  Carefully accounting for neutrino transport is an essential component of many
astrophysical studies. Solving the full transport equation is too expensive for
most realistic applications, especially those involving multiple spatial
dimensions. For such cases, resorting to approximations is often the only
viable option for obtaining solutions. One such approximation, which recently
became popular, is the M1 method. It utilizes the system of the lowest two
moments of the transport equation and closes the system with an ad hoc closure
relation. The accuracy of the M1 solution depends on the quality of the
closure. Several closures have been proposed in the literature and have been
used in various studies. We carry out an extensive study of these closures by
comparing the results of M1 calculations with precise Monte Carlo calculations
of the radiation field around spherically-symmetric protoneutron star models.
We find that no closure performs consistently better or worse than others in
all cases. The level of accuracy a given closure yields depends on the matter
configuration, neutrino type, and neutrino energy. Given this limitation, the
maximum entropy closure by Minerbo (1978) on average yields relatively accurate
results in the broadest set of cases considered in this work.
