Stars as Laboratories for Fundamental Physics - MPP Theory Group

480 Chapter 12
12.4.7 Limit on ν τ → ν e e + e −
Neutrinos with a mass exceeding 2m e can decay into ν e e + e − , a channel
which probably dominates over ν ′ γ. Among the standard neutrinos, the
role of the parent can be played only by ν τ (or rather ν 3 ) with its upper
experimental mass limit of about 24 MeV. Within the standard model
where the decay is due to flavor mixing the rate is given by Eq. (7.9).
In order to derive bounds on the e + e − channel from the GRS observations,
photons need to be produced. At first one may think that the
positrons would quickly annihilate so that a strong prompt γ flux can
be expected (Takahara and Sato 1987; Cowsik, Schramm, and Höflich
1989). Following Mohapatra, Nussinov, and Zhang (1994), however, the
gas density outside of the progenitor is too low, in spite of a substantial
stellar wind during the progenitor’s supergiant evolution. Also, the
annihilation of the charged leptons from the decay among each other is
moderately efficient only if the decays occur close to the source. Typical
galactic magnetic fields have a strength of about 3 µG; they may
well be larger in the Large Magellanic Cloud, and the circumstellar field
of the SN 1987A progenitor may have been larger still. The gyromagnetic
radii for 5 MeV positrons is then less than 10 10 cm ≪ R env so that
one may think that the charged leptons were locally trapped (Cowsik,
Schramm, and Höflich 1989). However, the momentum carried by the
flux of the charged decay products is so large that those fields would
have been swept away (Mohapatra, Nussinov, and Zhang 1994).
Altogether it appears that the decay positrons will linger in interstellar
space for a long time before meeting annihilation partners unless
most decays occur immediately outside of the progenitor. Therefore,
prompt photons are mostly produced by bremsstrahlung ν τ → ν e e + e − γ
which is suppressed relative to the decay rate only by a factor of about
α/π ≈ 10 −3 (Dar and Dado 1987).
Neutrinos with masses in the MeV range which are emitted at MeV
temperatures are nearly nonrelativistic. Their rest frame is then approximately
equal to the laboratory frame, but they still move essentially
with the speed of light. To escape from the progenitor before
decaying their rest-frame lifetime τ tot must exceed a few 100 s. This
also guarantees that the pulse of decay photons will outlast the GRS
integration time: one is automatically in the region of a “long” photon
burst which was “case 3” in Fig. 12.16. In fact, if one assumes that ν τ
decays are induced by mixing, the decay rate Eq. (7.9) together with
the laboratory bounds on U eh shown in Fig. 12.3 easily guarantees that
they fulfill this requirement.