Galaxies Astro 430/530 Prof. Jeff Kenney. CLASS 2 Jan 19, 2018 QuanDtaDve Morphology, Surface Brightness Profiles & Disks

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1 Galaxies Astro 430/530 Prof. Jeff Kenney CLASS 2 Jan 19, 2018 QuanDtaDve Morphology, Surface Brightness Profiles & Disks 1

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3 Color opdcal image of spiral galaxy Isophotes contours of equal surface brightness NGC 5533 SDSS gri Hogg Separate images taken in 3 bands: g, r, i 3 images combined to make color image

4 Surface brightness we observe 2D projecdon of 3D body (luminosity per area or surface brightness) galaxies are 3D bodies (luminosity per volume) Surface brightness at any posidon in a galaxy is the integrated light of all stars along that line- of- sight In principle, the SB profile can be deprojected to obtain the 3D spadal density distribudon of stars in a galaxy (but only by making assumpdons about symmetry)

5 unresolved (point) source L D (pc) Surface brightness & flux: unresolved sources If source smaller than beam, detect total flux of source beam = angle of sensidvity for detector small angle formula α rad = D/d α d (cm) solid angle of square patch Ω = α 2 detector pixel detects all of source flux

6 extended source I(x,y) D (pc) L Surface brightness & flux: resolved sources I(x,y) surface brightness I as a funcdon of of angular coordinates x,y) beam = angle of sensidvity for detector small angle formula α rad = D/d α d (cm) If source is resolved, a detector detects the flux per solid angle = surface brightness in erg s - 1 cm - 2 arcsec - 2 (or sr - 1 ) I = f/ω = f/α 2 solid angle of square patch Ω = α 2 detector pixel detects only part of source flux

7 extended source I(x,y) D (pc) L Surface brightness & flux: resolved sources beam = angle of sensidvity for detector d (cm) small angle formula α rad = D/d solid angle of square patch Ω = α 2 α detector pixel

8 Surface brightness is independent of distance! surface brightness = brightness or flux per solid angle Less light from each square meter of more distant source (Inverse square law B decreases by 1/d 2 ) But more square meters (surface area) of source within same solid angle of observer for more distant source (surface area increases by d 2 ) d 3d

9 Surface brightness is distance independent! If source is unresolved, a detector detects the flux in erg s - 1 cm - 2 If source is resolved, a detector detects the flux per solid angle = surface brightness in erg s - 1 cm - 2 arcsec - 2 (or erg s - 1 cm - 2 sr - 1 ) I = f/ω = f/α 2 Recall: angular size of source α = D/d angular area of source (square patch) Ω = α 2 = (D/d) 2 f = L/4πd 2 d = distance I = f/ω = (L/4πd 2 ) / (D/d) 2 = L/4πD 2 where D=size of patch on source So units of I are L sun pc - 2 or erg s - 1 cm - 2 arcsec - 2 Area on source (in pc 2 ) depends on distance (in cm) and angular area (in arcsec 2 ); so that s why units of cm - 2 arcsec - 2 are equivalent to pc - 2 in SB Luminosity and area of patch in source both increase as d 2 so rado doesn t depend on d!

10 Surface brightness in magnitudes arcsec - 2 µ = log I + C SB in mag arcsec - 2 SB in erg s - 1 cm - 2 arcsec - 2 magnitudes arcsec - 2 are strange units since magnitudes are not linear: if a point in a galaxy has a SB of 21 magnitudes arcsec - 2 this means an area of 1 square arcsecond around this point emits as much light as a star of apparent magnitude 21. warning! NotaDon in textbooks is not consistent! Both SG and BM use I to mean both L sun pc - 2 and magnitudes arcsec - 2

11 Color opdcal image of spiral galaxy Isophotes contours of equal surface brightness NGC 5533 SDSS gri Hogg Separate images taken in 3 bands: g, r, i 3 images combined to make color image Fit ellipses to isophotes

12 Isophotal analysis & aperture photometry for spiral galaxy R band opdcal image Fit ellipses to isophotes of image φ N a b Broeils & Knapen 1991 PosiDon angle Axial rado Surface brightness PA (φ) of ellipses vs radius gives esdmate of PA of galaxy (line of nodes) Axial rado (b/a) vs. radius of ellipses gives esdmate of disk inclinadon Average surface brightness in ellipdcal annuli vs radius gives radial light distribudon [& esdmate of bulge- to- disk rado]. Averages over substructure like spiral arms, bars, regions of star formadon 12

13 The radial distribudon of starlight in spiral galaxy disks is roughly exponendal NGC 4294 (Hα light) R- band light SDSS Hogg website Koopmann+2001 R- band radial light profile shows pure exponen)al disk NGC 4294 has li4le or no stellar bulge 13

14 FuncDons fit to Galaxy Radial light profiles ExponenDal disk: I(r) = I(0) exp (- r/r d )

15 EllipDcal galaxies have radial light distribudons different from disks more light in center and outskirts than exponen=al disk oken well fit by devaucouleurs r 1/4 profile : I(r) = I(r eff ) exp {- 7.67[( r/r eff ) 1/4-1]} E galaxy along minor axis along major axis Radial light distribudon well- fit by r 1/4 profile 15

16 FuncDons fit to Galaxy Radial light profiles ExponenDal disk: I(r) = I(0) exp (- r/r d ) DeVaucouleurs r 1/4 bulge law: I(r) = I(r eff ) exp {- 7.67[( r/r eff ) 1/4-1]}

17 Surface brightness profile of spiral with bulge+disk NGC 7331 is similar to M31 NGC 7331 B NGC µm NGC 7331 R SG 2D projected image with isophotal contours (contours of equal surface brightness) Bulge and disk apparent (Affected by dust exdncdon) Ideal galaxy Disk n=1 n=4 NGC 7331 Disk scale length 1D radial profile EllipDcally averaged ; Corrected for inclinadon (but not for dust) 17

18 FuncDons fit to Galaxy Radial light profiles ExponenDal disk: I(r) = I(0) exp (- r/r d ) devaucouleurs r 1/4 bulge law: I(r) = I(r eff ) exp {- 7.67[( r/r eff ) 1/4-1]} Sersic law: I(r) = I(r eff ) exp {- b n [( r/r eff ) 1/n - 1]} n = Sersic index b n chosen to make r eff the effecdve radius (encloses ½ the light) b n = 1.999n for n>1 n = 1-4 typically If n=1 exponendal (all disk) disks of spirals, S0s, dwarf Es If n=4 devaucouleurs r/4 law (all bulge) giant E s, globular clusters 1<n<4 bulges of spirals and S0s (higher n for large L bulges) If n<2 for endre spiral or S0: small bulge- disk rado If n>2 for endre spiral or S0: large bulge- disk rado BM eq is wrong! Has 10 rather than e Advantage of Sersic law: can describe en)re profile shape with just 1 number n

19 MacArthur Sersic profiles n=1 Sérsic n profiles for different values of n. The top panel shows profiles with µ e = 21 mag arcsec - 2 and r e = 3.5 for values of n in the range 0.2 < n < 4. n=1 The table lists the reladve light contribudons of the different profiles normalized to the n = 1 case. 2 different ways to normalize: at effecdve radius (top), and at center (bovom) The bovom panel shows the same profiles except for a constant CSB of µ 0 = 18 mag arcsec

20 Radial light profiles of disks vs. E s + bulges n=4: Light profile of E s and bulges n=1 (exponendal): Light profile of spiral disks and de s Compared to an exponendal (n=1) distribudon, an n=4 distribudon has more stars at small & large radii, and fewer at intermediate radii 20

21 what is best radius to characterize a galaxy? surface brightness I radius

22 Different photometric radii in small- bulge spiral galaxy NGC 4294 (Hα light) SDSS Hogg website R- band radial light profile shows pure exponen)al disk r d scale length of exponendal disk where SB falls to e - 1 of central SB I(r d ) = e - 1 I(0) r eff effecdve radius (contains 50% of total light) ; r eff R- band light Koopmann+2001 L(<r eff ) = 0.5 L tot r 24 isophotal radius (SB falls to 24 mag arcsec - 2 ) ; simplest to measure, oken less meaningful 22

23 effecdve radius = half- light radius cumuladve light integrated from center of galaxy outwards total light intensity (counts) total of all integrated light distance from center (pixels) 23

24 effecdve radius = half- light radius cumuladve light integrated from center of galaxy outwards total light intensity (counts) total of all integrated light distance from center (pixels) hard to measure radius containing all the light, so total light radius very uncertain half- light radius is more robust parameter 24

25 Different photometric radii in small- bulge spiral galaxy with only disk NGC 4294 (Hα light) R- band light SDSS Hogg website r eff Koopmann+2001 R- band radial light profile shows pure exponen;al disk r d scale length of exponendal disk (I ~ I 0 e - r/rd ) r eff effec;ve radius (contains 50% of total light) r 24 isophotal radius (SB falls to 24 mag arcsec - 2 ) 25

26 Different photometric radii in small- bulge spiral galaxy with only disk NGC 4294 (Hα light) R- band light SDSS Hogg website r eff Koopmann+2001 R- band radial light profile shows pure exponen;al disk r d scale length of exponendal disk (I ~ I 0 e - r/rd ) = 1.6 kpc r eff effec;ve radius (contains 50% of total light) = 3 kpc r 24 isophotal radius (SB falls to 24 mag arcsec - 2 ) = 6 kpc 26

27 Different photometric radii in small- bulge spiral galaxy with only disk NGC 4294 (Hα light) R- band light SDSS Hogg website r eff Koopmann+2001 R- band radial light profile shows pure exponen;al disk r d scale length of exponendal disk (I ~ I 0 e - r/rd ) = 1.6 kpc r eff effec;ve radius (contains 50% of total light) = 3 kpc r 24 isophotal radius (SB falls to 24 mag arcsec - 2 ) = 6 kpc r vir ~ kpc 27

28 Why are disks exponendal? Not understood in detail Stellar disks are thin because they form from gas disks, which experience (energy) dissipadon Stellar disks are exponendal (in radius) because they form from gas disks, which experience energy dissipadon and angular momentum transport

29 Not all disks are perfectly exponendal Bars, rings, spiral arms, interacdons modify radial distribudons Extra light due to ring HST Ringed galaxy NGC 4622 Buta+03

30 Not all disks are perfectly exponendal Pohlen+02 break radius UGC 9837 break radius Outer disks of some spiral galaxies fit by steeper exponendal than inner disk not well understood but clearly not )dal trunca)on, could be )dal interac)on or less efficient SF in outskirts

31 Truncated disks in edge- on spiral galaxies The disk starlight becomes much fainter than an extrapoladon of the exponendal disk at r~2-5 scale lengths in many galaxies (easier to observe in edge- ons) Kregel+2002

32 Q: How many galaxies can you see during the day?

33 Q: How many galaxies can you see during the day? A: NONE

34 Q: How many galaxies can you see during the day? A: NONE Followup Q: WHY?

35 Night sky brightness **Earth s Atmosphere: Airglow from upper atmosphere ***Solar System: Zodiacal light from dust in solar system *GalacDc: Faint unresolved stars in Milky Way Galaxy ExtragalacDc: Faint unresolved distant galaxies Typical night sky brightness: 23 B- mag arcsec - 2 for a good site & moonless night (or 21.5 R- mag arcsec - 2 )

36 Night sky brightness **Earth s Atmosphere: Airglow from upper atmosphere ***Solar System: Zodiacal light from dust in solar system *GalacDc: Faint unresolved stars in Milky Way Galaxy ExtragalacDc: Faint unresolved distant galaxies Typical night sky brightness: 23 B- mag arcsec - 2 for a good site & moonless night (or 21.5 R- mag arcsec - 2 ) Day brightness 5 B- mag arcsec - 2 (18 mags = factor of 1.6x10 7 x brighter than nightsky!)

37 ExponenDal radial light profile in small- bulge spiral galaxy NGC 4294 (Hα light) Night sky brightness 21.5 R- mag arcsec - 2 R- band light SDSS Hogg website r eff Koopmann+2001 In most bright galaxies, much of starlight arises from regions where the galaxy light is fainter than the brightness of the night sky Some light from galaxies is at levels fainter than 26 B- mag arcsec - 2 (24.5 R- mag arcsec - 2 ). This is only ~6% of night sky SO must carefully subtract light from night sky to see fainter parts of galaxies! 37

38 why can t you perfectly subtract night sky light from astronomical images?

39 IllustraDon of surface brightness variadons # photons detected in each pixel varies with Dme due to stadsdcal nature of emission processes (variadon = poisson noise ) Noise from sky oken exceeds average signal from astronomical source Need to average over (long?) Dme to beat down the noise enough to detect source

40 why can t you perfectly subtract night sky light from astronomical images? stars and the sky and other things produce photons in a random Poisson process, so that there are random variadons in the number of photons which strike a detector each second. These variadons are somedmes called shot noise. The size of these random variadons is simply the square root of the number of photons. sky brightness is annoying source of noise it produces extra signal with uncertainty we can subtract average value of signal but we cannot subtract the uncertainty, which is propor)onal to the square root of the signal

41 how S/N varies with integradon Dme S=signal (avg # photons detected) N=noise (variadon in #photons detected) t = integradon Dme S ~ t N ~ S ~ t S/N ~ S/ S ~ S ~ t signal- to- noise ra;o the signal- to- noise rado improves by increasing integradon Dme, but only as t bever to avoid extra light from all non- astronomical sources if possible!

42 ExponenDal radial light profile in small- bulge spiral galaxy NGC 4294 (Hα light) Night sky brightness WITH NOISE! 21.5 R- mag arcsec - 2 R- band light SDSS Hogg website r eff Koopmann+2001 In most bright galaxies, much of starlight arises from regions where the galaxy light is fainter than the brightness of the night sky Some light from galaxies is at levels fainter than 26 B- mag arcsec - 2 (24.5 R- mag arcsec - 2 ). This is only ~6% of night sky SO must carefully subtract light from night sky to see fainter parts of galaxies! 42

43 maybe there are lots of galaxies that are fainter than the night sky, and therefore very hard to detect! à low surface brightness (LSB) galaxies

44 Malin 1 Bothun+1987 Giant LSB galaxy Malin 1 I(0) disk = 26.5 mag arcsec - 2 Center of disk is 100x (=5 mags) fainter than Freeman s Law!! Malin 1 Magellan Galaz+2015 very large D opt ~100 kpc total luminosity & stellar mass higher than MW V max =300 km/s so it s a massive galaxy A very large & massive spiral galaxy that is fainter than the night sky everywhere but very center!

45 ultradiffuse (LSB) galaxies in the Coma cluster Coma Cluster UDG locadons van Dokkum+2015 most LSB galaxies have small stellar masses 45

46 Surface brightness (SB) funcdon of galaxies # galaxies per Mpc 3 per magnitude bin Low SB galaxies High SB ( normal ) galaxies McGaugh (1996) Central surface brightness CSB of bright ( normal ) spirals ~ 21.5 B- mag arcsec - 2 Low surface brightness galaxies are common

47 if LSB galaxies are common, could they account for most of the stars in the universe?

48 Surface brightness (SB) funcdon of galaxies # galaxies per Mpc 3 per magnitude bin Low SB galaxies are less massive on average High SB galaxies are more massive on average Low surface brightness galaxies are common BUT most of the galaxy mass & stars in the universe are in high surface brightness galaxies (this is not obvious from this plot need other data to show this!) McGaugh (1996) Central surface brightness

49 Surface brightness (SB) funcdon of galaxies Very high surface brightness disks also exist! (with µ 0 <20 mag arcsec - 2 ) They are called pseudobulges and they exist in the centers of the main (& larger) galaxy disk

50 not all compact stellar components in galaxies are bulges, some are compact disks (pseudobulges)! PeleDer+2007 ; Kormendy & Fischer 2008 pseudobulge compact stellar component in NGC 4274 has Sersic index close to 1, high v/σ, so it is a disk not a bulge 50