Massive τ neutrino and SN 1987A

The emission of MeV-mass τ neutrinos from newly formed neutron stars is considered in a simple, but accurate, model based upon the diffusion approximation. The τ-neutrinosphere temperature is found to increase with mass so that the emission of massive τ neutrinos is not suppressed by the Boltzmann factor previously used, (${\mathit{m}}_{\nu }$/${\mathit{T}}_{\nu }$ ${)}^{1.5}$exp(-${\mathit{m}}_{\nu }$/${\mathit{T}}_{\nu }$), where ${\mathit{T}}_{\nu }$∼4 MeV–8 MeV. For short τ neutrino lifetimes (${\mathrm{\tau }}_{\nu }$≲${10}^{\mathrm{-}3}$ sec) decays and inverse decays lead to a reduction in the temperature of the τ neutrinosphere. Using our results, we revise limits to the mass and lifetime of an MeV-mass τ neutrino based upon SN 1987A. Our constraints, together with bounds based upon primordial nucleosynthesis and laboratory experiments, exclude the possibility of a τ neutrino more massive than 0.4 MeV if the dominant decay mode is radiative and ${\mathrm{\tau }}_{\nu }$≳2.5×${10}^{\mathrm{-}12}$ sec (${\mathit{m}}_{\nu }$/MeV). The lifetime restriction does not apply for the modes ${\nu }_{\mathrm{\tau }}$→${\nu }_{\mathit{e},\mathrm{\mu }}$+γ. Our technique and results are easily generalized to other hypothetical MeV-mass particles whose interactions are of roughly weak strength. Finally, we speculate on the possible role a 15 MeV–30 MeV τ neutrino might play in powering supernova explosions.