths represent the true

motions of the BLR gas — for example, if the BLR has a flattened disk-like geometry,

the unknown inclination of the system can result in a huge uncertainty in the mass

(Collin et al. 2006). For the moment, however, if we set aside the issue of these

calibration uncertainties (i.e., the accuracy of the RM measurements themselves),

the relevant question becomes: how well can the SE mass measurements reproduce

the RM measurements? Scaling relationships are being used with increased

frequency in the literature to indirectly measure black hole masses from single-epoch

spectra. Therefore, it is imperative that we understand the systematic uncertainties

163

introduced in measuring a SE black hole mass. In this work we will discuss four

systematics, in particular, that clearly affect how well SE mass estimates reproduce

the RM measurements of BH masses.

1. Variability: The most inherent and unavoidable systematic in measuring masses

of AGNs is intrinsic variability that causes the luminosity, line widths, and

reverberation lag to change with time. The variable luminosity leads to

variable BLR radius determinations when the RBLR–L relation is used, so

we are therefore likely to measure different SE masses for different epochs.

In the case of AGNs for which multiple measurements of line widths and

radii are available from reverberation studies, the relationship between line

width and BLR radius (i.e. reverberation lag) is consistent with a virial

relationship, ∆V ∝ R−1/2 (Peterson & Wandel 1999, 2000; Onken & Peterson

2002; Kollatschny 2003), as expected if the BLR dynamics are dominated

by gravity. This relationship also seems to hold at least approximately for

individual emission lines measured at different times (e.g. Peterson et al. 2004):

the size of the BLR as measured in a particular emission line scales with

luminosity approximately as R ∝ L1/2 so we would expect that the line width

would correspondingly decrease as ∆V ∝ L−1/4 in order to preserve the virial

relationship. Evidence to date suggests that the central mass deduced from

reverberation experiments at different epochs is constant or, at worst, a weak

function of luminosity (Collin et al. 2006). This is itself quite remarkable since

164

we are characterizing a region that is undoubtedly rather complex (cf. Elvis

2000) by two quantities, the average time for response of an emission line to

continuum variations and the emission-line width. In a previous investigation

of variability on SE mass measurements using C ivλ1549 emission, Wilhite

et al. (2007) show that the distribution of fractional change in MBH between

epochs for several hundred SDSS quasars has a dispersion of ∼ 0.3. Only

part of this dispersion can be accounted for by random measurement errors.

Similarly, Woo et al. (2007) estimate the uncertainty in SE mass measurements

based solely on propagating the variability in the measurement of the Hβ

FWHM. They demonstrate that the uncertainty is roughly 30%. However,

the S/N of their data was low (∼ 10 − 15 pixel−1), and they attribute a large

fraction of their measured uncertainty to random measurement errors in the

line width. Here we will investigate the effect of variability by determining the

consistency of masses based on the two observables from optical SE spectra:

the monochromatic luminosity at 5100A and the Hβ line width. We will use

several hundred spectra of the Type 1 AGN NGC 5548 and a smaller sample

of spectra of the Palomar Green (PG) quasar PG1229+204.

2. Contamination by Constant Components: The variable AGN spectrum

is contaminated by relatively constant components. These include narrow

emission lines and host galaxy starlight. As the AGN luminosity varies, so

does the relative contributions to the observed spectrum from these sources.

165

We will determine how the SE mass measurements are affected by these

non-variable features in the spectrum. In particular, we will examine changes

in the precision and accuracy of the masses when these contaminating features

remain in the spectrum, compared to when their contributions are subtracted

before luminosities and line widths are measured.

3. Signal-to-Noise Ratio: Accurately measuring the spectroscopic properties

needed for calculating the SE mass is highly dependent on the quality of the

spectra. This is particularly true for measuring emission-line widths. Certainly

not all spectra used for such calculations in the literature are of comparable

quality. Therefore, we will demonstrate how changes in the signal-to-noise ratio

(S/N) of the data affect SE mass measurements. To make this comparison, we

will artificially degrade the S/N of our sample to various levels and compare

the resulting masses. In addition, it is common practice (e.g., McLure &

Dunlop 2004; Woo et al. 2007; Shen et al. 2008b; McGill et al. 2008) to fit

functions to emission-line profiles in data with comparatively low S/N in the

hopes of yielding more accurate line-width measurements. Here we test the

usefulness of this practice by calculating and comparing SE masses using line

widths measured directly from the data to those using line widths measured

from fits to the line profiles of the original and S/N -degraded spectra.

4. Blending: The optical region of broad-line AGNs is often characterized by

blending from many broad emission features as well as contributions from

166

the host galaxy starlight and AGN thermal emission. Therefore, detailed

modeling and decomposition of a spectrum into individual spectral components

is useful for isolating the features required for accurately measuring SE

masses. However, this process is rather time consuming as well as non-unique,

since it requires assumptions about the types of templates to fit and the

relative contributions to fit for each SE spectrum. Instead, to make SE mass

measurements for a large number of AGNs, it is expedient to use simple

algorithms or prescriptions for these measurements. There is concern, however,

that AGN emission-line blending and host galaxy features can affect the

accuracy of the line width measurements that utilize these simple prescriptions.

With these considerations in mind, we will compare SE mass measurements

made from measuring spectral properties using a simple prescription for local

continuum fitting and subtraction versus detailed modeling and decomposition

of the optical region to remove any extraneous components.

This is not a comprehensive list of systematics, but these particular issues have

a common element: all can be addressed empirically using a large number of SE

spectra of a single variable source. The use of a single source (actually, two single

sources) is what sets this study apart from past investigations, particularly on the

point of understanding the effect of variability on SE masses. This is an important

distinction, given that Kelly & Bechtold (2007) show that an intrinsic correlation

between MBH and L that is statistically independent of the RBLR–L relationship

167

(supported by, e.g. Corbett et al. 2003; Netzer 2003; Peterson et al. 2004) can lead

to an artificially broadened SE mass distribution when it is composed of masses

from multiple sources. They suggest that because of this intrinsic MBH − L relation,

using the luminosity simply as a proxy for the BLR radius may cause additional

scatter in the mass estimates because additional information about the BH mass

that may be contained in L is ignored. By utilizing many epochs from the same

object, however, the effect on SE masses due strictly to variability can be isolated,

while the broadening caused by a possible MBH − L correlation is avoided, because

we are dealing with a single black hole mass. Therefore, any additional information

about MBH contained in the luminosity could only affect the overall accuracy of our

SE measurements, not the scatter in our mass distributions due to variability.

For each of the potential sources of uncertainty listed above, we consider the

effect on the precision of the SE mass estimates, which is determined from the

dispersion of these masses about the mean sample value. We will also consider the

accuracy of the SE measurements, which we define as the systematic offset between

the distribution average and a single mass based on reverberation mapping results for

the same sample. We are not, however, addressing the accuracy of the reverberation

mapping masses themselves. Better understanding and quantifying the systematic

uncertainties and zero-point calibration of the reverberation mapping mass scale is

an important but difficult endeavor and will therefore be the focus of future work.

Because the focus of this paper is not the accuracy of the RM measurements but

168

instead on the reproducibility of these values by SE measurements, we will work

only with the virial product, given by

Mvir =cτ(∆V )2

G, (6.1)

where τ is the measured time delay between the continuum and broad emission-line

variations (so that cτ is the effective BLR radius) and ∆V is the velocity dispersion

of the BLR gas. Here, we measure the velocity dispersion from the width of the

broad Hβ emission line. By dealing simply with the virial product, or virial mass,

we bypass the zero-point calibration issue with the actual black hole mass1, MBH.

In addition, we will consider without prejudice the two common measures for

characterizing line widths: the full width at half maximum (FWHM) and the line

dispersion, or second moment of the line profile, σline.

6.1. Data and Analysis

6.1.1. NGC 5548 Spectra

The extensive, multi-decade monitoring of the Seyfert 1 galaxy NGC 5548

has led to one of the largest collections of observations of any single AGN. The

1This mass can be determined by scaling Mvir by a factor, f , which accounts for the unknown

BLR geometry and kinematics (e.g., Onken et al. 2004; Collin et al. 2006; Labita et al. 2006; Decarli

et al. 2008).

169

size of this data set alone makes this object an obvious choice for studying SE

mass measurements. The spectra of NGC 5548 for this paper were selected from

the International AGN Watch public archives2. With spectral quality in mind, we

choose several subsets of the available 1494 spectra for the different analyses within

this paper. In our analysis of AGN variability and the effects due to the constant

spectral components in §§6.2.1 and 6.2.2, we use a total of 370 spectra, including

the “Revised selected optical spectra (1989-1996)” covering years 1 − 5 (Wanders &

Peterson 1996), as well as the remaining spectra from the 1.8m Perkins Telescope at

Lowell Observatory covering years 6− 10 (Peterson et al. 1999, 2002). This subset of

data represents a nearly homogeneous set of high-quality spectra that is centered on

the Hβ λ4861 region of the optical spectrum. We then use a smaller subset of this

NGC 5548 data set for the S/N analysis in §6.2.3, separating from the 370 spectra

only those 270 observations made with the Perkins Telescope. These 270 spectra

were all obtained with the same instrument and instrumental setup, which kept

properties such as the entrance aperture, spectral resolution, and wavelength range

nearly constant for all observations. This sample allows us to target the systematic

errors due to changes in S/N rather than additional observational systematics. For

the analysis of spectral component blending covered in §6.2.4, we focus on a set of 33

spectra from years 6 − 13 of the AGN Watch campaign (Peterson et al. 1999, 2002)

observed with the 3.0m Shane Telescope at Lick Observatory. These spectra have

2http://www.astronomy.ohio-state.edu/∼agnwatch/

170

full optical wavelength coverage spanning rest frame ∼ 3000 − 7000 A. Utilizing this

wide spectral coverage, we perform full AGN-host spectral decompositions using two

independent methods to better judge the effects of blending.

Each of the above data sets have been internally flux calibrated to the

[O iii]λ5007 line flux in the mean spectrum using a χ2 minimization algorithm

developed by van Groningen & Wanders (1992). In this method the narrow

emission-line flux can be taken as constant, since these lines arise in an extended, low

density region and are thus unaffected by short timescale variations in the ionizing

continuum flux. Following this internal flux calibration, all subsets were scaled to

the absolute [O iii]λ5007 line flux of 5.58×10−13 erg s−1 cm−2 (Peterson et al. 1991).

6.1.2. PG1229+204 Spectra

The PG quasar PG1229+204 (hereafter PG1229) from the Bright Quasar

Survey was chosen as an additional object for this study because it is also a Type 1

AGN with a reverberation mapping mass measurement. In contrast to NGC 5548,

however, it is a higher luminosity source where neglecting the host galaxy and narrow

lines is less likely to interfere with the SE mass measurement. In addition, results

for this object will allow for a more meaningful comparison (than the low-luminosity

Seyfert 1 NGC 5548) with other quasars for which the RBLR–L scaling method is

more relevant. The 32 optical spectra in our sample were originally published along

171

with reverberation mapping results for several PG quasars by Kaspi et al. (2000) and

reanalyzed by Peterson et al. (2004). Here, we are again interested in the Hβ region

of the optical spectrum. The absolute spectral fluxes of these data were calibrated

externally with comparison stars in the same field as the object (for further details

see Kaspi et al. 2000).

6.1.3. Methodology for Measuring Virial Masses

Virial Masses from Single-Epoch Spectra

The virial mass can be measured from a single optical spectrum by using the

width of the broad Hβ emission line as a measure of the BLR velocity dispersion and

λLλ at λ = 5100 A in the rest frame as a proxy for the BLR radius, cτ , through the

use of the RBLR–L scaling relation (e.g. Kaspi et al. 2000; Bentz et al. 2006a, 2009a).

We use the RBLR–L relation of Bentz et al. (2009a) because it includes the most

current reverberation mapping results and luminosities that have been corrected for

host galaxy starlight contamination. Using this form of the RBLR–L scaling relation

and the virial mass formula given by equation 6.1 (i.e., excluding any assumptions

about the scale factor, f), the SE virial mass is given by

log

(

MSE

M⊙

)

= −22.0 + 0.519 log

(

λL5100

erg s−1

)

+ 2 log(

VHβ

km s−1

)

, (6.2)

172

where λL5100 is the luminosity at rest frame wavelength 5100 A, and VHβ is the

line width of the broad Hβ emission line. SE masses have been calculated in the

literature using various combinations of line widths and luminosity measurements

(for examples and comparisons, see McGill et al. 2008). Therefore, we calculate eight

virial masses for each SE spectrum using different combinations of line width and

luminosity measurements. Through comparisons of these different mass estimates,

we observe how the systematics listed above affect the resulting SE masses in relation

to each of the spectral properties that we isolate in our calculation.

For the investigations of AGN variability, constant components, and S/N

in §§6.2.1 – 6.2.3, the continuum flux density is taken as the average between

observed-frame wavelengths 5170 A and 5200 A for NGC 5548 and between 5412 A

and 5456 A for PG1229. These flux densities were corrected for Galactic extinction,

and then luminosity distances were calculated assuming the following cosmological

parameters: Ωm = 0.3, ΩΛ = 0.70, and H0 = 70 km sec−1 Mpc−1. Luminosities

for each spectrum were calculated both from the measured continuum flux density

and from the host galaxy-subtracted flux density. For NGC5548 spectra the

AGN continuum was then subtracted from each spectrum based on a linearly

interpolated fit between two local continuum regions: one blueward of Hβ over the

observed-frame range 4825 − 4840 A and one redward of [O iii]λ5007 over the range

5170 − 5200 A. Similarly, local continuum regions were defined for PG1229 over the

ranges 5063 − 5073 A and 5412 − 5456 A.

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Following continuum subtraction, Hβ line widths are measured from each

spectrum within the following observed-frame wavelength ranges. For the majority

of the NGC 5548 data, Hβ is defined over the wavelength range 4845 − 5018 A for

spectra with narrow line components still present but was extended to the range

4845− 5036 A for spectra from which we have removed the narrow lines because it is

often clear that the Hβ profile extends under the [O iii]λ4959 emission line. However,

during year 4 of the AGN Watch campaign (JD2448636–JD2448898), NGC 5548 was

in an extremely low luminosity state, thus necessitating a different choice for the

Hβ line boundaries and local continuum region blueward of this line. For spectra

observed this year, we extended the boundaries of Hβ to 4810 − 5135A and defined

the local continuum region blueward of Hβ to be between 4782 − 4795A. For the

PG1229 data set, Hβ is defined over the range 5075 − 5248 A or 5075 − 5310 A for

spectra with and without narrow lines, respectively. We measure the line dispersion

from the blue side of the broad Hβ line, σblue, assuming a symmetric profile about

the line center. This is done to avoid residuals from the [O iii]λλ4959, 5007 narrow

emission-line subtraction as well as possible Fe ii contamination commonly present

on the red side of the profile. The FWHM is measured from the full line profiles

described above. The exact procedures used for measuring these line widths follow

those of Peterson et al. (2004). We measure the line widths directly from the data,

except in one subsection of the S/N analysis (§6.2.3), where line widths are measured

from Gauss-Hermite polynomial fits to the Hβ line profile. Figure 6.1 shows the

174

host-subtracted luminosity and line widths measured from the 370 narrow-line

subtracted SE spectra of NGC 5548; the left panels show these observables as a

function of time, and the right panels show corresponding distributions, with the

mean and dispersions listed. The dispersions in these quantities are non-random and

due primarily to the intrinsic variability of the AGN but also include small random

measurement uncertainties.

Reverberation Virial Masses

To effect the most meaningful comparison with the single-epoch masses, we

calculate reverberation-based virial products, Mvir, for each data set. Using radii

from reverberation mapping leads to masses that are independent of the uncertainties

introduced in obtaining SE radii measurements (i.e., AGN variability and calibration

uncertainties in the RBLR–L scaling relationship). We use the reverberation radii of

Peterson et al. (2004) that are derived from the rest-frame lag, τcent, the centroid of

the cross-correlation function.

We characterize the BLR velocity dispersion by both FWHM and σblue of the

broad Hβ emission line. Line widths are measured in the mean spectrum for each

observing season of NGC 5548 (years 1–13) created from the sample of SE spectra

used in each analysis and the full PG1229 data set after removal of the narrow-line

components. We use the same methods and line boundaries as were used for the SE

spectra. Here, we measure line widths in the mean spectrum (Collin et al. 2006)

175

rather than the rms spectrum (Peterson et al. 2004) because there is no analog for the

rms spectrum for a SE spectrum. Instead, by using the mean spectrum, we are still

measuring the approximate mean BLR velocity dispersion3 yet retain a comparable

line profile to a single-epoch spectrum to use for a direct comparison. Uncertainties

in these line width measurements are determined with the bootstrap method of

Peterson et al. (2004). We then combine the reverberation radii for each year of the

NGC 5548 sample and the single radius for PG1229 with the corresponding values

of each line width measurement to calculate two sets of RM virial products for each

data set: one using FWHM and one using σblue. Weighted mean virial products are

then calculated for the NGC 5548 data sets spanning multiple years: 1 − 10 for the

variability, constant component, and S/N analyses in §§6.2.1 – 6.2.3 and 6 − 13 for

the blending analysis in §6.2.4, providing two final reverberation virial masses for

each data set: one using σblue and one using FWHM.

Comparisons: Measuring Precision and Accuracy

We measure the precision of SE virial masses by creating distributions of the

SE virial masses calculated for each data set as described above. The dispersion,

σSE, of these distributions serves as a measure of the precision of the SE masses.

3The main justification for using the rms spectrum is that only the portions of the line profile

varying in response to the ionizing continuum contribute to the rms spectrum. See Collin et al.

(2006) for a discussion.

176

It gives an indication of how well multiple SE spectra can reproduce a single,

mean mass, 〈log MSE〉. In addition, the accuracy of the SE masses can be gauged

by measuring the systematic offset of this mean mass from the corresponding

reverberation virial mass determined for a given data set. We define this offset as

〈∆log M〉 = 〈log MSE〉− log Mvir and calculate a value for each SE mass distribution.

6.1.4. Evaluation of Constant Components

A copy of each flux calibrated spectrum was made, and the narrow emission

lines were removed from this copy to allow for the calculation and comparison

of virial products from spectra with and without narrow lines present. Narrow

Hβ λ4861 and the [O iii]λλ4959, 5007 lines were removed by first creating a template

narrow line from the [O iii]λ5007 line in the mean spectrum from each data set.

This template was then scaled in flux to match and remove the [O iii]λ4959 line and

narrow component of Hβ (Peterson et al. 2004).

Host galaxy starlight contributions to the flux were determined for the various

extraction apertures of all NGC 5548 and PG1229 spectra using the method of Bentz

et al. (2009a) and observations of both galaxies with the High Resolution Channel of

the Advanced Camera for Surveys on the Hubble Space Telescope. Luminosities (and

subsequently SE virial masses) were calculated for every spectrum with and without

the presence of this constant continuum component.

177

6.1.5. Spectral Decomposition: Deblending the Spectral

Features

The rather simple approach used above to measure line widths and to account

for host galaxy contamination using local continuum fitting techniques fails to

address certain spectral features or components that may systematically affect our

SE virial mass estimates. First, the global AGN continuum is power-law shaped,

rather than linear, as we fit above. This may lead to small uncertainties in our

continuum subtraction, possibly even over the small wavelength range used here.

Second, blended Fe ii emission exists throughout the optical spectrum. If strong, this

emission could complicate our definitions of local continua on either side of the Hβ,

[O iii]λλ4959, 5007 region, potentially adding flux both to these continuum regions

and to Hβ itself. Third, the red wing of broad He iiλ4686 emission may be blended

with the blue wing of Hβ. This could also contaminate the local continuum region

defined between these two lines as well as the line width measurement. Fourth, the

underlying galaxy spectrum has structure that may be imprinted on the broad line

profiles if not removed accurately.

Therefore, we undertake full spectral decompositions of a selection of NGC 5548

spectra. Our goal is to determine if the (potentially over-) simplified local

continuum-fitting prescription to account for the underlying host galaxy and

additional AGN emission skew the SE virial mass results in a significant, yet

178

correctable manner. The data set used in this section consists of the 33 Shane

Telescope spectra from the AGN Watch sample described above. Because spectral

decomposition gives model-dependent, non-unique solutions, we compare results

based on two independent methods utilizing multi-component fits to account for

contributions from the host galaxy, AGN continuum, and spectral emission lines.

Method A

Decomposition method A (e.g., Wills et al. 1985) assumes that the observed

spectra can be described as a superposition of five components (see Dietrich et al.

2002, 2005, for more details):

1. An AGN power law continuum (Fν ∼ να).

2. A host galaxy spectrum (Kinney et al. 1996).

3. A pseudo-continuum due to merging Fe ii emission blends.

4. Balmer continuum emission (Grandi 1982).

5. An emission spectrum of individual emission lines, such as Hα,

[N ii]λλ6548, 6583, He iλ5876, Hβ, [O iii]λλ4959, 5007, He iiλ4686.

The first four components are simultaneously fit to each single-epoch spectrum,

minimizing the χ2 of the fit. We tested several different host galaxy templates

(elliptical galaxies, S0, and spiral Sa and Sb galaxies). The best results were obtained

179

using a scaled spectrum of the E0 galaxy NGC1407, which is quite appropriate for

the bulge of NGC5548. From this template we measure an average host starlight

contribution of Fgal(5100 A) = (4.16±0.84)×10−15 ergs s−1 cm−2 A−1 for this sample.

This is highly consistent with the value of Fgal(5100 A) = (4.45 ± 0.37) × 10−15

ergs s−1 cm−2 A−1 derived with the Bentz et al. (2009a) procedure for the observed

aperture of (4′′ × 10′′) for this data. To account for the Fe ii emission, we use the

rest-frame optical template covering 4250 − 7000 A based on observations of I Zw1

by Boroson & Green (1992). The width of the Fe ii emission template was on

average FWHM=1160 ± 34 km s−1. For the Balmer continuum emission, we found

that the best fit was obtained for Te = 15, 000K, ne = 108 cm−3, and optically thick

conditions.

The best fits of these components, including the power-law fit to account

for AGN continuum emission, are subtracted from each spectrum, leaving the

AGN emission-line spectrum intact. Narrow emission-line components were then

subtracted by creating a template narrow line from a two-component Gaussian fit

to the [O iii]λ5007 narrow line and then scaling it to each individual narrow line

to be subtracted based on standard emission line ratios. Figure 6.2 illustrates the

different fit components and residuals for a typical spectrum of NGC5548. Overall,

the spectrum is quite well reconstructed. However, it can be seen that around

λ ≃ 5200 A to λ ≃ 5800 A the flux level is overestimated. This might indicate that it

is necessary to include an additional component due to Paschen continuum emission,

180

as suggested by Grandi (1982) and more recently by Korista & Goad (2001). This

may, in turn, result in the selection of a less red host galaxy spectrum but potentially

a better overall fit (Vestergaard et al. 2008). This component was not included here,

however, because the actual strength of the Paschen continuum emission is not yet

well constrained and will therefore be the topic of future work in this area.

Method B

This method first corrects the spectra for Galactic reddening using the

extinction maps of Schlegel et al. (1998) and the reddening curve of O’Donnell

(1994) with E(B − V ) = 0.0392. The continuum and emission lines were modeled

separately. The continuum components include the following:

1. A nuclear power-law continuum.

2. The Fe ii and Fe iii blends that form a “pseudo-continuum” across much of the

UV-optical range. Template modeling is the only way, at present, to provide a

reasonable iron emission model for subtraction (see, e.g., Vestergaard & Wilkes

2001; Veron-Cetty et al. 2004, and references therein). We used the optical

iron template of Veron-Cetty et al. (2004), varying only the strength of the

template and the line widths.

3. The Balmer continuum was modeled using the prescription of Grandi (1982)

and Dietrich et al. (2002), with an adopted electron temperature of 10, 000

181

K and an optical depth at the Balmer edge of 1.0. These Balmer continuum

parameters typically give good matches to quasar spectra (Vestergaard et al.

2008). We note that here, too, no attempt was made to model the Paschen

continuum as it is poorly constrained.

4. The underlying host-galaxy spectrum was modeled using the stellar population

model templates of Bruzual & Charlot (2003). The best-fit model was a single

elliptical galaxy template with stellar ages of 10 Gyr. This model seems to

slightly underestimate the stellar emission strength in NGC 5548 longward of

Hα (e.g., ∼> 7000A), but preliminary fits (not included) seem to indicate the

overall fit is better with the inclusion of the Paschen continuum.

The individual continuum model components were varied to provide the

optimum match to the observed spectrum using Levenberg-Marquardt least-

squares fitting and optimization. Based on the host galaxy template fits

for this decomposition method, we measure a host starlight contribution of

Fgal(5100 A) = (7.05 ± 1.28) × 10−15 ergs s−1 cm−2 A−1, larger than found by Bentz

et al. (2009a) and the method A value, but marginally consistent once these other

values take Galactic reddening into account. The best fit continuum components

were then subtracted from the spectrum, and the remaining emission-line spectrum

was modeled with Gaussian functions using the same optimization routine as for

the continuum. A single Gaussian profile, whose width was allowed to vary up to

182

600 km s−1 was used for each of the narrow emission lines, but the same width was

used for all narrow lines. The strength of the [O iii]λλ4959, 5007 doublet lines was

constrained to the 1:3 ratio set by atomic physics. Figure 6.3 shows the individual

and combined components fit to the same NGC 5548 spectrum as in Figure 6.2, as

well as the residual spectrum after subtraction of both continuum components and

the narrow emission lines.

Methodical Differences and Mass Calculations

Overall, the two methods for fitting the individual AGN spectral components

agree quite well. However, there are two differences worth noting. First, each

method uses a different optical Fe ii emission line template. The Fe ii template used

by method B (Veron-Cetty et al. 2004) includes narrow line region contributions

to the emission. In general, both templates are similar, but they differ in detail

at around λ ≃ 5000 A and λ >∼ 6400 A. However, the strength of the optical Fe ii

emission in NGC5548 is quite weak (Vestergaard & Peterson 2005), and the width

of the Fe ii emission is expected to be broad. Therefore, the choice of the Fe ii

emission template has little impact on the results in this case. Second, the modeling

of the narrow emission lines in the Hβ and [O iii]λλ4959, 5007 region with the

single Gaussian component of method B sometimes leaves some residuals around

the [O iii]λλ4959, 5007 lines. This typically happens when excess emission appears

in the red wing of Hβ which cannot be fully accounted for with only Gaussian

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components. Although these residuals do not account for a significant amount of

flux, the two-component Gaussian fit to the narrow lines used by method A tends to

better minimize these residuals.

Line widths are measured for Hβ from all epochs following analysis from both

spectral decomposition methods as well as the local continuum fitting method. For

this particular sample, the local continuum was defined between two continuum

windows over the rest-frame wavelength ranges 4730 − 4745A and 5090 − 5110A,

and line widths were measured in all spectra over the rest-frame wavelength range

4747−4931A, as determined from the mean spectrum. For the local continuum-fitted

spectra, L5100 was calculated from the average continuum flux density over the

rest-frame wavelength range 5090 − 5110A after correcting for host galaxy starlight.

For decomposition methods A and B, L5100 was taken to be the value of the

power-law fit to each SE spectrum at rest-frame 5100A. SE virial masses were then

calculated with equation 6.2 for line widths measured with both σblue and FWHM.

For comparison to the SE mass distributions of each of the three data analysis

methods, reverberation virial masses were calculated with each of the line width

measures, FWHM and σblue, similar to the previous NGC 5548 data sets spanning

multiple years. The weighted mean RM virial mass for each analysis method

(covering yrs 6–11 and 13 for this data set) was calculated by averaging the yearly

RM virial masses calculated by combining line widths measured from the mean

spectrum created from SE spectra spanning a single observing season and the BLR

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radius from the corresponding season as determined with reverberation mapping (for

results from individual years, see Peterson et al. 2004).

6.2. Analysis and Results

6.2.1. Effects of Variability

To investigate systematics associated strictly with AGN variability in SE virial

products (VPs), we first remove the contaminating constant spectral components

(i.e., narrow lines and host galaxy flux) as described in §6.1.4. Figure 6.4 shows

virial mass distributions created from all 370 spectra of NGC 5548 (Fig. 6.4a)

and 32 spectra of PG1229 (Fig. 6.4b). Results are shown for both line width

measures, σblue and FWHM (left and right panels, respectively), for both objects.

For each distribution we focus on the dispersion (i.e., precision) and the mean offset

(i.e., accuracy), 〈∆logM〉, from the reverberation result, as given in Table 6.1.

Column 1 gives the object name, column 2 shows the sample size, column 3 lists the

reverberation virial product and associated uncertainties when calculated with σblue,

column 4 lists the mean and standard deviation of the distribution utilizing σblue,

column 5 gives the mean offset between the reverberation VP (Col. 3) and mean of

the SE distribution (Col. 4). Columns 6, 7, and 8 are similar to columns 3, 4, and 5,

but for masses based on FWHM.

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Figure 6.4 shows that the widths of all four distributions are quite small.

The listed dispersions have not been corrected for measurement uncertainties in

line width and luminosity. However, we have estimated the average measurement

uncertainties for the full set of NGC 5548 SE spectra to be 0.08 dex in log(L),

0.01 dex in log(σblue), and 0.03 dex in log(FWHM). We can assume that these

measurement errors are independent of the dispersion due to variability alone and

that the distributions are close enough to Gaussian that we can add independent

errors in quadrature. Therefore, we can correct the observed dispersions in the SE

mass distributions for NGC 5548 for the contribution due to these measurement

uncertainties. Following this correction, the uncorrected dispersions listed in Figure

6.4a and Table 6.1 can be reduced to 0.11 dex for masses based on σblue and 0.14

dex for masses based on FWHM. The narrowness of these distributions indicates

that the scatter in SE masses due to intrinsic variability is remarkably small. This

is particularly true for PG1229, for which σSE ≈ 0.05 dex. Granted, PG1229 is less

variable, but with a scatter of only 0.11 − 0.14 dex, the uncertainty in MSE due to

variability for NGC 5548 is not large either.

The precision and accuracy in the MSE measurements seem only weakly

dependent on whether σblue or FWHM is used as the line-width measure. For both

AGNs, the scatter is apparently minimized and the accuracy (given by 〈∆logM〉)

maximized with the use of σblue. In terms of accuracy, 〈∆logM〉 should at least

partially represent the displacement of the particular AGN from the RBLR–L relation,

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regardless of which quantity is used to characterize the line width. Figure 6.5 shows

that the average luminosities of the NGC 5548 and PG1229 SE spectra place them

above the RBLR–L relation in r by ∼ 0.13 dex and ∼ 0.07 dex, respectively, after

accounting for host starlight contributions (as was done here). This explains why,

for a given SE luminosity, the resulting radius (and thus VP) is underestimated

compared to the reverberation results, confirmed by the negative 〈∆logM〉 values

found in Table 6.1. Since this effect depends on luminosity alone, the masses

calculated from both line width measures should be affected equally. However,

masses calculated from FWHM measurements result in larger 〈∆logM〉 values

for both objects. This additional component may be related to the fact that our

measurement uncertainties tend to be larger for FWHM compared to σblue, or it may

simply demonstrate one of the limitations of measuring masses from SE spectra with

FWHM.

The light curves of NGC 5548 span several years, much longer than the

reverberation time scale of tens of days. Indeed, the Hβ lag has been measured

year-to-year for over a dozen different years, and the lag and the mean luminosity

of the AGN are well-correlated on yearly timescales, and as noted earlier, the

reverberation-based mass is approximately constant with perhaps a weak dependence

on luminosity (Bentz et al. 2007). Given our goal of comparing SE predictions with

reverberation measurements, we have for NGC 5548 also computed the difference

between each SE virial product and the reverberation virial product for the specific

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year in which the SE observation was made. We show the distribution of these

differences in Figure 6.6, which is rather narrower than the similar distribution shown

in Figure 6.4a. This illustrates that masses from SE spectra seem to reproduce the

reverberation mass that would be measured at the same time quite accurately, to

∼ 25% or so. However, there are longer term secular changes that occur, as shown

in the top panel of Figure 6.1, that add to the observed dispersion due to variability

resulting in the total width of the distributions shown in Figure 6.4. Because of

these secular changes, even a reverberation-based mass measurement might change

slightly, say, over a dynamical time scale.

6.2.2. Accounting for Constant Components

Failing to account for the constant spectral components in the AGN spectrum

(i.e., the narrow emission lines and host galaxy starlight) affects both the precision

and accuracy of the SE mass estimates. We examine the effect of neglecting each

of these components individually and then in combination for both NGC 5548 and

PG1229.

Effect of Starlight

First, we examine the consequence of failing to remove the host starlight

contribution to the continuum flux density. We still subtract narrow emission-line

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components, however. Figure 6.7 shows SE virial mass distributions similar to

those in Figure 6.4, but here the host starlight was not subtracted from the

luminosity before the SE masses were calculated. In terms of precision, the virial

mass distributions in Figure 6.7 derived from non-host-corrected luminosities have

equal or even slightly smaller dispersions than their corrected counterparts (Fig.

6.4). This occurs simply because subtraction of the host starlight increases the

relative amplitude of the AGN continuum variations. NGC 5548 has a relatively

larger host galaxy contribution and is therefore more susceptible to this effect than

PG1229. The observable result is an overall increase in the dispersion of the mass

distribution and, in particular, the low-mass (i.e., low-luminosity state) wings of

the MSE distributions in Figure 6.7 are broadened compared to those in Figure 6.4.

Notably, over-subtracting the host galaxy flux could also lead to similar observable

consequences. However, the tail of the distribution appears to be nearly Gaussian,

which argues against any large error in the starlight flux estimate. In contrast, this

broadening affect is not observed for PG1229. This is expected because PG1229 has

a smaller host contribution to its total luminosity than NGC 5548, and its luminosity

varied less over the time period in which it was observed. Therefore, when we

subtract a relatively smaller constant host flux from a distribution of values with an

initially smaller luminosity dispersion, the effect on the SE mass distributions is less

significant.

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Failing to account for host starlight imposes a shift to the entire SE mass

distribution. Because the luminosity is larger when the host contribution is not

subtracted, a larger BLR radius is estimated with the RBLR–L relation. This, in

turn, produces larger virial products and affects the accuracy of the measurements.

Whereas Figure 6.4 shows an average underestimation of the SE masses compared

to the reverberation results, Figure 6.7 shows that on average, the SE masses

are overestimated (i.e. positive 〈∆logM〉 values), which is again explained by

the locations of NGC 5548 and PG1229 on the RBLR–L scaling relationship

(Fig. 6.5). Without accounting for the host starlight, both objects lie below the

relation. Therefore, the RBLR–L relation overestimates the radius of a SE luminosity

measurement that does not account for this contribution. This effect can be seen by

comparing the 〈∆logM〉 values in rows 2 and 5 of Table 6.2 with those of Table 6.1,

which are negative for in Table 6.1 but positive in Table 6.24. Failing to account

for the host contribution has roughly the same overall effect on the precision and

accuracy of SE mass distributions regardless of whether σblue or FWHM is used for

the calculation of MSE (a shift in 〈∆logM〉 of 0.17 dex for NGC 5548 and 0.12 dex

for PG1229 for both line width measures), as expected since this contribution does

not affect the line width.

4Results in Table 6.2 are presented in a similar manner as Table 6.1, except columns have been

added to distinguish whether or not narrow emission-line and/or host starlight contributions are

present in the results.

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Based on the results presented here, it is not completely clear that subtracting

the host contribution improves the overall accuracy of the mass estimates. In fact,

the SE masses of both NGC 5548 and PG1229 presented here are typically as

accurate or more accurate (i.e., the absolute value of 〈∆logM〉 is smaller) when the

starlight contribution is not subtracted. When considering the physics of AGNs,

however, the BLR radius should be correlated with only the AGN luminosity, since

the material in the BLR knows nothing of the luminosity originating from galactic

starlight. Furthermore, Bentz et al. (2009a) determine that calibrating the RBLR–L

relation with luminosity measurements that have been corrected for host starlight

contamination significantly reduces the scatter in the relationship and results in

a slope that is highly consistent with that predicted by simple photoionization

theory. These considerations, in addition to our use of the Bentz et al. (2009a) host

starlight-corrected calibration of the RBLR–L relation for SE mass determinations,

serve as motivation for removing this contamination before the RBLR–L relation is

used. This evidence suggests that the ambiguity between the theoretical expectation

that host-subtracted luminosities should yield more accurate masses and the fact

that the masses presented here are more accurate before host starlight subtraction

is simply because both NGC 5548 and PG1229 happen to lie above the RBLR–L

relation. However, in a general statistical sense, SE masses will be overestimated if

host starlight contamination is not taken into account before the RBLR–L relation

is used to determine BLR radii. This is particularly true for lower-luminosity,

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Seyfert-type galaxies that, in contrast to quasars, have larger relative host starlight

contributions to their measured luminosity.

Effect of Narrow Lines

The Hβ and [O iii]λλ4959, 5007 emission line profiles for NGC 5548 and PG1229

are shown in Figure 6.8. In NGC 5548 (left), the narrow line typically increases

the peak flux by ∼ 50%, compared to ∼< 10% in PG1229 (right). Given these

relative contributions of narrow-line fluxes (particularly in the case of NGC 5548),

failing to subtract the narrow line component from the broad emission line before

measuring the width can have a significant impact on the resulting mass estimate.

To demonstrate this, Figure 6.9 displays SE mass distributions for NGC 5548 and

PG1229; this time, however, we do not subtract the narrow lines from the spectra

before measuring line widths, although we do subtract the host galaxy contribution.

Statistics for the scenarios shown in Figure 6.9 can be found in Table 6.2, rows 3

and 6. Figure 6.9 clearly demonstrates that leaving the narrow lines present affects

both the precision and accuracy of the SE masses.

Failing to subtract the narrow lines tends to decrease the precision of the

SE mass estimates. This is evident by an increase in the width of the SE mass

distributions and is particularly pronounced for NGC 5548 when characterizing the

line with FWHM (by comparing Fig. 6.9a with Fig. 6.4a or Fig. 6.7a, in which

narrow lines were removed). In this case (Fig. 6.9a, right), the resulting width of

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the VP distribution is a factor of three to four larger than if σblue is used (Fig. 6.9a,

left). This effect of the narrow lines on the precision is less apparent in PG1229

because the narrow line constitutes only a small percentage of the Hβ line flux.

However, it is still observed when the FWHM is used for measuring the line widths

(compare Fig. 6.9b, left, to Fig. 6.4b, left), since, to reiterate, this trend is much

more apparent for the FWHM.

From a physical standpoint, only BLR emission varies in response to the ionizing

continuum on reverberation timescales, so only the broad emission component

should be used for the virial mass calculation. Because the square of the line width

enters into the BH mass calculation, relatively small changes in the line width can

significantly affect the mass estimate. When the narrow-line component is not

subtracted, the line width and hence the black hole mass is underestimated. Figure

6.9 shows evidence for this in both NGC 5548 and PG1229. As with the precision,

this effect is much stronger when the narrow component is a more prominent feature

in the emission-line profile, as is the case for NGC 5548 (refer back to Fig. 6.8).

For obvious reasons, removing the narrow lines is more important when the line

width is measured with the FWHM (right panels of Figs. 6.9a and 6.9b); the very

definition of the FWHM depends on the peak flux, so if the narrow component is

not subtracted, this peak flux can be greatly overestimated. An overestimation of

the peak flux results in an artificially small FWHM and, subsequently, a severely

underestimated mass. NGC 5548 affords a useful case in point: the masses calculated

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without removing narrow line components (Figure 6.9a) are underestimated on

average by a whole order of magnitude (〈∆logM〉 = −1.00) when line widths are

measured from the FWHM (right panel). In contrast, the dependence of the line

dispersion on the line center and peak flux is relatively weak, affecting the accuracy

of SE mass estimates by ∼ 0.1 − 0.2 dex for NGC 5548 and by an insignificant

amount for PG1229 (compare 〈∆logM〉 values for MSE ∝ σblue from Table 6.2, Rows

3 and 6 to Table 6.1 values). Regardless of the minimal effect when σblue is used, the

evidence presented here clearly indicates that the narrow line component should be

removed regardless of which prescription is used for measuring the line width.

Combined Effects of Starlight and Narrow Lines

Figure 6.10 shows mass distributions for both NGC 5548 and PG1229 when

neither of these constant components is removed from the spectra. Table 6.2 (Rows

1 and 4) displays the corresponding statistics. Generally, as expected, the precision

and accuracy are worse, or at least no better than when these constant components

are removed. However, these two constant components act opposingly on the mass:

failing to remove the narrow lines tends to decrease mass estimates, but failing to

subtract host galaxy flux increases mass estimates. Therefore, these two effects can

fortuitously cancel, resulting in an apparently smaller dispersion and/or mean offset.

This is the case for PG1229 when FWHM is used to measure the line width and

NGC 5548 when σblue is used. The chance cancellation in these cases should not

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distract from the otherwise well-supported conclusion that both of these components

should be removed to obtain the most accurate and precise SE mass estimates.

6.2.3. Systematic Effects due to S/N

Our goal here is to identify the point at which low S/N begins to compromise

the precision and accuracy of SE mass determinations. We start with our most

homogeneous data set, the 270 observations of NGC 5548 from the Perkins

Telescope. Based on conclusions from previous sections §§6.2.1 and 6.2.2, only

narrow-line-subtracted spectra that have been corrected for host galaxy starlight

are used. The S/N per pixel of the original spectra ranges significantly, with a

mean and standard deviation of 110 ± 50, as measured across the 5100A continuum

window given above. Using the S/N per pixel in the original spectra as a starting

point, we then increase the noise in each spectrum by applying a random Gaussian

deviate to the flux of each pixel across the whole spectrum. The magnitude of the

deviate is set to achieve degraded S/N levels of ∼ 20, ∼ 10, and ∼ 5 across the

5100A continuum window. Figure 6.11 shows an example degradation for a typical

NGC 5548 spectrum. Below, we discuss results for masses calculated from line

widths measured directly from the data as well as from Gauss-Hermite fits to Hβ in

the original and S/N degraded spectra.

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Direct Measurement of the Spectra

We measure line widths and luminosities directly from both the original and

S/N -degraded spectra and calculate virial masses. The resulting distributions are

shown in Figure 6.12 for both σblue (left) and FWHM (right). Statistics describing

the distributions of MSE are listed in Table 6.3 in a format similar to that of previous

tables. Figure 6.12 shows that the dispersions of the distributions broaden as the

S/N of the spectra decreases. Overall, low S/N begins to negatively affect the

precision of the virial mass estimates at S/N ∼< 10 for σblue (see third panel on left)

and at S/N ∼< 5 for FWHM (see bottom panel on right). Wilhite et al. (2007) find a

similar result, with the widths of their SE mass distributions increasing steadily with

decreasing S/N . However, measurements of σblue and FWHM are affected differently

by decreasing S/N and will therefore be discussed separately.

Measurements of virial masses from σblue in low S/N spectra sacrifices both

precision and accuracy primarily because the wings of the broad line become lost

in the noise and the line profile boundaries cannot be accurately defined for cases

where S/N ∼< 10. This results in smaller effective line widths. This effect decreases

the overall accuracy by shifting the whole distribution to artificially smaller masses.

However, at these low S/N limits (see bottom two plots of Fig. 6.12, left), the

distribution actually becomes highly non-Gaussian in shape, resulting in a much

peakier distribution, nearly centered on the corresponding reverberation virial

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product. This implies that although the overall dispersion has increased significantly

(by nearly a factor of 2) and individual measurements have the potential to be highly

inaccurate, a typical measurement will likely be more accurate with a much smaller

uncertainty than quoted through the overall distribution average.

Different systematics are introduced when using FWHM to characterize the

line width. Because FWHM does not depend on the line wings, lower S/N can be

tolerated before the precision is significantly sacrificed. When S/N is low enough to

affect FWHM, the line width is generally underestimated. Several effects contribute

to the difficulty in defining FWHM in low S/N data. First, the peak flux may

be incorrectly attributed to the highest noise spike, resulting in an overestimated

maximum. Second, the half-maximum may be difficult to define because the

continuum level cannot be accurately ascertained. Third, the width may also be

problematic to define because a noisy profile could mean that the half-maximum flux

value is shared by multiple wavelength values. These effects alter the precision at

our lowest degraded S/N level (∼ 5). However, they begin to affect the accuracy of

the measurement much earlier. Progressively poorer accuracy can be easily observed

from the increasingly negative 〈∆logM〉 values in the distribution statistics given in

Table 6.3 for FWHM and/or by comparing the mean values of the distributions in

Figure 6.12, right. Although higher precision VP measurements can be made from

lower S/N data with the FWHM than with σblue, there is a trade-off in accuracy.

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For this reason, we caution against measuring SE masses from spectra with S/N

lower than ∼ 20 pixel−1, regardless of the line-width measurement method.

Measurements from Gauss-Hermite Polynomial Fits

Recent work has been published in which the emission line profiles are fit with

either Gaussian and/or Lorentzian profiles (e.g., McLure & Dunlop 2004; Shen et al.

2008a,b) or Gauss-Hermite polynomials (e.g., Woo et al. 2007; McGill et al. 2008).

SE virial masses are then calculated with the line widths measured from these fits

rather than directly from the data in an attempt to mitigate the negative effects of

low S/N on line-width determinations. We test this technique by fitting a sixth-order

Gauss-Hermite polynomial to the narrow-line-subtracted Hβ profiles in the original

and S/N -degraded spectra used above. A linearly interpolated continuum defined by

the same regions as above was first subtracted from the spectra before the fits were

made. Our Gauss-Hermite polynomials utilize the normalization of van der Marel

& Franx (1993) and the functional forms of e.g. Cappellari et al. (2002). We then

use the method of least-squares to determine the best coefficients for the sixth-order

polynomial fit. The thick black curves in Figure 6.11 show an example of the fits

to the original and S/N -degraded forms of this typical NGC 5548 spectrum. Both

FWHM and σblue were measured from these fits with the same methods described

previously for the direct measurements and then combined with host-corrected

luminosities in order to calculate virial masses for all SE spectra in this sample.

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Figure 6.13 shows the resulting distributions for the virial masses calculated using

σblue (left) and FWHM (right). Distribution statistics are also given in Table 6.3.

We can now compare the mass distributions from the fitted data to our previous

results (Fig. 6.12; Table 6.3) based on direct measurement. We find that low S/N is

somewhat mitigated by using σblue to characterize the line width of fits to the data

(Fig 6.13, left). The fits allow increased precision at the S/N ∼ 10 level, compared

to measurements directly from the spectra. In addition, the accuracy of the VPs

resulting from the fits is also nearly unchanged down to S/N ∼ 10. Although the fits

routinely underestimate the line peak, this does not greatly affect the σblue results

because of the insensitivity of this line characterization to the line center. Therefore,

Gauss-Hermite fits are advantageous for extending the usefulness of data down to

S/N ∼ 10 if σblue is used to characterize the line width.

On the other hand, our fit results do not show an improvement if FWHM is used

for the line widths, at least as far as this object is concerned. The Gauss-Hermite fits

were often unable to accurately model the complex Hβ profile of NGC 5548, and the

underestimation of the line peak by the fits that was mentioned previously causes

a systematic overestimation of FWHM that increases with decreasing S/N . This

overestimation of FWHM acts in the opposite direction as the trend observed with

the direct FWHM measurements from the data (i.e. a typical underestimation of

FWHM). Therefore, as the S/N decreases, a significantly increasing difference results

between the mean value of the MSE distributions based on direct measurement and

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those based on the Gauss-Hermite fits. From a precision standpoint, the width of

the MSE distribution based on Gauss-Hermite fits to the original S/N -level spectra

is actually narrower than that of the equivalent distribution resulting from direct

measurement. This suggests that fitting the line profile when using FWHM may

actually be beneficial in high S/N data and reduce possible systematics such as

residuals from narrow-line subtraction. However, once the S/N is degraded, the

dispersions of the distributions composed of masses calculated from the fits (Fig.

6.13, right) quickly become larger than those composed of masses calculated from

direct measurement (Fig. 6.12, right). This shows that fitting the line profile when

using FWHM does not mitigate the effects of low S/N because the fit does not

accurately reproduce the true profile shape.

For the sake of completeness, we note that there are many different methods

described in the literature for measuring FWHM that are formulated to address

issues associated with noisy data and complex line profiles. Here, we have chosen

two methods (the formulation of Peterson et al. (2004) and the use Gauss-Hermite

polynomial fits) that differ in computational complexity and the assumptions made

about the underlying profile shape. However, other methods also attempt to mitigate

the effects of noise. For example, Brotherton et al. (1994) define the peak of the

line based on a flux weighted mean wavelength, the centroid, above a level that

is 85% of the line peak to decrease the likelihood that the peak used is simply a

noise spike. Similarly, Heckman et al. (1981); Busko & Steiner (1989) also calculate

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the centroid with ∼> 80% of the peak flux but use it in a slightly different way to

determine the line width. Results using any of these other methods are not expected

to differ greatly from the results that we show here, however, since our two methods

effectively represent the extremes for measuring this naively simple quantity.

6.2.4. Systematic Effects Due to Blending

As noted earlier, the best subset of NGC 5548 spectra to use to explore the

effects of blending of spectral features is the 33 spectra from the Lick Observatory

3m Shane Telescope. These are high S/N , homogeneous spectra that have the broad

spectral coverage necessary for spectral decomposition. Since spectral decomposition

does not necessarily lead to a unique solution, two independent methods were

employed as described earlier. Cumulative distribution functions created from

the SE masses measured from the 33 Lick Observatory spectra of NGC 5548 are

shown in Figure 6.14. Distributions of MSE are presented for all three data analysis

methods described above: the local continuum fitting method (left panels), spectral

decomposition method A (center panels), and spectral decomposition method B

(right panels). As in previous plots, mass results are shown for both σblue (Fig.

6.14a) and FWHM (Fig. 6.14b). Table 6.4 displays the corresponding statistics for

the distributions shown in Figure 6.14.

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When σblue is used in the VP calculation, a full spectral decomposition gains

a small amount of precision relative to the simple, local continuum fitting method.

More importantly though is that a systematic offset is seen between the mean values

of the local continuum-fitted distribution versus those of decomposition methods A

and B. Line dispersions measured from the deblended spectra (for both methods

A and B) are consistently larger than those measured using a local continuum fit.

This is demonstrated in Figure 6.15, where we have plotted the σblue measurements

from the spectra deblended with methods A and B against those based on a local

continuum fit. This difference is due to a combination of two factors5. First, the

host galaxy templates used for both decomposition methods contain a small Hβ

absorption feature that effectively adds additional flux to the center of the Hβ

emission line when the host is subtracted. This absorption is not accounted for by a

linear continuum fit. However, since σblue is only weakly dependent on the line peak,

this is unlikely to make a significant contribution to the observed difference. The

second and larger contributing factor to the differences in σblue measurements is a

result of blending of Hβ with He iiλ4686. Decarli et al. (2008) have suggested that

this blending with He iiλ4686 complicates the measurement of the line dispersion

5A third factor that could also lead to differing line dispersion measurements is the presence

of Fe ii emission. Strong Fe ii emission can obscure the line wings and line boundaries as well

as contaminate the true AGN continuum level, leading to smaller line dispersion measurements.

Fortuitously, Fe ii emission is very weak in NGC 5548, and therefore does not contribute to the

differences observed here. However, this may not be the case for other objects.

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for Hβ widths larger that 2500 km s−1. However, we observe larger differences for

narrower Hβ widths, and therefore deduce that this blending is a stronger function

of the flux of He iiλ4686 rather than the width of Hβ. The effects of blending are

therefore greater when the AGN is in a higher luminosity state, when He iiλ4686 is

stronger, even though the Hβ line is narrower in high states. This is supported by

the trend seen in Figure 6.15 of larger σblue differences for narrower Hβ widths.

The blending of He iiλ4686 and Hβ could cause an overestimation of the

continuum flux level in the local continuum window defined between these lines (see

§6.1.5). An overestimated continuum level leads to a steeper linear fit, a subsequent

over-subtraction of the blue wing region of Hβ, and finally, an underestimation

of σblue. The power-law continuum fit used for the decomposition methods is not

susceptible to this, since it is not fit based on local continuum regions. On the

other hand, the σblue measurements from the decompositions could be overestimated

if some of the flux attributed to Hβ is actually from the red wing of He iiλ4686.

Figure 6.16 shows a comparison of the continuum-subtracted mean spectrum formed

from all SE spectra from each of the three data analysis methods. It is clear that

more flux exists in the blue wing of the deblended spectra from both methods A

and B than in the spectrum formed by subtracting the local continuum fit. This is

a consequence of the way the continuum was fit in each case in connection with the

presence of He iiλ4686.

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Because of the large differences we observe in σblue measurements between

the decomposition methods and the local continuum fitting method, we return to

each of our decomposition methods and fit additional contributions to account for

helium emission. Starting with the deblended spectra we previously created with

decomposition method A, we first remove the Hβ profile by modeling the emission

with a scaled template created from a four-component Gaussian fit (two components

for the main emission and two to account for broader wings) to Hα, whose blue wing

is unobstructed by broad emission-line blending. The template is fixed in velocity

space and then scaled in flux to minimize the residuals of the fit. For these 33

spectra, the best fits result in Balmer decrements typically in the range of 2.8 − 3.2.

The Hβ fit is then subtracted from the spectrum, leaving the He iiλ4686 emission

line clearly visible. This emission is then fit with either a single broad Gaussian

profile or a double Gaussian profile (adding a narrower component in addition to

the broad component fits 19 out of the 33 epochs better than a single component,

possibly due to residual narrow-line emission). The best fit profile for each epoch

is subtracted from the initial, narrow-line subtracted, deblended spectrum. Figure

6.17 (top) shows the Hβ region of the mean spectrum formed from the SE spectra

after spectral decomposition with method A before and after subtracting the mean

He iiλ4686 fit, which is also shown. This method fits He iiλ4686 only as a means to

better understand the blending with Hβ.

204

In contrast, with method B, we return to the continuum-subtracted spectra (i.e.

after removing contributions from the host starlight, Balmer continuum, power-law

continuum, and FeII emission) and simultaneously fit both broad and narrow optical

emission lines. Similar to the method described above for the continuum component

fitting, method B uses Levenberg-Marquardt least-squares fitting and optimization

to obtain the best overall emission-line fits to the full spectrum. In addition to fitting

the narrow-line features as described above, the three strongest broad Balmer lines

are each fit with two Gaussian profiles, where the best fit velocity width is held fixed

for all three lines. Both He ii and He i emission lines are fit with a single Gaussian

profile, and although these widths are not tied to the Balmer line widths, the widths

of He iiλ4686 and the He i emission under the Hβ, [O iii]λλ4959, 5007 region are tied

to the width of the unblended He iλ5876 line in the same way the Balmer line widths

are tied together. Each set of emission lines of a given species and type of emission

(i.e. narrow or broad) is isolated in the total fit, so that only the emission of interest

can be subtracted. Since the narrow-line emission was subtracted previously, we

now subtract the broad helium emission, effectively deblending Hβ from He iiλ4686.

Figure 6.17 (bottom) shows the Hβ region of the mean spectrum created from the

33 SE spectra after decomposition with method B before and after subtracting the

average helium fit, which is also shown.

We measure line widths in these He-deblended spectra with a newly-defined

blue boundary for Hβ at 4720A (compared to 4747A previously). This boundary

205

was extended because the edge of the blue wing of Hβ is better discerned without

the presence of He iiλ4686. Figure 6.18 shows new σblue measurements for the

He-deblended Hβ line from the two decomposition methods compared again to σblue

from the local continuum method. The σblue measurements from method A still

disagree with the local continuum fitting method as much as, if not more than, before

subtraction of He iiλ4686. However, the new σblue measurements from method B are

now consistent with the local continuum fitting method.

The observed differences in these new σblue measurements between method A

and method B come from the procedure and assumptions that each method uses to

fit the spectral emission lines. The line widths from method B now agree with the

local continuum fitting method because the combined best fit to both lines tends to

result in an Hβ profile that basically sits on top of a broad He iiλ4686 profile. In the

wavelength region between the two emission lines (i.e. where the local continuum

is defined), the difference between the continuum level and the flux level observed

in the blended spectrum is usually attributed completely to He iiλ4686 emission by

method B. Therefore, when He iiλ4686 is subtracted, the flux level of this region is

reduced nearly to the level of the continuum, which is what is assumed by the local

continuum fitting method, thus making these two methods consistent. On the other

hand, method A subtracts the Hβ with an Hα template before fitting He iiλ4686.

Because the Hα profile has very extended wings, this method necessarily assumes

that Hβ also has this extended, broad component. Therefore, nearly opposite to

206

method B, method A effectively fits a He iiλ4686 profile that is sitting on top of a

very broad Hβ profile and consequently subtracts a smaller He iiλ4686 component.

This results in σblue measurements that are equally or even more inconsistent with

previous measurements because it extends the Hβ wing under the He iiλ4686 profile.

Because this extended blue wing is hidden under He iiλ4686, method A results

suggest that the local continuum fitting method is significantly underestimating σblue

(by as much as 40%).

Evidence suggests that the helium lines are consistently broader than the

Balmer lines in Type 1 AGNs (Osterbrock & Shuder 1982). This is always the case

in the rms spectrum of AGNs that have been monitored for reverberation mapping

studies, as well. Additionally, in the few cases for which reverberation lags could

be measured for He iiλ4686 the lags are shorter than the corresponding Hβ lag

in the same object (see Peterson et al. 2004). This suggests that given the virial

hypothesis for a single source, the material responsible for He iiλ4686 emission is

closer to the central source than that responsible for the Hβ emission and moving

at a faster velocity, thus producing broader emission lines. Method B supports this

evidence with the emission line models and results described above. On the other

hand, although the fits of method A do not reproduce the same broad He iiλ4686

emission, the assumption this method makes about the similarities that should

exist between the shape of the Hα and Hβ profiles are hard to discount, given that

these two species should exist in similar regions of the BLR. Instead, our analysis

207

demonstrates that there is not a unique method to account for the blending of

Hβ and He iiλ4686 that results in consistent line dispersion measurements of Hβ.

Therefore, we conclude that this blending is a potential problem for the use of σblue

in calculating MSE.

Blending is less likely to be a limitation for reverberation mapping studies

that use the line dispersion measured in the rms spectrum, however. Blending

between Hβ and He iiλ4686 is often lessened in the rms spectrum because the

broad wings of the lines that are the most blended tend not to be as variable as

the more central parts of the line. To test this, we characterized the Hβ line width

with σblue in the 3 rms spectra formed from the three sets of spectra created during

the deblending analysis (after the local continuum fit, decomposition method A,

and decomposition method B). We did not account for He iiλ4686 emission in

the rms spectrum before measuring σblue in the local continuum subtracted rms

spectrum. However, the He iiλ4686 emission in the two rms spectra formed after

decomposition methods A and B was modeled with a single Gaussian profile and

subtracted. We find that measurements of σblue from the rms spectra from all three

methods are consistent to within 1σ. This consistency suggests that the masses

determined through reverberation studies that use the line dispersion measured from

the rms spectrum are not as susceptible as SE masses to this bias in σblue caused by

blending. Additionally, it is worth noting that not all AGNs have strong blending of

He iiλ4686 and Hβ, superceding the need for such caution with the use of σblue.

208

Different concerns arise when FWHM is used to characterize the Hβ line width.

Figure 6.14b demonstrates that all three methods are in agreement, on average,

with equally good precision and moderately small offsets from their respective

reverberation results (given in Table 6.4). The small systematic difference between

the mean SE masses of the decomposition methods and the local continuum fit is

most likely due to the small Hβ absorption feature present in the host galaxy light,

as discussed above. Figure 6.19 shows that FWHM, unlike the line dispersion, is

less sensitive to the details of measurement, however. The differences seen in the

line dispersion measurements are not present for the FWHM measurements, since

blending in the wings and the definition of the continuum have a much smaller

effect on the FWHM value. However, these general observations and the FWHM

statistics in Table 6.4 exclude the outliers at the low-mass end of the distributions

in Figure 6.14b, shown by the thin black curves (also labeled in Fig. 6.19). These

points are outliers because of a particularly complex line profile, characterized by

an asymmetric red bump, present in these two epochs (JD2452030 and JD2452045).

These epochs illustrate that FWHM can be complicated by profile features such

as the gross asymmetries and double peaks that the broad Balmer lines sometimes

exhibit.

Figure 6.20 shows how FWHM is defined for the Hβ profile on JD2452030

for each of the two decomposition methods and for a local continuum fit. In each

case, we measure FWHM following the procedure of Peterson et al. (2004). The

209

differences in the FWHM measurements for this spectrum are due in part to the

complex profile of this line and in part to the differences in the peak flux of the line

for the different methods. Figure 6.20 shows that each of the three methods removes

slightly different amounts of narrow-line emission. These small differences change

the total flux in the line by at most a few percent, but the change in the line peak

combined with the complex profile are sufficient to cause large differences in the

measurements of FWHM, and thus MSE.

Despite the observed differences in the SE σblue measurements between each

decomposition method after accounting for He iiλ4686 blending, masses derived

from both methods otherwise differ very little. The dispersions in the SE mass

distributions from both methods are nearly equal, however masses derived with the

use of method A seem somewhat more accurate, with smaller 〈∆logM〉 values than

method B.

6.3. Discussion and Conclusion

We have undertaken a careful examination of some of the systematics associated

with measurements of emission-line widths for the purpose of calculating black hole

virial masses from single-epoch spectra. The systematics on which we focused our

attention are (i) intrinsic AGN variability, (ii) contributions by constant spectral

210

components, (iii) S/N of the data, and (iv) blending with the different spectral

components, particularly the underlying host galaxy.

Throughout this analysis we have not displayed a preference for either the line

dispersion or the FWHM to characterize the line width and have instead shown that

there are both advantages and limitations to each measure. Specifically, FWHM

provides consistent results for lower S/N spectra without the use of profile fits, and

it is much more robust in the presence of blending. However, FWHM should only

be used in spectra that have had the narrow line components carefully removed, as

the sensitivity of FWHM to the presence and/or removal method of narrow emission

lines is a serious limitation. On the other hand, the line dispersion is advantageous

in this respect, since it is rather insensitive to the details of narrow-line component

subtraction. However, its use should be limited to data characterized by relatively

high S/N or with profile fits to the emission lines. Unlike FWHM, the greatest

limitation of using the line dispersion is blending in the line wings, and use of the

line dispersion should therefore be avoided if there is emission line blending that has

not been modeled and removed. As we have shown here, however, even in the case of

modeling, the accuracy of the model may be questionable. In the case of NGC 5548,

if decomposition model B is correct (i.e., where the He iiλ4686 line is fit assuming

the same velocity width as the unblended He iλ5876 line), then correcting for the

blending of Hβ and He iiλ4686 by modeling and subtracting the helium emission

produces consistent results with the local continuum-fitting method. However,

211

if method A is the more accurate representation of the blending (i.e., where the

He iiλ4686 line was modeled assuming the line profile of Hβ is the same as Hα),

then there will be a resulting mean offset in the SE masses of ∼ 0.1 dex compared

to the local continuum-fitting method due to underestimation of the blended Hβ

line dispersion in the latter method. Because of these difficulties, when blending

complicates the line profile shape or boundaries of SE spectra, it is best to use

FWHM.

To summarize the effects of these systematics on SE masses, Table 6.5 gives

an error budget displaying how each systematic affects the uncertainties in SE

mass estimates in terms of increasing or decreasing the precision and accuracy

of the measurement, where we generalize our results here to both low luminosity

Seyfert-type AGNs and quasars. While nearly all of the systematic uncertainties we

investigated add to the dispersion in the SE mass distributions in varying amounts,

some effects also cause often severe systematic shifts in the distributions, leading

to overall under- or overestimations of SE masses. Readers should be particularly

cautious about these effects because large statistical studies cannot average out

these types of systematics. In summarizing the sources of error covered here, we

use the same description of the precision and accuracy as above, with the accuracy

described as an offset in the mean SE virial mass, and the precision described by the

dispersion in the mass distribution. In Table 6.5, however, we assume that errors

are independent and the distributions are close enough to Gaussian that we can add

212

independent errors in quadrature to determine the cumulative effect. We therefore

describe the additional offset and dispersion due to each systematic with respect to

the SE mass calculation which results in the minimum observed uncertainties (i.e.,

Fig. 6.4). In Table 6.5 we consider the following individual sources of error in the

SE masses for both characterizations of the line width:

1. Random measurement errors. These are simply due to inherent uncertainties

in any measurement of luminosity and line width. Empirically, we determine

these uncertainties by comparing measurements of closely spaced observations,

assuming that these parameters change little over very short time scales

(i.e., time scales much shorter than the reverberation time scale). We use

this empirical method to estimate the uncertainties for the line width and

luminosity of the NGC 5548 data set, which we propagate through to determine

uncertainties in the mass estimates, listed in Table 6.5. Uncertainties are not

listed for quasars because the size of the PG1229 data set is much smaller

and with fewer closely spaced observations than that of NGC 5548. We could

therefore not accurately estimate uncertainties in this manner. However, given

the small observed dispersion in the SE virial masses for PG1229 (∼ 0.05 dex),

measurement uncertainties are likely to be very small.

2. Variability on reverberation timescales (see Fig. 6.6 and Fig. 6.4b). Our

analysis on reverberation-timescale variability shows that SE spectra can

213

reproduce the reverberation-based virial product that would be measured

at the same time to about 0.10 dex (i.e., ∼ 25%) for Seyferts and to about

0.05 dex (i.e., ∼ 15%) for quasars. This is an interesting result, given the

quadrature sum of the individual dispersions in luminosity and line width

for NGC 5548 add to be ∼ 0.17 dex, regardless of line width measure. This

is significantly larger than the dispersion in the virial masses, and therefore

confirms the presence of a virial relation between the line width and luminosity

(i.e., the BLR radius). An additional ramification for quasars is that the

dispersion for PG1229 determined here represents more than a factor of two

less than even the formal, observational uncertainties in the reverberation

mass for this object. This suggests that once the zero point and slope of

scaling relations such as the RBLR–L relation are accurately determined, it

may be more accurate to simply use the scaling relations to determine masses

of individual sources than to make direct mass measurements. It also follows

that SE mass estimates can then easily be acquired with relative certainty for

high redshift objects, as long as the extrapolation of the scaling relations to

these luminosity regimes is valid.

3. Longer-term secular variations. At least in the case of NGC 5548, we see that

longer-term (dynamical timescale?) variations cause changes in both the SE

and reverberation-based virial product. The amplitude of these variations is

similar to those on reverberation time scales, creating an additional dispersion

214

in the SE virial products of about 0.09 or 0.05 dex for FWHM and σblue,

respectively. This longer-term secular variability adds to the reverberation-scale

variability described above (and seen in Figure 6.6) to produce the observed

dispersion (Fig. 6.4a) in the SE virial product for Seyferts. We cannot estimate

the contribution of secular variations to the observed dispersion for quasars,

since all the data available for PG1229 was used in a single reverberation

experiment and observations did not span dynamical timescales for this object.

4. Combined minimum uncertainty. The combination of the above effects sets

a “minimum observable uncertainty” for SE-based masses, given in line 4 of

Table 6.5 (see also Fig. 6.4). Adding measurement uncertainties, reverberation

timescale variability, and longer-term secular variability effects in quadrature

yields an estimate of the observable dispersion in SE masses for Seyferts of

0.12 − 0.16 dex (∼ 30 − 45%) and less for quasars (although the long-term

secular effects are unexplored in this case).

5. Failure to remove host galaxy starlight. Host galaxy contamination causes

an overestimation of the luminosity and thus the mass. The effect of this

contamination on the precision of SE mass estimates is minimal so it does not

further broaden the distribution of mass measurements. Instead, it affects the

accuracy of the mass estimate, resulting in an additional mean offset, listed

in Table 6.5, compared to the offset observed when the host contamination is

removed (Also compare the mean distribution values of Figs. 6.4 and 6.7).

215

The size of the systematic overestimation of the mass depends on the fraction

of host starlight contamination, however. Since both NGC 5548 and PG1229

lie near the middle of the sample of AGNs used to set the slope of the RBLR–L

relation, the effect due to host-galaxy contamination could be much worse or

more minimal depending on whether the luminosity is much smaller or larger

(respectively) than the objects presented here (Bentz et al. 2009a).

6. Failure to remove narrow Hβ. The Hβ narrow emission-line component is

by far the biggest source of error for both Seyferts and quasars when using

FWHM to characterize the line width, adding significantly to the dispersion

and offset, as shown in Table 6.5. In particular, this offset causes SE masses to

be underestimated by nearly an order of magnitude for Seyfert-type galaxies

that often have strong narrow-line components. Notice, however, that because

of the insensitivity of σblue to the line center, this effect increases the dispersion

of the SE mass distributions very little or not at all when the line width is

characterized by σblue. However, the systematic offset for the σblue case is still

nearly doubled compared to the offset observed for the minimum uncertainty

case. This makes it imperative to remove narrow line components before

measuring line widths, regardless of how the line width is characterized.

7. Limitations due to S/N . Direct measurements from low S/N spectra add

an additional systematic offset in the SE mass measurements because of a

systematic underestimation of the line width, as well as decreased precision in

216

these measurements. Our fits to the line profiles do increase the usefulness of

S/N -level ∼ 10 spectra with σblue. However, they generally make things worse

for FWHM, leading to lower precision masses than when direct measurements

of the line widths are used, as well as systematic overestimations of the line

width and mass, an effect that is opposite to that observed when measuring

FWHM directly from the data. Therefore, to avoid either underestimating SE

masses when measuring line widths directly from the data or overestimating

SE masses when line profiles are fit, SE mass studies should be conducted

using high S/N (∼> 20 pixel−1) spectra.

217

Fig. 6.1.— Starlight-corrected luminosity and narrow-line subtracted Hβ line widthmeasurements from the full set of NGC 5548 spectra. Left panels show individualSE measurements as a function of time, and right panels show distributions of eachmeasured quantity, with the mean and standard deviation of the sample given.

218

Fig. 6.2.— The multi-component fit to a typical spectrum of NGC 5548 fordecomposition method A. In the top panel, the rest-frame spectrum shown togetherwith a four-component fit: a power-law continuum, a host-galaxy spectrum, Balmercontinuum emission, and weak optical Fe ii emission. The combined fit is displayedin green. In the bottom panel, the corresponding residual spectrum is presented afteradditional subtraction of the narrow emission-line components (not shown).

219

Fig. 6.3.— The multi-component fit to a typical spectrum of NGC 5548 fordecomposition method B. In the top panel the rest frame spectrum shown has beencorrected for Galactic extinction and is shown together with a four-component fit:a power-law continuum, a host-galaxy spectrum, Balmer continuum and broad-lineemission, and weak optical Fe ii emission. The combined fit is displayed in green.Note: the Balmer line emission shown here is only included to prevent the fittingroutine from attempting to assign continuum emission components to the profile wingsand is not included in the final fit that is subtracted to create the residual spectrum(bottom). In addition, the residual spectrum presented also includes additionalsubtraction of narrow emission-line components, not shown.

220

Fig. 6.4.— Virial mass distributions for the full NGC 5548 (a) and PG1229 (b)data sets. The Solid lines show the distributions of virial masses calculated withequation 6.2 using both σblue (left) and the FWHM (right) to measure Hβ line widths:histograms for the larger NGC 5548 data set and cumulative distribution functions(CDFs) for the smaller PG1229 data set. Narrow lines and host galaxy starlight havebeen subtracted from all spectra before calculating masses. A Gaussian functionwith the same mean, dispersion, and area as the data is overplotted in gray. Thedistribution mean and dispersion is shown in each plot, where values listed have notbeen corrected for random measurement uncertainties (see §6.2.1). For each dataset and line width measure, the vertical lines represent the reverberation virial mass(dotted) with measurement uncertainties (dashed; not shown for PG1229 becausethey are typically larger than the widths of the distributions).

221

Fig. 6.5.— Broad line region radius-luminosity relationship for the PG1229 data andweighted mean as well as individual years of NGC 5548 data. Points are plotted forluminosities both before and after subtracting the host galaxy starlight contributionto the 5100 A continuum flux. The Bentz et al. (2009a) relation and the Kaspi et al.(2005) relation are shown for reference.

222

Fig. 6.6.— Distributions of the differences between each SE mass in a given observingyear and the reverberation virial mass from that same year, plotted for massescalculated with σblue (left) and FWHM (right). Mass differences are shown for everyspectrum in the full sample of 370 observations of NGC 5548 after subtraction ofnarrow emission-line components and host starlight contribution.

223

Fig. 6.7.— Same as Figure 6.4, except the host-galaxy flux contribution has not beenremoved. The narrow-line components have been subtracted from the spectra beforemeasuring the Hβ line width and calculating the black hole mass.

224

Fig. 6.8.— Mean spectra of NGC 5548 (left) and PG1229 (right) with narrow emissionlines (solid) and after subtraction of the narrow emission lines (dotted).

225

Fig. 6.9.— Same as Figure 6.4, except the narrow emission lines have not beenremoved from the spectra before measuring the Hβ line width. The host-galaxycontribution to the flux was removed before determination of the masses.

226

Fig. 6.10.— Same as Figure 6.4, except neither the narrow-line components nor thehost-galaxy flux contribution have been removed before determination of the masses.

227

Fig. 6.11.— Example spectrum of NGC 5548 (top left) and three artificialdegradations of the same spectrum with the resultant S/N labeled for each. Thesolid black lines are the Gauss-Hermite polynomial fits to each spectrum (gray lines)as described in §6.2.3. The vertical lines show the assumed boundaries of the broadHβ line used for measuring the line widths from both the actual data and the Gauss-Hermite fits.

228

Fig. 6.12.— Virial mass distributions for the original and S/N degraded NGC 5548Perkins data set, using line widths measured directly from the data. Virial masses arecalculated in all cases by measuring the velocity dispersion of the broad Hβ emissionfrom narrow line-subtracted spectra using σblue (left) and FWHM (right). All virialmasses are calculated using a value of L5100 that has been corrected for host galaxystarlight.

229

Fig. 6.13.— Virial mass distributions based on sixth order Gauss-Hermite polynomialfits to the original and S/N degraded NGC 5548 Perkins data set. Virial masses arecalculated by measuring the velocity dispersion of the Gauss-Hermite polynomial fitto narrow line-subtracted broad Hβ emission line with σblue (left) and the FWHM(right). All virial masses are calculated with a value of L5100 that has been correctedfor host galaxy starlight.

230

Fig. 6.14.— Cumulative distribution functions of NGC 5548 SE virial masses fordecomposition data sets with σblue (a) and FWHM (b). The panels show virialmass distributions that have been calculated using a local continuum fit to thecontinuum underneath the Hβ line (left), spectral decomposition method A (middle),and spectral decomposition method B (right). Statistics listed in the bottom threepanels do not include the outliers plotted in the thin black line, as described in §6.2.4.

231

Fig. 6.15.— Comparison of the Hβ line dispersion measurements (σblue) using thevarious techniques described in §6.2.4 to account for the continuum flux level underthe emission line. The open circles represent the line width measurements usingdecomposition method A results, and the black triangles show results using methodB. In the top panel, these values are plotted against widths measured using a localcontinuum fit, and the bottom panel shows the residuals with respect to the widthfrom the local continua method. The solid black line in each panel shows a 1:1correlation between the measured σblue values.

232

Fig. 6.16.— Mean spectra of NGC 5548 created using three different techniquesto account for the continuum flux level under the Hβ emission line (as describedin §6.2.4). The black line shows the mean spectrum formed after simply fittingand subtracting a local linear continuum to each of the 33 spectra. The gray lineshows the mean continuum-subtracted spectrum formed after deblending the spectralcomponents from the same 33 spectra with method A, and the dotted line is the same,but for method B.

233

Fig. 6.17.— Mean spectra of NGC 5548 both before (gray lines) and after (dottedlines) subtracting the He iiλ4686 emission line (black lines). The top panel show theresults from decomposition method A, where the He ii line was modeled assumingthe line profile of Hβ is the same as Hα. The bottom panel shows the results fromdecomposition method B, where the He ii line is fit assuming the same velocity widthas the unblended He iλ5876 line.

234

Fig. 6.18.— Same as Figure 6.15, except the He iiλ4686 emission line has beensubtracted from each of the spectra before measuring the Hβ line dispersion (σblue).

235

Fig. 6.19.— Same as Figure 6.15, except the width of the Hβ line is characterizedhere by FWHM rather than σblue. Outliers discussed in §6.2.4 are individually labeledby Julian Date.

236

Fig. 6.20.— FWHM measurements of the Hβ broad line for JD2452030 using each ofthe three spectral analysis methods discussed in §6.2.4. The spectra shown hereillustrate complications that arise when using FWHM to characterize a complexemission line structure, especially when the narrow emission-line components arenot well-determined. The Hβ profile after subtracting a local continuum fit (blackline) has FWHM= 5632 km s−1, the profile determined from decomposition methodA (gray line) has FWHM= 4511 km s−1, and the profile from decomposition methodB (dotted line) has FWHM= 6334 km s−1.

237

M (M⊙) ∝ σblue M (M⊙) ∝ FWHM

Object NSE logMvir 〈log MSE〉 ± σSE 〈∆logM〉 logMvir 〈log MSE〉 ± σSE 〈∆logM〉

NGC 5548 370 7.21±0.02 7.12 ± 0.12 −0.09 8.06 ± 0.02 7.95 ± 0.16 −0.11

PG1229+204 33 7.28±0.25 7.22 ± 0.05 −0.06 8.03 ± 0.25 7.92 ± 0.06 −0.11

Table 6.1. Systematic Effects due to Variability

238


Narrow Host 〈log MSE〉〈log MSE〉Object NSE Lines Starlight logMvir ±σSE 〈∆log M〉 logMvir ±σSE 〈∆log M〉

NGC 5548a 370 present present 7.21±0.02 7.21 ± 0.11 +0.00 8.06 ± 0.02 7.22 ± 0.47 −0.84

NGC 5548b 370 removed present 7.21±0.02 7.29 ± 0.11 +0.08 8.06 ± 0.02 8.12 ± 0.14 +0.06

NGC 5548c 370 present removed 7.21±0.02 7.05 ± 0.13 −0.16 8.06 ± 0.02 7.06 ± 0.52 −1.00

PG1229...a 33 present present 7.28±0.25 7.33 ± 0.05 +0.05 8.03 ± 0.25 8.00 ± 0.07 −0.03

PG1229...b 33 removed present 7.28±0.25 7.34 ± 0.05 +0.06 8.03 ± 0.25 8.04 ± 0.06 +0.01

PG1229...c 33 present removed 7.28±0.25 7.21 ± 0.05 −0.07 8.03 ± 0.25 7.88 ± 0.07 −0.15

aRefer to Figure 6.10.

bRefer to Figure 6.7.

cRefer to Figure 6.9.

Note. — See Table 6.1 for the case in which both the narrow emission lines and the host starlight are removed for the

virial mass calculations for both NGC 5548 and PG1229.

Table 6.2. Systematic Effects due to Constant Components

239


Data or 〈log MSE〉〈log MSE〉Fit S/N NSE logMvir ±σSE 〈∆log M〉 logMvir ±σSE 〈∆log M〉

Data Orig 270 7.23 ± 0.02 7.12 ± 0.14 −0.11 8.02 ± 0.02 7.96 ± 0.19 −0.06

Data ∼ 20 270 7.23 ± 0.02 7.11 ± 0.15 −0.12 8.02 ± 0.02 7.93 ± 0.18 −0.09

Data ∼ 10 270 7.23 ± 0.02 7.09 ± 0.22 −0.14 8.02 ± 0.02 7.85 ± 0.19 −0.17

Data ∼ 05 270 7.23 ± 0.02 7.04 ± 0.31 −0.19 8.02 ± 0.02 7.84 ± 0.21 −0.18

Fit Orig 270 7.23 ± 0.02 7.11 ± 0.14 −0.12 8.02 ± 0.02 8.03 ± 0.17 +0.01

Fit ∼ 20 270 7.23 ± 0.02 7.10 ± 0.17 −0.13 8.02 ± 0.02 8.08 ± 0.23 +0.06

Fit ∼ 10 270 7.23 ± 0.02 7.10 ± 0.17 −0.13 8.02 ± 0.02 8.08 ± 0.23 +0.06

Fit ∼ 05 270 7.23 ± 0.02 7.06 ± 0.28 −0.17 8.02 ± 0.02 8.13 ± 0.29 +0.11

Table 6.3. Systematic Effects due to Signal-to-Noise Ratio

240


Decomposition 〈log MSE〉〈log MSE〉Object NSE Method logMvir ±σSE 〈∆log M〉 logMvir ±σSE 〈∆log M〉

NGC 5548 33 Local Cont. Fit 7.22 ± 0.02 7.23 ± 0.13 +0.01 8.16 ± 0.02 8.16 ± 0.09 +0.00

NGC 5548 33 Method A 7.32 ± 0.02 7.31 ± 0.10 −0.01 8.11 ± 0.02 8.09 ± 0.08 −0.02

NGC 5548 33 Method B 7.38 ± 0.02 7.31 ± 0.09 −0.07 8.15 ± 0.02 8.08 ± 0.09 −0.07

Table 6.4. Systematic Effects due to Blending

241

Seyfert Quasar

M ∝ FWHM M ∝ σblue M ∝ FWHM M ∝ σblue

Effect on MSE offset dispersion offset dispersion offset dispersion offset dispersion

Random measurement error: · · · 0.07 · · · 0.04 · · · · · · a · · · · · · a

Variability (RM timescales): −0.11 0.11 −0.10 0.10 −0.11 0.06 −0.06 0.05

Longer term secular variations +

slight inhomogeneity of spectra: −0.00 0.09 +0.01 0.05 · · · b · · · b · · · b · · · b

Above effects (min. uncertainty): −0.11 0.16 −0.09 0.12 −0.11 0.06 −0.06 0.05

Additional systematics:

Failure to remove host galaxy: +0.17 −0.08 +0.17 −0.05 +0.12 0.00 +0.12 0.00

Failure to remove narrow Hβ: −0.89 0.49 −0.07 0.05 −0.04 0.04 −0.01 0.00

S/N limitation (data, S/N=10): −0.06 0.10 −0.05 0.18 · · · · · · · · · · · ·(data, S/N=05): −0.07 0.14 −0.10 0.29 · · · · · · · · · · · ·

S/N limitation (fit, S/N=20): +0.17 0.17 −0.04 0.12 · · · · · · · · · · · ·(fit, S/N=10): +0.17 0.17 −0.04 0.12 · · · · · · · · · · · ·(fit, S/N=05): +0.22 0.24 −0.08 0.25 · · · · · · · · · · · ·

aUncertainties could not be determined; see Discussion, §6.3, individual sources of error (1).

bUncertainties could not be determined; see Discussion, §6.3, individual sources of error (3).

Table 6.5. Individual Error Sources for SE Mass Measurements

242

Chapter 7

Conclusions

7.1. Summary of Completed Work

We have presented two spectroscopic reverberation-mapping monitoring

campaigns, whose primary goals were to improve the emission-line lag and black

hole mass measurements for some of the nearest, apparently brightest AGNs because

(1) the proximity of these AGNs makes them candidates for measuring their black

hole masses with dynamical methods, thus allowing constraints to be placed on

systematic uncertainties in the reverberation-based mass measurement, and (2)

measured properties of these local AGNs are crucial for calibration of local scaling

relationships. Such scaling relationships are used for making black hole mass

estimates in objects at cosmological distances and for better understanding black

hole and galaxy evolution over the age of the universe. To increase the probability of

success of these observational campaigns, program elements were organized such that

(1) observations were scheduled daily for several months (i.e., at least three times

longer than the expected reverberation time delay of the highest luminosity object

in the sample), (2) supporting observations were gathered from collaborators around

243

the world to mitigate the effects of gaps in the time series caused by weather, and

(3) the same telescope and instrumental setup were used throughout the campaign

for the main data collection at MDM observatory to produce a homogeneous data

set that permitted relative spectrophotometric flux calibration at better than the

2% level.

These campaigns resulted in new reverberation measurements of the

characteristic BLR radius from cross correlation of the Hβ broad emission-line

flux with the optical continuum flux for seven local Seyfert 1 AGNs: NGC4593,

NGC3227, NGC3516, NGC4051, NGC5548, Mrk 290, and Mrk 817. Combining

these radii with measurements of the emission line widths of the variable Hβ

emission, we also presented new measurements of the black hole masses in each of

these galaxies. For more than half the sample (i.e., NGC4593, NGC3227, NGC3516,

and NGC4051), our results represent a factor of several improvement over past

measurements, and our current results should supersede any past measurements

of these quantities for these four objects. In addition, the results for Mrk 290 are

entirely new, as this object had not been targeted for reverberation mapping prior to

our observing campaign. Finally, while our measurements of Mrk 817 and NGC5548

did not improve upon past measurements, they are consistent with past results, and

making repeat reverberation measurements of AGNs is also of merit, e.g., (1) to

explore the radius-luminosity relationship in a single source observed in different

luminosity states, and (2) to check the repeatability of the mass measurements

244

for AGNs at different times, in different luminosity states, and with different line

profiles. We also put our results into the context of the most recent calibration of

the RBLR–L relationship of Bentz et al. (2009b), based on the measured luminosities

of our sample over the course of our campaigns, and found that the Hβ lags we

measured are in excellent agreement with the expectations of this relationship.

Furthermore, our new measurements reduced the scatter in the low-luminosity AGN

sample on this relation.

As an additional goal of our second campaign (i.e., in 2007), we searched for

velocity-resolved reverberation lags across the extent of the Hβ-emitting region of

the BLR for use in future efforts to recover velocity–delay maps to help constrain the

geometry and kinematics of the BLR. Though the velocity structure in some of our

targets remained unresolved on sampling-rate-limited time scales, we still found some

statistically significant and kinematically diverse velocity-resolved signatures, even

within this small sample. In particular, we presented three clear cases of differing

velocity signatures of the Hβ-emitting gas in the BLRs of NGC3516, NGC3227,

and NGC5548, where we saw indications of infall, outflow, and virialized motions,

respectively. These results demonstrate the diversity and probable complexity of the

kinematics in this region. However, the reliability with which we were still able to

determine the mean BLR radius and black hole mass in these objects suggests that

it is unlikely that the steady-state dynamics within this region are truly this diverse.

Instead, the BLR could be made up of multiple kinematic components with possible

245

transient features such as winds and/or warped disks that travel through the line of

sight to the observer over dynamical timescales.

We also undertook a careful examination of some of the systematic uncertainties

associated with measurements of emission-line widths for the purpose of calculating

black hole virial masses from single-epoch spectra. The systematics on which

we focused our attention were (i) intrinsic AGN variability, (ii) contributions by

constant spectral components, (iii) S/N of the data, and (iv) blending with the

different spectral components, particularly the underlying host galaxy. We calculated

masses by characterizing the broad Hβ emission line by both the full width at half

maximum and the line dispersion. Through this investigation, we demonstrated

the importance of removing narrow emission-line components and host starlight.

We also found that the reliability of line width measurements rapidly decreases for

S/N lower than ∼ 10 to 20 (per pixel) and that fitting the line profiles instead of

direct measurement of the data did not mitigate this problem but could, in fact,

introduce systematic errors. We also concluded that a full spectral decomposition to

deblend the AGN and galaxy spectral features was unnecessary except to judge the

contribution of the host galaxy to the luminosity and to deblend any emission lines

that may have inhibited accurate line width measurements. Finally, we presented

an error budget that summarized the minimum observable uncertainties as well as

the amount of additional scatter and/or systematic offset that could be expected

from the individual sources of error investigated. In particular, we found that the

246

minimum observable uncertainty in single-epoch mass estimates due to variability is

∼< 0.1 dex for high S/N (∼> 20 pixel−1) spectra.

7.2. Future Work

Future work will focus on constructing velocity-delay maps for our current

sample of objects using the MEMECHO code of Horne (1994). We will place

particular emphasis on the objects in which we observed kinematically distinct

behaviors of infall, outflow, or Keplerian motions. In addition, future reverberation

campaigns will be planned to reobserve these same objects in an attempt to

characterize the extent to which these observed kinematic signatures are steady-state

or transcient in nature, and if they change on the same time scales as profile

shape changes, luminosity state, etc. Results of such analyses will likely be able to

constrain models of the kinematics in this region of the BLR as well as the scale

factor, f , in these particular targets.

I also plan to extend my analysis of systematic uncertainties in single-epoch

black hole masses to investigate the effects on masses determined with the C ivλ1549

broad emission line. At redshifts z > 1, where access to Hβ becomes difficult, it

is necessary to use other emission lines to estimate black hole masses. Previous

studies show that C iv reverberation mapping radii measurements follow an RBLR–L

relationship consistent with that of Hβ (Kaspi et al. 2007). However, since C iv

247

is a resonance line, it is often observed to be self-absorbed, to varying degrees, or

exhibit enhanced blueward emission, both properties of which can be attributed to

possible outflowing gas. For these and other reasons, measuring line widths to use

for calculating single-epoch black hole masses, and the subsequent reliability of such

mass estimates, has been controversial. Furthermore, our previous investigation of

Hβ has shown that S/N is a significant factor in the reliability of these SE mass

estimates, and as many spectra from which C iv line widths are measured come

from survey data of high redshift (i.e., apparently faint) quasars, low S/N may

be a significant contributor to the often observed large uncertainties and possible

systematic offsets of C iv-based masses from Hβ-based mass estimates (Baskin &

Laor 2005; Netzer et al. 2007; Shen et al. 2008b). We plan to investigate these

and other possible systematics when using C iv to make SE mass estimates, again

providing suggestions and an error budget for the best use of this line for these

purposes, similar to our investigation with Hβ.

248

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