rolf kudritzki ss 2015 8. surface brightness fluctuations · 1 8. surface brightness fluctuations...
Post on 13-Apr-2020
6 Views
Preview:
TRANSCRIPT
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
Rolf Kudritzki SS 2015
2
2 galaxies at different distance
Cantiello, MIAPP WS
Jacoby et al., 1992, PASP 104, 599
Rolf Kudritzki SS 2015
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
Rolf Kudritzki SS 2015
4
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
Rolf Kudritzki SS 2015
5
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
Rolf Kudritzki SS 2015
6
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
Rolf Kudritzki SS 2015
7
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
◆
Rolf Kudritzki SS 2015
8
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
Rolf Kudritzki SS 2015
9
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
Rolf Kudritzki SS 2015
10
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
Rolf Kudritzki SS 2015
11
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 +�
Rolf Kudritzki SS 2015
12
predicted Fourier power spectrum of noise image
SBF
Blakeslee, Naples WS
Rolf Kudritzki SS 2015
13
observed power spectrum Tonry & Schneider, 1988 M32 is at ~ 0.8 Mpc NGC 3379 at ~ 10 Mpc
Rolf Kudritzki SS 2015
14
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
Rolf Kudritzki SS 2015
15
sabato 7 maggio 2011
Blakeslee, Naples WS
Coma cluster SBF observations with HST
Rolf Kudritzki SS 2015
16
N4889 ACS
N4874 ACS
WFC3/IR par
WFC3/UVis par
GO-11711 orients
sabato 7 maggio 2011
Blakeslee, Naples WS
Rolf Kudritzki SS 2015
17 N4874 F160w
sabato 7 maggio 2011
Blakeslee, Naples WS
Rolf Kudritzki SS 2015
18
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
Rolf Kudritzki SS 2015
19
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.
sabato 7 maggio 2011
Blakeslee, Naples WS
Rolf Kudritzki SS 2015
20
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
sabato 7 maggio 2011
Blakeslee, Naples WS
Rolf Kudritzki SS 2015
21
ACS/F814W SBF converted to absolute
σ = 0.029 magBlakeslee et al. 2010
sabato 7 maggio 2011
Rolf Kudritzki SS 2015
22 Cantiello, MIAPP WS
Rolf Kudritzki SS 2015
23
Virgo in 3-D
sabato 7 maggio 2011
Blakeslee, Naples WS
Rolf Kudritzki SS 2015
24
The 3-D Structure of Virgo:Projections in the Supergalactic Plane
sabato 7 maggio 2011
Blakeslee, Naples WS
Rolf Kudritzki SS 2015
25
Distances$
Fornax$21%$±1%$more$distant$than$Virgo$Mei$et$al.$(2007)$
• Very$accurate$rela3ve$distance$between$Virgo$&$Fornax$
• 3D$Structure$of$Virgo$$
• SBF$distances$for$BH$studies$
Blakeslee$et$al.$(2009,$ACSVCS+ACSFCS)$
Gültekin$et$al.$(2009)$
Rolf Kudritzki SS 2015
26
When$SBF$met$$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
Rolf Kudritzki SS 2015
27
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
sabato 7 maggio 2011
Blakeslee, Naples WS
Rolf Kudritzki SS 2015
28
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
top related