Clustering and density profile of dark matter halos

Why dark matter halos ?
Self-gravitating Self-gravitating
Self gravitating virialized objects
Sites Sites for galaxies and clusters
radiative cooling of baryonic gas
energy and angular momentum transfer
star formation and supernova heating
More More directly related to cosmological initial
conditions than other small-scale objects
Easier Easier to predict/model theoretically since
gravity dominates
2/31

Topics in in this talk include …
Clustering:
dark dark matter clustering on the light-cone
(Yamamoto + YS 1998)
Comparison with simulations on the light-cone
(Hamana, Colombi + YS 2000)
Morphology-dependent galaxy bias from SDSS data
(Kayo, Nakamura, Fukugita + YS for for SDSS collaboration)
halo halo
clustering on the light-cone
(Hamana, Yoshida, YS + Evrard 2001)
Density profile:
High-resolution N-body simulation (Jing+YS 2000)
Implications from the gravitational arc statistics
(Oguri, Taruya + YS 2001)
Possible constraints from time-delay time time-delay delay statistics
(Oguri, Taruya, YS + Turner 2001)
Halo density profile to dark matter clustering:
(Hamana, Yoshida + YS 2001)
3/31

z=0.05
(150h -1 Mpc)
1986
Clustering on the light-cone
CfA redshift survey:
de Lapparent et al.(1986)
Evolution Evolution
along the
light-cone light light-cone cone
is essential
even in the
current
surveys !
1996
z=0.2
(600h -1 Mpc)
Las Campanas redshift survey:
Schectman et al. (1996)
2001
z=3
(~1h -1 Gpc)
2dF QSO survey: Shanks et al. (2001)
4/31

Cosmological light-cone effects
linear and nonlinear gravitational evolution
redshift-space
redshift redshift-space space distortion due to peculiar velocity
linear distortion (the Kaiser effect)
nonlinear distortion (finger-of-god effect)
evolution of objects on the light-cone light light-cone cone
number density and luminosity evolution
object-dependent spatial bias relative to to mass
observational selection function
magnitude-limit and luminosity function
shape of of the survey boundary
Matsubara, Suto & Szapudi (1997); Matarrese et al. (1997)
Yamamoto & Suto (1998); Suto, Suto,
Magira, Magira,
Jing, Jing,
Matsubara & Yamamoto (1999)
5/31

Predicting the clustering on on the light-cone
redshift-space redshift redshift-space space distortion
1
r;
z)
= 2
2π
0
2 R
k dkPnl
( k,
z)
f ( k,
β , σ 1D,
sin kr
)
kr
gravitational
nonlinear evolution
linear and nonlinear
redshift-space distortion
ξ ( ∫ vel
∞
average average over the light-cone light light-cone cone
z
∫
max
2 dVc
dzξ
( r;
z)[
φ(
z)
n(
z)]
LC zmin
ξ ( r)
=
dz
z
∫
max
2 dVc
dz[
φ(
z)
n(
z)]
zmin
dz
comoving
volume
element
selection function mean number density
Yamamoto & Suto (1998) ; Hamana, Hamana,
Colombi & Suto (2001)
6/31

Correlation functions of of dark matter on on the the light-cone
Dark matter particle distribution on the
light light-cone cone from NN-body
body simulations
Bias is ignored here.
Hamana, Hamana Hamana, , Colombi & Suto (2001)
7/31

Slices from SDSS spectroscopic galaxy samples
Clustering of galaxies on the light-cone light cone !
(although the light-cone light cone effect is not important)
9971 galaxies (r’

Sample-variance of of ξ(s)
Morphology dependent correlation
functions of SDSS galaxies
SDSS
early-type early type
SDSS
late-type late type
average
N-body body Mock samples and
the model predictions
redshift space
Redshift-space
distortion
real space
Kayo, Nakamura, Fukugita, Fukugita,
YS et al. in preparation
9/31

Phenomenological model
for scale- and mass-dependent halo biasing
mass-dependence mass mass-dependence dependence (Jing (Jing1998;Sheth Jing1998; 1998;Sheth Sheth & Tormen 1999)
+ scale-dependence
scale scale-dependence dependence (Taruya
Taruya & Suto 2000) in halo
biasing (cf., Yoshikawa et al. 2001; poster #63)
biasing (cf., Yoshikawa et al. 2001; poster #63)
b halo
( M , R,
z)
= b ( M , z)[
1+
b ( M , z)
σ ( R,
z)]
average average over the light-cone light light-cone cone
ξ
LC
halo
( >
ST
ST
mass
2
ξ halo(
M, R,
z)
= bhalo(
M,
R,
z)
ξ mass(
R,
z)
M,
r)
=
z
max
∫ ∫
z
min
dz
z
∞
max
∫ ∫
z
M
min
dMξ
dz
halo
∞
M
0.
15
2 dV
( M,
R,
z)
nST(
M,
z)
dz
2 dVc
dM nST(
M,
z)
dz
Hamana et al. (2001)
c
12/31

Calibrating the halo biasing model
with the Hubble volume simulation at at z=0
Cumulative
halo bias
b(>M, R,z=0)
massive halos
less massive halos
Hamana et al. (2001)
Our halo bias model works
quite well at R>20h-1Mpc. The suppression of
biasing in simulation at
R

Correlation functions of of halos on on the the light-cone
Hamana et al. (2001)
14/31

Topics in in this talk include …
Clustering:
dark dark matter clustering on the light-cone
(Yamamoto + YS 1998)
Comparison with simulations on the light-cone
(Hamana, Colombi + YS 2000)
Morphology-dependent galaxy bias from SDSS data
(Kayo, Nakamura, Fukugita + YS for for SDSS collaboration)
halo halo
clustering on the light-cone
(Hamana, Yoshida, YS + Evrard 2001)
Density profile:
High-resolution N-body simulation (Jing+YS 2000)
Implications from the gravitational arc statistics
(Oguri, Taruya + YS 2001)
Possible constraints from time-delay time time-delay delay statistics
(Oguri, Taruya, YS + Turner 2001)
Halo density profile to dark matter clustering:
(Hamana, Yoshida + YS 2001)
15/31

Why density profiles of of dark halos ?
Theoretical Theoretical interest: what is the final
state of the cosmological selfgravitating
system ?
forget forget cosmological initial conditions?
keep keep initial memory somehow?
Practical Practical importance: testable
predictions for galaxies and clusters
can distinguish the underlying cosmological
model through comparison with observations
(i.e., galactic rotation curve, gravitational
lensing, X-ray/SZ observation)
16/31

log(density)
NFW universal density profile
halo halo density
profile is
independent of
cosmological
initial
conditions
log(radius)
Navarro, Frenk
& White (1997)
δ cρ
crit
ρ(
r)
=
2
( r / rs
)( 1 + r / rs
)
rvir(
M )
cvir(
M ) ≡
rs
( M )
3
∆virΩ
0 c
δ c(
M ) ≡
3[ln(
1 + c)
− c /( 1 + c)]
17/31

galaxies
~ 5x1012 galaxies
~ 5x10 Msun 12Msun groups
~ 5x1013 groups
~ 5x10 Msun 13Msun clusters
~ 3x1014 clusters
~ 3x10 Msun 14Msun Jing & Suto
(2000)
Halo profiles in in higher-resolution
N-body simulations
inner slope in higherresolution
simulations
is steeper (~ –1.5) than
the NFW value (–1.0)
next two talks by
Y.P.Jing
and
T.Fukushige
18/31

Gravitational lensing of of CL0024+1654
HST image
Z=0.39, LX=5 =5×10
10 43 h-2 2 erg/s
reconstructed mass distribution
(with 512 parameters)
Tyson, Kochanski & Dell’Antonio
Dell Antonio (1998)
20/31

Reconstructed mass profile of of CL0024+1654
flat core !
no cusp !
Tyson, Kochanski & Dell’Antonio (1998)
21/31

Problems with cold dark matter ?
Observations Observations favor the presence of
core rather than cusp.
Rotation Rotation curves of low-surface brightness
galaxies
Cluster Cluster mass profile from gravitational lensing
still still controversial, but ...
Cold Cold dark matter is really collisionless ?
Self-interacting Self Self-interacting interacting dark matter
(Spergel & Steinhardt 1999)
Bar-driven Bar-driven Bar driven core formation ?
(Weinberg & Katz 2001)
22/31

Constraining halo central density
profiles with gravitational lensing
Number Number statistics of QSO multiple
images
(Wyithe, Turner & Spergel 2001; Keeton & Madau 2001;
Li Li & Ostriker 2001; Takahashi & Chiba 2001)
Arc Arc statistics
(Bartelmann et al. 1998; Molikawa & Hattori 2001;
Oguri, Taruya + YS 2001)
Time-delay Time-delay Time delay statistics of QSO multiple
images
(Oguri, Taruya, YS + E.L.Turner 2001)
23/31

MS2137-2353
MS2137 2353
(z=0.313)
Radial arc
Tangential
arc
Tangential and radial arcs
Hammer et al. (1997)
24/31

Model for halo density profile
Halo density profile
Concentration parameter
Log-normal Log Log-normal normal distribution for scatter in c norm
∆(log cvir )=0.18 (Bullock et al. 2001; Jing 2000)
Free parameters: c norm and norm and αα α
25/31

Expected number of of arcs
Number of arcs per unit solid angle
Number of arcs per given halo
Cross section of arc
formation in a given halo
halo mass function
(lens objects)
Galaxy
luminosity
function
(sources)
Oguri, Oguri Oguri, , Taruya & Suto (2001)
26/31

Constraints from the existing arc samples
tentative application to 13 galaxy clusters
with SX >10-12 erg/s/cm2 tentative application to 13 galaxy clusters
with SX >10 and 0.1

Dark halo approach to to clustering
Beyond this redshift,
dark matter clustering
below the mean
separation of particles
in N-body method is
seriously affected by
discreteness.
Dark matter clustering
= halo density profile
+ halo-halo correlation
(e.g., Peebles 1980; Seljak 2000;
Ma & Fry 2000)
Quantitative check of of the
accuracy of of N-body
simulations below the
mean particle separation
(Hamana, Yoshida + YS 2001)
30/31

Conclusions
Halo Halo clustering: a phenomenologically
successful model on the light-cone light light-cone cone
gravitational gravitational nonlinear evolution
redshift-space redshift-spacedistortion distortion
mass-, mass-, time-, and scale-dependent bias
selection selection function
evolution evolution in the survey volume itself
Halo Halo density profiles: still controversial
LSB/dwarf galaxies, CL0024-1654: a flat core
N-body simulations, gravitational lensing : a cusp
Needs further work from different aspects
31/31

Profiles in in higher-resolution simulations
Fukushige
& Makino (1997)
r[kpc]
1 10 100
Moore et al. (1998)
mass
resolution
inner slope in
higher-resolution
higher higher-resolution resolution
simulations is
steeper (~ –1.5) 1.5) than
the NFW value (–1.0) ( (–1.0) 1.0)
force
resolution
Moore et al. (1998)
33/31

Mass function of of dark halos
The Press-Schechter
mass function
underpredicts, while
an empirical
correction by Sheth &
Tormen (1999)
overpredicts, the
Hubble volume
simulation data at
high mass (Jenkins
et al. 2001).
Hamana, Hamana Hamana, , Yoshida, Suto & Evrard (2001)
34/31