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Zheng Zheng
I NSTITUTE
for ADVANCED STUDY
Cosmology and Structure Formation
KIAS
Sep. 21, 2006
Collaborators:
David Weinberg (Ohio State)
Andreas Berlind (NYU)
Josh Frieman (Chicago)
Idit Zehavi
(Case Western)
Jeremy Tinker (Chicago)
Jaiyul Yoo
(Ohio State)
Kev Abazajian (LANL)
Alison Coil
(Arizona)
SDSS collaboration
Light traces mass?
Snapshot @ z~1100
Light-Mass relation well understood
CMB from WMAP
Snapshot @ z~0
Light-Mass relation not well understood
Galaxies from SDSS
Cosmological Model
initial conditions
energy & matter contents
Galaxy Formation Physics
gas dynamics, cooling
star formation, feedback
m 8 ns 
Dark Halo Population
n(M)
(r|M)
v(r|M)
Weinberg 2002
Halo Occupation Distribution
P(N|M)
spatial bias within halos
velocity bias within halos
Galaxy Clustering
Galaxy-Mass Correlations
Halo Occupation Distribution (HOD)
• P(N|M)
Probability distribution of finding N galaxies in a halo of virial mass M
mean occupation <N(M)> + higher moments
• Spatial bias within halos
Difference in the distribution profiles of dark matter and galaxies within halos
• Velocity bias within halos
Difference in the velocities of dark matter and galaxies within halos
e.g., Jing & Borner 1998; Seljak 2000; Scoccimarro et al. 2001; Berlind &
Weinberg 2002; Yang, Mo, & van den Bosch 2003; …
Galaxies from SDSS
P(N|M) from galaxy formation model
For galaxies above a certain threshold
in luminosity/baryon mass
Mean:
Low mass cutoff
Plateau
High mass power law
Scatter:
Sub-Poisson (low mass)
Poisson (high mass)
Berlind et al. 2003
P(N|M) from galaxy formation model
It is useful to separate central and satellite galaxies
Central galaxies:
Step-like function
Satellite galaxies
Mean following a powerlaw-like function
Scatter following Poisson distribution
Kravtsov et al. 2004, Zheng et al. 2005
Probing Galaxy Formation:
--- Galaxy Bias (HOD) from Galaxy Clustering Data
HOD modeling of two-point correlation functions
• Departure from a power law
• Luminosity dependence
• Color dependence
• Evolution
Two-point correlation function of galaxies
Excess probability w.r.t. random distribution of finding galaxy pairs at a given separation
1-halo term
Galaxies of each pair from the same halo
2-halo term
Galaxies of each pair from different halos
Two-point correlation function:
Departures from a power law
SDSS measurements
Zehavi et al. 2004
Two-point correlation function:
Departures from a power law
The inflection around 2 Mpc/h can be naturally
explained within the framework of the HOD:
It marks the transition from a large scale
regime dominated by galaxy pairs in
separate dark matter halos (2-halo term)
to a small scale regime dominated by
galaxy pairs in same dark matter halos
(1-halo term).
2-halo term
1-halo term
Dark matter
correlation function
Divided by the
best-fit power law
Zehavi et al. 2004
Two-point correlation function:
Departures from a power law
Fit the data by assuming an
r-1.8 real space correlation
function
 r0 ~ 8Mpc/h
 host halo mass > 1013 Msun/h
HDF-South
Strong clustering of a population
of red galaxies at z~3
+ galaxy number density
 ~100 galaxies in each halo
Daddi et al. 2003
Two-point correlation function:
Departures from a power law
Less surprising models from HOD modeling
Signals are dominated by 1-halo term
M > Mmin ~ 6×1011Msun/h
(not so massive)
<N(M)>=1.4(M/Mmin)0.45
Predicted r0 ~ 5Mpc/h
Ouchi et al 2005
HOD modeling of the clustering
of z~3 red galaxies
Zheng 2004
Hogg & Blanton
Luminosity dependence of galaxy clustering
Zehavi et al. 2005
Luminosity dependence of galaxy clustering
The HOD and its luminosity
dependence inferred from
fitting SDSS galaxy
correlation functions have a
general agreement with galaxy
formation model predictions
Luminosity dependence of the HOD
predicted by galaxy formation models
Berlind et al. 2003
Luminosity dependence of galaxy clustering
Zehavi et al. 2005
Zheng et al. 2005
inferred from observation
prediction of theory
HOD parameters vs galaxy luminosity
Hogg & Blanton
Color dependence of galaxy clustering
Zehavi et al. 2005
Color dependence of galaxy clustering
Zehavi et al. 2005
Berlind et al. 2003, Zheng et al. 2005
Inferred from SDSS data
Predicted by galaxy formation model
Studying galaxy evolution
z~1
z~1
Star
Merging Formation
Merging
z~0
z~0
Establishing an evolution link
between DEEP2 and SDSS galaxies
Tentative results:
For central galaxies in z~0 M<1012 h-1Msun
halos, ~80% of their stars form after z~1
For central galaxies in z~0 M>1012 h-1Msun
halos, ~20% of their stars form after z~1
Zheng, Coil & Zehavi 2006
Probing Cosmology:
--- Constraints from Galaxy Clustering Data
Tegmark et al. 2004
Why useful ?
• Consistency check
• Better constraints on cosmological parameters (e.g., 8, m)
• Tensor fluctuation and evolution of dark energy
• Non-Gaussianity
Mass-to-Light ratio of large scale structure
At a given cosmology (σ8)
Mr<-21.5
Mr<-20
Modeling w_p as a function of luminosity
How light occupies halos Φ(L|M) (CLF)
Populating N-body simulation according to Φ(L|M)
Mass-to-light ratio in different environments
Comparison with observation
Tinker et al 2005
Mass-to-Light ratio of large scale structure
σ8=0.95
σ8=0.9
σ8=0.8
σ8=0.7
σ8=0.6
CNOC data
M<-18
M<-20
Tinker et al 2005
Galaxy cluster <M/L>=universal value only for unbiased galaxies (σ8g~ σ8)
Comparison with CNOC data indicates (σ8/0.9)(Ωm/0.3)0.6=0.75+/-0.06
Modeling redshift-space distortion
For each (m, 8), choose HOD to
match wp(rp)
Large scale
distortions degenerate along
axis   8 m0.6, as predicted
by linear theory
Small scale
distortions have different
dependence on m, 8, v
Tinker et al 2006
Recovering the linear power spectrum
Galaxy bias is linear at k < 0.1~0.2 hMpc-1
and becomes scale-dependent at smaller
scales. Power spectrum becomes nonlinear
at similar scales
HOD modeling helps to recover the linear
power spectrum for k>0.2hMpc-1 and extend
the leverage for constraining cosmology.
Yoo et al 2006
Breaking the degeneracy between bias and cosmology
Cosmology
A
HOD
A
Halo Population
A
Galaxy Clustering
Galaxy-Mass Correlations
A



=
Cosmology
B
Halo Population
B
HOD
B
Galaxy Clustering
Galaxy-Mass Correlations
B
Breaking the degeneracy between bias and cosmology
Changing m with
8, ns, and  Fixed
Zheng & Weinberg 2005
Influence Matrix
Zheng & Weinberg 2005
Constraints on cosmological parameters
Forecast :
~10% on m
~10% on 8
~5% on 8 m0.75
From 30 observables
of 8 different statistics
with 10% fractional errors
Zheng & Weinberg 2005
Joint constraints on m
and 8 from SDSS
projected galaxy
correlation function and
CMB anisotropy
measurements.
Abazajian et al. 2004
Summary and Conclusion
• HOD is a powerful tool to model galaxy clustering.
2-pt, 3-pt, g-g lensing, voids, pairwise velocity, mock galaxy catalogs …
• HOD modeling aids interpretation of galaxy clustering.
* HOD leads to informative and physical explanations of galaxy clustering
(departures from a power law, luminosity/color dependence).
* HOD modeling helps to study galaxy evolution.
* It is useful to separate central and satellite galaxies.
* HODs inferred from the data have a general agreement with those predicted by
galaxy formation models.
• HOD modeling enhances the constraining power of
galaxy redshift surveys on cosmology.
* Current applications alreay led to interesting results, improving cosmological constraints
* Galaxy bias and cosmology are not degenerate w.r.t. galaxy clustering. They can be
simultaneously determined from galaxy clustering data (constrain cosmology and theory
of galaxy formation).