High-resolution supernova neutrino spectra represented by a simple fit

To study the capabilities of supernova neutrino detectors, the instantaneous spectra are often represented by a quasithermal distribution of the form f_ν(E)∝E^αe^-(α+1)E/Eₐᵥ, where Eₐᵥ is the average energy and α a numerical parameter. Based on a spherically symmetric supernova model with full Boltzmann neutrino transport we have, at a few representative postbounce times, reconverged the models with vastly increased energy resolution to test the fit quality. For our examples, the spectra are well represented by such a fit in the sense that the counting rates for a broad range of target nuclei, sensitive to different parts of the spectrum, are reproduced very well. Therefore, the mean energy and root-mean-square energy of numerical spectra hold enough information to provide the correct α and to forecast the response of multichannel supernova neutrino detection.