  The Livermore Supernova Explosion Code was used to calculate the effect of a
massive Dirac neutrino on neutrino emission from SN 1987A in a fully
self-consistent manner. Spin-flip interactions lead to the copious emission of
sterile, right-handed neutrinos and cool the core faster than the observed
neutrino emission time for Dirac masses exceeding about 3$\,$keV. This limit is
relaxed to $7\,$keV if pion emission processes in the core are neglected. These
limits are compared with the previous less stringent limits of Burrows et al.
