New Supernova Constraints on Sterile-Neutrino Production

We consider the possibility that a light, sterile-neutrino species ${\nu }_S$ can be produced by ${\nu }_e$ scattering during the cooling of a proto-neutron star. If we parametrize the sterile-neutrino production cross section by a parameter $A$ as $\sigma ({\nu }_{e}X\to {\nu }_{S}X)=A\sigma ({\nu }_{e}X\to {\nu }_{e}X)$, where $X$ is an electron, neutron, or proton, we show that $A$ is constrained by limits to the conversion of ${\nu }_e$ to ${\nu }_S$ in the region between the sterile-neutrino trapping region and the electron-neutrino trapping region. This consideration excludes values of $A$ in the range ${10}^{-4\mathrm{}}\lesssim A\lesssim {10}^{-1\mathrm{}}$.