Astr 323: Extragalactic Astronomy andCosmology

Spring Quarter 2012, University of Washington, Zeljko Ivezic

Lecture 6:Galaxy luminosity function,

galaxy formation, and interactions

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SDSS Spectroscopic Galaxy Survey

• Two samples:

1. imaging data for > 100 million galaxies

2. the “main” galaxy sample (r < 18): ∼1 million spectra

3. luminous red galaxy sample (LRG, cut in color-magnitude

space): ∼100,000 spectra

• Spectra are correlated with morphology (and colors)

• Distance estimate allows the determination of luminosity func-

tion (Blanton et al. 2001)

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SDSS sources in color-magnitude diagram

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Luminosity Function

• Basic concepts

• Methods for estimating LF from data

• Application to SDSS galaxies

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Luminosity Function• Luminosity Function is the

distribution in the luminosity–

position plane; how many

galaxies per unit interval in lu-

minosity and unit volume (or

redshift): Ψ(M, z)

• Imagine a tiny area with the

widths ∆Mr and ∆z centered

at some Mr and z in the plot

to the left: count the number

of galaxies, divide by ∆Mr∆z,

and correct for the fraction of

sky covered by your survey:

this gives you Ψ(M, z).

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Luminosity Function

• Luminosity Function is the distribution in the luminosity–

position plane; how many galaxies per unit interval in lumi-

nosity and unit volume: Ψ(M, z)

• Often, this is a separable function: Ψ(M, z) = Φ(M)n(z),

where Φ(M) is the absolute magnitude (i.e. luminosity) dis-

tribution, and n(z) is the number volume density.

• Luminosity is a product of flux and distance squared (ignore

cosmological effects for simplicity): L = 4πD2F

• The samples are usually flux-limited (meaning: all sources

brighter than some flux limit are detected) – the minimum

detectable luminosity depends on distance: L > 4πD2Fmin,

or for absolute magnitude M < Mmax(D) (c.f. the first plot)

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Schechter Function

Galaxy luminosity distribution resembles a power-law, with an ex-

ponential cutoff. This distribution is usually modeled by Schechter

function:

Φ(L) = Φ∗(L

L∗

)αe−L/L∗ (1)

Or using absolute magnitudes:

Φ(Mr) = 0.4Φ∗ e−0.4(α+1)(Mr−M∗) e−e−0.4(Mr−M∗)(2)

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Note: this LF cannot be

expressed as Φ(M, z) = f(M) g(z)

– not separable!

The LF in the SDSS r band• The thick solid line is the

SDSS r band luminosity func-

tion, and the gray band is its

uncertainty.

• The dashed line is a

Schechter-like fit that

also includes the effects of

changing luminosity and the

number density with time

(i.e. distance, or redshift).

Q > 0 indicates that galaxies

were more luminous in the

past, and P > 0 that galaxies

were more numerous in the

past. For detailed discussion,

see Blanton et al. 2003

(Astronomical Journal, 592,

819-838)

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ALL

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SF

The dependence of LF on galaxytype

• The top panel shows the distribution of

SDSS galaxies in the absolute magni-

tude – color plane (in a narrow redshift

range)

• In the bottom three panels, the same

distribution is compared to the dis-

tributions for subsamples selected by

their emission line properties

• Note that the most luminous galax-

ies (Mr < −20) are predominantly red

(P1 > 0.2), while faint galaxies (Mr >

−19) are blue (P1 < 0.2)

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The dependence of LF on galaxytype

• The comparison of LFs for blue and

red galaxies (from Baldry et al. 2004,

ApJ, 600, 681-694)

• The red distribution has a more lumi-

nous characteristic magnitude and a

shallower faint-end slope, compared to

the blue distribution

• The transition between the two types

corresponds to stellar mass of ∼ 3 ×1010 M�• The differences between the two LFs

are consistent with the red distribution

being formed from major galaxy merg-

ers.

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1. Galaxy Formation

• The Monolithic Collapse Model (top-down)

• The Merger Model (bottom-up)

2. Galaxy Interactions

• Fast Encounters

• Slow Encounters

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Kinematics• Stars move in a gravitational poten-

tial

• Two types of motion: disk stars ro-

tate around the center, while halo

stars are on randomly distributed el-

liptical orbits

• The motion of stars was set during

the formation period

• The details are governed by the laws

of physics: conservation of energy

and conservation of angular mo-

mentum!

• As the cloud collapses, its rotation

speed must increase. As it spins

faster, it must flatten.

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Galaxy Formation

The ELS Monolithic Collapse Model

• The ELS model (Eggen, Lynden-Bell and Sandage, 1962):

the Milky Way formed from the rapid collapse of a large

proto-galactic nebula: top-down approach

– the oldest halo stars formed early, while still on nearly

radial trajectories and with low metalicity

– then disk formed because of angular momentum conserva-

tion, and disk stars are thus younger and more metal-rich

– first thick disk (∼ 1 kpc scale height) was formed, and

then thin disk (∼ 300 pc scale height)

– the ongoing star formation is confined to a scale height

of ∼50 pc, at a rate of a few M� per year

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Galaxy Formation

The ELS Monolithic Collapse Model

How fast did the Galaxy form?

The free-fall time is

tff =

√3π

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1

Gρo, (3)

where ρo is the mean density:

ρo =3M

4πr3. (4)

For M = 6×1011 M� and r = 100 kpc, tff = 7×108 yr ∼ 1 Gyr

(upper limit, centrally peaked clouds collapse somewhat faster)

NB the lifetime of most massive stars is ∼ 1 Myr: many stellar

generations lead to chemical enrichment

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Problems with the monolythic collapse scenario:

• Why are half the halo stars in retrograde orbits? We wouldexpect that most stars would be moving in roughly the samedirection (on highly elliptical orbits) because of the initialrotation of the proto-Galactic cloud.

• Why there is an age spread of ∼ 3 Gyr among globular clus-ters (GCs)? We would expect < 1 Gyr spread (free-fall time).

Some important questions that are left without robust answers:

• Why GCs become more metal-poor with the distance fromthe center?

• Detailed calculations of chemical enrichment predict about10 times too many metal-poor stars in the solar neighbor-hood (the G-dwarf problem), why?

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An alternative model for galaxy formation

• A bottom-up scenario: galaxies are built up from merging

smaller fragments (similar but not the same as hypothesis

that giant ellipticals formed from merging spiral galaxies)

• by observing galaxies at large redshifts (beyond 1), we are

probing the epoch of galaxy formation – indeed, galaxies

at large redshifts have very different morphologies, and the

fraction of spirals in clusters is greater than today (Butcher-

Oemler effect). Also, the volume density of galaxies was

larger in the past: consistent with the merger hypothesis

• We have some important evidence for galaxy merging in our

own backyard:

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Evidence for Galaxy’s cannibalistic nature

• The spatial distribution of halo stars is clumpy

• Tidal streams in the halo (e.g. Sgr dwarf tidal stream, the

Monoceros stream)

• Large scale stellar counts overdensities that are inconsistent

with standard thin/thick disk & power-law halo model

• Deviations from the expected velocity distribution (expect

3D Gaussian distribution, aka the Schwarzschild ellipsoid)

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Galaxy Interactions: basic considerations

It is much more likely for two galaxies to interact/collide than

for two stars becomes typical distance between two galaxies (say

∼ 1 Mpc) is only about 10-100 times larger than the size of a

typical galaxy. For stars, typical distance (say 1 pc) is about 108

times larger than typical stellar size!

E.g. Andromeda is coming overhere at 100 km/s – expect fire-

works 6 Gyr from now!

Fraction of the Milky Way’s disk that is covered by stars: 10−14!

Even if another galaxy, such as Andromeda with 1011–1012 stars,

would score a direct hit, the probability of a direct stellar collision

is still negligible.

The main effect of a galaxy collision is on interstellar gas, which

is shocked and heated. The compressed gas cools off rapidly and

fragments into new stars. A collision usually triggers a burst of

star formation!20

Collisions, Encounters, Tidal tails: basic physics

• Two regimes for galaxy encounters: fast, v∞ > vf (elasticbehavior, galaxies affect each other but do not merge, e.g.tidal tails) and slow v∞ < vf (inelastic behavior – galaxiesmerge), where v∞ is the relative velocity, and vf is somecritical velocity that depends on detailed structure of inter-acting galaxies (≈ a few hundred km/s)

• In the fastest encounters (v∞ >> vf), stars do not signifi-cantly change their positions – impulse approximation

• During the not-so-fast encounters, the orbital (kinetic) en-ergy can be transferred to the internal energy (galaxies arenot point masses – better described as viscous fluid thatabsorbs energy when deformed)

Let’s first see some N-body model results and then chat a bitmore about underlying physics:

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Model from Toomre, A. & Toomre, J. 1972, Galactic Bridgesand Tails, ApJ, 178, 623

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Another example: Antennae Galaxy

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Fast Galaxy Encounters

• Impulse approximation: the potential energy doesn’t changeduring the encounter, but the internal kinetic energy changesby, say, ∆K. This change of the kinetic (and total) energytakes the system out of virial equilibrium! What is the finalequilibrium state? (before the encounter: E = Eo and K =Ko, with Eo = −Ko)

• After the encounter, and before returning to the equilibrium:K1 = Ko + ∆K (= −Eo + ∆K) and E1 = Eo + ∆K (notethat it is NOT true that E1 = −K1).

• After returning to the equilibrium: E2 = E1, and it mustbe true that K2 = −E2 because of virial theorem. Hence,K2 = −E1 = −Eo −∆K = K1 − 2∆K! During the returnto virial equilibrium, the system loses 2∆K of kinetic en-ergy (which becomes potential energy because energy is con-served). Therefore, the (self-gravitating) system expands!

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Slow Galaxy Encounters

• Need N-body numerical simulations for the full treatment

• In a special case when galaxies are very different in size,

analytic treatment is possible to some extent

• Dynamical friction: a compact body of mass M (small galaxy)

passes through a population of stars with mass m (large

galaxy). The net effect is a steady deceleration parallel to the

velocity vector (just like ordinary friction). For small speed of

the impactor (compared to the internal velocity dispersion),

the deceleration is proportional to speed, for large speeds

to the inverse squared speed (c.f. Chandrasekhar dynamical

friction formula).

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