1. Dark Matter in the Universe Ue-Li Pen 彭威禮

2. Overview The observational case for dark matter dark matter candidates dark matter dynamics simulations conclusions

3. Observational Evidence CMB-structure formation cluster of galaxies strong gravitational lensing galaxy rotation curves

4. CMB-structure formation Perturbations grow in matter era after decoupling proportional to scale factor. Grows by factor of 1100/(1+z m ) where z m is the end of matter domination for open universes, 1+z m =1/  10, growth factor is only 100 BUT COBE perturbations are only 10 -5

5. Clusters of Galaxies In 20’s, Zwicky pointed out that the velocity dispersion of the Coma cluster is inconsistent with its self-gravity One expects v 2 =GM/R, the mass inferred this way is 100 times larger than the inferred stellar mass

6. The Coma Cluster Galaxies in optical X-ray image of coma from ROSAT

7. Rotation Curves Galaxy rotation curves tend to be inconsistent with light distribution. 21 cm gas curves. M33 rotation curve (points) compared with the best-fitting model (continuous line). Also shown are the halo contribution (dot-dashed line), the stellar disc (short-dashed line) and the gas contribution (long-dashed line). Edvige Corbelli; Paolo Salucci 2000: The extended rotation curve and the dark matter halo of M33, Monthly Notices of the Royal Astronomical Society, 311, 441-447

8. Dark Matter Candidates Weakly-Interacting-Massive-Particles (WIMPS): neutrinos, axions, etc Massive Compact Halo Objects (MACHOs): black holes, planets, brown dwarfs

9. Kinematic Classification Hot Dark Matter: v/c or order unity at matter radiation equality: neutrinos Cold Dark Matter: v/c << 1 at all times in matter domination

10. Dynamical Effects Transfer function: spatial clustering of dark matter. HDM does not cluster sufficiently. CMB  dark matter must be non-baryonic in order to start growing at matter-radiation equality (z  100 000) instead of decoupling (z  1000) most present epoch observations are of non- linear fluctuations, require massive computer simulations to predict quantitatively

11. Current Research Directions CMB: sub degree scale, polarization: detailed tracers of linear dark matter distribution Gravitational lensing: measures total mass distribution, I.e. dark matter Sunyaev-Zeldovich Effect: inverse Compton Scattering of CMB photons along line of sight: measures unbiased non-linear electron distribution -- requires simulations to model galaxy surveys

12. Cosmological Simulations Mean homogeneous Hubble expansion -- Friedman equation (relativistic) Most other physics is Newtonian: v/c < 0.01 3 fluids: , DM, baryons non-interacting DM given as collisionless fluid baryons are ideal Eulerian gas

13. Place universe in a box approximate local physics using constant density Box must be big enough that perturbations are small: L >> 32 Mpc cell must be small enough to resolve features of relevance Non-trivial non-linear dynamics through Newtonian gravity Gravitational clustering moves matter into small scales: adaptive resolution required

14. Initial Conditions Adiabatic, scale invariant super-horizon perturbations. Photon-baryon-dm-etc ratio constant in space and time (super-horizon) fluctuations in total density and curvature Harrison-Zeldovich-Peebles: power law fluctuations should not diverge on any scale

15. k^3 P(k)=10^-5 on all scales: mass fluctuations independent on smoothing scale. Dark matter perturbations grow in matter domination subhorizon wave of half the size entered the horizon at 1/4 the scale factor size perturbations grow as the scale factor transfer function goes as k^4 in MD P(k)=k on large, subhorizon scales

16. Hardware High resolution simulations now possible with new Canada Foundation for Innovation supercomputers at Toronto: 32 proc GS320 729 Mhz alpha, 64 G, 48 proc alpha cluster, 4 proc NEC SX-5, 48 proc SGI O2K, worth over CDN$ 15 million.

17. Software: MMH Moving Mesh Hydro/N-body General purpose cosmological N-body & hydro code high resolution TVD characteristic solver adaptive grid changes model diffuse X-ray emission, S-Z effect

18. Irrotational, stable grid

20. Single Slice Kinetic SZ effect

21. Ray-tracing through expanding universe

22. Kinetic SZ: Raytrace

23. Ray-traced gas density

24. Ray-traced dark matter

25. Ray-traced SZ effect

27. Conclusions Direct ab initio simulations of dark matter and gas now possible, can predict SZ effects. Full observable map and knowledge of dark matter and baryon distribution possible with upcoming SZ experiments (AMIBA, Planck, CBI) and galaxy/SZ cross-correlations. Dynamics seems to suggest Cold Dark Matter, underlying nature unknown.