1. Clustering and environments of dark matter halos
Yipeng Jing
Shanghai Astronomical Observatory

2. 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

3. Three important aspects of dark matter halos
Mean number: mass function f(m)dm;
Spatial distribution: correlation functions; bias factors, etc.
Internal properties of dark matter: density profile, spin,etc

4. Excursion Set Theory for “identifying” dark matter halos from Gaussian Initial density field
Bond et al. 1991, ApJ

5. Predictions of the Excursion Set TheoryM a s f u n c t i o ( P r e
& S h 1 9 7 ; B d l . ) = 2 x p W : 6 8 L + T y , g - v m

6. Test of the Excursion theory :mass function
Lee & Shandarin 1998, ApJ

7. Jing et al. 2006 in preparation
暗晕的质量函数也能很好地与模拟数据符合（Based on the background-split assumption and the bias model）

8. Test of the bias (Jing 1998, ApJL)

9. Empirical Modification for MF and bias (based on peak background split)
Sheth & Tormen (1999) MNRAS

11. Environmental effect
Lemson & Kauffmann (1999): spin, concentration, no dependence;
Percival et al. (2003): clustering vs age, no dependence;
Gao et al. (2005), MNRAS, found age dependence
Main Reason: Gao et al examine M<<M* halos
Formation time: at the time when the most massive pregenitor has accumulated a half mass

12. Concentration vs formation time
Jing (2000) ApJ; see also Bullock et al. (2001), Wechsler et al. (2002), Zhao et al (2003a,b)

13. Clustering vs concentration
Wechsler et al. 2006/astroph
Small halos: agree with Gao et al.
Big halos: reversed
Small and big halos Not at the same epoch

14. Reversal not found for formation time ??
Wetzel, et al. 2006
Astroph/
For massive halos: confirmed the dependence on c; but not found for the formation time

15. An accurate determination at high halo mass
Jing, Suto, Mo 2006, to be submitted
A set of N-body simulations of 1 billion particles
Using cross-power spectrum method
Superior over the correlation function method b = P c m ( k ) h i 1

16. Cosmological N-body simulations at SHAO with 10243 particles
Box size
(Mpc/h)
M_p
(M_sun/h)
realizations
LCDM1
300
1.8 E9 1
LCDM2
600
1.5 E10
LCDM3
1200
1.2 E 11
LCDM4
1800
4.0 E 11 4

17. The dependence on the formation time is detected at >10sigma for large halos, though small !

18. Why old, low mass halos are more strongly clustered?
Wang, Mo, Jing (2006), astroph/ (MN in press)

19. Association with high initial collapse region (SC) leads to high clustering of old population

20. Tidal stripping/pancake heating suppress formation of low mass halos in high density regions (cf. Mo et al 2005 MN, Lee 2006 astroph/ )

21. Observational Evidence?
Using 2dF catalogs of galaxies and groups, and the cross correlation
Using η (current SFR)of the central as the proxy for z_f
Yang et al. (2005) ApJL

22. Consequences for Halo Occupation Distribution Studies (Zhu et al
Consequences for Halo Occupation Distribution Studies (Zhu et al. 2006, ApJL)

23. Limitation for precision measurement with HOD
Croton et al. 2006
Astroph/

24. Summary
The dependences of halo clustering on both formation time and the concentration are well established;
The dependence at low mass is largely due to the failure of the spherical model; providing clues to improve EST;
The dependences at high mass still are challenging to Excursion Set Theory
Preliminary observational evidence, but not fully consistent;
Important for precision cosmology studies with HOD: color dependence