TIP OF THE RED GIANT BRANCH AS DISTANCE

INDICATOR

ESO KES, October 2019

Marina Rejkuba

Lemaitre

1927

Robertson

1928

Hubble

1929

Jan Oort

Sandage

Baade

Allan Sandage &

Gustav Tammann

Gerard de Vauculeurs

1996 Scale of the Universe debate:

Gustav Tammann vs Sidney van den Bergh

HST KEY PROJECT

• 1990 launch of the Hubble Space Telescope

• R. Giacconi (first director) established HST Key Projects:

1. Measure H0 with an accuracy of 10%

2. Study of the IGM through quasar absorption lines

3. Medium-deep survey of galaxies

2001: HST Key Program:

𝐻0 = 72 ± 8 𝑘𝑚 𝑠−1𝑀𝑝𝑐−1

Age of the Universe in the Einstein-de Sitter model: 9.1 Gyr

(still younger than some of the oldest stars)

Wendy Freedman

THE CARNEGIE-CHICAGO HUBBLE PROGRAM

RED GIANT BRANCH TIP THEORETICAL BACKGROUND

Solar composition tracks:

M= 0.9, 1, 1.2 …. 2.1 Mo

2.3, 2.5, 3 , 4, 5, 6 Mo

7 , 8 , 9 , 10 Mo

from BaSTI database

Dashed lines: constant radii

R=0.01,0.1,1,10,100,1000 Ro

Dot-dashed for WDs:

R= 0.008,0.013 Ro

(MWD=1,0.6 Mo)

Hot HB, AGB-Manque’,

normal HB tracks for

MHB=0.48,0.5,0.55 Mo

Stellar Evolutionary Tracks

PN

RED GIANT BRANCH EVOLUTION

RGB: He-core supported by e- degeneracy pressure surrounded by a H-burning shell that provides the luminosity

RGB evolution:

core mass increases → radius shrinks →

shell T & consequently the luminosity

generated in the shell increases → star

climbs along the RGB with increasing luminosity and core temperature

RGB Tip:

He core ignition → lifts e- degeneracy in the

core → core flash quenched within seconds → core inflates & star settles at lower

luminosity burning He in the core

H-R DIAGRAM FOR OLD STELLAR POPULATIONS

Stellar

evolutionary

tracks from

ZAMS to TRGB

for stars with masses: 0.8, 1,

and 1.3 M

i.e. age > 4 Gyr

Serenelli et al.

2017

Note:

Age-Metallicity

Degeneracy

RED GIANT BRANCH TIP

• Theoretically well understood: discontinuity for old metal-poor stars evolving on RGB

• Attractive alternative for RR Lyr & Cepheid distance scale

• Population II: lower extinction and crowding

• Single epoch observations – easy to observe/measure

• I-band TRGB nearly constant for old metal-poor stars

• 4 mag brighter than RR Lyr, less extinction than Cepheids

• Da Costa & Armandroff 1990 (DA90): “Standard Globular Cluster Giant Branches in the [MI vs (V-I)0] Plane”

• Lee, Freedman & Madore 1993: “The Tip of the Red Giant Branch as Distance Indicator for Resolved Galaxies”

DA COSTA & ARMANDROFF 1990: “STANDARD GLOBULAR CLUSTER

GIANT BRANCHES IN THE [MI VS (V-I)0] PLANE”

“In Sec. IV the cluster giant branch results are compared with the predictions of theory. … The agreement found is quite satisfactory

indicating, inter alia, that the giant branch tip luminosity can be used as a distance indicator for old stellar populations.”

MI assuming HB distances based on

Lee, Demarque & Zinn 1990 calibration:

MV(RR) = 0.82 + 0.17 [Fe/H]

DA90 Standard GC RGBs

𝐵𝐶𝐼 = 0.881 − 0.234 𝑉 − 𝐼 𝑇𝑅𝐺𝐵

𝑀𝑏𝑜𝑙𝑇𝑅𝐺𝐵 = −0.19

𝐹𝑒

𝐻−3.81

𝑚 −𝑀 𝐼 = 𝐼𝑇𝑅𝐺𝐵 − 𝑀𝐼,𝑇𝑅𝐺𝐵 = 𝐼𝑇𝑅𝐺𝐵 + 𝐵𝐶𝐼 −𝑀𝑏𝑜𝑙𝑇𝑅𝐺𝐵

𝑀𝐼 ≅ −4.05

𝐹𝑒/𝐻 = −15.16 + 17.0 𝑉 − 𝐼 −3 − 4.9 𝑉 − 𝐼 −32

LEE, FREEDMAN & MADORE 1993:“THE TIP OF THE RED GIANT

BRANCH AS A DISTANCE INDICATOR FOR RESOLVED

GALAXIES”

LEE ET AL. 1993

• Edge detection – zero sum Sobel Kernel [-2, 0, 2] convolution with I-band luminosity function

Madore & Freedman ‘95

LEE ET AL. 1993

• Method as in DA90 with slight modification:𝐹𝑒/𝐻 = −12.64 + 12.6 𝑉 − 𝐼 −3.5 − 3.3 𝑉 − 𝐼 −3.5

2

• Since 𝑀𝐼 ≅ −4 ± 0.1 𝑚𝑎𝑔 with little variation with metallicity for [Fe/H]≤ −0.7 dex, the method can be used up to ~4 Mpcfrom the ground and up to Virgo and Fornax with the HST

EARLY WORKS

• Sakai et al. 1996:

• replace the discrete LFs with their respective Gaussians (smooth)

• apply adaptive edge-detection – localised slope estimator with 4-point smoothing

• Madore & Freedman 1995: extensive computer simulations

• Signal-to-noise – larger than 5 to limit photometric errors

• Crowding – less than 25% (one star every 3 contaminated)

• Population size – need ~50 stars within upper 1 mag

• Contamination from non-RGB stars – work in outer halo

𝐸 𝑚 = Φ 𝐼 + ത𝜎𝑚 −Φ 𝐼 − ത𝜎𝑚

Sakai+1996: Sextans A

TRGB brightness in the main body 21.64

and in the halo 21.79

• Authors attribute to crowding

• Age may play a role as well

MEASURING TRGB

• Cioni et al. 2000

• LMC & SMC – TRGB in I, J, K band

• Bolometric correction using J-K color

• Using Savitzky-Golay filter to estimate the 2nd

derivative

• Use Gaussian fit to identify TRGB

• Systematic correction up to ~0.02 mag (AGB, photometric errors)

MAXIMUM LIKELIHOOD

• Mendez, B. et al. 2002, Makarov et al. 2006

• Maximum likelihood

• logarithmic edge detection to smooth the luminosity function

• RGB LF is a power law: 𝑁 𝑚 𝑑𝑚 ∝ 10𝑎𝑚 & 𝑎 = 0.30 ± 0.04

• Marginalising over free parameters: TRGB mag, LF slope brighter than TRGB, discontinuity strength

Makarov et al. 2006

TRGBDETECTION

Edge detection + smoothing due to

Poisson noise in the LF

Smoothing incorporated:

(i) in the edge detection of the kernel(ii) applied to the LF itself

(iii) folded in the model

Edge detection:

1. Discrete approx. to derivative (Sobel kernel)

2. Discrete approx. to derivative that

incorporate smoothing (Gaussian

formulation of Sobel kernel)

3. Maximum likelihood fitting

TRGB CALIBRATION

GCs: Ferraro+2000, Bellazzini+2004; Valenti+2004

Galaxies: Rizzi et al. 2007, Jang & Lee 2017

Bellazzini et al. 2004

Large dots:

Omega Cen

47 Tuc

Solid lines:

Empirical calibrations

Dashed lines:Fit to data

Open squares:

theoretical models

Salaris & Cassisi ‘98

RED GIANT BRANCH TIPNGC 5128

IRGBT=24.1± 0.1 mag

D = 3.8 ± 0.1 Mpc Rejkuba et al. 2005

I-BAND COLORDEPENDENT CALIBRATION

Rizzi et al. 2007:

• Slope is always the same

• Zero point calibrated via

HB in 5 Local Group

galaxies & applying

Carretta et al. 2000 calib

• MI = - 4.05 +/- 0.02 at

(V-I) = 1.6

TRGB: METALLICITY CORRECTION

𝑀𝐼𝑇𝑅𝐺𝐵 = 0.14

𝐹𝑒

𝐻

2

+ 0.48𝐹𝑒

𝐻− 3.629

𝑉 − 𝐼 = 0.581𝐹𝑒

𝐻

2

+ 2.472𝐹𝑒

𝐻+ 4.013

Belazzini et al. 2001, 2004:

Mager et al. 2008

Jang & Lee 2017

Quadratic fit to measure TRGB vs color

Zero point anchors:

• LMC (eclipsing binaries)

• NGC 4258 (Maser)

ERROR BUDGET

Jang & Lee

2017

aF555W – F814W to F606W – F814W transformation.

SUMMARY: I-BAND CALIBRATIONS

Beaton et al. 2018

TRGB IN INFRARED

Z = 0.004, 0.001, 0.004,

0.008, 0.19, and 0.30

Girardi+02 isochrones

NIR data for

24 GCs

Valenti + 2004

AGE DEPENDENCY

Salaris & Girardi 2005:

“… the TRGB method for distance determinations has to be applied with

caution to all galaxies that present signatures of intermediate-age stars.”

TRGB CALIBRATION WITH GAIA DR2

SkyMapper Gaia DR2 RGB with overplotted calibration of

the TRGB by Rizzi et al. 2007 (solid line)

Mould,

Clementini

& Da Costa

2019

BOLOMETRIC CORRECTION

Serenelli et al. 2017 𝑀𝐼𝑇𝑅𝐺𝐵 = 𝑀𝑏𝑜𝑙

𝑇𝑅𝐺𝐵 − 𝐵𝐶𝐼

Full age range

NGC 4258

THE CARNEGIE-CHICAGO HUBBLE PROGRAM

Extragalactic distance scale using only Population II distance indicators

Beaton+2018

Beaton et al. 2018

TAKE HOME MESSAGES

• TRGB potential for Cepheid-independent precise & accurate distance scale measurement

• TRGB as RELATIVE distance indicator – precision < 5%

• TRGB as ABSOLUTE distance indicator – accuracy > 5%

• Need better I-band bolometric corrections

• Future application for H0 measurements with ELT, JWST:

• K-band (and J, H) calibration work ongoing

• application possibly more complex

REFERENCES AND FURTHER MATERIAL

• Freedman, Wendy & Madore, Barry F., 2010, ARA&A: “The

Hubble Constant”

• Beaton, R. L., et al. 2018: “Old Aged Stellar

Population Distance Indicators”

• Serenelli, A, Weiss, A., Cassisi, S., et al., 2017: “The

brightness of the RGB tip. Theoretical framework, a set of

reference models, and predicted observables”