The Non-Isotropic Diffusion Approximation in Wolf-Rayet Winds

Abstract

We derive the dynamics of a steady-state Wolf-Rayet wind using a non-isotropic diffusion approximation applied to the transfer between strongly overlapping spectral lines. Following the approach of Friend and Castor (1983), the line list is assumed to approximate a statistically parametrized Poisson distribution in frequency, so that photon transport is controlled by an angle-dependent, effectively gray opacity. We find that multiple radiative momentum deposition is greatest when photons undergo a nearly local diffusion, e.g. through scattering between many lines closely spaced in frequency. Our results reiterate the view that the so-called “momentum problem” of WR winds is better characterized as an “opacity problem” of simply identifying enough driving lines. One way of increasing the number of thick lines in WR winds is to transfer opacity from saturated to unsaturated lines, yielding a steeper opacity distribution than that found in OB winds. We also consider the growth of instabilities, and find that WR winds are up to an order of magnitude less unstable than OB winds if both are driven radiatively. However, initially small perturbations can still be multiplied by many orders of magnitude as they advect through WR winds.