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The halo model & galaxy formation. 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. Dark matter. Galaxies. Connecting Galaxies with dark matter halos.
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The halo model & galaxy formation 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.
Dark matter Galaxies 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?
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
Galaxies are biased tracers of the dark matter Matter Galaxy Galaxy bias Jing et al. 1998
An novel scheme: HOD Original HOD model: One step further: HOD for galaxies of different luminosities: P(N|M) Conditional Luminosity Function: P(L|M) Jing et al. 1998
(1) Better match/model observation / Put constraints on the galaxy formation Yang et al. 2003; van den Bosch et al.2003
(2a) Better constrain the cosmology van den Bosch et al. 2003b
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 Dark matter Galaxies
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…
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
central and satellite galaxies, separately Direct measurement: CLF & CSM Yang et al. 2008a
central galaxy, as a function of host halo mass Model the local central-halo relation
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
The subhalo mass functions Giocoli et al. 2008
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…
(A1) The satellite: prediction (original) vs. observation (survived)
(A2) The satellite: part of them are either stripped or disrupted.
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 quench limit Star formation in small halos
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.
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