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 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 with N-body simulations?

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. 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 M 2, if define its formation time as the epoch when its largest progenitor have half of the mass, the conditional probability is Conditional mass function

Let t 2 ＝ t 0 ， M 2 ＝ M 0 ， and

So that we can derive the halo formation time: tf zf tf zf

zfzf

M * ≈1.66x10 13 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

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 -1 Mpc (small haloes), B 100 h -1 Mpc(sub- M * haloes), C 300 h -1 Mpc(Large haloes)  CDM power spectrum:  ＝ 0.2 ，  8 ＝ 0.9/1.0/1.0  Total Number of Particles: A/B 256 3, C  Mass of particles: A 7.7x10 7 h -1 M ⊙, B 4.9x10 9 h -1 M ⊙, C 1.67x10 10 h -1 M ⊙  P 3 M ； softening 2.5 h -1 kpc  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 to10 -2 M * 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.

Sub-M* haloes 100 Mpc/h 0.03 to 0.3 M* 3 realizations

300 h -1 Mpc particles 1 realizations 0.17 to 8.74 M *

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 N- body simulations NFW density profile

Example of NFW fitting

Redshift evolution of Cvir From top to bottom: z=0, 0.5, 1.0, 2.0

Black ： M ⊙ ， slop -0.99± 0.08 Red ： M ⊙ ， slop -0.94± 0.08 Green ： M ⊙, slop -0.90± 0.08

Black ： M ⊙ ， slop -0.91± 0.07 Red ： M ⊙ ， slop -0.88± 0.07 Green ： M ⊙, slop -0.82± 0.07 Blue Curve: progenitor

Zhao et al.(2003)found there is close correlation between r s 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 r s is in physical scale LCDM

Zhao et al 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 c vir  c vir  (1+z f ) 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 c vir ： deviation from NFW, fitting errors, sub-structure, non- equilibrium halo, halo ellipsoidal halo, etc.

C vir ∝ (1+z f ) M vir 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 ：Observations of galaxy clusters in the central part of clusters of galaxies, the density profiles are more flat than NFW profile, i.e.,   r 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.El-Zant et al.(2002, 2004)  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.hydro-dynamical N-body simulations

Our simulations  A set of simulations: one is adiabatic, one with weak cooling and another with strong cooling. Each have DM and 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 DM and gas particles using Gadget (Springel, Yoshida & White 2001) to study the adiabatic case.

128 3 P 3 M M gas =2.4E9M  M dm =2.2E10M 

256 3 Gadget: Tree-code M gas =3.0E8M  M dm =2.8E9M 

Fitting from 2% virial radii simul 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 DM and 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 Dynamical Friction 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.

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  Simulations with gas particles and DM particles. Particle mass of gas and DM will be almost comparable. Simulation done!  Using simulations with star formation and feedback. With 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: DM, DM GAS (adiabatic), DM GAS (adiabatic/star formation), all with the same IC, 100 h -1 Mpc simulations with DE  Simulations in preparation: re-simulations, DM GAS (adiabatic/star formation, 300 h -1 Mpc)

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