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

Sino-France Workshop – Dark Universe Sep 2005@ CPPM, France

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 N-body/SPH simulations

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!

Part I The formation-time distribution of halos

(Lin, Jing & Lin 2003, MNRAS)

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 wit

h N-body simulations?

Press－ Schechter formalism Extended PS theory,e.g.,Lacey & Cole (199

3) ： simple linear growth of over-density field. simple threshold for over-dense regions to c

ollapse and form virial objects. predict the formation of haloes, mass functi

on, conditional mass function, halo formation redshift, halo survival time, halo merger rate, etc.

What theory?

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, non-linear 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

)(),2/( where

),|,()(

)(

),|,2/(),|(

22

122111

2

22121221

12

MSMSS

dSSSfSM

SM

tMtMMPtMttP

h

s

S

S

f

h

Conditional mass

function

Let t2 ＝ t0 ， M2 ＝ M0 ， and

SSSK

SM

SMSSS

SdSKSSSPtP

SS

SSSSS

f

h

fhff

h

h

2

)(exp

)()2(

1)~,

~(

)(

)(),;

~( where

,~

)~,~

(),;~

()~()(

have we

)(/)(~),/()(

~

2

3/22/1

00

1

0 0

00

00

So that we can derive the halo formation time:

. offunction

a is and field,y overdensit ofgrowth linear

from reduced becan It halo. a into collapse to

region afor density -over critical theis )(

)()2/(~)()(

0

02

02

0

t

MMtt

c

fcfc

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:

The unconditional mass function and conditional mass function are modified

2

2

)](/)([

])(1)[(),(

mz

azazB

sc

sc

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(sub-

M* 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

Green: Simulations

Black: EPS

Red: EC

Cyan: NCB

25 Mpc/h

10-3 to10-2 M*

2 realizations

Results for small mass haloes In contrast to the anticipations, the formation red

shifts 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-colo

r” 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 red

shifts 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.

Sub-M* haloes

100 Mpc/h

0.03 to 0.3 M*

3 realizations

300 h-1Mpc

5123 particles

1 realizations

0.17 to 8.74 M*

More to be doneThe 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 N-body simulations

22

crit3

vir

virvir

virvirvir

3

2virvir

vir critvir

]1)([39]1)([82π18

ρ 4π

M3

/ ,/

)1/()1ln(3)(

x)cx(1c

)(ρ )(ρ

zz

r

RrxrRc

ccc

ccf

cfx

s

NFW density profile

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

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

LCDM

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 formation-time distribution.

Other reasons of scatter of cvir ： deviation from NFW, fitting errors, sub-structure, non-equilibrium halo, halo ellipsoidal halo, etc.

Cvir (1+z∝ f)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 formation-redshift

Part III The halo structure in N-body/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 w

eak 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 (cluster-s

ize). An additional high-resolution simulation with 256

3 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

2563 simul.

1283 simul.

Over-cooling

?

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 den

sity 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, th

ey 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

DynamicalFriction

Winner in our simulations

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.

DiscussionsTwo-body heating (Steinmetz & White

1997)

gas particle are much lighter than DM particles in the simulations

Yoshikawa, Jing & Suto 2000

Works in progressSimulations 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……

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/st

ar formation, 300 h-1Mpc)

Thanks for patience!

Welcome to visit the Partner Group of MPA in Shanghai Observatory

and welcome for collaborations!