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

F Mass function (Press & Schechter 1971; Bond et al. 1991 )

n(M )dM =½0M 2

¯¯¯¯dln¾(M )dlnM

¯¯¯¯

r2¼º exp

歧2

2

¶dM (1)

Where º =±c=¾(M ) and ±c = 1:68.F Bias factor (Linear; Mo & White1996)

B(M ) = 1+º2 ¡ 1±c

(2)

F The internal physical properties of halos (spin, shape, ageetc.) are inde-pendent of environment (Bond et al. 1991; White1996)

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 concentrationWechsler et al. 2006/astroph0512416

1. Small halos: agree with Gao et al.

2. Big halos: reversed

3. 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=Pcm(k)Pmm(k) =

h±c(k)±m(k)ih±m(k)±m(k)i

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 1

LCDM3 1200 1.2 E 11 1

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 correlationUsing 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. 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