rolf kudritzki ss 2015 8. surface brightness fluctuations · 1 8. surface brightness fluctuations...

Rolf Kudritzki SS 2015

1

8. Surface Brightness Fluctuations

Basic Idea •  Elliptical galaxies have smooth and regular surface brightness profiles

•  However, more distant galaxies look smoother with pixel-to-pixel variations much smaller

•  this has a simple reason: number of stars per pixel in a galaxy increases with distance à assuming Poissonian fluctuations of the number of stars in a galaxy between volume elements we expect smaller variance

Key Papers •  Tonry & Schneider, 1988, AJ 96, 807 •  Tonry et al., 1997, ApJ 475, 399 •  Tonry et al., 2001, ApJ 546, 681


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2 galaxies at different distance

Cantiello, MIAPP WS

Jacoby et al., 1992, PASP 104, 599


3

SBF: Galaxy surface brightness is independent of distance, but the variance (measured in

Fourier space) goes as d-2

globular star cluster

N ~ 106 stars

d ~ 10 kpc

M32 (Andromeda)

N ~ 109 stars

d ~ 770 kpc

M49 (Virgo)

N ~ 1012 stars

d ~ 16 Mpc

sabato 7 maggio 2011 Blakeslee, Naples WS


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simple approach: consider elliptical galaxy with -  a constant surface brightness profile -  consisting of one type of stars only with stellar luminosity in photometric band used stellar flux observed with telescope Then with angular area of spatial resolution element average number of stars in resolution element column number density of stars in galaxy average flux in each resolution element Poissonian fluctuation

f⇤ =L⇤4⇡

1

d2

L⇤

F⇤ = N · f⇤�F⇤

F⇤=

1pN

�F⇤ =F⇤pN

�⇥2

N = n ·�⇥2

n = n0 · d2 n0


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because of and à does not depend on distance or surface brightness independent of distance However, à surface brightness fluctuation flux (1) decreases with distance !!!

N ⇠ d2 f⇤ ⇠ 1

d2

F⇤

F⇤�⇥2

= n · f⇤

�2F⇤

F⇤=

1

N· F⇤ = f⇤ =

L⇤4⇡

1

d2

FSBF =�2F⇤

F⇤=

L⇤4⇡

1

d2


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in reality, not only one type of star, but luminosity function à average flux in each resolution element or the Poissonian scatter of each between resolution elements is then (analogous to eq. 1) and à (2)

F⇤ =�⇥2

4⇡d2

XniLi

F⇤ =X

Fi

Fi

�2F⇤ =

X�2i

niLi

FSBF =�2F⇤

F⇤=

1

d21

4⇡

PniL2

iPniLi

ni =

✓ni

n0

◆n0 · d2

Fi = NiLi

4⇡d2

Ni = ni�⇥2

�i =p

NiLi

4⇡d2�2i = �⇥2

✓1

4⇡d2

◆2

niL2i


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introducing magnitudes we obtain distance (3) modulus measured surface (4) brightness magnitude absolute surface (5) brightness magnitude

mSBF �MSBF = 5 · log(d/pc)� 5

mSBF = �2.5log�

2F⇤

F⇤+ const.

MSBF = �2.5log

✓1

4⇡

PniL

2iP

niLi

◆


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measurement of SBF method developed by Tonry & Schneider (1988) – 4 steps: 1.  prepare CCD image excise cosmic rays, bad columns, saturation tracks, point sources (for instance globular clusters), foreground and background sources 2.  derive smooth local mean across whole image - fit isophotal model to galaxy image - subtract model - remove remaining point sources 3.  carefully measure PSF (seeing, in case of HST telescope PSF)

4.  Fourier transform remaining “noise image” power spectrum of Fourier transform has the form where is the Fourier transform of the PSF

|I(k)|2 = �

2SBF · P 2

SBF + const.

PSBF


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Why Fourier transform?? One could simply use processed image and measure mean flux pixel-to-pixel fluctuation However, such measurement would mix different sources of noise (detector, photons, etc.) with SBFs •  SBFs in a galaxy are distributed in the image over a spatial scale determined by the FWHM of the PSF (seeing or in case of HST the telescope PSF). FWHM is larger than pixel size. •  photon noise, detector noise etc. are on pixel scale.

Fp =1

Np

NpX

p=1

Fp

�2 =1

Np

NpX

p=1

�Fp � Fp

�2


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simple consideration of “noise image” consider a 1-dimensional azimuthally averaged image I(x) of the remaining noise is the flux from the area of the galaxy corresponding to the projected pixel size. It is different from because of SBF. It is distributed over many pixels through the PSF. is the additional noise coming from the detector or Poisson photon noise. It varies from pixel to pixel.

I(x) =X

j

�jPPSF (x� xj) +X

j

�j�(x� xj)

�j = FSBFj � F

FSBFj

�j

F


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The Fourier transforms are à à This is for a Gaussian PSF. In reality the PSF is more complex. à  Fourier transform of image

à  power spectrum

f(x) = �(x� xj)

f(x) =1

�PSF

1p2⇡

e

� (x�x

j

)2

2�2PSF

f(k) = e�ikxj

f(k) = e�ikxj · e� 12�

2PSF k

2

I(k) = PPSF

(k)X

j

�j

e�ikxj +X

�j

e�ikxj

|I(k)|2 ⇡ P 2PSF (k)

X

j

�2j +

X�2

j

|I(k)|2 ⇡ P 2PSF (k) · �2

SBF +�


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predicted Fourier power spectrum of noise image

SBF

Blakeslee, Naples WS


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observed power spectrum Tonry & Schneider, 1988 M32 is at ~ 0.8 Mpc NGC 3379 at ~ 10 Mpc


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Limitations obviously, the method needs in order to work, where corresponds to the photon and detector noise à high spatial resolution is good, good seeing (Mauna Kea), AO, space telescopes perfect detectors, long exposures help to reduce maximum distance with HST à 200 Mpc? JWST à 2� HST ELTs + AO à 10� HST So far, observations out to Coma cluster

�2F⇤ � �2

�2F⇤ ⇠ 1

N⇠ 1

�⇥2d2

�2

�2


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sabato 7 maggio 2011


Coma cluster SBF observations with HST


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N4889 ACS

N4874 ACS

WFC3/IR par

WFC3/UVis par

GO-11711 orients




17 N4874 F160w




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calibration of -  originally Tonry & Schneider (1988) used the study by Gunn, Stryker, Tinsley, 1981, ApJ 249, 48 which combined population synthesis calculations with multi-color photometry and spectrophotometry of giant ellipticals -  almost all contribution comes from low mass stars at the main sequence turn-off up to the tip of the RGB -  original value used was mag

-  however, dependence on metallicity and age of populations already discussed à calibration in different filter bands as a function of color using ellipticals in galaxy clusters and population synthesis

MSFB

LSFB(V ) = 58L� MSFB(V ) = 0.41


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Measure amplitude of thefluctuations in Fourier space(variance convolved with PSF)

Convert to magnitudes and calibrate dependence on stellar pop (color, Mg2, etc) for galaxies at same distance:normalized fluctuations (SBF) fainter in redder galaxies.

Set zeropoint from Cepheid distances to these groups or individual galaxies.




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SBF “fluctuation magnitude” versus (g-z) color:elliptical galaxy stellar population VRIz predictions

Other SBF models:

Worthey 1993

Liu et al. 2000

Cantiello et al. 2003

Raimondo et al. 2005

Marin-Franch & Apparicio 2006

Lee et al. 2010

z-band SBF bright; ~ 0.06 mag scatter.

Blakeslee, Vazdekis, & Ajhar 2001

composite models.

bright

red

Mei et al. 2005 z-bandempirical calibration




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ACS/F814W SBF converted to absolute

σ = 0.029 magBlakeslee et al. 2010



22 Cantiello, MIAPP WS


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Virgo in 3-D




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The 3-D Structure of Virgo:Projections in the Supergalactic Plane




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Distances$

Fornax$21%$±1%$more$distant$than$Virgo$Mei$et$al.$(2007)$

•  Very$accurate$rela3ve$distance$between$Virgo$&$Fornax$

•  3D$Structure$of$Virgo$$

•  SBF$distances$for$BH$studies$

Blakeslee$et$al.$(2009,$ACSVCS+ACSFCS)$

Gültekin$et$al.$(2009)$


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When$SBF$met$$H0$

Michele$Can3ello$N$MIAAP$May/June$2014$

Author" H0"(km"sA1"MpcA1)" ΔH0""StaEsEcal""

ΔH0""SystemaEc"

Notes"

Tonry$et$al.$

(2000)$

$

77$ ±4$ ±7$ SBF$survey,$smooth$

cosmic$flows.$$

Cepheids$ZP$

Jensen$et$al.$

(2001)$

$

76$ ±1.3$ ±6$ NearNIR$NICMOS/HST$

data.$

Cepheids$ZP$

Blakeslee$et$al.$

(2002)$

73$ ±4$ ±11$ SBF$Survey$+$FP$+$IRAS$

Vel.$Field$model$

Biscardi$I.$et$al.,$

(2008)$$

76$ ±6$ ±5$ ACS$op3cal$

Model$calibra3on$

Mould$&$Sakai$

(2009)$

68$ ±6$ ±4$ TRGB$calibra3on$

Cantiello, MIAPP WS


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Infrared SBFSBF is ~30× more luminous at K than at I

✦Dominated by luminous RGB stars

Increased contrast with (less contamination from)

globular clusters & background galaxies

Seeing is better in the near-IR

Extinction is much lower than in the optical

Sensitive to young populations and AGB stars

Age-metallicity degeneracy is broken




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Problems •  undetected dust and extinction affects SBF and distance

•  PSF still an issue in particular with AO

•  IMF changes affect calibration

•  correlated noise in images

•  near IR: uncertainties of AGB models

rolf kudritzki ss 2015 8. surface brightness fluctuations · 1 8. surface brightness fluctuations...

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