Lecture Notes for Astronomy 321, W 2004 1 Stellar Energy ...

are a lot of them around us from the decoupling, then perhaps this gives an
appreciable contribution to the estimated dark matter mass density. We find
that to make a critical density from cosmic neutrinos requires that the mass
of the 3 species total 47 eV/c 2 , that is
ρ ν = ρ c ⇒ ρ ν = 340 × 47 eV/cm 3 . (41)
We would require about 30% of this in order for neutrinos to give the “right”
contribution to dark matter. The data suggests it is about 10 3 short of this.
So it seems that neutrinos contribute rather insignificantly to dark matter.
There is one other reason why it was not expected that neutrinos would
contribute to this. Structure formation (companion lecture) demands that
the dark matter be “cold,” that is, that the particles be non-relativistic during
the early era of structure formation. Recall that the netrinos decouple with
an average energy kT ≈ 1 MeV, much larger than the rest energies. Indeed,
at the dawn of structure formation, the neutrinos would have only cooled to
∼ 10 eV, still relativistic. Therefore, neutrinos are not only too light, but
also too “hot” to be an important contributor to dark matter.
9.4 WIMPs
We didn’t discuss this in much depth in class. But this is an important
topic for both astrophysics/cosmology and elementary particle physics (aka
HEP). An important issue in HEP theory is that basic calculations become
untenable at energies which are about 10 times higher than the reach of our
current accelerators, which currently probe elementary particle interactions
at energies of ∼ 200 GeV. One solution to this is a theory called supersymmetry,
aka SUSY. A prediction of SUSY is that there is a stable, neutral,
weakly interacting particle, usually called the neutralino, χ ◦ . For our present
purpose we can simply think of these as heavy neutrinos. Generically, such
dark matter candidates are called WIMPs, for weakly-interacting massive
particle.
Just as with neutrinos, we can evaluate WIMP decoupling using Eqs.
38 and 38. However, because they are massive, they will be non-relativistic
at decoupling, and hence will contribute to cold dark matter (CDM). The
decoupling temperature is about Mc 2 /kT ≈ 25 ± 5 for a WIMP of mass
M. The WIMP energy distribution will follow a Boltzmann function after
decoupling. Generically, the WIMP energy density is found to follow
ρ wimp /ρ c ∼ [ 10 −25 cm 3 s −1] /(σv) .
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