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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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14 stars
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14 galaxies
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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
0.028 < redshift < 0.032
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NOEML
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AGN
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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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