The Mu and Tau Number of Supernovae

Abstract

The neutrino-nucleon cross section is slightly larger than that for $\bar\nu-N$. Therefore, $\bar\nu$ will escape more quickly from core collapse supernovae leaving the star $\nu$ rich. A diffusion formalism is used to calculate the time evolution of the mu and tau lepton number densities. These quickly reach steady state equilibria. We estimate that a protoneutron star with a maximum temperature near 50 MeV will contain over 50 % more $\nu_\mu$ and $\nu_\tau$ than $\bar\nu_\mu$ and $\bar\nu_\tau$. Supernovae may be the only known systems with large mu and or tau lepton numbers.