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8. Surface Brightness Fluctuations

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8. Surface Brightness Fluctuations Rolf Kudritzki SS 2015 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 1 Rolf Kudritzki SS 2015 2 galaxies at different distance Jacoby et al., 1992, PASP 104, 599 Cantiello, MIAPP WS 2 Rolf KudritzkiSBF SS 2015: Galaxy surface brightness is independent of distance, but the variance (measured in Fourier space) goes as d-2 globular star cluster M32 (Andromeda) M49 (Virgo) N ~ 106 stars N ~ 109 stars N ~ 1012 stars d ~ 10 kpc d ~ 770 kpc d ~ 16 Mpc 3 sabato 7 maggio 2011 Blakeslee, Naples WS Rolf Kudritzki SS 2015 simple approach: consider elliptical galaxy with - a constant surface brightness profile - consisting of one type of stars only with L stellar luminosity in photometric band used ⇤ L 1 ⇤ stellar flux observed with telescope f = 2 ⇤ 4⇡ d Then with ⇥ 2 angular area of spatial resolution element 2 N = n ⇥ average number of stars in resolution element · 2 n = n 0 d n 0 column number density of stars in galaxy · F = N f average flux in each resolution element ⇤ ⇤ σF 1· F ⇤ = ⇤ Poissonian fluctuation σ F = F pN ⇤ ⇤ pN 4 Rolf Kudritzki SS 2015 1 because of N d 2 and f ⇤ ⇠ d2 ⇠ à F does not depend on distance or ⇤ F ⇤ surface brightness independent of distance 2 = n f ⇥ · ⇤ However, 2 σF 1 L 1 ⇤ = F = f = ⇤ F N · ⇤ ⇤ 4⇡ d2 ⇤ à surface brightness fluctuation flux 2 σF L 1 ⇤ ⇤ F SBF = = 2 (1) F 4⇡ d ⇤ decreases with distance !!! 5 Rolf Kudritzki SS 2015 in reality, not only one type of star, but luminosity function niLi ⇥2 à average flux in each F = 2 niLi ⇤ 4 ⇡ d resolution element or X Li F = Fi Fi = Ni ⇤ 2 4⇡d X n 2 n = i n d2 Ni = ni⇥ i 0 n0 · ✓ ◆ the Poissonian scatter of each F i between resolution elements is then (analogous to eq. 1) 2 Li 1 2 2 2 and 2 2 σi = Ni 2 σi = ⇥ 2 niLi σF = σi 4⇡d 4⇡d ⇤ ✓ ◆ p X 2 2 σF 1 1 niLi à ⇤ (2) FSBF = = 2 F d 4⇡ niLi ⇤ P 6 P Rolf Kudritzki SS 2015 introducing magnitudes we obtain distance m SBF M SBF =5 log ( d/pc ) 5 (3) modulus − · − 2 σ F measured surface m = 2.5log ⇤ + const. SBF − F (4) brightness magnitude ⇤ 2 1 n i L i absolute surface MSBF = 2.5log − 4 ⇡ n L (5) brightness magnitude ✓ P i i ◆ P 7 Rolf Kudritzki SS 2015 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 I˜(k) 2 = σ2 P˜2 + const. | | SBF · SBF where P˜ SBF is the Fourier transform of the PSF 8 Rolf Kudritzki SS 2015 Why Fourier transform?? One could simply use processed image and measure N 1 p F ¯ = F p N p p p =1 mean flux X N p 2 1 ¯ 2 σ = F p F p pixel-to-pixel fluctuation Np − p=1 X 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. 9 Rolf Kudritzki SS 2015 simple consideration of “noise image” consider a 1-dimensional azimuthally averaged image I(x) of the remaining noise I(x)= σjPPSF(x xj)+ ∆jδ(x xj) − − j j X X σ = F SBF F¯ j j − SBF F j is the flux from the area of the galaxy corresponding to the projected pixel size. It is different from F ¯ because of SBF. It is distributed over many pixels through the PSF. ∆ j is the additional noise coming from the detector or Poisson photon noise. It varies from pixel to pixel. 10 Rolf Kudritzki SS 2015 The Fourier transforms are ikxj f ( x )= δ ( x x ) à f˜(k)=e− − j (x x )2 − j 1 1 2 1 2 2 − 2σ ikxj σ k f ( x )= e PSF à f ˜(k)=e− e− 2 PSF σPSF p2⇡ · This is for a Gaussian PSF. In reality the PSF is more complex. à Fourier transform of image ikxj ikxj I˜(k)=P˜PSF(k) σje− + ∆je− j X X à power spectrum I˜(k) 2 P˜2 (k) σ2 + ∆2 | | ⇡ PSF j j j X X I˜(k) 2 P˜2 (k) σ2 + ∆ | | ⇡ PSF · SBF 11 Rolf Kudritzki SS 2015 predicted Fourier power spectrum of noise image SBF 12 Blakeslee, Naples WS Rolf Kudritzki SS 2015 observed power spectrum Tonry & Schneider, 1988 M32 is at ~ 0.8 Mpc NGC 3379 at ~ 10 Mpc 13 Rolf Kudritzki SS 2015 Limitations 2 2 obviously, the method needs σ F ∆ in order to work, ⇤ ≥ where ∆ 2 corresponds to the photon and detector noise 2 1 1 à high spatial resolution is good, σF 2 2 ⇤ ⇠ N ⇠ ⇥ d good seeing (Mauna Kea), AO, space telescopes perfect detectors, long exposures help to reduce ∆2 maximum distance with HST à 200 Mpc? JWST à 2 HST ELTs + AO à 10 HST So far, observations out to Coma cluster 14 RolfComa Kudritzki cluster SS 2015 SBF observations with HST 15 Blakeslee, Naples WS sabato 7 maggio 2011 Rolf Kudritzki SS 2015 N4889 ACS N4874 ACS WFC3/IR par WFC3/UVis par GO-11711 orients 16 Blakeslee, Naples WS sabato 7 maggio 2011 Rolf Kudritzki SS 2015 17 Blakeslee, Naples WS N4874 F160w sabato 7 maggio 2011 Rolf Kudritzki SS 2015 calibration of MSFB - 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 L SFB ( V ) = 58 L M SFB ( V )=0 . 41 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 18 Rolf Kudritzki SS 2015 Measure amplitude of the fluctuations 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. Blakeslee, Naples 19WS sabato 7 maggio 2011 Rolf KudritzkiSBF SS “fluctuation 2015 magnitude” versus (g-z) color: elliptical galaxy stellar population VRIz predictions z-band SBF bright; ~ 0.06 mag scatter. bright Blakeslee, Vazdekis, & Ajhar 2001 composite models. 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 Mei et al. 2005 z-band empirical calibration red Blakeslee, Naples 20WS sabato 7 maggio 2011 Rolf Kudritzki SS 2015 ACS/F814W SBF converted to absolute σ = 0.029 mag Blakeslee et al. 2010 21 sabato 7 maggio 2011 Rolf Kudritzki SS 2015 Cantiello, MIAPP WS 22 Rolf Kudritzki SS 2015 Virgo in 3-D 23 Blakeslee, Naples WS sabato 7 maggio 2011 Rolf Kudritzki SS 2015 The 3-D Structure of Virgo: Projections in the Supergalactic Plane Blakeslee, Naples 24WS sabato 7 maggio 2011 Rolf Kudritzki SS 2015 • Very$accurate$rela3ve$distance$Between$Virgo$&$Fornax$ • 3D$Structure$of$Virgo$$ Distances$ • SBF$distances$for$BH$studies$ Mei$et$al.$(2007)$ Fornax$21%$±1%$more$distant$than$Virgo$ Blakeslee$et$al.$(2009,$ACSVCS+ACSFCS)$ 25 Gültekin$et$al.$(2009)$ Rolf Kudritzki SS 2015 When$SBF$met$$H0$ A1 A1 Author" H0"(km"s "Mpc )" ΔH0"" ΔH0"" Notes" StaEsEcal"" SystemaEc" Tonry$et$al.$ 77$ ±4$ ±7$ SBF$survey,$smooth$ (2000)$ cosmic$flows.$$ $ Cepheids$ZP$ Jensen$et$al.$ 76$ ±1.3$ ±6$ NearNIR$NICMOS/HST$ (2001)$ data.$ $ Cepheids$ZP$ Blakeslee$et$al.$ 73$ ±4$ ±11$ SBF$Survey$+$FP$+$IRAS$ (2002)$ Vel.$Field$model$ Biscardi$I.$et$al.,$ 76$ ±6$ ±5$ ACS$op3cal$ (2008)$$ Model$calibra3on$ Mould$&$Sakai$ 68$ ±6$ ±4$ TRGB$calibra3on$ (2009)$ Cantiello, MIAPP WS Michele$Can3ello$N$MIAAP$May/June$2014$ 26 Rolf Kudritzki SS 2015 Infrared SBF SBF 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 Blakeslee, Naples 27WS sabato 7 maggio 2011 Rolf Kudritzki SS 2015 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 28 .
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