The anisotropic radiation field approximation and its effect on wave equation solutions in the solar photosphere

Abstract

An approximation is developed which more accurately “solves” the radiative transfer equation than does the standard Eddington approximation. The difference between the two approaches is greatest in the optically thin region of the photosphere, where the new approximation more accurately represents the physics. Solutions of the wave equations for photospheric oscillations in both of the above approximations were generated by a linear, nonadiabatic, radial modeling program. Differences were found to exist between the sets of solutions obtained from the two transfer equation techniques. As to the effect on measurable quantities, such as the Eulerian perturbation in intensity and the radial displacement, the impact of varying the radiative transfer treatment was dependent on the outer solar boundary conditions. A solar model with standard outer boundary conditions produced observables which were less sensitive to the radiative transfer treatment than a solar model having anomalous outer boundary conditions (cf. Hill, Rosenwald and Caudell 1978). Since several observations indicate that the latter model is more realistic, the new approximation may be important in accurately studying the solar photosphere.