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The method of moments is widely used for the reduction of kinetic equationsinto fluid models. It consists in extracting the moments of the kineticequation with respect to a velocity variable, but the resulting system is apriori underdetermined and requires a closure relation. In this paper, we adaptthe $\varphi$-divergence based closure, recently developed for rarefied gasesi.e. with a velocity variable describing $\mathbb{R}^d$, to the radiativetransfer equation where velocity describes the unit sphere $\mathbb{S}^2$. Thisclosure is analyzed and a numerical method to compute it is provided.Eventually, it provides the main desirable properties to the resulting systemof moments: Similarily to the entropy minimizing closure ($M_N$), it dissipatesan entropy and captures exactly the equilibrium distribution. However,contrarily to $M_N$, it remains computationnally tractable even at high orderand it relies on an exact quadrature formula which preserves exactly symmetryproperties, i.e. it does not trigger ray effects. The purely anisotropicregimes (beams) are not captured exactly but they can be approached as close asdesired and the closures remains again tractable in this limit.

Moment Methods for the 3D Radiative Transfer Equation Based on $\varphi$-Divergences