Stars as Laboratories for Fundamental Physics - MPP Theory Group

338 Chapter 9
Fig. 9.4. In the hatched parameter range ν µ or ν τ would achieve chemical
equilibrium with ν e in a SN core within about one second after collapse.
The cosmological mass limit of about 30 eV prevents ν µ or ν τ from
playing any novel role in the cooling or deleptonization of a SN core.
However, only a very small mixing angle is required to achieve equilibrium
if one of the neutrinos defied either standard particle physics
or standard cosmology and had a mass in the keV range or above. Of
course, if the mass were of Dirac type the cooling effect from the production
of spin-flipped neutrinos would be too large to be compatible
with the SN 1987A neutrino signal, yielding a bound on Dirac neutrino
masses in the 10 keV range (Sect. 13.8.1). It is in this context that flavor
conversion was first discussed by Maalampi and Peltoniemi (1991),
Turner (1992), and Pantaleone (1992a).
9.6 Sterile Neutrinos and SN 1987A
If a hypothetical sterile neutrino ν x existed, it would be produced in
the inner core of a SN by virtue of its assumed mixing with ν e . The ν x
would escape directly from the inner SN core, carrying away energy and
lepton number. If this process occurred too fast the observed neutrino
signal of SN 1987A would have been unduly shortened, allowing one
to exclude a certain range of ν x masses and mixing angles with ν e
(Kainulainen, Maalampi, and Peltoniemi 1991).
For small mixing angles one may use Eqs. (9.40) and (9.50) as a
starting point for the rate of change of the ν x occupation numbers fp.
x