1. Xiaohu Yang ( 杨小虎 ) Shanghai Astronomical Observatory Partner group of MPA Collaborators: H.J. Mo (UMass), F.C. van den Bosch (MPIA), A. Pasquali (MPiA), S. Weinmann (MPA), etc.

2. Connecting Galaxies with dark matter halos Galaxies are formed in dark matter halos How many galaxies are formed per halo? What luminosity does each galaxy have? Color? What is their spatial distribution? GalaxiesDark matter

3. Outline What is HOD/CLF? Can we directly measure the HOD/CLF? Can we model the evolution of the satellite galaxies?  To probe the fate of the disrupted satellite galaxies

4. Galaxy Matter Galaxies are biased tracers of the dark matter Jing et al. 1998 Galaxy bias

5. An novel scheme: HOD Jing et al. 1998 Original HOD model: One step further: HOD for galaxies of different luminosities: P(N|M) Conditional Luminosity Function: P(L|M)

6. Yang et al. 2003; van den Bosch et al.2003 (1) Better match/model observation / Put constraints on the galaxy formation

7. (2a) Better constrain the cosmology van den Bosch et al. 2003b

8. (2b) Better constrain the cosmology

9. Progresses in HOD/CLF models Probe the connection between galaxies and HOST halos The halo Occupations  e.g. Jing, Mo & Borner 1998; Berlind & Weinberg 2002; Zheng et al. 2005; 2008… The Conditional Luminosity Function  e.g. Yang et al. 2003; van den Bosch et al. 2003; 2007; Cooray 2006… The non-parametric CLF  e.g. Vale & Ostriker 2004; 2006; Conroy et al. 2006… Model the central and satellite galaxies separately Log-normal distribution model for the central galaxies  Yang et al. 2003; 2008; Zheng et al. 2006; Cooray 2006; van den Bosch et al. 2007 Power law or (modified) Schetchter form CLF for satellite galaxies  Berlind & Weinberg 2002; Yang et al. 2003; van den Bosch et al. 2003 GalaxiesDark matter

10. Part II: Direct measurement? The HOD/CLF model  Need to assume a functional form  Constrained using the observational data Do we have direct measure of these functions?  Yes!  If the galaxies can be grouped according to their common halos…

11. Galaxy groups in the SDSS DR4 ( Yang et al. 2007 ) Sky coverage: 4514 deg^2 Galaxies with redshifts: 369447 (408119) Groups selected: 301237 (300049) Galaxies are grouped according to their common halos Halo mass is assigned for each group The most massive galaxy is defined as the central galaxy

12. central and satellite galaxies, separately Direct measurement: CLF & CSM Yang et al. 2008a

13. central galaxy, as a function of host halo mass Model the local central-halo relation

14. Part III: Model the satellite evolution Satellite galaxies are connected with subhalos  Before their accretion into host halos, they are central galaxies  They may have different evolution process after their accretion into the host halos Probe the evolution of the satellite galaxies  The original stellar mass?  The survived stellar mass? What we have?  Observation: CSMF for satellite galaxies (survived)  Observation: the central – host halo relation  Theory: the models of the subhalo population (SHMF) Assumption :  If the subhalo at the time of its accretion into host halo and the host halo have the same central – host halo relation, we can predict the original CSMF for satellite galaxies Used in recent models: Vale & Ostriker 2006; Conroy et al. 2006; 2007; 2008; Cooray 2005

15. Weinberg et al. 2006 Left: SPH galaxies Middle: SPH subhalos Right: DM subhalos The general correspondence between satellite galaxies and subhalo Small galaxies are less disrupted relative to the DM subhalos The connection between satellite and subhalo (SAM)

16. Weinberg et al. 2006 Left: SPH galaxies Middle: SPH subhalos Right: DM subhalos The general correspondence between satellite galaxies and subhalo Small galaxies are less disrupted relative to the DM subhalos The connection between satellite and subhalo (SPH)

17. The subhalo mass functions Giocoli et al. 2008

18. Predict the original satellite galaxy population What we have?  Observation: CSMF for satellite galaxies (survived)  Observation: the central – host halo relation  Theory: the models of the subhalo population (SHMF) Assumption :  If the subhalo and the host halo have the same central – host halo relation, we can predict the original CSMF for satellite galaxies Predictions…

19. (A1) The satellite: prediction (original) vs. observation (survived)

20. (A2) The satellite: part of them are either stripped or disrupted.

21. (B) various stellar mass in satellite galaxies

22. The fate of the disrupted satellite galaxies:  Case 1: merged to the central galaxies  Case 2: remain scattered as intra-cluster (group) stars  Case 3: in-between Case 1 ruled out Star formation in small halos Star formation quench limit

23. The fraction of stellar mass associated with central galaxy ICS observational proof  Our prediction of about 8  Gonzalez et al. 2005; 2007; ~ 90% light associated with central galaxies is in the ICS  A factor of 10 more light in ICS than in the central galaxy  Various observational proofs of ICS.

24. Main results Observational constraints:  The satellite galaxies in more massive subhalos are disrupted at a higher fraction  Star formation in the central galaxy is necessary to halos of mass >10^{12.4}M_{sun}  Not all the stars in the disrupted satellite galaxies are merged to the central galaxy, especially in clusters.  The large amount ICS observed by Gonzalez et al. is predicted in our model. Impacts:  The galaxy formation models  The amount of AGN feedback Yang et al. 2008 b

25. Discussion: if halos form different galaxies at different redshift Impacts  Higher total star formation in high redshift halo: more satellite galaxies are disrupted.  More complicated case: need to consider the accretion of subhalo as a function of time  Since most of the subhalos are accreted recently, the impact is small Conroy et al. 2008 See also Cooray 2005