An excessive core collapse and its limitation in cosmological simulations

1. An excessive core collapse and its limitation in cosmological simulations Weike Xiao xwk@mail.tsinghua.edu.cn

2. N-body Simulation Method • Have got huge success in cosmological studies • For LCDM model: Nice agreement with observations: Power spectrum Correlation function Mass function Halo model … …

3. Some problem on small scale • DM halo density profile • NFW model: Navarro,Frenk & White (1996,97) the Halo(10^4 particle)density profile, can be discribed with an uniform func: • Higher resolution results (10^6): Moore 1999, Ghigna 2000,Klypin 2001 • More higher results even < 1 Power 2002, Stoehr 2003. • “the cusp problem”

4. Gentile et al.对dwarf galaxy DDO 47

5. W.J.G. de Blok et al. LSB galaxies (with two different methods)

7. “the substructure problem” • Less than 50 dwarf galaxies in the local group was found. • Similar results in neighbor clusters • Simulation results predict 10-100times of substructures (10^10-11 M_sun)

9. Explanations • LCDM model should be changed: SIDM WDM Modified Newtonian Dynamics(MOND) • Effects of baryons on small scales: feedback model, SBH…. • Delay of Observations: small dark halo gravitational lensing method…

10. The particle number N in simulations • Started 1970th, 400 particles • Yasushi Suto found: • At Dec. of 2348, • Astro/ph-0311575

11. The Particle number in simulations

12. The limitation of N: • To keep the mean density, large particle mass: • It’s acceptable for large scale problems. each particle  one galaxy ( or one Halo)

13. But for small scale topics: • We got the statistical property of the “Huge mass particle system” from simualtion • But in particle physics:  GeV candidates

14. Dark Matter Particle Candidates

15. A Physical Bias Exist • For a given box size L:

16. The problems • Do they have the same dynamic and stitistical property? • How will it affect the simulation results? • At what time should it be considered? • any relationship with the “cusp problem” and the ”substructure problem”? • How to avoid the result of such a bias?

17. From the viewpoint of each particle: • Different density fluctuation • The two-body relaxation

18. Define the “mean free path” Ls: • For a virialized spherical system:

19. The relaxation time scale: • For a given halo, Ls ~ N. • If the AE bias calls:

20. equivalent scattering cross section • Follow the way of SIDM: • In simulation: • Near the value needed in SIDM • an excessive cross section exist!

21. How will it affect the whole system? • Excessive scatter cross section can make E and L transition more effectively • Relaxation  Ei and Li be changed • Evaporation : Ei > 0  fly away • 2T+U=0 • Negative thermal capacity • Core collapse

22. Core collapse process of one globular cluster (M. Freitag 2001)

23. Time scale of core collapse • Based on Fokker-Planck eq., • Follow the way of Spitzer & Hart(1971)

24. What can we see? • For the same halo, (given M,rh) different m: • For one simulation, (given m) different halo:

25. If tcc < tu  introduce an excessive core collapse of the halo! • For one halo of the Milky Way, need more then 10^4 particles in sim. • The nowaday simulation, low z 10^6~10^8

26. Evolution scenario at the halo center (Toshiyuki Fukushige, 2003)

27. But in cosmological sim • CDM model, hierarchical clustering small halos, at high z, 10~10^2 particles For people use Kny when generate the initial conditions

28. For small halos in early univ • An excessive core collapse was introduced! • They will have a too cuspy center • How will it affect the simulation result?

29. Major merger M1<~10 M2 • Center part will soon merge • Cusp center can be kept, densiter profile keeps to be the deeper one only core+core = > core • Stelios Kazantzidis et al 2006 • Boylan-Kolchin et al.2004 • Astro-ph/0301271

30. Minor merger M1 >> M2 • core center small halo, will soon melt together with large halo • Cusp center small halo, the cusp center won’t be demaged, be a new substructure

31. How will the results be affected? • Init small halos will experience an excessive core collapse, got an unexpeted cusp center • In merging process, they can be kept: Major merger: the new halo will get a too cusp center .cusp problem Minor merger : the cusp can be kept as one more unexpected substructure of the large halo too many substruc: substructure problem

34. How to avoid it? • One reliable simulation result should avoid such excessive core collapse • To avoid the excessive core collapse for the init small halos • Make sure they can include enough particles

35. Limitation for generiting the initial condition • The mass within one shortest wavelenth: • The half mass radio: • The mass of each particle

37. For nowaday simulations • Ng for FFT trasition: (Ng/2)^3=N K_max == K_Nyquist • There will must be many small halos with 10~10^3 particles experence the excessive core collapse  excessive cusp problem & substructure problem.

38. How to avoid it? • Sensitive to : N, L, Kmax • 1. Increase N, but Kmax should be kept! • 2. When generating the initial condition, cut P(k) with K<Kcut • 3. Smaller L • resimilation: L’<L keeping : K<Kcut. L’<L  K’cut>Kcut. different with HDM model

41. Expecting numerical testing What can we expect • When N increased, but still use(k_max=k_Nyquist), substructure will increase, cusp still exists. • To keep Kmax & L unchanged, N’=N*(2Pi)^3~250 N, we can avoid the excessive core collapse • N,Lunchanged, to use K<Kcutfor P(k)_ini

42. Thank you!

43. Halo Model

44. Ant-Elephant bias Ant-Elephant (AE) Bias