  The $\phi$-divergence-based moment method was recently introduced Abdelmalik
et al. (2023) for the discretization of the radiative transfer equation. At the
continuous level, this method is very close to the entropy-based MN methods and
possesses its main properties, i.e. entropy dissipation, rotational invariance
and energy conservation. However, the $\phi$-divergence based moment systems
are easier to resolve numerically due to the improved conditioning of the
discrete equations. Moreover, exact quadrature rules can be used to compute
moments of the distribution function, which enables the preservation of energy
conservation, entropy dissipation and rotational invariants, discretely. In
this paper we consider different variants of the $\phi$-divergence closures
that are based on different approximations of the exponential function and the
Planck function. We compare the approximation properties of the proposed
closures in the numerical benchmarks.
