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

1
Formation and structure of dark matter halos in
N-body and SPH simulations
Sino-France Workshop Dark Universe Sep 2005_at_
CPPM, France

• Wei-Peng Lin
• The Partner Group of MPI for Astrophysics,
  Shanghai Astronomical Observatory, CAS, P.R.China

2
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.

3
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

4
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

5
Why and what to do?
Part I The formation-time distribution of halos
(Lin, Jing Lin 2003, MNRAS)

• 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!

6
F.C.van den Bosch 2002 (MNRAS 332, 456)
red
?
blue
The impact of cooling and feed back on disc
galaxies
7
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?

8
Press-Schechter formalism
What theory?

• 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.

9
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

10
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

Conditional mass function
11
Let t2t0, M2M0,and
12
So that we can derive the halo formation time
tf ?zf
13
(No Transcript)
14
zf
15
M1.66x1013 M?/h
16
50
17
The improvement of the excursion set approaches

• Ellipsoidal collapseSheth Tormen 1999 Sheth,
  Mo Tormen 2001, Sheth Tormen 2002
• Non-spherical collapse boundary (Chiueh Lee
  2001, Lin, Chiueh Lee 2002) 6-D random walks

18
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

19
Black EPS Red EC Blue NCB
20

• previous comparison with simulationsunconditiona
  l/conditional mass function,formation time(mainly
  for high mass haloes,because of low resolution)

21
F.C.van den Bosch 2002
22
The N-body simulations

• ?CDM?m0.3, ?? 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,?80.9/1.0/1.0
• 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?
• P3Msoftening 2.5 h-1kpc
• Time-steps/outputs A 5000/165 B 600/30
  C1200/36

23
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 redshiftwhen the largest
  progenitor for the first time has half of the
  parent-halos mass, the redshift at this epoch is
  defined as the formation redshift of the parent
  halo.

24
Methods

• Particle tracing methodsselect 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
25 Mpc/h
10-3 to10-2 M
Green Simulations Black EPS Red EC Cyan
NCB
2 realizations
26
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.

27
More results

• We found 1015 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.

28
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.

29
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.

30
100 Mpc/h
0.03 to 0.3 M
Sub-M haloes
3 realizations
31
300 h-1Mpc 5123 particles
0.17 to 8.74 M
1 realizations
32
More to be done

• The improvement of conditional mass function to
  lower mass end (in progress by using simulation
  with 10243 particles).
• The survival probability of haloes.
• The dynamical evolution of haloes.

33
Part II The structure of haloes in N-body
simulations
NFW density profile
34
Example of NFW fitting
35
Redshift evolution of Cvir From top to bottom
z0, 0.5, 1.0, 2.0
36
Black1012M?, slop -0.99 0.08 Red1013M? ,
slop -0.94 0.08 Green1014M?, slop -0.90 0.08
37
Black1012M?, slop -0.91 0.07 Red1013M? ,
slop -0.88 0.07 Green1014M?, slop -0.82
0.07 Blue Curve progenitor
38
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
(z0) 1.96 dot (z1.0) 1.93 dash
(z2.0) 1.72 Here rs is in physical scale
LCDM
39
Zhao et al. 2003
This relation has been used to predict halo
concentration accurately
40
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 ?(1zf)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 cvirdeviation from
  NFW, fitting errors, sub-structure,
  non-equilibrium halo, halo ellipsoidal halo, etc.

41
Cvir ?(1zf)0.603Mvir-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
42
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?

43
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?

44

• 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

45

• 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.

46

• 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.

47
(No Transcript)
48
(No Transcript)
49
(No Transcript)
50
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
  (cluster-size).
• An additional high-resolution simulation with
  2563 DM and 2563 gas particles using Gadget
  (Springel, Yoshida White 2001) to study the
  adiabatic case.

51
1283 P3M
Mgas2.4E9M? Mdm2.2E10M?
52
2563 Gadget Tree-code
Mgas3.0E8M? Mdm2.8E9M?
53
(No Transcript)
54
(No Transcript)
55
Fitting from 2 virial radii
1283 simul.
Over-cooling?
2563 simul.
56

• 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 .

57
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.

58
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.

59
Adiabatic Compression
Dynamical Friction
Winner in our simulations
60
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.

61
Discussions

• Two-body heating (Steinmetz White 1997)
• gas particle are much lighter than DM
  particles in the simulations

62
Yoshikawa, Jing Suto 2000
63
Works in progress

• Simulations 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

64
(No Transcript)
65
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)

66

• Thanks for patience!
• Welcome to visit the Partner Group of MPA in
  Shanghai Observatory
• and welcome for collaborations!