Photometric Properties of Spiral Galaxies

Disk scale lengthCentral surface brightness (Id in BM)

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

Disks•Many are well-represented by an exponential profile

I(R) = Ioe-R/Rd (Freeman 1970)

NGC 7331 Sb galaxyR-band isophotes

In magnitudes μ(R) = μ(0) +1.086 (R/Rd)

•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

(Rd)

(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!)

• 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

15

5

(van der Kruit 1978)

•Some low-surface brightness (LSB) galaxies have been identified -extreme case - Malin 1 (Io = 25.5 and Rd=55 kpc!)

•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

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

z-direction

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

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?)

Homework SB Profile fittingChoose 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 = Re

2Ie

Re2Ie + 0.28Rd

2Io

S0

Sa

Sb

ScB

/T

T-type

0.8

0

Bulge fraction: in spirals, determine the ratio of bulge to disk or total luminosity – follows Hubble type

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:

Vz2 = 2GΣMzo

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 Vz decrease with radius ?

•Disk is continually heated by random acceleration of disk stars by Giant Molecular Clouds (GMCs)

•Number of GMCs decrease with radiusSome 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)