Transcript Surface Brightness Properties of Spiral Galaxies

Photometric Properties of Spiral Galaxies
Bulges
•Luminosity profiles fit r1/4 or r1/n laws
NGC 7331
Sb galaxy
R-band
isophotes
•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)
Central surface brightness (Id in BM)
In magnitudes
Disk scale length
μ(R) = μ(0) +1.086 (R/Rd)
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
Face-on
15
5
20
(van der Kruit 1978)
21
22
23
24 25
B
• 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!)
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
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)
z-direction
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
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 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
B/T =
Re2Ie
0.8
S0
Sa
B/T
the ratio of bulge to disk or total
luminosity – follows Hubble type
Sb
Sc
Re2Ie + 0.28Rd2Io
0
T-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 = 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 Vz 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)