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

2. Bulge dominates in center and again at very large radii (if bulge obeyed r 1/4 to large R) Disk dominates at intermediate radii R d ~ 1 - 10 kpc (I-band; 20% longer in B-band) Disks appear to end at some R max around 10 to 30 kpc or 3 to 5R d (R d ) (R)(R) NGC 7331 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!)

3. 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 Face-on 20 21 22 23 24 25 BB 15 5 (van der Kruit 1978) Some low-surface brightness (LSB) galaxies have been identified -extreme case - Malin 1 (I o = 25.5 and R d =55 kpc!)

4. 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 Ursa Major galaxy group Open circles: fainter  o

5. 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) = j o e -R/Rd sech 2 (z/2z o ) for R<R max z-direction Scale height (sometimes z e which is 2z o ) van der Kruit and Searle (1981,1982) At face-on inclination, obeys exponential SB law At large z, j(z) ~ j o exp(-z/z o ) in SB  I(R,z) = I(R)exp(-z/z o ) Disks fit well with typical R d and R max values and constant z o with R

6. Scale height varies strongly with stellar type z o ~ 100 pc for young stars z o ~ 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 z o =1 kpc Mostly older stars Formed either through puffing up of disk stars (e.g. via minor merger?)

7. 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 r 1/4 and exponential functions, respectively. Derive a)effective radius and surface brightness for the bulge (I e and R e ) – give in mag/arc 2 b)scale length and central surface brightness for the disk (R d and I 0 ) c)bulge/disk luminosity ratio B/T = Re2IeRe2Ie R e 2 I e + 0.28R d 2 I o S0 Sa Sb Sc B/T T-type 0.8 0 Bulge fraction: in spirals, determine the ratio of bulge to disk or total luminosity – follows Hubble type

8. How does the vertical distribution of starlight in disks compare with the theoretical distribution of a self-gravitating sheet? 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:

9.   V z 2  = 2  GΣ M z o where Σ M is mass surface density = 4ρ o z o If z o is constant with R, and Σ M decreases with increasing R,  V z 2  must also decrease with increasing R. Why does V z 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 z o may not be constant and may increase with R (models include mass density of atomic and molecular gas). (Narayan & Jog 2002)