Stars as Laboratories for Fundamental Physics - MPP Theory Group

Radiative Particle Decays 475
Fig. 12.14. Lower limit on m ν τ γ for 200 eV ∼ < m ν ∼
< 1 MeV, assuming
m ν τ tot ∼
> 10 10 eV s.
For Dirac neutrinos the most conservative case is α = −1 and the
temperature range relevant for ν µ and ν τ is between 6 and 8 MeV. This
yields an approximately temperature independent bound of m ν τ γ >
7×10 18 eV s. For Majorana neutrinos (α = 0) the limit is about 77
m ν τ γ > 12×10 18 eV s. The most conservative case (α = −1) translates
with Eq. (7.12) into
µ eff < 1.6×10 −10 µ B m −1
eV, (12.31)
assuming m ν τ tot ∼ > 10 10 eV s. Note the different dependence on m eV
relative to the low-mass result Eq. (12.17).
If m ν τ tot violates this condition because it is below 10 10 eV s means
that the neutrinos decay so fast that the photon burst effectively ends
before the GRS integration time t GRS is over. Then the photon burst is
again “short” even though the neutrino mass is large. In this case one
can state a limit on B γ as in Sect. 12.4.3. If τ tot is only slightly shorter
so that m ν τ tot ∼ < 4×10 8 eV s, all photons arrive within t GRS = 10 s
and one may directly apply Eq. (12.19), originally derived for small
neutrino masses. For the narrow region where the photon burst ends
between 10 and 223.2 s this bound must be discounted by about a
factor of 2 because of the less restrictive fluence limits for the larger
integration time.
77 The result here is after Oberauer et al. (1993) which is similar to 6×10 18 eV s
of Bludman (1992) but substantially more restrictive than 0.84×10 18 eV s of Kolb
and Turner (1989). These works all refer to the isotropic case (α = 0).