Large scale structure in the SDSS

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Large scale structure in the SDSS

• The ISW effect
• The Ly-alpha forest
• Galaxies and Clusters
• Marked correlations Theres more to the points
• Ravi K. Sheth (UPitt/UPenn)

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The ISW effect
Cross-correlate CMB and galaxy distributions Inte
rpretation requires understanding of galaxy
population
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Expected scaling of signal
Expect NO signal in Einstein de-Sitter! Recent
(2003) detections in X-ray and radio-selected
catalogs
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Cross-correlate LRGs with CMB
Measured signal combination of ISW and SZ
effects Estimate both using halo model
(although signal dominated by linear theory)
Signal predicted to depend on b(a) D(a) d/dt
D(a)/a
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Evolution and bias
Work in progress to disentangle evolution of
bias from z dependence of signal (Scranton
et al. 2004)
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Spherical harmonic analysis similar (Padmanabhan
et al 2004)
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The Ly-a forest

• Evolution measured over 2.2ltzlt4.2
• Consistent with WMAP LCDM cosmology (hi-z
  universe EdS)
• Series of papers by McDonald, Seljak et al.
  (2004)
• (Alternative analysis by Hui et al. 200?)

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Galaxy Surveys
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Spatial Clustering

• Large scale measurements can detect baryon
  wiggles/bump
• LRG clustering
• QSO clustering
• Smaller scale measurements constrain galaxy
  formation models

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(Cole et al. 2000)
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Kauffmann, Diaferio, Colberg White
1999 Also Cole et al., Benson et al.,
Somerville Primack, Colin et al.
Colors indicate age
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Halo-model of galaxy clustering

• Two types of pairs only difference from dark
  matter is that now, number of pairs in m-halo is
  not m2
• ?dm(r) ?1h(r) ?2h(r)
• Spatial distribution within halos is small-scale
  detail

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Comparison with simulations
Sheth et al. 2001
steeper

• Halo model calculation of x(r)
• Red galaxies
• Dark matter
• Blue galaxies
• Note inflection at scale of transition from
  1-halo term to 2-halo term
• Bias constant at large r

shallower
?x1hx2h
x1hx2h ?
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Galaxy clustering depends on type
Large samples now available to quantify this
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Power-law x(r) (r0/r)g slope g
-1.8
Totsuji Kihara 1969
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Not a power law
Feature on few Mpc scale expected as transition
from 1halo to 2halo term (Zehavi et al. 2004)
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N-body simulations of gravitational clustering
in an expanding universe Lots of substructure!
(Model by Lee 2004)
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Galaxies and halo substructure

• Better to think in terms of center satellite
• g1(m) 1 m/23m1(L)a(L) for mgtm1(L)
• Higher order moments from assumption that
  satellite distribution is Poisson
• Poisson model consistent with assumption that
  halo substructure galaxies

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Linear bias on large scales
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Color dependence and cross-correlations
consistent with simplest halo model
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fingers of god
Redshift space trends qualitatively consistent
with v2 m2/3 scalingquantitative agreement
also?
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Galaxy formation models correctly identify the
halos in which galaxies form Galaxy halo
substructure is reasonable model
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Extensions

• Poisson model implies a complete model of point
  distribution
• Can now make mock catalogs that have correct LF
  and 2pt function---check using n-pt,
  Minkowskis,
• Assume monotonic relation between subclump mass
  and galaxy luminosity to get L-s relations
• Include correlations between L, size, color, etc.
• Relate galaxy distribution to cluster
  distribution (what is better tracer of mass L?
  Ngal? S?)
• Model of BCGs (e.g. use C4 catalog)

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The galaxy correlation function

• ?dm(r) ?1h(r) ?2h(r)
  
• ?1h(r) ?dm n(m) g2(m) ?dm(mr)/r2
• n(m) number density of halos
• g2(m) total number of galaxy pairs
• ?dm(mr) fraction of pairs which have separation
  r depends on density profile within m-halos
• Need not know spatial distribution of halos!
• This term only matters on scales smaller than the
  virial radius of a typical M halo ( Mpc)
• ?2h(r) larger scales, depends on halo clustering

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Successes and Failures

• Distribution of sizes Lognormal seen in SDSS
• Morphology-density relation (oldest stars in
  clusters/youngest in field)
• Type-dependent clustering red galaxies have
  steep correlation function clustering strength
  increases with luminosity
• Distribution of luminosities
• Correlations between observables
  (luminosity/color, luminosity/velocity dispersion)

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Sizes of disks and bulges
Observed distribution Lognormal Distribution
of halo spins Lognormal Distribution of halo
concentrations Lognormal (Bernardi et al.
2003 Kauffmann et al. 2003 Shen et al. 2003)
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Environmental effects

• Fundamental assumption all
  environmental trends come from fact that massive
  halos populate densest regions

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Halo clustering
massive halos

• Massive halos more strongly clustered
• Clustering of halos different from clustering of
  mass

non-
linear theory
dark matter
Percival et al. 2003
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Halo clustering ? Halo abundances

• Clustering is ideal (only?) mass calibrator
  (Sheth Tormen 1999)

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Color and Luminosity
Hogg et al. 2004
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Density and Lumi-nosity
Hogg et al. 2004
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Marked correlation functions
Weight galaxies by some observable (e.g.
luminosity, color, SFR) when computing clustering
statistics (standard analysis weights by zero or
one)
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Theres more to the point(s)

• Multi-band photometry becoming the norm
• CCDs provide accurate photometry possible to
  exploit more than just spatial information
• How to estimate clustering of observables, over
  and above correlations which are due to spatial
  clustering?
• Do galaxy properties depend on environment?
  Standard model says only dependence comes from
  parent halos

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Early-type galaxies

• Models suggest cluster galaxies older, redder,
  more massive
• Weak, if any, trends seen

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Age and environment
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Marked correlations
(in volume-limited catalogs) Close pairs are
redder, and have larger D4000, suggesting they
are older, even though no strong trend seen with
s Environment matters!
hi-z
low-z
D4000
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Marked correlations
(usual correlation function analysis sets m 1
for all galaxies)
W(r) is a weighted correlation function, so
marked correlations are related to weighted ?(r)
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Luminosity as a mark

• Mr from SDSS
• BIK from semi-analytic
• model
• Little B-band light
• associated with
• close pairs more B-band
• light in field than clusters
• Vice-versa in K
• Feature at 3/h Mpc in all
• bands Same physical
• process the cause?
• e.g. galaxies form in groups
• at the outskirts of clusters

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Colors and star formation

• Close pairs tend to be redder
• Scale on which feature
• appears smaller at higher z
• clusters smaller at high-z?
• Amplitude drops at lower z
• close red pairs merged?
• Close pairs have small
• star formation rates scale
• similar to that for color even
• though curves show
• opposite trends!
• Same physics drives both
• color and SFR?

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Stellar mass

• Circles show M, crosses show LK
• Similar bumps, wiggles in both offset related to
  rms M, L
• Evolution with time M grows more rapidly in
  dense regions

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Halo-model of marked correlations
Again, write in terms of two components W1gal(r)
?dm n(m) g2(m) Wm2 ?dm(mr)/rgal2 W2gal(r)
?dm n(m) g1(m) Wm b(m)/rgal2 ?dm(r) So,
on large scales, expect
1W(r) 1?(r)
1 BW ?dm(r) 1 bgal ?dm(r)
M(r)

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Most massive halos populate densest regions
over-dense
under-dense
Key to understand galaxy biasing (Mo White
1996 Sheth Tormen 2002)
n(md) 1 b(m)d n(m)
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Conclusions (mark these words!)

• Marked correlations represent efficient use of
  information in new high-quality multi-band
  datasets (theres more to the points)
• No ad hoc division into cluster/field,
  bright/faint, etc.
• Comparison of SDSS/SAMs ongoing
• test Ngalaxies(m)
• then test if rank ordering OK
• finally test actual values
• Halo-model is natural language to interpret/model

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Halo-model calculations

• Type-dependent (n-pt) clustering
• ISW and tracer population
• SZ effect and halo shapes/motions
• Weak gravitational lensing
• Absorption line systems
• Marked correlations

Review in Cooray Sheth 2002

Work in progress
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