Stars as Laboratories for Fundamental Physics - MPP Theory Group

164 Chapter 4
energy-loss rates are
Q scat = G2 Fm 2 νn B T 4
4π 4
Q pair = G2 Fm 2 νn B T 4
4π 4
∫ ∞
0
∫ ∞
0
dω
[ ( ω
T
dω 1 12
( ω
T
) 2
+ 6
ω
T + 12 ]
S(ω),
) 4
S(ω), (4.94)
where the detailed-balance condition S(−ω) = S(ω)e ω/T was used.
These rates include a factor of 2 for the emission of ν R and ν R .
As noted by Raffelt and Seckel (1995), unless the functional form
of S(ω) is very bizarre one has Q scat ≫ Q pair . This is easily understood
if one observes that in a scattering process the energy available
for the final-state ν R is that of the initial-state ν L plus energy that
is contributed by the medium. For pair emission, the energy for the
final-state ν L and ν R both have to be provided by the medium. Therefore,
the spin-flip scattering process is favored by the neutrino phase
space. 27 In a SN core the production of right-handed Dirac neutrinos
is given essentially by the standard scattering rate times the factor
(m ν /2E ν ) 2 .
27 This conclusion is in contrast to a suggestion that the pair-emission rates
could be relatively important in a SN core (Turner 1992). This statement was
not based on a self-consistent treatment of the medium structure functions, but
rather on a perturbative treatment of the processes involved. The conflict between
Turner’s statement and our finding, which essentially was based on phase-space
considerations, highlights the inadequacy of naive perturbative results in a nuclear
medium.