AST 346, Galaxies, Part 1 - Stony Brook University · r d 0:1 m pc with ‘the mean free path....

Major Topics1. Introduction

Stars, the Milky Way, Other Galaxies, Cosmology2. The Galaxy and its Components

Luminosity/Mass Functions, Distances, Clusters, Rotation3. The Interstellar Medium

Gas, Dust, Emission and Absorption4. Galactic Dynamics

Gravity, Encounters, Epicycles, Boltzmann Equation5. The Local Group6. Spiral and S0 Galaxies

Starlight Distribution, Gas Motions, Spiral Structure, Bulges7. Elliptical Galaxies

Photometry, Motions, Dark Matter, Black Holes8. Galaxy Groups and Clusters

Galaxy Formation, Intergalactic Matter and Gravitational Lensing9. The Large Scale Distribution of Galaxies

Cosmology, Growth of Structure10. 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 4000A break⇓

CH

H neutral⇐ Balmer lines

H nearly totally ionizedBalmer jump⇑

3646A Paschen jump⇑

8250A


Stars – A Dwarf, Giant and Supergiant Spectra

Effect of gravity on line width – the Stark effect

⇐ broad Balmer lines

⇐ narrow Balmer lines


Stars – Basic Relations for Main Sequence Stars

I Masses between 0.08 M and 100 MI Radii between 0.1 R and 25 R

I R ∼ R(

MM

)0.7

I L ∼ L(

MM

)5

(M ≤ M), L ∼ L(

MM

)3.9

(M ≤ 10M ≤ M)

I L ∼ 50L(

MM

)2.2

(M ≥ 10M)

I τMS ' τMS,

(M

M

)(LL

)' 10Gyr

(M

M

)−2.5

' 10Gyr(

LL

)−5/7

I log(τMS/Gyr) ' 1.015− 3.49 log(

MM

)+ 0.83

[log(

MM

)]2

I MV , = 4.83,MB, = 5.48,MK , = 3.31,MI , = 4.11

I Mbol, = 4.76, L = 3.9× 1033 erg s−1,Teff , = 5780K


Abundances

[A/B] = log10

[(A/B)∗(A/B)

]


PhotometrySky emission from La Palma

A0Fλ

FBP =∫∞

0TBP,λFλdλ

≈ Fλeff

∫∞0TBP,λdλ

≡ Fλeff∆λBP

m2 −m1 = 2.5 log10

(F1

F2

)mBP = 2.5 log10

(FV ,0∆λBP

FBP

)FV ,0 ≈ 3.63× 10−9

erg s−1 cm−2 A−1

mBP = −21.1

+2.5 log10

(∆λBPFBP

)' −21.1− 2.5 log10 Fλeff

TBP(λ)


Milky Way

4 × 106 M BH

⇓

H I

Disc stellar mass: 6× 1010 MDisc luminosity: 2× 1010 LBulge stellar mass: 2× 1010 MBulge luminosity: 5× 109 L

Halo stellar mass: 1× 109 M

8.5 kpc


Gas and Dust in the Milky WayI Solar neighborhood: 1 star per 10 pc−3, 1 atom per cm3

I H II region: ionizing photons λ < 912 A, Eγ > 13.6 eVI Emission timescale typically 10−8 sI Collisional excitation A + B → A∗ + B, A∗ → A + hνI Forbidden line: collisons rare (gas density low), timescale ∼ 1 sI Fine structure transition: spin-orbit coupling in atoms, 1/1372 less

energy: far-infraredI Hyperfine transition: nuclear spin coupling with electron spin, 2000

times less energy than fine structure: mm and radioI Spin flip 21 cm radiation of H I. Takes about 11 Myr to

spontaneously transition to ground state. Collision times of orderthousands of years.

I Molecular emission from electronic, vibrational and rotationaltransitions

I CO emission (1.3 mm, 2.6 mm) is strongest after H2

I OH (1.7 GHz) and H2O (22 GHz) masingI Continuum radiation (free-free or bremstrahlung, and synchotron)

from ionized gasI Dust absorption (optical and UV) and emission (infrared)


21 cm Emission

Strength of 21 cm emission depends on collision rate. In general, rate =density × cross section × velocity. T ∼ 100 K.

mHv2H/2 = 3kT/2, ⇒ vH ' 1.6 km s−1

Cross section of a sphere with a radius equal to the Bohr radius

a0 = ~c/(αmec2) = 197.3× 137/0.511 fm = 50A

is πa20. The inverse collision rate is(

nhπa20vH

)−1= 3000

(1 cm−3

nH

)√100 K

Tyr.

An H atom in the upper level (electron and proton spins aligned)spontaneously decays with a halflife of 11 Myr. Since the energydifference corresponding to 21 cm emission is much smaller than T ,collisions drive the abundances of the two states to equilibrium. Thepopulation ratio upper/lower is 3. So the emission rate of 21 cmradiation is (3/44)nH photons per Myr, independent of T .


Dust Absorption

Dust is about 1% of the interstellar mass, primarily in the form ofsilicates and carbon with sizes rd ∼ 0.1µm. For radiation withwavelengths smaller than this size, absorption and scattering are quiteefficient, so the effective cross section is πr2

d . Long wavelength light isscattered less efficiently, κ ∝ λ−1, leading to preferential removal of bluelight and reddenning.The number density nd of dust grains is

ndmd = 0.01nHmH , nd =.01× 3nHmH

4πρd r3d

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:

dFλdx

= −κρFλ = −Fλ`, ` =

(ndπr2

d

)−1 ' 300

(rd

0.1µm

)pc

with ` the mean free path. Thus, for a path length x ' `, Fλ is decreasedby a factor e. The column density of hydrogen over a path length x is

NH = nHx = 3× 1021( nH

1 cm−3

)( x

1 kpc

)cm−2.


Galactic and Sky Coordinates

Sun-centered Galactic-centered


Other Galaxies

100 LMW, 300 kpc

10 LMW, 30 kpc

0.1 LMW


Galaxy Photometry

Surface brightness IBP(x),measured in LBP pc−2

or magBP arcsec−2.Observed area on galaxy is D2,distance to galaxy is d ,α2 = (D/d)2 is angular areaobserved on sky.

IBP(x) =FBP(x)

α2=

LBP(x)/4πd2

(D/d)2

which is independent of d!Centers of galaxies: IB ≈ 18 magarcsec−2 = 4000LB pc−2 orIR ≈ 16 mag arcsec−2.Galactic discs have IB ∼ 27 magarsec−2 ∼ 1 LB pc−2.For comparison, the backgroundbrightness of the night sky isabout IB = 22.7 mag arsec−2.

Sky emission Las Palma

Sky emissionMauna Kea


Numbers of Galaxies

Number of galaxies between luminosities L and L + dL (Schechter function):

Φ(L)dL =n∗L∗

(L

L∗

)αexp

(−L

L∗

)dL

For the bandpass BJ ,α ∼ −0.5,n∗ = 0.02h3 Mpc−3 '0.007 Mpc−3, L∗ '9× 109h−2 L ' 2× 1010 L.For α ≤ −1, total number∫∞

LΦ(L)dL→∞ for L→ 0.

The luminosity density in eachluminosity interval dL isρL(L) = Φ(L)L which peaksnear L∗. The total luminositydensity is

Φ(M)

ρM (M)

ρL =

∫ ∞0

Φ(L)LdL = n∗L∗Γ(α + 2) ' 2× 108h L Mpc−3.

For the K band, ρL ' 6× 108h L Mpc−3.J.M. Lattimer AST 346, Galaxies, Part 1

Hubble’s Law

Vr = H0d , d = h−1

(Vr

100 km s−1

)Mpc, h =

H0

100 km s−1Mpc−1

When d determined from Vr ,

L ∝ h−2, n ∝ h3, M ∝ V 2r d ∝ h−1.

Vr ' cz

Vr = H0d + Vpec

Brightest galaxies in rich clusters

dmV = 5d log10 z

d = 3h−1z Gpc


Cosmic Parameters

Hubble time

tH =1

H0= 9.78h−1 Gyr

Age of universe in the standard model (ΩΛ = 0.7,Ωm = 0.3)

tH =0.964

H0= 9.43h−1 Gyr

Critical density

ρcrit(now) =3H2

0

8πG= 1.9× 10−29h2 g cm−3 = 2.8× 1011h2 M Mpc−3


The Big Bang

I Planck epoch: t < 10−43 sGR predicts gravitational singularity before this, but quantum effectsprevent it.

I Grand unification epoch: 10−43 s < t < 10−36 sGravitation separates from the fundamental gauge interactions

I Inflationary epoch: 10−36 s < t < 10−32 sUniverse flattened by homogenous, isotropic rapid expansion,triggered by separation of strong force from electroweak forces,resulting in a primordial spectrum of nearly scale-invariantfluctuations. Potential energy of the inflation field decays into a hot,relativistic plasma.

I Electroweak epoch: 10−36 s < t < 10−12 sProduction of W and Z bosons and Higgs bosons.

I BaryogenesisUniverse becomes asymmetric with respect to baryons andanti-baryons. Why?


The Big Bang

I Quark epoch: 10−12 s < t < 10−6 sFundamental particles acquire mass (Higgs mechanism), quarks toohot to bind into hadrons

I Hadron epoch: 10−6 s < t < 1 sQuark-gluon plasma cools and hadrons form, neutrinos decouple.

I Lepton epoch: 1 s< t < 10 sMajority of hadrons and anti-hadrons annihilate, leaving leptons andanti-leptons to dominate mass, which themselves finally annihilate.Small residues of hadrons and leptons survive.

I Photon epoch: 10 s< t < 0.38 MyrUniverse energy dominated by photons

I Nucleosynthesis: 3 m< t <20 mProtons and neutrons fuse, neutrons decay, forming D and He, Li,and Be isotopes.


Nucleosynthesis

Neutrons are more massive than protons by1.293 MeV, resulting in a proton excess:

n/p = e−(1.293 MeV/kT ).

Neutrinos decouple at t = 1 s, T = 0.8MeV. 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 inHe nuclei. Therefore n/p = 1/7 andHe/H=1/12. By mass, Y /X = 1/3.Y is insensitive to nB , but D/H is verysensitive. D forms easily, but He requiresweak interactions. If nB is relatively small,D/H becomes large. If nB is relativelylarge, D/H becomes small. Thus, D/H is asensitive measure of ΩB .

Abundances of other light nucleilike 3He, 6Li and 7 Li can also beused to estimate nB . Theestimates of all but 7Li convergeon 0.02 < ΩBh2 < 0.025.


The Big BangI Matter domination: t < 0.07 Myr

Jeans length falls below fluctuationmasses and smallest structuresform. Cold dark matter dominates(but when did that form?).

I Recombination: t = 0.38 MyrProtons and electrons form neutralH, opacity decreases, photonsdecouple and form the CMB. Nowredshifted by factor 1 + z ≈ 1100to 2.73 K.

I Dark ages: 150 Myr < t < 500 MyrOnly emitted radiation is 21 cm.

I Structure formation, reionization:500 Myr< t < 1 GyrQuasars and Pop III stars (not yetobserved) form and re-ionizesurroundings. Sub-galactic objectwith z = 10.2, t = 480 Myr,observed Jan 2011. Star-forminggalaxies observed at t = 500 Myr.


The CMB fluctuations

The small fluctuations in the CMB remaining after subtraction of theDoppler effect are acoustic oscillations due to a competition between thegravitational attraction of the baryons and the smoothing of photons.The angular scale of the first peak depends on the curvature of theuniverse. The next peak depends on nB . The third peak depends on thedark 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


The CMB and the Sun

The radiation from the CMB is farlarger than that from the extragalacticbackground at IR, optical, UV, X-rayand γ-ray energies.

The CMB is uniform to within 1 part in105 with the exception (besides theannual motion of the Earth about theSun) of a dipole anisotropy in thedirection ` = 265, b = 48, with anamplitude of 0.1% (hottest in thatdirection). The higher temperaturerepresents a Doppler blue shift

T (θ) = TCMB

(1 +

V

ccos θ

).

This gives V = 370 km s−1. Aftercorrection for the solar motion in theGalaxy and the Milky Way’s motionrelative to nearby galaxies, one hasVpec ≈ 600 km s−3. The origin of thislarge motion is not understood.


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