The Physical Properties of Cosmological Halos: Environmental Effects

1. The Physical Properties of Cosmological Halos: Environmental Effects Juhan Kim & Changbom Park Korea Institute for Advanced Study

2. History of Universe

3. Large-scale Structures Dubinski 2003

4. dark matter hot intracluster medium (ICM) Galaxies (Coma) What is dark matter halo? ROSAT Not spherical! Evrard and White et al. (1993)

5. what we don’t see Dark Matter Halo much larger than the galaxy itself! How do we know this? From the circular velocities of stars and molecular hydrogen in the disk of spirals (recall “flat rotation curves”) and from the highly non-circular stellar orbits in elliptical galaxies. Key property Same velocity spread of particles independent of position within the halo and density of material ∝ 1 / r2

6. Basic picture of the formation process Gravity baryons baryons Hydrodynamics dark matter Chemical reactions r, T Cooling/ Star formation

7. A New Parallel N-body Code • C2AP (Cosmological Code for Astrophysical Problems) • An improved version of the former code, GOTPM (2-3 times faster) • Supporting arbitrary number of CPUs (but not for serial) • using z-directional domain slabs with variable widths  equal load of memory (& equal CPU time is possible.) & maximizing the usage of memory space • Using FFTW (ver. 2) for full parallel Fast-Fourier-Transform (FFT) • Supporting OpenMP ( but not in the FFT)

8. Force Measuring (hybrid method) PM force (measuring global force) Tree force (correcting local force) r  d  dk  jk j  force FFT

9. Oct-Sibling Tree (OST) Oct Tree: spatially decomposes particles into hierarchical particle groups Sibling Tree: rather than using eight daughter pointers, it uses one sibling pointer

10. Dynamic Domain Decomposition Except for the FFT When calculating FFT

11. Parallel Performance For 40963 particle simulation, it will take about one hour with 512 IBMSP3 CPUs.

12. Effect of Gravitational Evolution High density region collapse forming galactic & cluster halos Low density region  expand forming cosmic voids

13. Density Evolution from Quantum Fluctuations Nearly smooth homogeneous & isotropic background A few hundreds galaxies

14. PSB Halos • Group finding from particle distribution • PSB (Physically Self-Bound) method (Kim & Park 2006) • Halo-halo boundary Constraints • Total Energy • Tidal Radius • subhalo in halo • Assumed to be individual halo • Subhalo ~ galaxy • Halo information  galaxy information • Mock galaxy redshift survey • What we can get from simulation are.. • xcorrelation • Genus statistics • Halo massfunction, shape, rotation angle, spin parameters • We can compare the simulation results with observations directly. PSB Halos

15. Halo Mass Function Z=0 • Sheth & Tormen: the best fitting MF for FoF groups proved in others’ simulation results • FoF:only FoF group are counted. • Well fitted by the S-T at z=0 • Well fitted by the P-S at z=7 • Different from other researches. The reason of difference of FoF MF from others • Different simulation resolution in mass & force • PSB:subhalos are counted as individual halos. • Difference of MF btw. FoF & PSB • At z=7, same MF • At z=0, significantly different at high mass tail Z=7 FoF PSB

16. Halo Shape Fitting • Shape Tensor : Sij = S xi xj • 3 eigen vectors : directional cosine of axes • 3 eigen values : two ratios  ratios of radii oblate a=b=c : sphere a=b>c : oblate spheroid (disk-shaped) a>b=c : prolate spheroid (cigar-shaped) a>b>c : scalene (triaxial) prolate

17. Definition of Local Density • Using spline kernel to measure local density with a variable smoothing length ( = distance to 20’th neighboring seed halo) • How to define density seeds? • Observation: L* (-21<Mr<-20) galaxies(Park et al. 2006) • Simulation: using • Model: more massive halo has one and only one brighter galaxy • Halo mass function + Galaxy luminosity function --> Mass to Luminosity correspondence • Producing L* mock galaxies

18. SDSS & Simulation density histogram • M<-20 : • general agreement btw. SDSS and Simulation • But not in High r region  sample variance in SDSS but still higher than Sim. • M<-21: • Sim: slightly underestimate # in lower r underdense region, since galaxies are brighter than in dense region?

19. Halo Shape halo Triaxiality (Warren et al. (1992); Bailin & Steinmetz (2004): dense 0 < T < 1/3 : Oblate “pancake like” 1/3 < T < 2/3 : scalene 2/3 < T < 1 : Prolate “needle like” massive • Halos In denser environment  more oblate • More massive halos  more prolate • Roundness: qxs = bc/a2 Oblate Prolate

20. Spin Distribution • Spin : • Well fitted by the Gamma distribution rather than log-normal • No significant change of k (~ 3.6) • In denser region smaller b  halo rotate faster • Massive halo  higher b  rotate slower

21. Relation btw. Rotation & Shape Axes • Rotation & major axes  orthogonal • Rotation & intermediate axes  no relation • Rotation & minor axes  parallel • No obvious environmental effect on these relations

22. summary • A new version of GOTPM • Faster & less usage of memory space • Halos tend to be more prolate. • but in dense region they tend to be more oblate. • more massive halos tend to be more prolate • spin distribution  well described by the Gamma distribution • In denser region, halos rotate faster. • More massive halos rotate slower. • Halo rotation axis ~ halo minor axis