ASTRO 310: Galac/c & Extragalac/c Astronomy Prof. Jeff Kenney Class 17 Mar 30, 2016 Starlight Distribu/ons in Disk Galaxies
reminder no class next Monday, April 3!!
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Color op/cal 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
Surface brightness we observe 2D projec/on of 3D body (luminosity per area or surface brightness) galaxies are 3D bodies (luminosity per volume) Surface brightness at any posi/on 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 spa/al density distribu/on of stars in a galaxy (but only by making assump/ons about symmetry)
unresolved (point) source L D (pc) Surface brightness & flux: unresolved sources If source smaller than beam, detect total flux of source beam = angle of sensi/vity for detector d (cm) small angle formula α rad = D/d solid angle of square patch Ω = α 2 α detector pixel detects all of source flux
extended source I(x,y) D (pc) L Surface brightness & flux: resolved sources I(x,y) surface brightness I as a func/on of of angular coordinates x,y) 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
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
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 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 ra/o doesn t depend on d!
Surface brightness in magnitudes arcsec - 2 µ = - 2.5 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! Nota/on in textbooks is not consistent! Both SG and BM use I to mean both L sun pc - 2 and magnitudes arcsec - 2
Color op/cal 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
Isophotal analysis & aperture photometry for spiral galaxy R band op/cal image Fit ellipses to isophotes of image φ N a b Broeils & Knapen 1991 Posi/on angle Axial ra/o Surface brightness PA (φ) of ellipses vs radius gives es/mate of PA of galaxy Axial ra/o (b/a) vs. radius of ellipses gives es/mate of disk inclina/on Average surface brightness in ellip/cal annuli vs radius gives radial light distribu/on [& es/mate of bulge- to- disk ra/o]. Averages over substructure like spiral arms, bars, regions of star forma/on 12
The radial distribu/on of starlight in spiral galaxy disks is roughly exponen/al NGC 4294 (Hα light) R- band light SDSS Hogg website Koopmann+2001 R- band radial light profile shows pure exponen)al disk 13
Func/ons fit to Galaxy Radial light profiles Exponen/al disk: I(r) = I(0) exp (- r/r d )
Surface brightness profile of spiral with bulge+disk NGC 7331 B NGC 7331 3.6µm NGC 7331 R SG 2D projected image with isophotal contours (contours of equal surface brightness) Bulge and disk apparent (Affected by dust ex/nc/on) Ideal galaxy Disk n=1 n=4 NGC 7331 Disk scale length 1D radial profile Ellip/cally averaged ; Corrected for inclina/on (but not for dust) 15
Disks have very different radial light profiles from bulges & ellip/cals Surface Brightness (mag arcsec - 2 )
Ellip/cal galaxies have radial light distribu/ons different from disks more light in center and outskirts than exponen5al disk olen well fit by devaucouleurs r 1/4 profile : I(r) = I(r eff ) exp {- 7.67[( r/r eff ) 1/4-1]} E galaxy Radial light distribu/on well- fit by r 1/4 profile 17
Func/ons fit to Galaxy Radial light profiles Exponen/al 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]}
Func/ons fit to Galaxy Radial light profiles Exponen/al 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 n = 1-4 typically If n=1 exponen/al (all disk) [b n chosen to make r eff the effec/ve radius] If n=4 devaucouleurs r/4 law (all bulge) If n<2 small bulge- disk ra/o If n>2 large bulge- disk ra/o Advantage of Sersic law: can describe en5re profile shape with just one number n
MacArthur + 2003 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 rela/ve light contribu/ons of the different profiles normalized to the n = 1 case. 2 different ways to normalize: at effec/ve radius (top), and at center (botom) The botom panel shows the same profiles except for a constant CSB of µ 0 = 18 mag arcsec - 2. 20
what is best radius to characterize a galaxy? surface brightness I radius
Different photometric radii in small- bulge spiral galaxy NGC 4294 (Hα light) R- band light SDSS Hogg website r eff Koopmann+2001 R- band radial light profile shows pure exponen5al disk r d scale length of exponen/al disk (I ~ I 0 e - r/rd ) = 1.6 kpc r eff effec5ve radius (contains 50% of total light) = 3 kpc r 24 isophotal radius (SB falls to 24 mag arcsec - 2 ) = 6 kpc r vir ~ 100-200 kpc 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 exponen/al disk where SB falls to e - 1 of central SB I(r d ) = e - 1 I(0) r eff effec/ve 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, olen less meaningful 23
Why are disks exponen/al? Not understood in detail Stellar disks are thin because they form from gas disks, which experience (energy) dissipa/on Stellar disks are exponen/al (in radius) because they form from gas disks, which experience energy dissipa/on and angular momentum transport
Not all disks are perfectly exponen/al Bars, rings, spiral arms, interac/ons modify radial distribu/ons Extra light due to ring HST Ringed galaxy NGC 4622 Buta+03
Not all disks are perfectly exponen/al UGC 9837 Pohlem+02 Outer disks of some spiral galaxies fit by steeper exponen/al than inner disk not well understood but clearly not )dal trunca)on, could be )dal interac)on or less efficient SF in outskirts
Truncated disks in edge- on spiral galaxies The disk starlight becomes much fainter than an extrapola/on of the exponen/al disk at r~2-5 scale lengths in many galaxies (easier to observe in edge- ons) Kregel+2002
Q: How many galaxies can you see during the day? A: NONE Followup Q: WHY?
Night sky brightness **Earth s Atmosphere: Airglow from upper atmosphere ***Solar System: Zodiacal light from dust in solar system *Galac/c: Faint unresolved stars in Milky Way Galaxy Extragalac/c: 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!)
Exponen/al 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! 30
why can t you perfectly subtract night sky light from astronomical images?
Illustra/on of surface brightness varia/ons # photons detected in each pixel varies with /me due to sta/s/cal nature of emission processes (varia/on = noise ) Noise from sky olen exceeds average signal from astronomical source Need to average over (long?) /me to beat down the noise enough to detect source
Exponen/al 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! 33
stars and the sky and other things produce photons in a random Poisson process, so that there are random varia/ons in the number of photons which strike a detector each second. These varia/ons are some/mes called shot noise. The size of these random varia/ons 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
signal (avg # photons detected) S ~ t (t = integra/on /me) noise (varia/on in #photons detected) N ~ S ~ t signal- to- noise ra/o S/N ~ S/ S ~ S ~ t the signal- to- noise ra/o improves by increasing integra/on /me, but only as t beter to avoid extra light from all non- astronomical sources if possible!
maybe there are lots of galaxies that are fainter than the night sky, and therefore very hard to detect! à low surface brightness galaxies
Low surface brightness galaxy Malin 1 I(0) disk = 26.5 mag arcsec - 2 Center of disk is 100x (=5 mags) fainter than Freeman s Law!! Yet V max =300 km/s so it s a massive galaxy A large & massive spiral galaxy that is fainter than the night sky everywhere but very center!
Surface brightness (SB) func/on 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
if LSB galaxies are common, could they account for most of the stars in the universe?
Surface brightness (SB) func/on 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
reminder no class next Monday, April 3!!