1.  CDM Subhalos P.Nurmi, P.Heinämäki, E. Saar, M. Einasto, J. Holopainen, V.J. Martinez, J. Einasto Subhalos in LCDM cosmological simulations: Masses and abundances, astro-ph/0611941

2. Dark matter cosmological simulations have had considerable success in modeling large-scale-structure in the Universe: CMB to present structures, abundance of massive galaxy clusters… Dark matter cosmological simulations have had considerable success in modeling large-scale-structure in the Universe: CMB to present structures, abundance of massive galaxy clusters… More detail simulations shows that there are still a number of discrepancies on smaller scales: More detail simulations shows that there are still a number of discrepancies on smaller scales: CDM predicts one-to-two orders of magnitude more satellite galaxies (subhalos) orbiting their host halos.. CDM predicts one-to-two orders of magnitude more satellite galaxies (subhalos) orbiting their host halos.. In simulations the density profiles of virialized galaxy scale CDM halos are too steep with respect to what is inferred from rotation curves of dwarf spiral and low surface brightness galaxies. In simulations the density profiles of virialized galaxy scale CDM halos are too steep with respect to what is inferred from rotation curves of dwarf spiral and low surface brightness galaxies. Probably mass is more smoothly distributed on smaller scales, baryonic physics causes small halos to remain starless? (Bullock et al. 2000,Somerville 2002, Springel et al. 2001). Galaxies and suhalos represent different population (Gao et al. 2004)? Probably mass is more smoothly distributed on smaller scales, baryonic physics causes small halos to remain starless? (Bullock et al. 2000,Somerville 2002, Springel et al. 2001). Galaxies and suhalos represent different population (Gao et al. 2004)? If predicted subhalos exist most of the satellites are completely (or almost completely) dark If predicted subhalos exist most of the satellites are completely (or almost completely) dark The predicted mini-halos are not observed Strong gravitational lensing (multiple quasar images and giant arc systems) provides an unique way to study the dark matter content of galaxies. The predicted mini-halos are not observed Strong gravitational lensing (multiple quasar images and giant arc systems) provides an unique way to study the dark matter content of galaxies.

3. Provide physical understanding: qualitative predictions of theoretical models Make observable predictions for testing models Knebe astro-ph/0412565

4. Different N-body codes are needed Different N-body codes are needed Numerical methods themselves are approximations: limitations in resolution, physics, numerical errors, bugs… Numerical methods themselves are approximations: limitations in resolution, physics, numerical errors, bugs… Different halo finding algorithms are needed Different halo finding algorithms are needed FOF, SKID, SO, DENMAX, BDM…. FOF, SKID, SO, DENMAX, BDM…. Large enough volume, sufficient mass resolution Large enough volume, sufficient mass resolution m p =(L/N) 3  0  c m p =(L/N) 3  0  c

5. N-body code MLAPM (Multi-Level-Adaptive-Particle-mesh) 1992-1997 (Andrew Green) MLAPM (Multi-Level-Adaptive-Particle-mesh) 1992-1997 (Andrew Green) First release (Alexander Knebe) First release (Alexander Knebe) Lightcone package (Enn Saar) Lightcone package (Enn Saar) Halo identification, AHF, Amiga Halo Finder (Stuart Gill) Halo identification, AHF, Amiga Halo Finder (Stuart Gill)  AMIGA (2005) Adaptive Mesh Investigations of Galaxy Assembly) Hydrodynamics already Parallelisation under way

6. AMIGA open source C-code open source C-code Tree-code which recursively refines cells – subgrids being adaptively formed in regions where the density exceeds a spesified threshold number of particles). Tree-code which recursively refines cells – subgrids being adaptively formed in regions where the density exceeds a spesified threshold number of particles). memory efficient memory efficient fast fast support for all sorts of input data support for all sorts of input data analysis tools analysis tools

7. A. Knebe astro-ph/0412565

8. The general goal of a halo finder is to identify gravitationally bound objects. The general goal of a halo finder is to identify gravitationally bound objects. Subhalos are virialized objects inside the virial radius of main halos. Subhalos are virialized objects inside the virial radius of main halos. Assuming each of density peaks in adaptive grids is the centre of a halo. Step out in (logarithmically spaced) radial bins until the radius r vir 1) where the density reaches  satellite(r vir ) =  vir (z)  b (z),  b is background density and  vir (z) is overdensity of the viralized objects or 2) radial density profile starts to rise. Assuming each of density peaks in adaptive grids is the centre of a halo. Step out in (logarithmically spaced) radial bins until the radius r vir 1) where the density reaches  satellite(r vir ) =  vir (z)  b (z),  b is background density and  vir (z) is overdensity of the viralized objects or 2) radial density profile starts to rise. Each branch of the grid tree represents a single dark matter halo within the simulation Each branch of the grid tree represents a single dark matter halo within the simulation From S. Gill thesis (2005) N-bodyGrid hierarchy

9. Essential parameter free Essential parameter free Halos on-the fly ( uses the adaptive grids of AMIGA to locate the satellites of the host halo.) Halos on-the fly ( uses the adaptive grids of AMIGA to locate the satellites of the host halo.) Halos, subhalos, sub-sub halos Halos, subhalos, sub-sub halos From A.Knebe talk in Helmholtz summer school 2006

10. Merger trees, tracking halos through time Merger trees, tracking halos through time

11. to reach the mass resolution we have in our B10 simulation for a single 80 Mpc/h cube would require 2048 3 particles,

12. Mass function Differential mass functions of all haloes in three simulations at two different redshifts z= 0 and z = 5 (see the legend in the Figure). The theoretical Press- Schechter (PS) and Sheth & Tormen (ST) predictions are also shown.

13. Resolution limit 10000 particles Resolution limit 10000 particles Subhalo MF seems to be universal : do not depend on the mass of the main halo.  -0.9 (Gao et al. 2004, Ghigna et al. 2000 Helmi et al. 2002). Weak dependence suggested by Reed et al. 2005. Reliable regions 100 particles

14. Evolution of the subhalo mass function Hints that slope of the subhalo MF is a function of redshift. (Subhalo MF might be steeper) Hints that slope of the subhalo MF is a function of redshift. (Subhalo MF might be steeper)

15. Subhalo mass fraction/Total halo mass Depends slightly on the total halo mass Mass fraction between 0.08-0.2. Might depend on the redshift

16. Subhalo mass fraction/Main halo mass Mass fraction varies 0.08- 0.33 Mass fraction varies 0.08- 0.33 Mass fraction larger at earlier redshifts ( van de Bosch et al. opposite results with semi-analytical model) Mass fraction larger at earlier redshifts ( van de Bosch et al. opposite results with semi-analytical model) More massive halos have a larger fraction of their mass in substructure: functional dependence: More massive halos have a larger fraction of their mass in substructure: functional dependence:

17. The distribution for logarithm of mass fraction can be approximated by a Weibull distribution. The distribution for logarithm of mass fraction can be approximated by a Weibull distribution. Distributions at different redshifts are similar but Distributions at different redshifts are similar but At earlier times the mass ratio were higher in the mean and small ratio wing not so prominent At earlier times the mass ratio were higher in the mean and small ratio wing not so prominent  Tidal distribution of subhalos - as the main halo evolves, subhalos gradually lose their mass

18. Halo environment Sphere of influence up to 16*r/r vir. Halo distribution not uniform Depends on redshift

19. Total mass fraction + subhalo MF + spatial distribution can be used to find the radial mass density distributions of subhalos, and the surface mass densities necessary for gravitational lensing studies. Total mass fraction + subhalo MF + spatial distribution can be used to find the radial mass density distributions of subhalos, and the surface mass densities necessary for gravitational lensing studies.

20. Conclusions Number of N-body particles to reliably select a halo: about 100 particles for subhalos, 10000 particles for main haloes harboring subhalos. Number of N-body particles to reliably select a halo: about 100 particles for subhalos, 10000 particles for main haloes harboring subhalos. Functional form of the mass function agrees well with earlier studies Gao et al. 2004, Kravtsov et al. 2004 Functional form of the mass function agrees well with earlier studies Gao et al. 2004, Kravtsov et al. 2004 The MF slope is same for main halos and subhalos. Slope is a function of redshift. The MF slope is same for main halos and subhalos. Slope is a function of redshift. Subhalo mass fraction depends on the main halo mass – more massive halos have larger mass fraction. Within the same main halo mass range, the subhalo mass fraction is larger at earlier epochs. Subhalo mass fraction depends on the main halo mass – more massive halos have larger mass fraction. Within the same main halo mass range, the subhalo mass fraction is larger at earlier epochs. The distribution for the logarithm of mass fraction can be approximated by a Weibull distribution. There is a systematic change in the distribution parameters as a function of redshift. The distribution for the logarithm of mass fraction can be approximated by a Weibull distribution. There is a systematic change in the distribution parameters as a function of redshift. The number density of haloes surrounding main haloes drops quickly as we move beyond the virial radius of the halo. However, the slope stays the same after that, up to distance about 3 *rvir. The sphere of influence of a halo reaches out to the distance of 16 times of its virial radius. Beyond this limit the number density of haloes is uniform. The number density of haloes surrounding main haloes drops quickly as we move beyond the virial radius of the halo. However, the slope stays the same after that, up to distance about 3 *rvir. The sphere of influence of a halo reaches out to the distance of 16 times of its virial radius. Beyond this limit the number density of haloes is uniform.

21. From V. Springel’s talk: Computers double their speed every 18 months (Moore's law) N-body simulations have doubled their size every 16-17 Months.