Photometric Properties of Spiral Galaxies

1. Photometric Properties of Spiral Galaxies • Bulges • Luminosity profiles fit r1/4 or r1/n laws • Structure appears similar to E’s, except bulges are more “flattened” and can have different stellar dynamics NGC 7331 Sb galaxy R-band isophotes • Disks • Many are well-represented by an exponential profile • I(R) = Ioe-R/Rd (Freeman 1970) Central surface brightness (Id in BM) Disk scale length In magnitudes μ(R) = μ(0) +1.086 (R/Rd)

2. 1-d fit to azimuthally averaged light profile with 2 components (A 2-d fit to the image may be better since bulge and disk may have different ellipticities!) NGC 7331 (Rd) (R) • Bulge dominates in center and again at very large radii (if bulge obeyed r1/4 to large R) • Disk dominates at intermediate radii • Rd ~ 1 - 10 kpc (I-band; 20% longer in B-band) • Disks appear to end at some Rmax around 10 to 30 kpc or 3 to 5Rd

3. Face-on 15 5 20 21 22 23 24 25 B (van der Kruit 1978) • Freeman’s Law (1970) - found that almost all spirals have central disk surface brightness oB= 21.5  0.5 • Turns out to be a selection effect yielding upper limit since fainter SB disks are harder to detect! • Disks like bulges show that larger systems have lower central surface brightness • Some low-surface brightness (LSB) galaxies have been identified -extreme case - Malin 1 (Io = 25.5 and Rd=55 kpc!)

4. 0.8 S0 Sa B/T Sb Re2Ie Sc B/T = 0 Re2Ie + 0.28Rd2Io T-type • Homework SB Profile fitting • Choose one galaxy, extract an azimuthally averaged surface brightness profile, calibrate counts to surface brightness units, and fit the bulge and disk to r1/4 and exponential functions, respectively. Derive • a) effective radius and surface brightness for the bulge (Ie and Re) – give in mag/arc2 • b) scale length and central surface brightness for the disk (Rd and I0) • c) bulge/disk luminosity ratio Bulge fraction:in spirals, determine the ratio of bulge to disk or total luminosity – follows Hubble type

5. Ursa Major galaxy group Open circles: fainter o • Spirals get bluer and fainter along the sequence S0  Sd • S0 color is similar to K giant stars; younger, bluer stars absent • Later types have more young stars

6. z-direction Disks - Vertical Distribution of Starlight • Disks are puffed up by vertical motions of stars • Observations of edge-on disks (and MW stars) show the luminosity density is approximated by j(R,z) = joe-R/Rdsech2(z/2zo) for R<Rmax Scale height (sometimes ze which is 2zo) van der Kruit and Searle (1981,1982) • At face-on inclination, obeys exponential SB law • At large z, j(z) ~ joexp(-z/zo) in SB  I(R,z) = I(R)exp(-z/zo) • Disks fit well with typical Rd and Rmax values and constant zo with R

7. How does the vertical distribution of starlight in disks compare with the theoretical distribution of a self-gravitating sheet? <VZ2>1/2 (z component of stellar velocity dispersion) is constant with z Poisson’s Equation Liouville’s Equation (hydrostatic equilibrium state for system of collisionless particles) Substituting and solving: Solution:

8.  Vz2 = 2GΣMzo • where ΣM is mass surface density = 4ρozo • If zo is constant with R, and ΣM decreases with increasing R, Vz2 must also decrease with increasing R. Why does velocity dispersion decrease with radius ? • Disk is continually heated by random acceleration of disk stars by Giant Molecular Clouds (GMCs) • Number of GMCs decrease with radius Some observations suggest that zo may not be constant and may increase with R (models include mass density of atomic and molecular gas). (Narayan & Jog 2002)

9. Scale height varies strongly with stellar type • zo ~ 100 pc for young stars • zo ~ 400 pc for older stars • In addition to the main disk, there is evidence for a thick disk in some galaxies (including our own) with zo=1 kpc • Mostly older stars • Formed either through puffing up of disk stars (e.g. via minor merger?)