1. 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:

2. Light traces mass?

3. Snapshot @ z~1100 Light-Mass relation well understood CMB from WMAP Galaxies from SDSS Snapshot @ z~0 Light-Mass relation not well understood

4. Cosmological Model initial conditions energy & matter contents Galaxy Formation Theory gas dynamics, cooling star formation, feedback  m  8 n  Dark Halo Population n ( M )  ( r | M ) v ( r | M ) Halo Occupation Distribution P(N|M) spatial bias within halos velocity bias within halos Galaxy Clustering Galaxy-Mass Correlations Weinberg 2002

5. Halo Occupation Distribution (HOD) P(N|M) Probability distribution of finding N galaxies in a halo of virial mass M mean occupation + 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

6. Part I Constraining Galaxy Bias (HOD) Using SDSS Galaxy Clustering Data HOD modeling of two-point correlation functions Departure from a power law Luminosity dependence Color dependence

7. Two-point correlation function of galaxies 1-halo term 2-halo term

8. HOD of sub-halos Central: =1, for M  M min Satellite: =(M/M 1 ) , for M  M min Close to Poisson Distribution (  ~1) Galaxies Zheng et al. 2004 HOD Parameterization Kravtsov et al. 2004 Sub-halos

9. Two-point correlation function: Departures from a power law Zehavi et al. 2004a SDSS measurements

10. 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).

11. 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  r 0 ~ 8Mpc/h  host halo mass > 10 13 M sun /h + galaxy number density  ~100 galaxies in each halo

12. 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 > M min ~ 6×10 11 M sun /h (not so massive) =1.4(M/M min ) 0.45 Predicted r 0 ~ 5Mpc/h Less surprising models from HOD modeling

13. Luminosity dependence of galaxy clustering Zehavi et al. 2004b

14. Luminosity dependence of galaxy clustering Zehavi et al. 2004bDivided by a power law

15. 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

16. 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 derived from different methods Agreement at high mass end Systematics at low mass end

17. Luminosity dependence of galaxy clustering HOD parameters as a function of galaxy luminosity Zehavi et al. 2004bZheng et al. 2004 SA model

18. Luminosity dependence of galaxy clustering Predicting correlation functions for luminosity-bin samples Zehavi et al. 2004b

19. Luminosity dependence of galaxy clustering Zehavi et al. 2004b Predicting the conditional luminosity function (CLF)

20. Zheng et al. 2004 Conditional luminosity function (CLF) predicted by galaxy formation models

21. Color dependence of galaxy clustering Zehavi et al. 2004b

22. Color dependence of galaxy clustering Zehavi et al. 2004bBerlind et al. 2003, Zheng et al. 2004 Inferred from SDSS dataPredicted by galaxy formation model

23. Color dependence of galaxy clustering Zehavi et al. 2004b -20<M r <-19-21<M r <-20

24. Color dependence of galaxy clustering Zehavi et al. 2004b Red-blue cross-correlation: Prediction vs Measurement What we learn: Red and blue galaxies are nearly well-mixed within halos.

25. Part II Constraining Galaxy Bias (HOD) and Cosmology Simultaneously Using Galaxy Clustering Data A Theoretical Investigation 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

26. Cosmology A Halo Population A HOD A Galaxy Clustering Galaxy-Mass Correlations A Cosmology B Halo Population B HOD B Galaxy Clustering Galaxy-Mass Correlations B  ==

27. Halo populations from distinct cosmological models Zheng, Tinker, Weinberg, & Berlind 2002 Changing  m with  8, n, and  Fixed

28. 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 *  m 0.6 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 velocities Halo Populations from distinct cosmological models are NOT degenerate. (Zheng, Tinker, Weinberg, & Berlind 2002)

29. Cosmology A Halo Population A HOD A Galaxy Clustering Galaxy-Mass Correlations A Cosmology B Halo Population B HOD B Galaxy Clustering Galaxy-Mass Correlations B  == 

30. HOD parameterization P(N|M) Mean occupation M 2 nd momentum 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 v g =  v v m Motivated by results from semi-analytic galaxy formation models and SPH simulations

31. Observational quantities Galaxy overdensity  g (r) Group multiplicity function n group (>N) Two-point correlation function of galaxies  gg (r)  m 0.6 / b g Pairwise velocity dispersion  v (r) Average virial mass of galaxy groups Galaxy-mass cross-correlation function  m  gm (r) 3-point correlation function of galaxies

32. Constraints on HOD and cosmological parameters Changing  m with  8, n, and  Fixed Zheng & Weinberg 2004

33. Constraints on HOD parameters Changing  m with  8, n, and  Fixed

34. Constraints on cosmological parameters Changing  m onlyChanging  8 only Cluster-normalizedHalo MF matched

35. 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]