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Carefully accounting for neutrino transport is an essential component of manyastrophysical studies. Solving the full transport equation is too expensive formost realistic applications, especially those involving multiple spatialdimensions. For such cases, resorting to approximations is often the onlyviable option for obtaining solutions. One such approximation, which recentlybecame popular, is the M1 method. It utilizes the system of the lowest twomoments of the transport equation and closes the system with an ad hoc closurerelation. The accuracy of the M1 solution depends on the quality of theclosure. Several closures have been proposed in the literature and have beenused in various studies. We carry out an extensive study of these closures bycomparing the results of M1 calculations with precise Monte Carlo calculationsof the radiation field around spherically-symmetric protoneutron star models.We find that no closure performs consistently better or worse than others inall cases. The level of accuracy a given closure yields depends on the matterconfiguration, neutrino type, and neutrino energy. Given this limitation, themaximum entropy closure by Minerbo (1978) on average yields relatively accurateresults in the broadest set of cases considered in this work.

Analytic Closures for M1 Neutrino Transport