Zheng Zheng

I N S T I T U T E

for ADVANCED STUDY

Cosmology and Structure Formation KIAS Sep. Cosmology and Structure Formation KIAS Sep. 21, 200621, 2006

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

Collaborators:

Light traces mass?

Galaxies from SDSS

Snapshot @ z~0Light-Mass relation not well

understood

Snapshot @ z~1100Light-Mass relation well

understood

CMB from WMAP

Cosmological Modelinitial conditions

energy & matter contents

Galaxy Formation Physicsgas dynamics, cooling

star formation, feedback

m 8 ns

Dark Halo Population n(M)

(r|M) v(r|M)

Halo Occupation Distribution P(N|M)

spatial bias within halosvelocity bias within halos

Galaxy ClusteringGalaxy-Mass CorrelationsWeinberg

2002

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

Berlind et al. 2003

P(N|M) from galaxy formation model

For galaxies above a certain For galaxies above a certain threshold threshold in luminosity/baryon massin luminosity/baryon mass

Mean: Mean:

Low mass cutoff Low mass cutoff PlateauPlateau High mass power lawHigh mass power law

Scatter: Scatter:

Sub-Poisson (low mass)Sub-Poisson (low mass) Poisson (high mass)Poisson (high mass)

P(N|M) from galaxy formation model

Kravtsov et al. 2004, Zheng et al. 2005

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

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

1-halo term

2-halo term

Excess probability w.r.t. random distribution of finding galaxy pairs at a given separation

Galaxies of each pair from the same halo

Galaxies of each pair from different halos

Two-point correlation function: Departures from a power law

Zehavi et al. 2004SDSS measurements

Two-point correlation function: Departures from a power law

Zehavi et al. 2004

2-halo term

1-halo term

Divided by the best-fit power law

Dark matter correlation function

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).

Two-point correlation function: Departures from a power law

Daddi et al. 2003

Strong clustering of a population of red galaxies at z~3

HDF-South

Fit the data by assuming an r-1.8 real space correlation function

r0 ~ 8Mpc/h

host halo mass > 1013 Msun/h

+ galaxy number density ~100 galaxies in each halo

Two-point correlation function: Departures from a power law

Zheng 2004

HOD modeling of the clustering

of z~3 red galaxies

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

Less surprising models from HOD modeling

Ouchi et al 2005

Hogg & Blanton

Luminosity dependence of galaxy clustering

Zehavi et al. 2005

Luminosity dependence of galaxy clustering

Berlind et al. 2003

Luminosity dependence of the HOD

predicted by galaxy formation models

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 galaxy clustering

HOD parameters vs galaxy luminosity

Zehavi et al. 2005

inferred from observation

Zheng et al. 2005

prediction of theory

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 dataPredicted by galaxy formation

model

MergingStar

Formation

z~0

z~1

Merging

z~1

z~0

Studying galaxy evolution

Establishing an evolution link between DEEP2 and SDSS galaxies

Zheng, Coil & Zehavi 2006

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

Why useful ?

• Consistency check• Better constraints on cosmological parameters (e.g., 8, m)• Tensor fluctuation and evolution of dark energy• Non-Gaussianity

Tegmark et al. 2004

Probing Cosmology: --- Constraints from Galaxy Clustering Data

Tinker et al 2005

Mr<-20

Mr<-21.5

Mass-to-Light ratio of large scale structure

At a given cosmology (σ8)

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

Mass-to-Light ratio of large scale structure

σ8=0.95 σ8=0.9

σ8=0.8

σ8=0.7

σ8=0.6

M<-18 M<-20

CNOC data

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

Tinker et al 2005

Modeling redshift-space distortion

For each (m, 8), choose HOD to match wp(rp)

Large scale distortions degenerate along axis 8 m

0.6, as predicted by linear theory

Small scale distortions have different dependence on m, 8, v

Tinker et al 2006

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.

Recovering the linear power spectrum

Yoo et al 2006

CosmologyA

Halo PopulationA

HODA

Galaxy ClusteringGalaxy-Mass Correlations

A

CosmologyB

Halo PopulationB

HODB

Galaxy ClusteringGalaxy-Mass Correlations

B

=

Breaking the degeneracy between bias and cosmology

Changing m

with 8, ns, and Fixed

Zheng & Weinberg 2005

Breaking the degeneracy between bias and cosmology

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

Abazajian et al. 2004

Joint constraints on m and 8 from SDSS projected galaxy correlation function and CMB anisotropy measurements.

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).