1. Evolution of galaxies and dark matter halos Yipeng Jing Shanghai Astronomical Observatory Main Collaborators: Chunyan Jiang ( 姜春艳）, Cheng Li （李成）, Donghai Zhao （赵东海）, Lan Wang （王岚） …….

2. Taken from S. Faber Theoretical framework for understanding evolution of galaxies and dark matter halos

3. Taken-away conclusions The mass accretion history and the structure evolution of halos established by Zhao et al. (2009) is universally valid not only for LCDM, but also for WDM, HDM (Zhao et al. 2012); A reliable stellar mass-halo mass is directly measured from SDSS, putting useful constraints both on galaxy formation and on cosmology (Li, Cheng et al. 2012); The merger time scale of galaxies is about two times longer than previously thought ( Jiang et al. 2008); Merger leading to a increase of 50-100% in stellar mass of massive galaxies (Wang & YPJ 2010) from z=1 to z=0, consistent with our recent analysis of CFHT data (YPJ 2012)

4. The universal mass accretion history of dark matter haloes

5. N-body cosmological simulations Assumption: MAHs are well simulated with pure dark matter (incomplete, 1024**3) modelnini Γσ8σ8 Ω0Ω0 Λ0Λ0 NpNp LN NQ ηzizi SF11K cut110512 3 1605120.0161481.3 SF20110512 3 1605120.016363.2 SF3110512 3 1605120.01675.0 SF4-2110512 3 1605120.01611.3 LCDM110.20.90.30.7256 3 255120.002572 LCDM210.20.90.30.7512 3 1005120.0172 LCDM310.20.90.30.7512 3 3005120.0336 OCDM110.21.00.30256 3 502560.0272 SCDM110.50.5510256 3 255120.002572 SCDM210.50.5510512 3 1002560.0272

7. Choosing proper variables for modeling Given cosmology and power spectrum, after extrapolated linearly to z=0, linear mass variance of given volume σ is determined by M, and linear critical collapse overdensity δ c by z.

8. Growth rate as a function of scaled “mass” D.H. Zhao et al. (2010)

9. Universal differential relation w-p determines growth rate of halo of mass M D.H. Zhao, et al. ApJ (2009)

10. LCDM Much more accurate than van den Bocsh (2002) or Wecshler et al. (2002)

11. –SCDM & OCDM

12. Another universal correlation t : universe age of final halo t 0.03 : universe age when main progenitor mass is 4% of final halo mass Important Finding!

13. Evolution of halo density profile Combined with MAHs model we presented in part I, c-t correlation can be used to predict the evolution of halo density profile –LCDM1-3

14. Evolution of halo density profile –SCDM1-3

15. Prada et al. (2012) does not work!

16. Zhao et al. (2009) for HDM, without any tuning the parameters, universal indeed

17. Zhao et al. (2009) for Warm DM, without any tuning the parameters, universal indeed (Zhao et al. 2012)

18. Taken from S. Faber Relation between the stellar mass of the central galaxy and host dark matter halo

19. Group catalog of SDSS DR7 (Yang et al. 2008) Sky coverage: 4514 deg^2 Galaxies with redshifts: 369447 (408119) Groups selected: 301237 (300049)

20. Measure the redshift cross correlation function for groups with a given central stellar mass (Li et al. 2012

21. Velocity dispersion – stellar mass relation

22. Halo mass-stellar mass relation

23. Luminosity – halo mass relation

24. Velocity dispersion – stellar mass relation

25. Constraint on cosmology Sigma_8 =0.88 \pm 0.04 Consiste nt with WMAP7 <2sigma

26. Taken from S. Faber Galaxy merger timescale

29. Using ln(m_h/m_sub) for Coulomb logarithm (c.f. Navarro et al. (1994) Predicted friction timescale Measured merger timescale repeated Navarro et al. 1994 But our conclusion is different from theirs

30. Fitting formula Merger timescale for all mergers

31. arXiv:1204.6319

32. Summary The Chandrasekhar formula, as is usually used, under(over)-estimates merger time for minor(major) mergers ; If the Coulomb logarithm is replaced ln(1+lambda), the mass dependence is accounted for correctly; but underestimate The dependence on the circularity is much weaker than the 0.78 power; We have presented a fitting formula and circularity distribution which are sufficient for modeling the merger rate; the scatters are 40%

33. Evolution of the stellar mass and halo mass relation with Halo Occupation Model Halo (and subhalo) catalog from an high resolution N- body simulation Galaxies in halos (central) and subhalos (satellites) are determined by the host halos at infall (Lan Wang et al. 2006), Using the mass functions and correlation functions from SDSS and VVDS (z=0.8) Linear interpolation Unified model Jing & Suto (2000)

34. HOD method: assuming N galaxies in halo of mass M ； First applied to Las Campanas Redshift survey ， getting alpha ＝ 0.09 Jing, Mo, Boerner 1998, ApJ, 494, 1

35. Fitting to SDSS (Wang & YPJ 2010)

36. Fitting to VVDS

37. The stellar mass –halo mass relation

38. Stellar mass functions at high redshift

39. How many mergers

40. CFHT and COSMOS (preliminary)

41. Remarks Well understood for the evolution of dark matter halos Still very poorly for evolution of galaxies Combining deep catalogs of galaxies with the dark matter model can yield important clues to the evolution of galaxies