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