Evolution of large scale structures

1. Evolution of large scale structures The importance of studying dark matter halos: 1)in CDM models, all dark matter is in halos of different mass; 2) shaping up luminous objects, such galaxies and clusters; 3) dark matter halos could be directly detected by gravitational lensing

2. Physical (Internal) Properties of dark matter halos

3. Contents • Density profiles • Shape and triaxial model of density profiles • Subhalos and their spatial distribution • Spin and angular momentum distribution

4. Brief introduction to the simulation methods • Cosmological simulation • Cosmological multiple-mass particle resimulation

5. Density profile

9. c(M)

10. NFW Recipe for predicting c(M) Formation time of progenitor fM: Characteristic Density from the formation time:

11. Selection and Scatters • NFW valid only for ~30 percent most virialized halos; • Lognormal distribution with sigma_c about 0.2 for ~30 % subpopulation or 0.5 for all halos at the same mass Jing (2000)

12. Lognormal distribution Jing (2000); Bullock et al. 2001

13. Fails to explain the z-dependence of c(M,z) c(M,z)∝1/(1+z) Bullock et al. 2001

18. Conclusion for this part • A prescription based MAH for predicting c for hierarchical models, is more accurate than previous empirical models. • The prescription, based on the tight relation found for Ms-rs, works for individual halos based on their MAH; • MAH is universal after scaling at the turning point, for halos of 1010 to 1015 Msun

19. Debate on the inner slope of NFW Moore et al (1998) ApJ 499 L5 Jing & Suto (2000),ApJ, 529,L69 Beta=1.1 for clusters; 1.3 for groups; 1.5 for galaxies

20. JYP & Suto, Y. 2000, ApJ, 529, L69

21. summary • NFW is a good approximation; • c is log-normal distributed • The c parameter is determined from MAH (Zhao et al. 2004) • It is still in debate that the inner slope may be steeper than NFW and may even depend on halo mass.

23. JYP & Suto,Y. 2000,ApJ, 529, L69

24. Determine local density for each particle from 32 nearest neighbors; Get iso-density surfaces after excluding subhalos;

26. Feature1: concentric triaxial model works better than spherical model

28. Feature2: density along the major axis fit with NFW

32. We need to fix the shapes of halos in order to quantify the density distribution in the triaxial model Feature3：scaling relation and universal distributions exists for the shape distributions

37. Feature4: more elongated at the central region; easy to be included

38. Summary • Used two large samples of HR simulations • the concentric triaxial model more accurate; • a COMPLETE set of formulae which can predict the tri-axial density profile of halos for a CDM model • can adopt a/c (R) • Many applications: lensing, S-Z effect, x-ray distribution of clusters, modeling non-linear clustering of DM……

39. Mass function of subhalos:

40. JYP & Suto,Y. 2000,ApJ, 529, L69

41. Radial distribution of subhalos: much shallower than DM

42. Comparing with observation of clusters

43. Comparing with our Milky way

44. Angular Momentum distribution and Spin distribution