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TIP OF THE RED GIANT BRANCH AS DISTANCE
INDICATOR
ESO KES, October 2019
Marina Rejkuba
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Lemaitre
1927
Robertson
1928
Hubble
1929
Jan Oort
Sandage
Baade
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Allan Sandage &
Gustav Tammann
Gerard de Vauculeurs
1996 Scale of the Universe debate:
Gustav Tammann vs Sidney van den Bergh
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HST KEY PROJECT
β’ 1990 launch of the Hubble Space Telescope
β’ 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:
π»0 = 72 Β± 8 ππ π β1πππβ1
Age of the Universe in the Einstein-de Sitter model: 9.1 Gyr
(still younger than some of the oldest stars)
Wendy Freedman
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THE CARNEGIE-CHICAGO HUBBLE PROGRAM
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RED GIANT BRANCH TIP THEORETICAL BACKGROUND
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Solar composition tracks:
M= 0.9, 1, 1.2 β¦. 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-Manqueβ,
normal HB tracks for
MHB=0.48,0.5,0.55 Mo
Stellar Evolutionary Tracks
PN
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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 β radius shrinks β
shell T & consequently the luminosity
generated in the shell increases β star
climbs along the RGB with increasing luminosity and core temperature
RGB Tip:
He core ignition β lifts e- degeneracy in the
core β core flash quenched within seconds β core inflates & star settles at lower
luminosity burning He in the core
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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
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RED GIANT BRANCH TIP
β’ Theoretically well understood: discontinuity for old metal-poor stars evolving on RGB
β’ Attractive alternative for RR Lyr & Cepheid distance scale
β’ Population II: lower extinction and crowding
β’ Single epoch observations β easy to observe/measure
β’ I-band TRGB nearly constant for old metal-poor stars
β’ 4 mag brighter than RR Lyr, less extinction than Cepheids
β’ Da Costa & Armandroff 1990 (DA90): βStandard Globular Cluster Giant Branches in the [MI vs (V-I)0] Planeβ
β’ Lee, Freedman & Madore 1993: βThe Tip of the Red Giant Branch as Distance Indicator for Resolved Galaxiesβ
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DA COSTA & ARMANDROFF 1990: βSTANDARD GLOBULAR CLUSTER
GIANT BRANCHES IN THE [MI VS (V-I)0] PLANEβ
βIn Sec. IV the cluster giant branch results are compared with the predictions of theory. β¦ 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.β
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MI assuming HB distances based on
Lee, Demarque & Zinn 1990 calibration:
MV(RR) = 0.82 + 0.17 [Fe/H]
DA90 Standard GC RGBs
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π΅πΆπΌ = 0.881 β 0.234 π β πΌ ππ πΊπ΅
ππππππ πΊπ΅ = β0.19
πΉπ
π»β3.81
π βπ πΌ = πΌππ πΊπ΅ β ππΌ,ππ πΊπ΅ = πΌππ πΊπ΅ + π΅πΆπΌ βππππππ πΊπ΅
ππΌ β β4.05
πΉπ/π» = β15.16 + 17.0 π β πΌ β3 β 4.9 π β πΌ β32
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LEE, FREEDMAN & MADORE 1993:βTHE TIP OF THE RED GIANT
BRANCH AS A DISTANCE INDICATOR FOR RESOLVED
GALAXIESβ
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LEE ET AL. 1993
β’ Edge detection β zero sum Sobel Kernel [-2, 0, 2] convolution with I-band luminosity function
Madore & Freedman β95
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LEE ET AL. 1993
β’ Method as in DA90 with slight modification:πΉπ/π» = β12.64 + 12.6 π β πΌ β3.5 β 3.3 π β πΌ β3.5
2
β’ Since ππΌ β β4 Β± 0.1 πππ with little variation with metallicity for [Fe/H]β€ β0.7 dex, the method can be used up to ~4 Mpcfrom the ground and up to Virgo and Fornax with the HST
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EARLY WORKS
β’ Sakai et al. 1996:
β’ replace the discrete LFs with their respective Gaussians (smooth)
β’ apply adaptive edge-detection β localised slope estimator with 4-point smoothing
β’ Madore & Freedman 1995: extensive computer simulations
β’ Signal-to-noise β larger than 5 to limit photometric errors
β’ Crowding β less than 25% (one star every 3 contaminated)
β’ Population size β need ~50 stars within upper 1 mag
β’ Contamination from non-RGB stars β work in outer halo
πΈ π = Ξ¦ πΌ + ΰ΄€ππ βΞ¦ πΌ β ΰ΄€ππ
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Sakai+1996: Sextans A
TRGB brightness in the main body 21.64
and in the halo 21.79
β’ Authors attribute to crowding
β’ Age may play a role as well
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MEASURING TRGB
β’ Cioni et al. 2000
β’ LMC & SMC β TRGB in I, J, K band
β’ Bolometric correction using J-K color
β’ Using Savitzky-Golay filter to estimate the 2nd
derivative
β’ Use Gaussian fit to identify TRGB
β’ Systematic correction up to ~0.02 mag (AGB, photometric errors)
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MAXIMUM LIKELIHOOD
β’ Mendez, B. et al. 2002, Makarov et al. 2006
β’ Maximum likelihood
β’ logarithmic edge detection to smooth the luminosity function
β’ RGB LF is a power law: π π ππ β 10ππ & π = 0.30 Β± 0.04
β’ Marginalising over free parameters: TRGB mag, LF slope brighter than TRGB, discontinuity strength
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Makarov et al. 2006
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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
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TRGB CALIBRATION
GCs: Ferraro+2000, Bellazzini+2004; Valenti+2004
Galaxies: Rizzi et al. 2007, Jang & Lee 2017
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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 β98
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RED GIANT BRANCH TIPNGC 5128
IRGBT=24.1Β± 0.1 mag
D = 3.8 Β± 0.1 Mpc Rejkuba et al. 2005
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I-BAND COLORDEPENDENT CALIBRATION
Rizzi et al. 2007:
β’ Slope is always the same
β’ Zero point calibrated via
HB in 5 Local Group
galaxies & applying
Carretta et al. 2000 calib
β’ MI = - 4.05 +/- 0.02 at
(V-I) = 1.6
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TRGB: METALLICITY CORRECTION
ππΌππ πΊπ΅ = 0.14
πΉπ
π»
2
+ 0.48πΉπ
π»β 3.629
π β πΌ = 0.581πΉπ
π»
2
+ 2.472πΉπ
π»+ 4.013
Belazzini et al. 2001, 2004:
Mager et al. 2008
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Jang & Lee 2017
Quadratic fit to measure TRGB vs color
Zero point anchors:
β’ LMC (eclipsing binaries)
β’ NGC 4258 (Maser)
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ERROR BUDGET
Jang & Lee
2017
aF555W β F814W to F606W β F814W transformation.
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SUMMARY: I-BAND CALIBRATIONS
Beaton et al. 2018
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TRGB IN INFRARED
Z = 0.004, 0.001, 0.004,
0.008, 0.19, and 0.30
Girardi+02 isochrones
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NIR data for
24 GCs
Valenti + 2004
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AGE DEPENDENCY
Salaris & Girardi 2005:
ββ¦ the TRGB method for distance determinations has to be applied with
caution to all galaxies that present signatures of intermediate-age stars.β
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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
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BOLOMETRIC CORRECTION
Serenelli et al. 2017 ππΌππ πΊπ΅ = ππππ
ππ πΊπ΅ β π΅πΆπΌ
Full age range
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NGC 4258
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THE CARNEGIE-CHICAGO HUBBLE PROGRAM
Extragalactic distance scale using only Population II distance indicators
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Beaton+2018
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Beaton et al. 2018
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TAKE HOME MESSAGES
β’ TRGB potential for Cepheid-independent precise & accurate distance scale measurement
β’ TRGB as RELATIVE distance indicator β precision < 5%
β’ TRGB as ABSOLUTE distance indicator β accuracy > 5%
β’ Need better I-band bolometric corrections
β’ Future application for H0 measurements with ELT, JWST:
β’ K-band (and J, H) calibration work ongoing
β’ application possibly more complex
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REFERENCES AND FURTHER MATERIAL
β’ Freedman, Wendy & Madore, Barry F., 2010, ARA&A: βThe
Hubble Constantβ
β’ Beaton, R. L., et al. 2018: βOld Aged Stellar
Population Distance Indicatorsβ
β’ Serenelli, A, Weiss, A., Cassisi, S., et al., 2017: βThe
brightness of the RGB tip. Theoretical framework, a set of
reference models, and predicted observablesβ