A preliminary discussion of Hose-Einstein diffusion in supernovae

Abstract

It has been argued that Bose-Einstein diffusion is a conceptual improvement in the treatment of radiative transport in supernovae. First and foremost, it represents a two-parameter description of the radiation field, the two parameters being µ and T_γ whose associated integrals, the total photon number and the total photon energy, can be budgeted independently. As the first iteration in a bootstrap process to achieve an internally consistent SN model and to develop general techniques of handling radiative transport at all optical depths, it seems clear from the above discussion that such a two-parameter fit is a step toward these goals. Secondly, the microphysics of the relevant photon/matter interactions in the SN strongly suggests that the appropriate two-parameter function is indeed Bose-Einstein, since it gives the correct physical limits of photon equilibrium whenever the appropriate conditions as dictated by the laws of statistical mechanics apply. A major difficulty is the explicit formulation of the interaction terms in the dynamical equations. These integrals over frequency must be made computationally tractable and require more knowledge of the energy spectrum of the radiation. The simplest approach would be to employ the nondegenerate BE energy distribution; however, it should be kept in mind that although the frequency integrated moments of a Maxwell-Boltzmann gas can approximate the degenerate limit with an 8 % error, the corresponding energy distribution is a poor approximation of the Rayleigh-Jeans portion of the blackbody spectrum. Nevertheless, such an approach may be preferable in a first set of calculations.