Stars as Laboratories for Fundamental Physics - MPP Theory Group

518 Chapter 13
too different from that found in the dilute-medium limit. If one applies
the analytic criterion Eq. (13.8) one finds
m ν ∼ < 30 keV (13.15)
as a limit on a possible Dirac neutrino mass. This agrees with the
bounds originally estimated by Raffelt and Seckel (1988) and Gaemers,
Gandhi, and Lattimer (1989) while Grifols and Massó (1990a) estimated
a slightly more restrictive limit (14 keV). This sort of bound
only applies if the mass is not so large that the “wrong-helicity” states
interact strongly enough to be trapped themselves. This would occur
for a mass beyond a few MeV. Therefore, a Dirac-mass ν τ with, say,
m ντ = O(10 MeV) is not excluded by this argument.
In a numerical study Gandhi and Burrows (1990) implemented the
spin-flip energy-loss rate and calculated the expected event counts and
signal durations at the IMB and Kamiokande II detectors. They found
a bound almost identical with Eq. (13.15). A similar numerical study
by Burrows, Gandhi, and Turner (1992) corroborated this result. Another
numerical study was performed by Mayle et al. (1993) who found
a somewhat more restrictive limit of about 10 keV, essentially because
their equation of state allows the core to heat up to much higher temperatures
than are found in Burrows’ implementation with a stiff EOS.
In the Mayle et al. (1993) study, a more restrictive bound of around
3 keV was claimed if the pion-induced pair emission process π + N →
N +ν R +ν L was included. This result is incorrect if one accepts the predominance
of the spin-flip scattering over the pair-emission processes
that was discussed in Sect. 4.10. It does not seem believable that the
presence of pions would enhance the scattering cross section on nucleons.
In the form implemented by Mayle et al. (1993), the pair emission
rate and their neutrino opacities were not based on a common and
consistent axial-vector dynamical structure function.
A massive ν µ or ν τ likely would mix with ν e . In this case the degenerate
ν e sea initially present in a SN core would partially convert into a
degenerate ν µ or ν τ sea (Maalampi and Peltoniemi 1991; Turner 1992;
Pantaleone 1992a). In Sect. 9.5 it was shown that the flavor conversion
would be very fast even for rather small mixing angles. In this case the
spin-flip scattering energy-loss rate involves initial-state neutrinos with
much larger average energies than those of a nondegenerate distribution
that was used above. However, even though the initial energy-loss
rate in r.h. neutrino is much larger than before, the degeneracy effect
disappears after the core has been deleptonized and so the late-time