Dark Matter in the Universe Ue-Li Pen 彭威禮

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

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

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

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

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

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,

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

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

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  ) instead of decoupling (z  1000) most present epoch observations are of non- linear fluctuations, require massive computer simulations to predict quantitatively

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

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

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

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

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

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

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

Irrotational, stable grid

Single Slice Kinetic SZ effect

Ray-tracing through expanding universe

Kinetic SZ: Raytrace

Ray-traced gas density

Ray-traced dark matter

Ray-traced SZ effect

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.