Sep 16, 2015
• Luminosity and mass functions, initial mass function, star formation
rate, star formation history
• Intro to galaxy photometry
• HW#3 is due next Monday
• Part of it is a group project. I hope you have already been in
touch.
• Do not wait until the last minute to work on this!
• If you have questions, ask me!
• Reading: Chapter 3
• There is a handout today.
• (Hopefully) Arecibo remote observing Fri/Sat Oct 16&17
HW #3
Includes a group project: You will work with 2 classmates on one
project and prepare a presentation for class next week.
Team
Who
A
1. Gabe
2. Zach
3. JiSoo
B
1.
2.
3.
4.
James
John
Samuel
Paola
Seyfert’s Sextet
The group around
Messier 81 and 82
M82
M81
NGC3077
Optical image:
traces starlight
The map of hydrogen gas
reveals an interaction
Optical image:
traces starlight
Radio image, traces gas
M81/M82/NGC3077 movie
The Hubble “Tuning Fork” Diagram
Image from Galaxy Zoo
Why do galaxies look the way they do?
Stars: (Initial) Mass Function
• Mass function
The number of stars that form with masses
between M and M + M is (M) M
 (M) = 0 M-
Constant which sets
local stellar density
http://i.stack.imgur.com/sgrnw.jpg
Stars: (Initial)Mass Function (M)
 (M) = 0 M-
Total mass of stars with
masses between Mlower
and Mupper is:
M =
𝑴𝒖
𝑴
𝑴𝒍
𝑴 𝒅𝑴
Salpeter (1955)
 (M) = 0 M-2.35
Note: sometime
exponent is written x+1
and sometimes as x;
check definition!
Describing Populations of Stars/Galaxies
• Luminosity function
• Need to
understand
survey
“completeness
”
• Flux-limited
vs volumelimited
Schechter Luminosity Function
• The “Schechter function” is useful in fitting luminosity and mass
functions
• Can also be expressed in terms of absolute magnitude or luminosity
• Two important parameters:
• Faint end slope 
• “knee” (or “characteristic”) luminosity/mass/magnitude
Star formation/evolution=> color change
Star formation rate: SFR
• Rate at which gas is converted into stars
• In MW, about 3 M yr-1
• Arp 220, about 1000 M yr-1
• High redshift starbursts 5000 M yr-1

Star formation history SFR(t)
Single, early burst:
SFR(t > o) = 0
Exponential decline
SFR(t) = (0) exp (-t/c)
Single later burst:
SFR(t < o and
t > o + t) = 0
Multiple bursts on top of
exponential decline
Quantitative morphology
Levels of symmetry:
1. spherical: glob. clusters, E0 galaxies (some round by projection)
2. axial: natural result of rotation => disk
- basic shape for most galaxies
3. triaxial: (less recognized); results in strongly anisotropic velocity
distributions.
Fundamental planes of galaxy properties (are there more?)
1. Form: morphology, color, star formation rate, specific angular momentum
2. Scale: luminosity, linear size, mass
Question: Is the shape of a galaxy, in the absence of active perturbations,
dominated by:
1. present equilibrium conditions?
2. initial (or early) conditions?
Surface brightness
I(x) = F/2 = L/(4d2)(d/D)2 = L/(4D2)
• Units: L⊙/pc2
• Nearby, S.B. is independent of D
• Often, use magnitudes to denote flux at given point in image
(x) = -2.5 log10 I(x) + const
Units are [mag/arcsec2]
Galaxy photometry
•Fitting isophotes: in practice
• Fix center
• Allow smooth
variation in position
angle (of major axis),
ellipticity
Where does the image
above come from?
Surface brightness profile => I(r) in L⊙ pc-2
(r) in mag arcsec-2
Photometric Properties of Galaxies
Surface brightness measured in mag/arcsec2 (I, B, R, etc.)
is independent of distance since light falls as 1/d2, but the area
subtended by 1 sq arcsec increases as 1/d2.
• however, cosmological dimming of 1/(1+z)4 causes higher z
galaxies to have lower surface brightnesses
• SB profiles are produced by
azimuthally averaging around the
15
galaxy along isophotes of constant
Night sky at 22.7
brightness.
20
B
• Must understand viewing geometry.
• Seeing effects on SB profiles 25
unresolved points spread out due to
effects of our atmosphere, etc.
30
• makes central part of profile
radius
flatter
Much of the galaxy structure is
• makes isophote rounder
fainter than the sky which must
be accurately subtracted.
Elliptical isophotes
Ellipticity = 1 – (b/a)
where a,b are the
major,minor axes.
PA = position angle =
angle (measured from
north towards east) of
the major axis
Surface brightness =
µ(r) = azimuthally
averaged brightness in
mag/arcsec2 along the
major axis
Quantitative Morphology
• Sérsic profile:
I(r) = I(0) exp (-k r1/n)
= Ie exp { -bn [(r/re)1/n – 1]}
where bn must be determined
numerically from the condition
re
0
∫
r In(r) dr = ½∫0 r In(r) dr
∞
• “de Vaucouleurs’ profile”:
I(r)= I(re) exp[-(r/re)¼]
where re is the “effective
radius” and L(<re)=½ Ltotal
• “exponential profile”:
I(r)= I(0) exp[-r/rd]
where rd is the “exponential scale length” or “disk scale length”
Spiral: I(r) = Ibulge(r) + Idisk(r)… [+ Ibar(r)]
The R1/4 Law
µ(r) = Ie exp { -7.67 [(r/re)1/4 – 1]}
Fits many Es
Van Albada (1992) showed
that dissipationless collapse
(gravitating particles without
losing energy by heating or
turbulence) can lead to the
R1/4 shape.
Re = effective radius = radius
encompassing half the light
Ie = I(Re)
Note that the SB falls > 10 magnitudes from center
to outskirts
Range of Elliptical properties
Photometry of spiral galaxies
Separating disk from bulge
Internal extinction
• Large amounts of dust affect
observed SB
• Disks optically thick in inner
regions; transparent outside
• Hence various components
affected differently; depend on
geometry.
•Scattering and
absorption have
competing effects. Which
one dominates depends
strongly on viewing
geometry (both bulge &
disk)
•High and low inclination:
dimming/reddening
•Intermediate inclination:
(forward) scattering
• Dust preferentially
scatters blue light
• Scattering is not
isotropic (dust grains not
round) => forward
scattering (small angles)
Disk + bulge
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 - why?)
• Disk in many spirals appear to end at some Rmax around 10 to 30 kpc
or (3-5Rd)
n=1
exponential
n=4 deVauc
Sérsic + Exponential profiles
I(R) = I(Re) exp {-b[ (R/Re)1/n – 1]}
ell
0.2
0.3
0.4
An understanding of the Hubble sequence
Elliptical galaxies
• Formed all stars long ago (red)
• Little gas (fuel for new stars)
• Random stellar motions
• Found in clusters
Spiral galaxies
• Still forming stars today (blue)
• Lots of gas and dust
• Rotation in disk plane
• Avoid clusters
The Spiral Sequence
• Prominence of bulge
• Windy-ness of spiral arms (tight versus open)
• Barred versus unbarred
• Degree of development of
spiral arms:
• Flocculent (fleecy)
• Grand design
Overall trends along the Spiral sequence
• Important structural differences among o, disk size, n, B/D
• Also difference in gas content and SFR/stellar content
“Early”
“Late”
Decreasing:
o, disk size, B/D, Sersic n, Ltot, Vrot, mean stellar age, metallicity
Increasing:
Gas content, star formation rate (per unit mass = SSFR),
lopsidedness/asymmetry
Elliptical
Galaxies
• Morphology-density
relation => found in
regions of high
galaxy density
• Often show hints of
interactions/merger
M87 jet
Offset M87 field:
Point sources are
globular clusters
CenA