We constrain energy spectra of supernova neutrinos through the avoidance of an overproduction of the ${}^{11}\mathrm{B}$ abundance during Galactic chemical evolution. In supernova nucleosynthesis calculations with a parametrized neutrino spectrum as a function of temperature of ${\nu }_{\mu ,\tau }$ and ${\overline{\nu }}_{\mu ,\tau }$ and total neutrino energy, we find a strong neutrino temperature dependence of the ${}^{11}\mathrm{B}$ yield. When the yield is combined with observed abundances, the acceptable range of the ${\nu }_{\mu ,\tau }$ and ${\overline{\nu }}_{\mu ,\tau }$ temperature is found to be 4.8 to 6.6 MeV. Nonzero neutrino chemical potentials would reduce this temperature range by about 10% for a degeneracy parameter ${\eta }_{\nu }={\mu }_{\nu }/k{T}_{\nu }$ smaller than 3.

• Received 27 October 2004

DOI:https://doi.org/10.1103/PhysRevLett.94.231101