A class of physically motivated closures for radiation hydrodynamics

Radiative transfer and radiation hydrodynamics use the relativistic Boltzmann equation to describe the kinetics of photons. It is difficult to solve the six-dimensional time-dependent transfer equation unless the problem is highly symmetric or in equilibrium. When the radiation field is smooth, it is natural to take angular moments of the transfer equation to reduce the degrees of freedom. However, low order moment equations contain terms that depend on higher order moments. To close the system of moment equations, approximations are made to truncate this hierarchy. Popular closures used in astrophysics include flux-limited diffusion and the M₁ closure, which are rather ad hoc and do not necessarily capture the correct physics. In this paper, we propose a new class of closures for radiative transfer and radiation hydrodynamics. We start from a different perspective and highlight the consistency of a fully relativistic formalism. We present a generic framework to approximate radiative transfer based on relativistic Grad's moment method. We then derive a 14-field method that minimizes unphysical photon self-interaction.