Massive Tau Neutrino and SN 1987a

The emission of $\MeV$-mass tau neutrinos from newly formed neutron stars is considered in a simple, but accurate, model based upon the diffusion approximation. The tau-neutrinosphere temperature is found to increase with mass so that emission of massive tau neutrinos is not suppressed by the Boltzmann factor previously used, $(\mnu /T_\nu )^{1.5}\exp(-\mnu/T_{\nu})$, where $T_{\nu}\sim 4\MeV -8\MeV$. If the tau neutrino decays to electron neutrinos, then for short lifetimes ($\taunu\la10^{-3}\sec$) the location of both the tau and electron neutrinospheres can be affected, and, for very short lifetimes ($\tau_\nu \la 10^{-6}\sec$) its temperature falls below $1\MeV$, in conflict with neutrino observations of Supernova 1987A (SN 87A). Using our results, we revise limits to the mass/lifetime of an $\MeV$-mass tau neutrino based upon SN 87A. Our constraints, together with bounds based upon primordial nucleosynthesis and the laboratory mass limit of around $30\MeV$, exclude the possibility of a tau neutrino more massive than $0.4\MeV$ if the dominant decay mode is radiative. Finally, we speculate on the possible role a $15\MeV -25\MeV$ tau neutrino might play in the supernova explosion itself.