1. Cosmological N-body simulations of structure formation Jürg Diemand, Ben Moore and Joachim Stadel, University of Zurich

2. Main Goals: large scale structure of CDM large scale structure of CDM internal properties of CDM halos (profiles, substructure) internal properties of CDM halos (profiles, substructure)Challenges: large dynamic range large dynamic range two body relaxation, “Ant-Elephant Bias”??? Methods: two body relaxation, “Ant-Elephant Bias”??? Methods: refinements of the initial conditions refinements of the initial conditions multi-mass halos multi-mass halos

3. Relaxation Time Def: Time when rms of energy changes due to encounters becomes equal to mean energy. Def: Time when rms of energy changes due to encounters becomes equal to mean energy. Fokker-Planck estimate: Fokker-Planck estimate: Globular clusters: T ≃ 100 Myr to 10 Gyr Globular clusters: T ≃ 100 Myr to 10 Gyr Stars in a galaxy: T ≃ 10 15 yr Stars in a galaxy: T ≃ 10 15 yr CDM in a galaxy halo: T ≃ 10 65 yr CDM in a galaxy halo: T ≃ 10 65 yr

4. Two Body Relaxation N =10 000 Equilibrium Hernquist Model with massless tracers (green) in a plane

5. Two body relaxation DM in N-body simulation: T = one Hubble time in a halo with N = 5'000, and DM in N-body simulation: T = one Hubble time in a halo with N = 5'000, and T(r) = one Hubble time, for r = 0.01 rvir in a system with N = 1 million. (Power et al. 2003) T(r) = one Hubble time, for r = 0.01 rvir in a system with N = 1 million. (Power et al. 2003) "Resolved radius" ~ N -0.5 "Resolved radius" ~ N -0.5 2 WIMPs at 1kpc 2 bodies at 1kpc

6. Two body relaxation DM in N-body simulation: T = one Hubble time in a halo with N = 5'000, and DM in N-body simulation: T = one Hubble time in a halo with N = 5'000, and T(r) = one Hubble time, for r = 0.01 rvir in a system with N = 1 million. (Power et al. 2003) T(r) = one Hubble time, for r = 0.01 rvir in a system with N = 1 million. (Power et al. 2003) "Resolved radius" ~ N -0.5 "Resolved radius" ~ N -0.5 2 WIMPs at 1kpc 2 bodies at 1kpc ● BUT: N is always small in the first CDM objects, also at high resolution! (Moore 2001, Binney & Knebe, 2002)

7. cluster with 650'000 particles log densitylog "relaxation" Relaxation in cosmological runs cluster with 650'000 particles

8. Effect on final object? N=4'000 Hernquist halo, IC and after 1 and 3 mean relaxation times: merging... final profile also shallower

9. Relaxation in cosmological simulations Relaxation is present in CDM simulations Relaxation is present in CDM simulations Increasing N helps, but slowly ( N -0.25 ) Increasing N helps, but slowly ( N -0.25 ) Continue to look for convergence by using more particles!

10.  Refinement: Resimulating halos with better mass resolution

11. Highest resolution numerical simulations of the structure of dark matter halos 10 5 steps 10 8 particles High mass and force resolution

12. Cluster formation movie

13. Convergence tests in CDM clusters  Numerical flattening due to two body relaxation: slow convergence, 1 million to resolve 1% of Rvirial, 1000 to resolve 10% ! (Moore et al. 1998; Diemand et al. 2004) 14 million 6 million 1.7 million 0.2 million

14. Convergence tests in CDM clusters  Numerical flattening due to two body relaxation: slow convergence, 1 million to resolve 1% of Rvirial, 1000 to resolve 10% ! (Moore et al. 1998; Diemand et al. 2004)  Numerical Overmerging: incomplete subhalo sample for N<100 14 million 6 million 1.7 million 0.2 million

15. Our clusters (PKDGRAV) Fukushige et al. 2004 (treecode on GRAPE) Hayashi et al. 2004, Navarro et al. 2004 (GADGET) Tasitsiomi et al. 2004 (ART) Wambsganss, Bode, Ostriker 2004 (TPM)

16. CDM clusters profiles  Agreement among simulators. 5 different groups using different codes and initial conditions.  Generalized NFW profiles with inner slopes of -1.16 +- 0.14 fit our 6 cluster profiles very well.  Cored or cusped in the center? Still open at this resolution...

17. Resolving the inner halo with a multimass approach Reducing the high resolution region to the core forming part reduces CPU time by a factor of 10 ! Works well for the 6 million particles cluster Now we are running the same system at an effective resolution of 130 million particles inside the virial radius

18. Resolving the inner halo with a multimass approach Preliminary results show convergence towards a power-law inner profile Density profile: logarithmic slope:

19. First objects in a SUSY-CDM universe 3 kpc (comoving) box containing a 60 pc high resolution region. 100 Gev SUSY-CDM power spectrum with a cutoff at 10 -6 solar masses (Green etal.2004) Mass resolution of 2x10 -10 solar masses

20. First objects in a SUSY-CDM universe 3 kpc (comoving) box containing a 60 pc high resolution region. 100 Gev SUSY-CDM power spectrum with a cutoff at 10 -6 solar masses (Green etal.2004) Mass resolution of 2x10 -10 solar masses

21. First objects in a SUSY-CDM universe 3 kpc (comoving) box containing a 60 pc high resolution region. 100 Gev SUSY-CDM power spectrum with a cutoff at 10 -6 solar masses (Green etal.2004) Mass resolution of 2x10 -10 solar masses Cumulative mass function

22. First objects in a SUSY-CDM universe Very dense objects R ~ 0.01 pc ~ 5000 AU They should survive as subhalos in the halo of the Milky Way Expected abundance: 10 15 Expected mean separation: 0.5 pc The solar system moves through one every 10 000 years. Bright annihilation signal in gamma-rays Typical density profiles at z = 26

23. Conclusions Structure of CDM halos is now well known, except: - in the very center (< 0.001 virial radii) - low mass substructure (fraction of smooth vs. clustered halo material?) For many astrophysical problems the influence of gasdynamics, star formation, black holes and various feedback(s) on CDM has to be included to make progress, e.g.: - adiabatic contraction - survival of subhalos in clusters - DM cusps or cores in galaxy halos