  We point out the following astrophysical consequences of a tau neutrino with
mass in the MeV range:
  (i) if it has a small electric charge which will allow it to become a cold
dark matter of the universe, then present limits on the 511 KeV gamma ray line
rule out the possibility that it contributes an $\Omega_{\nu_{\tau}}$ between
.1 to 1 making it unsuitable as a cold dark matter candidate;
  (ii) if an electrically neutral MeV range $\nu_{\tau}$ decays to $\nu_e +
\chi$ ( where $\chi$ is a massless boson) , then its lifetime is bounded by
SN1987A observations to be within a window $.05~~sec.\leq \tau(\nu_{\tau})~\leq
300~sec./(m_{\nu_{\tau}}~in~ MeV)$ a range which may be of interest from the
point of view of structure formation.
  Encouraged by the overlap between the range allowed in (ii) above and that
required for a proposed structure formation mechanism by Dodelson et al., we
search for simple extensions of the standard model, where such masses and
lifetimes may arise for natural values of parameters and show that the already
existing singlet majoron and low scale left-right models have this property. We
also comment on possible familon models for this decay.
