1. semi-analytical model of galaxy formation Xi Kang Purple Mountain Observatory, CAS

2. Outline galaxy formation: semi-analytical model model predictions and observational data WDM as an alternative solution ?

3. Galaxy formation model: framework Concordance Model (LCDM): dark energy dominated, cold dark matter as main mass component Cosmic structure forms hierarchically: small halo forms first, and merger to form massive ones (well understood from N-body simulation and EPS theory) Galaxy formation in collapsed DM halo: via gas cooling and star formation semi-analytical model: simple formula to describe physics governing galaxy formation,fast to population large sample of dark matter haloes with galaxies, easy to change parameters (effects on galaxy properties) But need to disentangle physics uncertainty from cosmology uncertainty

4. Model ingredients (most important) Cold gas accumulation: how many gas can cool in given halo (gas accretion manner) Star formation efficiency (redshift evolution) SN feedback, Black Hole feedback (fate of reheated gas, BH accretion rate) Central galaxy ->satellite: ram-pressure stripping, stellar stripping, disruption, merger rate (partly understood) Stellar population evolution (IMF) Others: galaxy merger, morphology transform, star burst,,,

5. Model predictions vs Observational data LCDM simulations: WMAP one, three, seven-year cosmologies (σ 8= 0.9,0.73,0.81) Box: 200Mpc/h, particles number 1024 3 (mp=3X10 9 M ⊙ ) Semi-analytical model: Kang & van den Bosch 2008, ApJL; Kang et al. 2012, MNRAS

6. Results at z=0: galaxy stellar mass function M cool =f*M hot /t dyn lower f --> less low mass galaxies f=1.0 f=0.15 Kang et al. 2011, MNRAS

7. Results at z=0: two-points correlation function small-scale clustering is too strong Guo et al. 2010 MNRAS σ 8 =0.9 (too high?)

8. Results at z=0: Ms-Mhalo relation leauthaud et al. 2011, ApJ

9. Results at z=0: Conditional stellar mass function data points: Yang et al. (2010, MNRAS) from SDSS DR7 red line: satellites, blue: centrals too many satellites or satellites mass are too large

10. why above results at z=0 ? the above: the stellar mass-halo mass relation, stellar mass function, two-points correlation function are the most important observational data at z=0 these data tell us: the efficiency of star formation in given halo, how many haloes, how galaxy are distributed in halo --> all are complementary with CDM model with stellar mass function well matched, most other results: color distribution, Tully-Fisher relation, radial distribution in clusters, etc, can be also well reproduced

11. Stellar mass functions at z>0 Model predicts less massive galaxies at z>2 Too many galaxies at M_*=10^10 at z>0 Note: high-z data are not well measured, larger discrepancies among data Cosmic variance for massive galaxies Evolution of galaxy at z>0 is not well constrained !!

12. Main problems of Sam (small scale crisis!) Too many satellites (or satellites are too massive) Solutions: ❖ cosmological model? (lower σ 8 ) ❖ warm dark matter? ❖ galaxy formation physics?

13. small-scale clustering problem: (σ 8 ?) red WMAP1 (σ 8 =0.9 ) blue WMAP7(σ 8=0.81 ) green WMAP3(σ 8=0.73 )

14. small-scale clustering problem: WDM? power on small scales suppressed ! but still higher Ms=0.75, 0.5kev other problems for this WDM mass(Ms=0.5kev)

15. Suppress of satellites growth: 1: Instantaneous stripping of hot halo gas? But satellites are too red !!

16. Suppress of satellites growth: SN feedback effect ? In KB08, for satellites at accretion, V reheated =V host, Not V disk (before accretion) for satellites accreted at high-z, V host > V disk, so SN feedback efficiency suppressed too much (equally: stellar mass grows too much)

17. conditional stellar mass function

18. warm dark matter? Milky Way satellites are too concentrated for CDM Boylan-kolchin et al. 2011, MNRAS Lovell et al. 2012, MNRAS

19. galaxy formation with WDM Menci et al. 2012, MNRAS Ms=0.75 kev

20. stellar mass functions (ms=0.75, 0.5 kev) fc=0.15

21. galaxy formation with ms=0.5 & 0.75kev ms=0.5kev,fc=1.0 Tully-Fisher ms=0.75kev,fc=0.3 5

22. summary semi-analytical model can reproduce many local and high-z observations small-scales problem: satellites are too massive cosmological model & WDM do not solve this problem physical model works better (satellite mass should increased limited)