Zheng Zheng

Dept. of Astronomy, Ohio State University

David Weinberg (Advisor, Ohio State)Andreas Berlind (NYU)Josh Frieman (Chicago)Jeremy Tinker (Ohio State)Idit Zehavi (Arizona)SDSS et al.

Collaborators:

Light traces mass?

Light traces mass?

Snapshot @ z~1100Light-Mass relation well

understood

CMB from WMAP

Galaxies from SDSS

Snapshot @ z~0Light-Mass relation not well

understood

Cosmological Modelinitial conditions

energy & matter contents

Galaxy Formation Theorygas dynamics, cooling

star formation, feedback

m 8 n

Dark Halo Population n(M) (r|M) v(r|M)

Halo Occupation DistributionP(N|M) spatial bias within halos velocity bias within halos

Galaxy ClusteringGalaxy-Mass CorrelationsWeinberg

2002

Halo Occupation Distribution (HOD)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., Seljak 2000, Scoccimarro et al. 2001, Berlind & Weinberg 2002

Part IPart I

Constraining Galaxy Bias (HOD) Using Constraining Galaxy Bias (HOD) Using SDSS Galaxy Clustering DataSDSS Galaxy Clustering Data

HOD modeling of two-point correlation functions• Departure from a power law

• Luminosity dependence

• Color dependence

Two-point correlation function of galaxies

1-halo term

2-halo term

HOD of sub-halos

Central:

<Ncen>=1, for MMmin

Satellite:

<Nsat>=(M/M1) , for MMmin

Close to Poisson Distribution (~1) Galaxies

Zheng et al. 2004

HOD Parameterization

Kravtsov et al. 2004

Sub-halos

Two-point correlation function: Departures from a power law

Zehavi et al. 2004aSDSS measurements

Two-point correlation function: Departures from a power law

Zehavi et al. 2004a

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

Luminosity dependence of galaxy clustering

Zehavi et al. 2004b

Luminosity dependence of galaxy clustering

Zehavi et al. 2004bDivided by a power law

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

• From 2-point correlation functions (Zehavi et al. 2004b)

• From group multiplicity functions (Berlind et al. 2004)

• From populating Virgo simulations (Wechsler et al. 2004)

Comparison of HODs derivedfrom different methods

Agreement at high mass endSystematics at low mass end

Luminosity dependence of galaxy clustering

HOD parameters as a function of galaxy luminosity

Zehavi et al. 2004b Zheng et al. 2004

SA model

Luminosity dependence of galaxy clustering

Predicting correlation functions for luminosity-bin samples

Zehavi et al. 2004b

Luminosity dependence of galaxy clustering

Zehavi et al. 2004bPredicting the conditional luminosity function (CLF)

Zheng et al. 2004

Conditional luminosity function (CLF) predicted by galaxy formation models

Color dependence of galaxy clustering

Zehavi et al. 2004b

Color dependence of galaxy clustering

Zehavi et al. 2004b Berlind et al. 2003, Zheng et al. 2004

Inferred from SDSS dataPredicted by galaxy formation

model

Color dependence of galaxy clustering

Zehavi et al. 2004b

-20<Mr<-19 -21<Mr<-20

Color dependence of galaxy clustering

Zehavi et al. 2004bRed-blue cross-correlation:Prediction vs Measurement

What we learn:

Red and blue galaxies are nearly well-mixed within halos.

Part IIPart II

Constraining Galaxy Bias (HOD) Constraining Galaxy Bias (HOD) and Cosmology Simultaneously and Cosmology Simultaneously

Using Galaxy Clustering DataUsing Galaxy Clustering Data

A Theoretical Investigation

Why useful ?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

CosmologyA

Halo PopulationA

HODA

Galaxy ClusteringGalaxy-Mass Correlations

A

CosmologyB

Halo PopulationB

HODB

Galaxy ClusteringGalaxy-Mass Correlations

B

=

Halo populations from distinct cosmological models

Zheng, Tinker, Weinberg, &

Berlind 2002

Changing m

with 8, n, and Fixed

Halo populations from distinct cosmological models

• Changing m only

Halo mass scale shifts (m)

Same halo clustering at same M/M*

Pairwise velocities at same M/M* m0.6

• Changing m but keeping Cluster-normalization

Similar halo clustering and pairwise velocities at fixed M

Different shapes of halo mass functions

• Changing m and P(k) to preserve the shape of halo MF

Similar halo mass functions

Different halo clustering and halo velocitiesHalo Populations from distinct cosmological models are NOT

degenerate. (Zheng, Tinker, Weinberg, & Berlind 2002)

CosmologyA

Halo PopulationA

HODA

Galaxy ClusteringGalaxy-Mass Correlations

A

CosmologyB

Halo PopulationB

HODB

Galaxy ClusteringGalaxy-Mass Correlations

B

=

HOD parameterization

• P(N|M) Mean occupation <N>M

2nd momentum <N(N-1)>M

[Transition from a narrow distribution to a wide distribution]

• Spatial bias within halos Different concentrations of galaxy distribution and dark

matter distribution (c)

• Velocity bias within halos vg= vvm

Motivated by results from semi-analytic galaxy

formation models and SPH simulations

Observational quantities

• Galaxy overdensity g(r)

• Group multiplicity function ngroup(>N)

• Two-point correlation function of galaxies gg(r)

m0.6/bg

• Pairwise velocity dispersion v(r)

• Average virial mass of galaxy groups <Mvir(N)>

• Galaxy-mass cross-correlation function mgm(r)

• 3-point correlation function of galaxies

Constraints on HOD and cosmological parameters

Changing m

with 8, n, and Fixed

Zheng & Weinberg 2004

Constraints on HOD parameters

Changing m

with 8, n, and Fixed

Constraints on cosmological parameters

Changing m only

Changing 8 only

Cluster-normalized

Halo MF matched

Summary and Conclusion • HOD is a powerful tool to model galaxy clustering.

• HOD modeling aids interpretation of SDSS galaxy clustering.

* HOD leads to informative and physical explanations of galaxy clustering (departures from a power law in 2-point correlation function, the luminosity dependence, and the color dependence) .

* 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.

• Galaxy bias and cosmology are not degenerate w.r.t. galaxy clustering.

* Using galaxy clustering data, we can learn the HOD of different classes of galaxies, and thus provide useful constraints to the theory of galaxy formation.

* Simultaneously, cosmological parameters can also be determined from galaxy clustering data. [future applications to SDSS data]