Cosmic evolution of galaxy clustering

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Cosmic evolution of galaxy clustering
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Large scale structureobservations and N-body
simulationsStatistical description of the
matter/galaxy distributionthe two-point
correlation functionGalaxy clustering
dependencies on color, luminosityGalaxy
clustering measurements from low to high
redshiftsClustering evolution and bias, some
(little) theoryHow to guess progenitors and
descendants of a galaxypopulation observed at a
given redshift.
Main topics / outline
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Galaxy distribution in the local Universe
From the Sloan Digital Sky Survey (SDSS) 7000
deg2 800000 redshifts
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Galaxy distribution in the local Universe
From Colless et al. (2001) 1500 deg2, 250000
redshifts
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N-body simulations(dark matter)
Millennium simulation (Springel et al.
2005) 1010 dark matter particles of 8.6 x 108
Msun each 5003 Mpc3/h3 volume resolution 5/h kpc
12.6 billion yr ago z5.7
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N-body simulations(dark matter)
9.0 billion yr ago z1.4
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N-body simulations(dark matter)
Now z0.0
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A few questions
Do galaxies trace the dark matter
distribution? Or are they biased tracers? Do
different galaxy types cluster the same way?
What do we expect? How do galaxy clustering
evolve? Can we use clustering evolution to
estimate descendant and progenitors of a given
population?
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Statistical description of galaxy distribution

• Gravity make the distribution of matter/galaxies
• everything but random.
• Search for a statistical description of the dark
  matter / galaxy distribution
• Foundation and formalism in the 1970s,
• Main references Peebles 1980
• The two-point correlation function

w(?) excess probability over random of finding
one galaxy within the solid angle dO1 and
another galaxy within dO2 separated by an angle ?
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Random distribution
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Highly clustered distribution
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Regular distribution (grid)
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Correlation function estimators
Counting galaxy pairs at a given separation and
compare with the expectations from a random
distribution ?(r) DD/RR - 1 ?(r) DD/DR -
1 ?(r) (DD - 2DR RR) / RR Landy Szalay
(1993) ?(r) (DD RR ) / (DR)2 - 1
Hamilton (1993)
DD normalized number of data-data pairs within
r and rdr DR normalized number of data-random
pairs within r and rdr RR normalized number of
random-random pairs within r and rdr
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Angular correlation function of local galaxies
d 0.7-0.8
Power law
Cut off
4000 deg2, 2 x 106 objects
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Spatial correlation function
?(r) excess probability over random of finding a
source in dV1 and another in dV2 separated by a
distance r
Two ways of measuring ?(r) 1) If redshifts are
available, measure separation in redshift
space 2) If redshifts are not available use
w(?) Limbers equation (Limber 1958) w(?) f
N(z), ?(r,z)
d comoving distance
observer
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Example of correlation function in redshift space
s06.8 Mpc/h ?1.6
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Distortions in redshift space
Coherent infall
?(s) ? ?(rp,rv)
?(rp,rv)
Unbiased pattern
rp (d1d2)tan(?/2) separation along the line
of sight rv d1-d2 transverse separation
rv (Mpc/h)
Peculiar velocities
rp (Mpc/h)
Observed pattern
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The projected correlation function
Projected correlation function w(rp) integral
of ?(rp,rv) along the line of sight
Allows to get rid of distortions in redshift
space (i.e. peculiar velocities, redshift errors)
w(rp) is the most common statistics used to
measure the spatial clustering of galaxies
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Galaxy clustering the local Universe (z0.1)
SDSS galaxies
2dFGRS
Hawkins et al. 2003
Zehavi et al. 2005
w(rp)/rp
rp Mpc/h
Redshift space s06.8 Mpc/h ?1.6
Real space r05.0 Mpc/h ?1.7
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Galaxy bimodal distribution
luminous/massive objects are red/ellipticals/old
Mass function and luminosity function by color
types red galaxies dominate the
luminouse/massive part (Baldry et al. 04, Bell
et al. 03)
SDSS, Baldry et al. 2004
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Clustering vs galaxy color
Red galaxies cluster more strongly larger r0
and steeper slope
Red r06 Mpc/h ?2.0 Blue r0 4 Mpc/h ?1.5
SDSS, (Zehavi et al. 2005)
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Clustering vs galaxy luminosity
Brighter galaxies cluster more strongly
From SDSS (Zehavi et al. 2005)
Giant ellipticals, L L r0 8-10 Mpc/h
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Clustering of galaxy clusters (z0)
Galaxy clusters are strongly clustered
r0 13 Mpc/h
Croft et al. (1997)
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Surveys of galaxies at z1
VVDS VIMOS-VLT, purely magnitude selected, 5
fields DEEP 17.517.5600 arcmin² 9600 redshifts
DEEP2 DEIMOS-Keck 1.5deg2, 19000 0.4color selected gals, 4583 with zspec RCOSMOS Multiwavelenght coverage of 2 deg2, in
progress
Ideally one would need several deg2 of sky to
beat cosmic variance
Peebles (1980)
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z1 clustering dependence on luminosity
Even at z1 brighter galaxies cluster more
strongly
VVDS (Pollo et al. 2006)
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z1 clustering dependence on color
Even at z redder galaxies cluster more strongly
Red r05.3 Mpc/h ?2.1 Blue r0 3.9
Mpc/h ?1.6
DEEP2 (Coil et al. 2007)
BUT mid-IR selected sources at z1 (large SFR)
cluster as strongly as passive z1 galaxies,
consistent with the SFR vs Mass results at
z1 (downsizing)
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The most clustered galaxies at z1
Extemely Red Objects (EROs, R-K5) at z1. About
80 of brigth (Kellipticals, 20 are dusty starforming galaxies
Brown et al. 2005
Daddi et al. 2000
EROs at z1 are strongly clustered r010 Mpc/h
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Galaxy clustering at high z
z3
U-dropout technique to select objects at z3
B-,V-,R-, dropout techniques to select objects
at higher z
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Galaxy clustering high z
Steidel et al. 03
Observed distribution Expected distribution if
z3 galaxies were arranged randomly in space.
Very distant galaxies are strongly
clustered. Red (J-K1.7) distant galaxies (Daddi
et al. 2003) cluster even stronger than LBGs.
Adelberger et al. 05
Star forming galaxies at z2-3 r04-4.5 Mpc/h
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Galaxy clustering r0 vs z
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Clustering evolution
How do we relate galaxy populations at different
z? That is, what are the progenitors and
descendants of a given galaxy population? Need
to know 1) How galaxies are related to dark
matter. In other words, how well the galaxy
distribution trace the dark matter distribution.
Are galaxies biased tracers of the mass? 2)
How dark matter clustering evolves with z 3) In
which DM halos galaxies reside?
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Dark matter clustering
From Moustakas Somerville (2004) Based on
GIF/VIRGO N-body simulations by Jenkins et al.
(1998)
At z3 r01 Mpc/h, ?1.2 At z0 r05 Mpc/h,
?1.7
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Galaxy bias b
Galaxy corr. function dark matter corr.
function
Example z3 Dark matter r01 Mpc/h,
?1.2 LBG galaxies r04 Mpc/h, ?1.5
LBGs at z3 are much more clustered than the dark
matter ? biased tracers of DM distribution
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Biased galaxy formation
From Djorgovski 2003
The LBGs strong clustering represents strong
support for the idea that galaxies form at the
highest peaks in the distribution of matter
these high peaks are themselves expected to be
strongly correlated in space.
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Bias of the different galaxy populations
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Conserving model
Hypothesis galaxies form within collapsed DM
structures at a given epoch and then evolve
without merging, simply following the surrounding
density field. The bias evolution in this
scenario (conserving model, Fry 1996, Moscardini
1998) has the form
D(z) growth factor of perturbations ? known
from N-body simulations and approximated
analytically (for reference D(z) 1/(1z) in
Einstein-de Sitter)
What is the corresponding evolution in r0?
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Conserving model
Warning. bias evolution depends on ?,s8,etc..
Also, conserving scenario is a simplistic model.
See e.g. Moscardini et al. 1998 for other
possible scenarios which include merging
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Conserving model
LBGs at z5 may evolve into z0 gEs EROs, RGs
at z1 may indicate the site of protoclusters
Warning. r0 evolution depends on ?,s8,etc.. Also,
conserving scenario is a simplistic model. See
e.g. Moscardini et al. 1998 for other possible
scenarios which include merging
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Estimate host dark matter halos
In a simulation halos are defined as regions
above a given density contrast (e.g.
d?/?200) At any given redshift, r0 increases
with halo mass For any given halo mass, r0
increases with redshift

GIF simulation (Kauffman et al. 1999, Frenk et
al. 2000)
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Dark matter halos
LBGs at z2-3 logM 12 EROs at z 1 logM
13 Clusters logM14
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AGN clustering
AGN can trace the Large Scale Structure of the
Universe to cosmologically significant redshifts
(z2) AGN physics from clustering - host halo
mass - host galaxy type - AGN lifetimes
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AGN clustering
Bright QSOs in the 2dFGRS (2QZ)
Croom et al. (2005)
Croom 05
Increase with z? Likely, but also degeneracy with
MB see also Porciani et al. (2005)
s05.5 Mpc/h
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AGN Correlation length vs redshift(and
luminosity)
Bright QSOs in early type gals and faint AGN in
late type gals? maybe, but see other results.
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From minimum halo mass to AGN lifetime
QSOs density above a given luminosity (hypothesis
LQSO Mhalo) measured
Halo density known from N-body, CDM models
Mmin known from r0 comparison
Once an estimate for the halo lifetime tH is made
(e.g. tH tu Hubble time at that z), the QSO
lifetime tQ is obtained
For X-ray AGN at z2 tQ3-10 107 yr For Optical
AGN (2QZ) at z2 tQ108 yr
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Summary
Clustering analysis, statistics of galaxy
distribution two-point correlation
function Red,massive galaxies cluster more
strongly than blue less massive galaxies from z0
to z1 Eros, RGs are the most clustered
population at z1 Likely evolve into galaxy
clusters High-z galaxies (e.g. LBGs) are
strongly biased tracers of DM distribution. They
form in the highest density peaks, in the
first collapsed structures. With clustering one
can estimate host and lifetime of AGN (e.g.
bright QSOs in early type and faint AGN in late
type galaxies?)