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

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

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

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

Predictions of the Excursion Set Theory M a s f u n c t i o ( P r e & S h 1 9 7 ; B d l . ) = ½ 2 ¯ ¾ ¼ º x p µ ¡ ¶ W ± : 6 8 L + T y , g - v m

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

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）

Test of the bias (Jing 1998, ApJL)

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

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

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

Clustering vs concentration Wechsler et al. 2006/astroph0512416 Small halos: agree with Gao et al. Big halos: reversed Small and big halos Not at the same epoch

Reversal not found for formation time ?? Wetzel, et al. 2006 Astroph/0606699 For massive halos: confirmed the dependence on c; but not found for the formation time

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

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

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

Why old, low mass halos are more strongly clustered? Wang, Mo, Jing (2006), astroph/0608690 (MN in press)

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

Tidal stripping/pancake heating suppress formation of low mass halos in high density regions (cf. Mo et al 2005 MN, Lee 2006 astroph/0605697)

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

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

Limitation for precision measurement with HOD Croton et al. 2006 Astroph/0605636

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