Transcript Formation and structure of dark matter halos in N-body and SPH simulations

Sino-France Workshop – Dark Universe Sep 2005@ CPPM, France
Formation and structure of dark
matter halos in N-body and SPH
simulations
Wei-Peng Lin
The Partner Group of MPI for Astrophysics,
Shanghai Astronomical Observatory, CAS,
P.R.China
Introduction of our group



The Partner Group of Max-Planck-Institute for Astrophysics,
Shanghai Astronomical Observatory was founded in year
2000 through the exchange program between CAS and
Max-Planck Society (MPG). The goal of establishing this
group is to create an active research group which will play
an important role in promoting cosmological research in
China, in enhancing the existing exchanges between
Chinese and German astronomers, & in training
outstanding young cosmologists.
The group is carrying out research on numerical
simulations of galaxy formation and on statistical analysis
of large scale structures.
Group Head: Dr Yi-Peng Jing. We now have 6 faculty
members, 8 graduate students and several visitors.
Our Interests
Dark Energy
 Large Scale Structure, statistic, 3PCF, PVD
 Galaxy Formation, semi-analytical model, HOD
 Weak lensing, cosmic shear, spin-spin correl.
 Strong lensing, giant arc
 Sunyav-Zedovich effect, x-ray
 Simulations, N-body, SPH
 Halo formation, structure, angular momentum
 Quasar Absorption Line Systems

Contents
 Part
I: The formation-time distribution of
halos in N-body simulations
 Part II: The structure of halos in N-body
simulations
 Part III: The structure of halos in Nbody/SPH simulations
Part I The formation-time distribution of halos
(Lin, Jing & Lin 2003, MNRAS)
Why and what to do?
 The
“blue-color” problems of dwarf
galaxies
Small halo forms earlier than large one,
thus stars form earlier and they are “old”,
metal-rich, red!
 Theories of galaxy formation can hardly
solve this problem!
F.C.van den Bosch 2002 (MNRAS 332, 456)
red
？
blue
The impact of cooling and feed back on disc galaxies
Questions
How many fraction of dwarf galaxies form at
low redshift?
From tidal debris or just newly form out of
over-dense regions?
Can theories predicted consistent results
with N-body simulations?
What theory?
Press－Schechter formalism
Extended PS theory,e.g.,Lacey & Cole
(1993)：
simple linear growth of over-density field.
simple threshold for over-dense regions to
collapse and form virial objects.
predict the formation of haloes, mass
function, conditional mass function, halo
formation redshift, halo survival time, halo
merger rate, etc.
PS formalism
 Has
been used to construct galaxy
“Merger Trees” in semi-analytical models
of galaxy formation: cooling, star formation,
feedback, yield, outflow (super-wind), etc.
Kind of Successful!
Shortcoming: no environmental effect, no
interaction between different scales, nonlinear evolution of structures
The formation-redshift distribution of
dark matter haloes
Example: EPS approach by Lacey & Cole (1993)
 A parent halo with mass of M2, if define its
formation time as the epoch when its largest
progenitor have half of the mass, the conditional
probability is

P(t f  t1 | M 2 , t2 )  P( M 1  M 2 / 2, t1 | M 2 , t2 )
M (S2 )

f s1 ( S1 , 1 | S 2 ,  2 )dS1
S2 M (S )
1
Sh
where S h  S ( M 2 / 2), S   ( M )
2
Conditional
mass
function
Let t2＝t0， M2＝M0，and
~
S  ( S  S 0 ) /( S h  S 0 ),
~  (   0 ) / ( S h  S 0 )
we have
1
~
~ ~ ~
~
P( t f )  P(  f )    ( S ; S 0 , S h ) K ( S ,  f )dS ,
0
M (S0 )
~
where  ( S ; S 0 , S h ) 
M (S )
~ ~
K (S , f ) 
1
(2 )1/ 2
2


(  ) 
exp 

2/3
(S )
2

S


So that we can derive the halo formation time:
2
2
~
 c (t f )   c (t0 )   f  ( M 0 / 2)   ( M 0 )
 c (t ) is the critical over - density for a region
to collapse into a halo. It can be reduced from
linear growth of overdensit y field, and is a
function of  0 .
tf zf
zf
M*≈1.66x1013 M⊙/h
50
%
The improvement of the excursion set
approaches
 Ellipsoidal
collapse：Sheth & Tormen
1999; Sheth, Mo & Tormen 2001, Sheth &
Tormen 2002
 Non-spherical collapse boundary (Chiueh
& Lee 2001, Lin, Chiueh & Lee 2002) 6-D
random walks
EC or NCB models
** For EC/NCB models, the threshold is higher
for smaller haloes. Not a constant!
 The moving barrier for EC model:
B( 2 , z )  a sc ( z )[1   (a )  ]
  [ sc ( z ) /  (m)]
 The unconditional mass function and
conditional mass function are modified
2
Black: EPS
Red: EC
Blue: NCB

previous comparison with simulations：
unconditional/conditional mass function，
formation time（mainly for high mass haloes，
because of low resolution）
F.C.van den Bosch 2002
The N-body simulations
CDM：m＝0.3， ＝ 0.7
 Box: A 25 h-1Mpc (small haloes), B 100 h-1Mpc(subM* haloes), C 300 h-1Mpc(Large haloes)
 CDM power spectrum: ＝0.2，8＝0.9/1.0/1.0
 Total Number of Particles: A/B 2563, C 5123
 Mass of particles: A 7.7x107h-1M⊙, B 4.9x109h-1M⊙,
C 1.67x1010 h-1M⊙
 P3M；softening 2.5 h-1kpc
 Time-steps/outputs A: 5000/165; B: 600/30;
C:1200/36

Definitions of halo and formation redshift
 FOF
group method to select haloes; The
points with min-potential as halo center;
spherical virial halo assumption
 The formation redshift：when the largest
progenitor for the first time has half of the
parent-halo’s mass, the redshift at this
epoch is defined as the formation redshift
of the parent halo.
Methods…
 Particle
tracing methods：select a parent
halo, find its member particles, trace these
particle back at the last output step and
check if they inhabit in some progenitor
haloes, calculate the fraction of member
particles inside each progenitor halo, and
so on
 Calculate the redshift distribution
possibility of the formation redshifts and
compare with theory predictions
25 Mpc/h
10-3 to10-2 M*
Green: Simulations
Black: EPS
Red: EC
Cyan: NCB
2 realizations
Results for small mass haloes
In contrast to the anticipations, the formation
redshifts of small haloes are averagely larger
than the theoretical predictions by EPS
 At low redshifts, the prediction by ellipsoidal
collapse (EC) are consistent with simulated
results; at high redshifts, the EPS prediction is
better, while EC/Non-spherical collapse
boundary model (NCB) predict too large fraction
of haloes formed.
 The simulated profile of formation redshift
distribution is narrow but higher than prediction,
and shift to higher redshift.

More results…
 We
found 10~15% small haloes once sink
into some big halo within its half virial radius
and then come out.
These strong interaction may trigger star
bursts and form lots of young stars (thus
make the color blue), however, the physics
for gas procedures is complex.
Discussion
If simulation results are believable, the “blue-color”
problem of dwarf galaxies can not be solved
directly (formation shifts to higher redshift).
 other ways to solve the problems:
1. Even if the fraction of haloes formed at low
redshifts is small, however they posses enough
number of blue dwarf galaxies in observations.
2. When small haloes formed at high redshifts,
they are pre-heated, gas temperature is too high
to be cooled down to form stars, i.e. the star
formation was delayed.

Discussion..
3. Gas in small haloes was stripped off at
high redshifts, thus can not form large
amount of stars; They accrete gas again
at some lower redshift to form stars (so
that the stars are young, mental poor
and blue).
4. Other possibilities, for example:
environmental effects, star formation by
galaxy interaction, other unknown
physics, etc.
100 Mpc/h
0.03 to 0.3 M*
Sub-M* haloes
3 realizations
300 h-1Mpc
5123 particles
0.17 to 8.74 M*
1 realizations
More to be done
 The
improvement of conditional mass
function to lower mass end (in progress
by using simulation with 1024^3
particles).
 The survival probability of haloes.
 The dynamical evolution of haloes.
Part II The structure of haloes in Nbody simulations
 vir ρ crit f (cvir )
ρ ( x) 
2
c vir x(1  c vir x)
NFW density profile
3
c
f (c ) 
3ln( 1  c)  c /(1  c)
cvir  Rvir / rs , x  r / Rvir
3M vir
 vir 
3
4π rvir
ρ crit
 18π  82[( z )  1]  39[( z )  1]
2
2
Example of NFW
fitting
Redshift
evolution of Cvir
From top to
bottom: z=0, 0.5,
1.0, 2.0
Black：1012M⊙，
slop -0.99± 0.08
Red：1013M⊙ ，
slop -0.94± 0.08
Green：1014M⊙,
slop -0.90± 0.08
Black：1012M⊙，
slop -0.91± 0.07
Red：1013M⊙ ，
slop -0.88± 0.07
Green：1014M⊙,
slop -0.82± 0.07
Blue Curve: progenitor
LCDM
Zhao et
al.(2003)found there
is close correlation
between rs and Ms for
main progenitor
haloes
The same relation
was found for all
haloes
solid (z=0) 1.96
dot (z=1.0) 1.93
dash (z=2.0) 1.72
Here rs is in physical
scale
Zhao et al. 2003
This relation has been used to predict halo concentration accurately
The relation of halo structure and
formation epoch
As a halo formed earlier, its environmental
mass density is higher, therefore its core is
denser and more compact, hence with bigger
concentration factor cvir
 cvir (1+zf)0.6,the dependence is much more
stronger than that on halo mass（M-0.1）; its
scatter span reflects the span of halo formationtime distribution.
 Other reasons of scatter of cvir：deviation from
NFW, fitting errors, sub-structure, nonequilibrium halo, halo ellipsoidal halo, etc.

Cvir
∝(1+zf)0.603M
vir-0.065
Dependence on
formation redshift:
Formed earlier,
when mass density
is higher, halo core
is more compact
Dependence on
halo mass: Larger
halo has averagely
smaller formationredshift
Part III The halo structure in Nbody/SPH simulations
The dynamical interaction between baryonic matter
and DM
 Would the relatively small fraction of gas has
impact on the distribution of dark matter in halo?
(adiabatic/with cooling/with star formation)
 Who will win, dynamical friction of big galaxy
clumps sinking in to halo center or adiabatic
compress effect?
 Two body heating, as artificial fact in simulations?
The problems of the central distribution of matter of
dark haloes are hot topic
The central density profiles have cusps in
(CDM) N-body simulations, while
observations of galaxies and clusters show
at least some objects have shallow density
profiles and even have core-like structures.
SIMP, WIMP, WDM?
Why to study the density profiles of clusters of
galaxies? No strong effects from complex star
processes, relatively clean and simple in some
sense.
So far, people have just begun to study the
structures of haloes by simulations with gas and to
investigate dynamical interaction of dark matter
with gases components.
Only 16 percents of mass in baryons (WMAP
results); Weak interaction between DM and baryon
particles
•Observations of galaxy clusters（Sand et al.
2002,2003）concluded：
in the central part of clusters of galaxies, the
density profiles are more flat than NFW profile,
i.e.,   r-0.5.
However, Bartelmann & Meneghetti 2004, Dalal
& Keeton 2004 weaken this constrain by taking
into account the non-spherical structures of
haloes.

Assuming a NFW halo and simulating the infall of
galaxies, El-Zant et al.(2002, 2004) found the
dynamical friction on the galaxies can transfer
orbital energy to and heat up DM in the central
part of the halo, thus make shallow density profile.

Counter effect: adiabatic compression from
baryonic matter. (Blumenthal et al. 1986, Mao, Mo
& White 1998, Rasia et al. 2004): the adiabatic
contraction of baryon can transfer energy from
DM to gas therefore make the density profile
steeper.

So, we use hydro-dynamical N-body simulations
to find whether the dark matter profile can be
affected by gaseous components.
Our simulations
A set of simulations: one is adiabatic, one with
weak cooling and another with strong cooling.
Each have 1283 DM and 1283 gas particles.
 A pure DM simulation provides control sample.
 All realizations have the same initial condition.
 We selected the first 12 biggest haloes (clustersize).
 An additional high-resolution simulation with
2563 DM and 2563 gas particles using Gadget
(Springel, Yoshida & White 2001) to study the
adiabatic case.

1283
P3M
Mgas=2.4E9M
Mdm=2.2E10M
2563
Gadget:
Tree-code
Mgas=3.0E8M
Mdm=2.8E9M
Fitting from 2% virial radii
1283 simul.
2563 simul.
Overcooling?
results:
•We find that adiabatic compression can make
the DM density profile steeper even if the
dynamical friction effect has been taken into
account in the simulations.
•In simulations with cooling, DM density
profiles become even steeper than in adiabatic
case.
•The additional simulation using Gadget and
with 2563 DM and 2563 gas particles confirm our
result with low-resolution .
Implications:
 If
our results are correct, the overall
density profiles of haloes remains NFW
form but with larger concentration
factors and the DM-only profiles
become even steeper. This may have
effects in the observations of
gravitational lensing.
Discussions
Why in El-Zant et al’ (2002,2004) simulations,
they got flat density profile?
The possible reasons are:
a very strong working assumption is that there
has been already a NFW halo where galaxy
clumps spiral in. In fact, the hierarchical growth
of halo by merger and accretion were omitted;
in their simulation, adiabatic compression
effect and tidal stripping were not taken into
account.
Adiabatic
Compression
Winner in our
simulations
Dynamical
Friction
Discussions

We need simulations with higher resolution to
confirm our results. There could be some
resolution effects, for example, gas particle are
much lighter then DM particles in the
simulations, softening length is too large, etc.

Over-cooling problems: thermal
feedback,thermal conduction, AGN, particle
annihilation, etc.

Dynamical friction and tidal stripping on
substructures and/or luminous systems.
Discussions
 Two-body
heating (Steinmetz & White
1997)
gas particle are much lighter than DM
particles in the simulations
Yoshikawa, Jing & Suto 2000
Works in progress
with 2563 gas particles and 5123
DM particles. Particle mass of gas and DM
will be almost comparable. Simulation done!
 Using simulations with star formation and
feedback. With 5123 DM and the same
number of gas particles. Simulation done!
 Re-simulations of some regions with much
higher-mass and force resolutions. Outside,
DM only. In preparation……
 Simulations
Parallel simulations in Shanghai
Supercomputer Center
SSC: 2048 Processors (512 nodes, Myrinet), once
ranked among Top 10 (we were permitted to use
512 CPUs)
 Simulations done so far:
10243 DM, 5123 DM+ 2563 GAS (adiabatic) , 5123
DM+ 5123 GAS (adiabatic/star formation), all with
the same IC, 100 h-1Mpc
simulations with DE
 Simulations in preparation:
re-simulations, 10243 DM+ 10243 GAS
(adiabatic/star formation, 300 h-1Mpc)

Thanks for patience!
Welcome to visit the Partner Group of
MPA in Shanghai Observatory
and welcome for collaborations!