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
BM 4.4, SG 5.1
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) (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)
R_d is 55” in this figure or about 3.6 kpc
Bulge dominates in center and again at very large radii (if bulge obeyed r1/4 to large R)
Disk dominates at intermediate radii
Rd ~ 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 B 15 5
(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. 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
B/T =
Re2Ie
Re2Ie Rd2Io S0 Sa Sb Sc
B/T
T-type
0.8
Bulge fraction: in spirals, determine the ratio of bulge to disk or total luminosity – follows Hubble type
Eq 4.46 in BM

5. Spirals get bluer and fainter along the sequence S0  Sd
Ursa Major galaxy group
Open circles: fainter o
B is at 4500 A and K is at 2.2 microns or A
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. 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
z-direction
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)
Generally R_d = 0.1 z_o
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?)