The role of a resonant $\nu_e$-$\nu_s$ oscillation is discussed in the event of a supernova explosion. It is concluded that a significant $\nu_e$-$\nu_s$ mixing may hinder the ability of the supernova to explode. It may also cool the proto-neutron star too quickly with respect to the observed cooling time of several seconds. The constraints on the $\nu_e$-$\nu_s$ mixing parameters based on the above arguments are calculated.
Categories: hep-ph astro-ph