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Constrains on Dark Matter

The Dark Matter Universe

Last time we saw that clusters of galaxies generally have virial masses which are significantly larger than can be accounted for by the mass of individual cluster galaxy members. Much of this "extra" mass is distributed in the Intracluster Medium. However, when substructure is accounted for, the M/L ratio for clusters is no longer exceedling high but is generally in the range of 200-400.

Two Kinds of Non-Baryonic Dark Matter: Cold vs Hot

Non-baryonic dark matter comes in two basic forms: hot and cold. These terms refer to the ability for this dark matter to cool to non-relativistic velocities and clump into smaller units. A cold dark matter (CDM) universe gives rise to much different structure formation modes than a hot dark matter (HDM) universe.

CDM consists of weakly interacting massive particles (WIMPs) that become non-relativistic at temperatures well above 104K. As such, they are excellent candidates for producing small scale structure as prior to recombination they would have easily clumped together. This requires the rest mass of most CDM WIMPs to be extraordinarily high (1016 Gev).

WIMPs could have been created very early on through quantum fluctuations and if they did not immediately annihilate with their respective anti-WIMPS, could survive as the dominant relic mass today.

Many of these particles are naturally created in the supersymmetric theories (SUSY) of particle physics. SUSY makes use of a conserved quantum number called R parity. R = +1 for particles and -1 for their SUSY partner. R parity can be linked to baryon number B and lepton number L conservation through the spin, S as

R = -1(3B+L+2S)

The conservation of R parity has three important implications

Current potential dark matter SUSY particles are the neutralino,gravitino,photino and higgsino.

Another favorite CDM particle is known as an axion. In contrast to other CDM particles, the axion is relatively light. The axion is predicted to exist as a result of a symmetry breaking associated with the strong-CP problem in quantum chromodynamics. Although the axion mass is arbitrary over the range 10-12 eV to 1 Mev, the symmetry breaking occurs at high energy scale and hence early in the Universe

Although axions are created in the very early Universe when it was quite hot, axions have very small momenta and are born cold and hence begin to clump early on.

In contrast, HDM consists of particles that remain relativistic for significantly longer times. This requires their masses to be < 100 ev . Unlike CDM, HDM has one real particle candidate, the neutrino .

Once the total number of neutrino species is known, the density of neutrinos (as well as their cosmic temperature) can be determined. LEP tells us that the number of species is 3 (electron, muon, and tau) and the cosmic density of neutrinoes per species is then

neutrino density = 100 cm-3

Any neutrino mass (electron, muon or tau) above 1 eV would represent a significant contribution to the overall cosmological mass density.

Key point about Neutrino Dominated Universes:

The freestreaming of neutrinos stops when they become non-relativistic. This occurs through expansion and cooling of the Universe. When the universe has cooled to the point where kT is equal to the rest mass energy of the neutrino, whatever that is (< 100 eV tho), they become non-relativistic.

In other words, the halo of our galaxy has a velocity dispersion of 300 km/s. A cluster of galaxies has a velocity dispersion of 1000 km/s. Hence neutrinoes must have cooled from v ~ c to v ~ 300 -1000 km/s before these structure could have formed.

At the point where kT = neutrino rest mass the universe has some horizon size, rhor and variations in neutrino density can only occur on scales larger than rhor. The total mass within the horizon is approximately

rhor3Mnu4

For Mnu ~ 30 eV this is ~ 1016 Solar Masses, which is an order of magnitude larger than the mass of a large cluster of galaxies.

For a neutrino dominated Universe, potentials of this mass would be the first to form. The formation of smaller scale structure would occur from fragmentation of gas within these potentials.

Why We can't live in a Neutrino Dominated Universe

The Electronic Universe Project
e-mail: nuts@moo.uoregon.edu