Dispersed Fixed-Delay Interferometry and its Application in SDSS-III MARVELS

Dispersed Fixed-Delay Interferometry and its

Application in SDSS-III MARVELS

Dispersed Fixed-Delay Interferometry and its

Application in SDSS-III MARVELS

Brian Lee,for the MARVELS collaboration,Aug. 31, 2011

Lots of early SDSS-III MARVELS collaborators- (list still growing!)

Principal investigator: Jian Ge (UF)

Survey scientist: Scott Gaudi (OSU)

Science Team Chair: Keivan Stassun (VU)

Instrument scientist: Xiaoke Wan (UF)

SWG coordinator : Eric Agol (UW)

Data coordinator: Brian Lee (UF)

Basic physics of Dispersed Fixed-Delay Interferometry

(DFDI)

Basic physics of Dispersed Fixed-Delay Interferometry

(DFDI)

B1 B2Input light

Beamsplitter

Mirror 1

Mirror 2

MARVELS basic physics

Physical path difference: B2-B1

(DFDI Refs.: Erskine & Ge (2000), Ge et al. 2001, Erskine 2003, Ge 2002, Mosser et al. 2003, Mahadevan et al. 2008, van Eyken et al. 2010)

B1 B2Input light

Beamsplitter

Mirror 1

Mirror 2


Physical path difference: B2-B1 = N*lambda-> constructive interference


B1 B2Input light

Beamsplitter

Mirror 1

Mirror 2


Physical path difference: B2-B1 = N*lambda + 0.5*lambda-> destructive interference

(0.5*lambda of added delay)


B1 B2Input light

Beamsplitter

Mirror 1

Mirror 2


Tilt mirror 2 over, so path length is a function of height Y

->Intensity is now a function of height Y = fringes

Y

Y

B1 B2Input light

Beamsplitter

Mirror 1

Mirror 2


Now consider slightly longer wavelength of input light

Y

Y

Old lambda

New lambda

B1 B2Input light

Beamsplitter

Mirror 1

Mirror 2


So multiple wavelengths look like this:

Y

Y

lambda


Zooming out in lambda, you’d see more strongly the dependence of periodicity of interference on wavelength. We call that the “interferometer fan”:


m=1

m=2

m=3

m=4

Orders m are evenly spaced in y…


(The MARVELS instrument can only collect a small cutout from the fan, with m~13000 and 5000A~<lambda~<5700A. We typically refer to the small cutout as, “comb.”)

m=1

m=2

m=3

m=4this way to m=13000…

B1 B2Input light

Beamsplitter

Mirror 1

Mirror 2


(Have to add a low-resolution spectrograph so the fringes aren't all on top of each other)

Y

Spectrograph

Y

lambda

B1 B2Input light

Beamsplitter

Mirror 1

Mirror 2


Gradient in tilt of fringes across lambda is present, but fairly small.

Y

Spectrograph

Y

lambda


Y

lambda

This was for a continuum light source...


Y

lambda

Now multiply in a stellar source with absorption lines instead.


Y

lambda

Now multiply in a stellar source with absorption lines instead.

Note intersections.


Y

lambda

Small x shift (e.g., from RV) of stellar lines gives larger y shift in intersections (amplification higher if slope is steeper)!

Y shift

X shift


Y

lambda

Actual intensities follow a sinusoidal model, in theory.

Y

Inten.

Co

ntin

uu

m le

vel

Line depth


Y

lambda

Y

Inten.

Co

ntin

uu

m le

vel

Line depth

Okay, now what messes this up?

Slanted spectral lines…

…tilted trace apertures…

…illumination profile of the slit…

…higher order distortions (probably time-variable)…

…PSF (not necessarily constant across CCD)…

…a touch of scattered light…

…integrated onto the CCD (still assuming infinite SNR).Can you still track the intersections?

The final image: Sample full 4kx4k real data frame (ThAr lamp calib.) (60 objects give 120 spectra)

Pipeline flow: attempting to remove the optical effects

Pipeline flow: attempting to remove the optical effects

Pipeline flow- current preprocessing order (not necessarily the ideal one!)

0. Starting point (assume bias,

dark, flat already done)

1. Try to measure (using calib. lamp)

& undo trace

2. Try to measure (using calib. lamp)

& undo slant

3. Try to measure & divide out slit

illumination profile (using current image

itself)

4. Try to measure (using calib. lamp) & undo vertical distortions

5. Apply a horizontal spatial freq. filter to subtract

continuum fringes (since unaffected by star RV)

6. Trim the image down and fit a sinusoidal model to the intensity at each wavelength

Pipeline flow- intermediate data product “whirl” and RV extraction

7. Record sine fit parameters (and errors) and fluxes at each wavelength into a multi-extension FITS file (“whirl”)

Phases (radians): [ 1.3, 1.4, 6.28, 2.0]Sine amplitude/DC offset: [0.02, 0.05, 0.00001, 0.034]Normalized fluxes: [0.98, 0.56, 0.9999, 0.71]

8. For each star or calibration source to have differential radial velocity measured, choose template epoch

8a. For each other epoch, do chi-squared minimization to find best fitting velocity (x and y axes treated as separate velocity

parameters; final answer used is the y-velocity only)

10. For star exposures only, subtract off apparent lamp velocity derived from adjacent lamp exposures from the final

star velocity.

9. For star exposures only, subtract off barycentric velocity

11. Write RV’s to disk as a FITS table.

Zoom of raw MARVELS data (Tungsten lamp behind Iodine cell):

Above fringing spectrum, fully preprocessed:

MARVELS survey stats: what data are available?

MARVELS survey stats: what data are available?

Vital stats

• Site: SDSS 2.5-m Telescope (3 deg. FOV)

• Multi-object feed: 60 fibres

• Spectrograph R~10000, wavelength 500-570nm

• Interferometer operating order m~13000

• Throughput of telescope plus instrument: 2-3%

• Magnitudes surveyed: 7.6<V<12

• Stellar types F9 through K

• Up to 30% giant stars per field; similarly large % of subgiants

Data: Yrs. 1-274,040 RV points

1234 Observations

43 Fields > 18 Epochs

2,580 Total Stars

Min Epochs: 18

Max Epochs: 42

(Median: 28)

Data: Year 320,880 RV points

348 Observations

6 Fields > 18 Epochs

2,460 Total Stars

Min Epochs: 1

Max Epochs: 29

(Median: 5)

Data collection will end in year 4 with completion of a dozen spring Year 3 fields

MARVELS KEPLER overlap fields

Field RA DEC Epochs

K15 296.12 43.53 21

K4 295.69 49.90 20

K10 294.12 46.01 21

K8 281.91 43.44 26

K21 291.58 38.15 18

TRES-2 285.90 49.20 23

K7 285.05 45.20 20

KEPLER4

282.52 47.46 23

K5 291.93 48.45 21

K20 294.71 39.63 23

K14 299.64 44.87 2438

Bonus SEGUE spectra

600 spectra per Kepler field ->

R=2000, wavelength 380-920nm

Current RV performance

Current 1 month stellar RV rms scatter (rerun v001.17)- (seems okay)-300 stars (5 plates) from Oct. 2009

-Noise floor @ 10 m/s

-One-month timescales are basically okay, with rms approximately at the level of the instrument requirements

-Green squares = median phot. limits of mag. bins

-Magenta squares = median total rms of mag. bins

Current multi-month (<17 mo.) stellar RV rms scatter (rerun v001.17)-1680 stars (28 plates) from yrs. 1-2

-rms scatter ~2x the phot. limit at faint magnitudes

-Bright-end noise floor@ 50 m/s- much larger than the one-month floor

-Noise due to slowly-varying month-to-month offsets (see next slide for specific example)

-Green squares = median phot. limits of mag. bins

-Magenta squares = median 1-month total rms of mag. bins

-Blue squares = median multi-month total rms of mag. bins

Orange=giantsRed=<1.5% visib.

5 M_Jup det. thresh

1 M_Jup det. thresh

Specific example of multi-month systematic noise (400 days)-Planet-bearing RV reference star HD 68988

-RV offsets and varying background slopes between months

Current Science Current Science ProjectsProjects

Project 119 (3): MARVELS-1c (b)

Project 3: TYC 1240-945-1 (PUBLISHED)

Lee et al. 2011: MARVELS-1b discovery

msini ~ 28 Jupiter Masses, Period ~ 5.89 days.

Project 119: follow-up to Project 3

A second Coherent RV signal is present in the data

49

Project 119: The Plot Thickens (a bit)

AO image of system (courtesy Justin Crepp). Initial photometry by Ji Wang shows that the secondary is ~3.5 mags fainter in Kp and the tertiary is ~4 mags fainter

50

Project 119: Summary

•Intriguing inner signal on Brown Dwarf

•If inner signal is a planet, this would be the first example of a combined short-period BD / Planet system

•This is a very dynamically interesting system- not many stable scenarios

• 3:1 period ratio (possibly a resonance?)

• Further N-body simulations could be helpful

• Temporary “Working group” to try and understand this system

Project 87: Defringed Project 87: Defringed MARVELS spectraMARVELS spectra

Project 87: Defringed Project 87: Defringed MARVELS spectraMARVELS spectra• MARVELS resolution → MARVELS resolution →

Problems for EWs.Problems for EWs.

• Spectral indices Spectral indices →→ [Fe/H], log g, T[Fe/H], log g, Teffeff and and [[αα/Fe] (?)./Fe] (?).

• Catalogue along with 3-Catalogue along with 3-D vels. from MARVELS D vels. from MARVELS RVs and Tycho proper RVs and Tycho proper motionsmotions

• Galactic chemical and Galactic chemical and dynamical evolution in dynamical evolution in solar neighborhood?solar neighborhood?

• Statistical studies of Statistical studies of stars with and without stars with and without companions?companions?

Project 31: Statistics of binaries in MARVELS

Sample binary RV

Project 31: Statistics of binaries in MARVELS

Example binary completeness prediction for just one month of data collection (~4 epochs) @ 100 m/s err. (slice @ 0.6 solar mass primary)

Project 31: Statistics of binaries

MARVELS preliminary binary star orbit fits: eccentricity-period relation (high eccentricity fits less reliable to fit)

Project 31: Statistics of binaries

Raghavan 2010MARVELS prelim.

Project 24: Statistics of brown dwarfs in MARVELS

Project 24: Statistics of brown dwarfs in MARVELS

Grether and Lineweaver (2006)

The desert

Project 24: Filling in the Desert

Project 24: BD Temperatures

Project 24: Family Portrait

Summary

• MARVELS current RV syst. noise floor 50 m/s, but is ample to find brown dwarfs and binaries

• Broad, shallow survey strategy especially suited for finding rare objects

• Follow-up RV and AO studies often show extra complexity of objects

• Spectra can be used without the fringes for traditional analyses. Available for solar neighbourhood and Kepler.

Documents

Dispersed Fixed-Delay Interferometry and its Application in SDSS-III MARVELS