Major Topics
1. Introduction
Stars, the Milky Way, Other Galaxies, Cosmology
2. The Galaxy and its Components
Luminosity/Mass Functions, Distances, Clusters, Rotation
3. The Interstellar Medium
Gas, Dust, Emission and Absorption
4. Galactic Dynamics
Gravity, Encounters, Epicycles, Boltzmann Equation
5. The Local Group
6. Spiral and S0 Galaxies
Starlight Distribution, Gas Motions, Spiral Structure, Bulges
7. Elliptical Galaxies
Photometry, Motions, Dark Matter, Black Holes
8. Galaxy Groups and Clusters
Galaxy Formation, Intergalactic Matter and Gravitational Lensing
9. The Large Scale Distribution of Galaxies
Cosmology, Growth of Structure
10. Active Galaxies and Pre-Galactic History
Active Galactic Nuclei, Jets, Intergalactic Clouds, the First Galaxies
J.M. Lattimer
AST 346, Galaxies, Part 1
Stars – Main Sequence Spectra
metal 4000Å break
⇓
CH
H neutral
⇐ Balmer lines
⇑
Balmer jump
3646Å
H nearly totally ionized
J.M. Lattimer
⇑
Paschen jump
8250Å
AST 346, Galaxies, Part 1
Stars – A Dwarf, Giant and Supergiant Spectra
Effect of gravity on line width – the Stark effect
⇐ broad Balmer lines
⇐ narrow Balmer lines
J.M. Lattimer
AST 346, Galaxies, Part 1
Stars – Basic Relations for Main Sequence Stars
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Masses between 0.08 M and 100 M
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Radii between 0.1 R and 25 R
0.7
R ∼ R MM
5
3.9
(M ≤ 10M ≤ M )
L ∼ L MM (M ≤ M ), L ∼ L MM
2.2
L ∼ 50L MM
(M ≥ 10M )
−2.5
−5/7
L
M
L
τMS ' τMS, MM
'
10Gyr
'
10Gyr
L
M
L
h i2
log(τMS /Gyr) ' 1.015 − 3.49 log MM + 0.83 log MM
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MV , = 4.83, MB, = 5.48, MK , = 3.31, MI , = 4.11
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Mbol, = 4.76, L = 3.9 × 1033 erg s−1 , Teff , = 5780K
J.M. Lattimer
AST 346, Galaxies, Part 1
Abundances
[A/B] = log10
h
(A/B)∗
(A/B)
i
J.M. Lattimer
AST 346, Galaxies, Part 1
Photometry
Sky emission from La Palma
R∞
FBP = R0 TBP,λ Fλ dλ
∞
≈ Fλeff 0 TBP,λ dλ
≡ Fλeff ∆λBP
m2 − m1 = 2.5 log10
mBP = 2.5 log10
F1
F2
FV ,0 ∆λBP
FBP
FV ,0 ≈ 3.63 × 10−9
erg s−1 cm−2 Å
mBP = −21.1
∆λBP
FBP
−1
TBP (λ)
A0
Fλ
+2.5 log10
' −21.1 − 2.5 log10 Fλeff
J.M. Lattimer
AST 346, Galaxies, Part 1
Milky Way
Disc stellar mass: 6 × 1010 M
Halo stellar mass: 1 × 109 M
4 × 106 M BH
⇓
Disc luminosity: 2 × 1010 L
Bulge stellar mass: 2 × 1010 M
Bulge luminosity: 5 × 109 L
8.5 kpc
HI
J.M. Lattimer
AST 346, Galaxies, Part 1
Gas and Dust in the Milky Way
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Solar neighborhood: 1 star per 10 pc−3 , 1 atom per cm3
H II region: ionizing photons λ < 912 Å, Eγ > 13.6 eV
Emission timescale typically 10−8 s
Collisional excitation A + B → A∗ + B, A∗ → A + hν
Forbidden line: collisons rare (gas density low), timescale ∼ 1 s
Fine structure transition: spin-orbit coupling in atoms, 1/1372 less
energy: far-infrared
Hyperfine transition: nuclear spin coupling with electron spin, 2000
times less energy than fine structure: mm and radio
Spin flip 21 cm radiation of H I. Takes about 11 Myr to
spontaneously transition to ground state. Collision times of order
thousands of years.
Molecular emission from electronic, vibrational and rotational
transitions
CO emission (1.3 mm, 2.6 mm) is strongest after H2
OH (1.7 GHz) and H2 O (22 GHz) masing
Continuum radiation (free-free or bremstrahlung, and synchotron)
from ionized gas
Dust absorption (optical and UV) and emission (infrared)
J.M. Lattimer
AST 346, Galaxies, Part 1
21 cm Emission
Strength of 21 cm emission depends on collision rate. In general, rate =
density × cross section × velocity. T ∼ 100 K.
⇒ vH ' 1.6 km s−1
mH vH2 /2 = 3kT /2,
Cross section of a sphere with a radius equal to the Bohr radius
a0 = ~c/(αme c 2 ) = 197.3 × 137/0.511 fm = 50Å
is πa02 . The inverse collision rate is
−1
nh πa02 vH
= 3000
1 cm−3
nH
r
100 K
yr.
T
An H atom in the upper level (electron and proton spins aligned)
spontaneously decays with a halflife of 11 Myr. Since the energy
difference corresponding to 21 cm emission is much smaller than T ,
collisions drive the abundances of the two states to equilibrium. The
population ratio upper/lower is 3. So the emission rate of 21 cm
radiation is (3/44)nH photons per Myr, independent of T .
J.M. Lattimer
AST 346, Galaxies, Part 1
Dust Absorption
Dust is about 1% of the interstellar mass, primarily in the form of
silicates and carbon with sizes rd ∼ 0.1µm. For radiation with
wavelengths smaller than this size, absorption and scattering are quite
efficient, so the effective cross section is πrd2 . Long wavelength light is
scattered less efficiently, κ ∝ λ−1 , leading to preferential removal of blue
light and reddenning.
The number density nd of dust grains is
.01 × 3nH mH
nd md = 0.01nH mH ,
nd =
4πρd rd3
which is about 4 × 10−12 cm−3 if ρd ∼ 1 g cm−3 .
For uniformly distributed dust, the flux is diminished with path length:
rd
dFλ
Fλ
2 −1
= −κρFλ = − ,
` = nd πrd
' 300
pc
dx
`
0.1µm
with ` the mean free path. Thus, for a path length x ' `, Fλ is decreased
by a factor e. The column density of hydrogen over a path length x is
n
x H
21
NH = nH x = 3 × 10
cm−2 .
1 cm−3
1 kpc
J.M. Lattimer
AST 346, Galaxies, Part 1
Galactic and Sky Coordinates
Sun-centered
J.M. Lattimer
Galactic-centered
AST 346, Galaxies, Part 1
Other Galaxies
100 LMW , 300 kpc
10 LMW , 30 kpc
0.1 LMW
J.M. Lattimer
AST 346, Galaxies, Part 1
Galaxy Photometry
Surface brightness IBP (x),
measured in LBP pc−2
or magBP arcsec−2 .
Observed area on galaxy is D 2 ,
distance to galaxy is d,
α2 = (D/d)2 is angular area
observed on sky.
IBP (x) =
Sky emission Las Palma
LBP (x)/4πd 2
FBP (x)
=
2
α
(D/d)2
which is independent of d!
Centers of galaxies: IB ≈ 18 mag
arcsec−2 = 4000LB pc−2 or
IR ≈ 16 mag arcsec−2 .
Galactic discs have IB ∼ 27 mag
arsec−2 ∼ 1 LB pc−2 .
For comparison, the background
brightness of the night sky is
about IB = 22.7 mag arsec−2 .
J.M. Lattimer
Sky emission
Mauna Kea
AST 346, Galaxies, Part 1
Numbers of Galaxies
Number of galaxies between luminosities L and L + dL (Schechter function):
α
−L
n∗ L
exp
dL
Φ(L)dL =
L∗ L∗
L∗
For the bandpass BJ ,
α ∼ −0.5,
n∗ = 0.02h3 Mpc−3 '
0.007 Mpc−3 , L∗ '
9 × 109 h−2 L ' 2 × 1010 L .
α ≤ −1, total number
RFor
∞
Φ(L)dL
→ ∞ for L → 0.
L
The luminosity density in each
luminosity interval dL is
ρL (L) = Φ(L)L which peaks
near L∗ . The total luminosity
density is
Z
Φ(M)
ρM (M)
∞
Φ(L)LdL = n∗ L∗ Γ(α + 2) ' 2 × 108 h L Mpc−3 .
ρL =
0
For the K band, ρL ' 6 × 108 h L Mpc−3 .
J.M. Lattimer
AST 346, Galaxies, Part 1
Hubble’s Law
Vr = H0 d,
d =h
−1
Vr
100 km s−1
Mpc,
h=
H0
100 km s−1 Mpc−1
When d determined from Vr ,
L ∝ h−2 ,
M ∝ Vr2 d ∝ h−1 .
n ∝ h3 ,
Brightest galaxies in rich clusters
Vr = H0 d + Vpec
dm = 5d log z
V
10
Vr ' cz
J.M. Lattimer
AST 346, Galaxies, Part 1
d = 3h−1 z Gpc
Cosmic Parameters
Hubble time
tH =
1
= 9.78h−1 Gyr
H0
Age of universe in the standard model (ΩΛ = 0.7, Ωm = 0.3)
tH =
0.964
= 9.43h−1 Gyr
H0
Critical density
ρcrit (now) =
3H02
= 1.9 × 10−29 h2 g cm−3 = 2.8 × 1011 h2 M Mpc−3
8πG
J.M. Lattimer
AST 346, Galaxies, Part 1
The Big Bang
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Planck epoch: t < 10−43 s
GR predicts gravitational singularity before this, but quantum effects
prevent it.
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Grand unification epoch: 10−43 s < t < 10−36 s
Gravitation separates from the fundamental gauge interactions
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Inflationary epoch: 10−36 s < t < 10−32 s
Universe flattened by homogenous, isotropic rapid expansion,
triggered by separation of strong force from electroweak forces,
resulting in a primordial spectrum of nearly scale-invariant
fluctuations. Potential energy of the inflation field decays into a hot,
relativistic plasma.
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Electroweak epoch: 10−36 s < t < 10−12 s
Production of W and Z bosons and Higgs bosons.
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Baryogenesis
Universe becomes asymmetric with respect to baryons and
anti-baryons. Why?
J.M. Lattimer
AST 346, Galaxies, Part 1
The Big Bang
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Quark epoch: 10−12 s < t < 10−6 s
Fundamental particles acquire mass (Higgs mechanism), quarks too
hot to bind into hadrons
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Hadron epoch: 10−6 s < t < 1 s
Quark-gluon plasma cools and hadrons form, neutrinos decouple.
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Lepton epoch: 1 s< t < 10 s
Majority of hadrons and anti-hadrons annihilate, leaving leptons and
anti-leptons to dominate mass, which themselves finally annihilate.
Small residues of hadrons and leptons survive.
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Photon epoch: 10 s< t < 0.38 Myr
Universe energy dominated by photons
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Nucleosynthesis: 3 m< t <20 m
Protons and neutrons fuse, neutrons decay, forming D and He, Li,
and Be isotopes.
J.M. Lattimer
AST 346, Galaxies, Part 1
Nucleosynthesis
Neutrons are more massive than protons by
1.293 MeV, resulting in a proton excess:
n/p = e −(1.293
MeV/kT )
.
Neutrinos decouple at t = 1 s, T = 0.8
MeV. Neutrons freeze out with n/p ≈ 1/5.
Neutrons have a finite lifetime, τn ' 886 s.
After 20 minutes, when fusion terminates,
only 1/4 are left. These become bound in
He nuclei. Therefore n/p = 1/7 and
He/H=1/12. By mass, Y /X = 1/3.
Y is insensitive to nB , but D/H is very
sensitive. D forms easily, but He requires
weak interactions. If nB is relatively small,
D/H becomes large. If nB is relatively
large, D/H becomes small. Thus, D/H is a
sensitive measure of ΩB .
J.M. Lattimer
Abundances of other light nuclei
like 3 He, 6 Li and 7 Li can also be
used to estimate nB . The
estimates of all but 7 Li converge
on 0.02 < ΩB h2 < 0.025.
AST 346, Galaxies, Part 1
The Big Bang
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Matter domination: t < 0.07 Myr
Jeans length falls below fluctuation
masses and smallest structures
form. Cold dark matter dominates
(but when did that form?).
Recombination: t = 0.38 Myr
Protons and electrons form neutral
H, opacity decreases, photons
decouple and form the CMB. Now
redshifted by factor 1 + z ≈ 1100
to 2.73 K.
J.M. Lattimer
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Dark ages: 150 Myr < t < 500 Myr
Only emitted radiation is 21 cm.
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Structure formation, reionization:
500 Myr< t < 1 Gyr
Quasars and Pop III stars (not yet
observed) form and re-ionize
surroundings. Sub-galactic object
with z = 10.2, t = 480 Myr,
observed Jan 2011. Star-forming
galaxies observed at t = 500 Myr.
AST 346, Galaxies, Part 1
The CMB fluctuations
The small fluctuations in the CMB remaining after subtraction of the
Doppler effect are acoustic oscillations due to a competition between the
gravitational attraction of the baryons and the smoothing of photons.
The angular scale of the first peak depends on the curvature of the
universe. The next peak depends on nB . The third peak depends on the
dark matter density. They depend on ΩΛ and ΩB .
ΩΛ = 0.7, Ωm = 0.3
ΩΛ = 0.85, Ωm = 0.15
ΩΛ = 0, Ωm = 0.3
J.M. Lattimer
AST 346, Galaxies, Part 1
The CMB and the Sun
The radiation from the CMB is far
larger than that from the extragalactic
background at IR, optical, UV, X-ray
and γ-ray energies.
The CMB is uniform to within 1 part in
105 with the exception (besides the
annual motion of the Earth about the
Sun) of a dipole anisotropy in the
direction ` = 265◦ , b = 48◦ , with an
amplitude of 0.1% (hottest in that
direction). The higher temperature
represents a Doppler blue shift
V
T (θ) = TCMB 1 + cos θ .
c
This gives V = 370 km s−1 . After
correction for the solar motion in the
Galaxy and the Milky Way’s motion
relative to nearby galaxies, one has
Vpec ≈ 600 km s−3 . The origin of this
large motion is not understood.
J.M. Lattimer
AST 346, Galaxies, Part 1
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AST 346, Galaxies, Part 1
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J.M. Lattimer
AST 346, Galaxies, Part 1