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Dark Matter in the Universe
Ue-Li Pen
彭威禮
Overview
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The observational case for dark matter
dark matter candidates
dark matter dynamics
simulations
conclusions
Observational Evidence
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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+zm) where zm is
the end of matter domination
• for open universes, 1+zm=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 v2=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, 441-447
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100 000) instead of decoupling
(z  1000)
• most present epoch observations are of nonlinear 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 < 0.01
• 3 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 GS320
729 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
Ray-tracing through expanding universe
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.