Stars as Laboratories for Fundamental Physics - MPP Theory Group

What Have We Learned from SN 1987A 521
13.8.3 Magnetic Dipole Moments
Turning to neutrino magnetic dipole moments, the main production
process of r.h. states would be spin-flip scattering on charged particles,
notably on protons. The scattering cross section was discussed in
Sect. 7.4. It involves the usual Coulomb divergence which in a medium
is cut off by screening effects. In a SN core, the electrons are initially
very degenerate while the protons are essentially nondegenerate and
so the main contribution to screening is from the protons. According
to Eq. (D.17) they are electrically weakly coupled at the prevailing
temperatures and densities so that Debye screening should be an approximately
adequate prescription; the Debye scale for the protons is
found to be around 30 MeV. As typical neutrino energies are somewhat
larger but of the same order, the Coulomb logarithm is approximately
unity. Thus the cross section is approximately αµ 2 ν with µ ν the magnetic
dipole or transition moment.
This is to be compared with the spin-flip cross section from a Dirac
mass which is approximately G 2 Fm 2 ν/4π. In Sect. 13.8.1 a Dirac mass
bound of about 30 keV was derived which translates into
µ ν ∼ < 4×10 −12 µ B (13.20)
with µ B = e/2m e the Bohr magneton. This bound is similar to that
derived by Barbieri and Mohapatra (1988), but less restrictive by about
an order of magnitude than that claimed by Lattimer and Cooperstein
(1988). See also Nussinov and Rephaeli (1987), Goldman et al. (1988),
and Goyal, Dutta, and Choudhury (1995).
Eq. (13.20) applies to all magnetic, electric, and transition moments
of Dirac neutrinos. Numerically, it is similar to the bound Eq. (6.97)
derived from the absence of excessive plasmon decay in globular cluster
stars. However, because this latter result applies also to Majorana
transition moments it is more general than the SN limit. The SN limit,
on the other hand, applies to masses up to a few MeV while the globular
cluster bound only for m < ν ∼ 5 keV.
The simple cooling argument that led to Eq. (13.20) is not necessarily
the end of the story of neutrino magnetic dipole moments in SNe. If
r.h. neutrinos were indeed produced in the inner core and escaped freely,
they could rotate back into l.h. ones in the magnetic field around the
SN and in the galaxy. For a galactic magnetic field of order 10 −6 Gauss,
extended over, say, 1 kpc (the field is confined to the disk, the LMC lies
far above the disk) this effect would be important for µ > ν ∼ 10 −12 µ B .