1. Zheng I N S T I T U T E for ADVANCED STUDY Cosmology and Structure Formation KIAS Sep. 21, 2006

2. 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:

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

4. Cosmological Model initial conditions energy & matter contents Galaxy Formation Physics gas dynamics, cooling star formation, feedback  m  8 n s  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., Jing & Borner 1998; Seljak 2000; Scoccimarro et al. 2001; Berlind & Weinberg 2002; Yang, Mo, & van den Bosch 2003; …

8. Galaxies from SDSS

9. Berlind et al. 2003 P(N|M) from galaxy formation model For galaxies above a certain threshold in luminosity/baryon mass Mean: Low mass cutoff Low mass cutoff Plateau Plateau High mass power law High mass power lawScatter: Sub-Poisson (low mass) Sub-Poisson (low mass) Poisson (high mass) Poisson (high mass)

10. 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

11. 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

12. 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

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

14. 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).

15. 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

16. 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 Ouchi et al 2005

17. Hogg & Blanton

18. Luminosity dependence of galaxy clustering Zehavi et al. 2005

19. 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

20. Luminosity dependence of galaxy clustering HOD parameters vs galaxy luminosity Zehavi et al. 2005 inferred from observation Zheng et al. 2005 prediction of theory

21. Hogg & Blanton

22. Color dependence of galaxy clustering Zehavi et al. 2005

23. Color dependence of galaxy clustering Zehavi et al. 2005Berlind et al. 2003, Zheng et al. 2005 Inferred from SDSS dataPredicted by galaxy formation model

24. Merging Star Formation z~0 z~1 Merging z~1 z~0 Studying galaxy evolution

25. Establishing an evolution link between DEEP2 and SDSS galaxies Zheng, Coil & Zehavi 2006 Tentative results: For central galaxies in z~0 M<10 12 h -1 M sun halos, ~80% of their stars form after z~1 For central galaxies in z~0 M>10 12 h -1 M sun halos, ~20% of their stars form after z~1

26. 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

27. Tinker et al 2005 M r <-20 M r <-21.5 Mass-to-Light ratio of large scale structure At a given cosmology (σ 8 ) 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

28. Mass-to-Light ratio of large scale structure σ 8 =0.95 σ 8 =0.9 σ 8 =0.8 σ 8 =0.7 σ 8 =0.6 M<-18M<-20 CNOC data Galaxy cluster =universal value only for unbiased galaxies (σ 8g ~ σ 8 ) Comparison with CNOC data indicates (σ 8 /0.9)(Ω m /0.3) 0.6 =0.75+/-0.06 Tinker et al 2005

29. Modeling redshift-space distortion For each (  m,  8 ), choose HOD to match w p (r p ) 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

30. 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

31. 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  ==  Breaking the degeneracy between bias and cosmology

32. Changing  m with  8, n s, and  Fixed Zheng & Weinberg 2005 Breaking the degeneracy between bias and cosmology

33. Influence Matrix Zheng & Weinberg 2005

34. Constraints on cosmological parameters Forecast : ~10% on  m ~10% on  8 ~5% on  8  m 0.75 From 30 observables of 8 different statistics with 10% fractional errors Zheng & Weinberg 2005

35. Abazajian et al. 2004 Joint constraints on  m and  8 from SDSS projected galaxy correlation function and CMB anisotropy measurements.

36. 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).