Zheng Zheng Dept. of Astronomy, Ohio State University

1. Constraining Galaxy Bias and Cosmology Using Galaxy Clustering Data Zheng Zheng Dept. of Astronomy, Ohio State University Collaborators: David Weinberg(Advisor, Ohio State) Andreas Berlind(NYU) Josh Frieman(Chicago) Jeremy Tinker(Ohio State) Idit Zehavi(Arizona) SDSS et al.

2. Light traces mass?

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

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 <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

6. Part IConstraining 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. Zheng et al. 2004 Sub-halos Galaxies HOD Parameterization HOD of sub-halos Central: <Ncen>=1, for MMmin Satellite: <Nsat>=(M/M1) , for MMmin Close to Poisson Distribution (~1) Kravtsov et al. 2004

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

10. 2-halo term 1-halo term Dark matter correlation function Divided by the best-fit power law 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). Zehavi et al. 2004a

11. 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 + galaxy number density  ~100 galaxies in each halo HDF-South Strong clustering of a population of red galaxies at z~3 Daddi et al. 2003

12. 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 HOD modeling of the clustering of z~3 red galaxies Zheng 2004

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

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

15. 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

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) Agreement at high mass end Systematics at low mass end Comparison of HODs derived from different methods

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

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

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

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

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

22. Color dependence of galaxy clustering Zehavi et al. 2004b Berlind et al. 2003, Zheng et al. 2004 Inferred from SDSS data Predicted by galaxy formation model

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

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

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

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

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

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

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

30. HOD parameterization Motivated by results from semi-analytic galaxy formation models and SPH simulations • 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

31. 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 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 only Changing 8 only Cluster-normalized Halo 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]