Long-Wavelength, Free-Free Spectral Energy Distributions from Porous   Stellar Winds
  The influence of macroclumps for free-free spectral energy distributions (SEDs) of ionized winds is considered. The goal is to emphasize distinctions between microclumping and macroclumping effects. Microclumping can alter SED slopes and flux levels if the volume filling factor of the clumps varies with radius; however, the modifications are independent of the clump geometry. To what extent does macroclumping alter SED slopes and flux levels? In addressing the question, two specific types of macroclump geometries are explored: shell fragments ("pancake"-shaped) and spherical clumps. Analytic and semi-analytic results are derived in the limiting case that clumps never obscure one another. Numerical calculations based on a porosity formalism is used when clumps do overlap. Under the assumptions of a constant expansion, isothermal, and fixed ionization wind, the fragment model leads to results that are essentially identical to the microclumping result. Mass-loss rate determinations are not affected by porosity effects for shell fragments. By contrast, spherical clumps can lead to a reduction in long-wavelength fluxes, but the reductions are only significant for extreme volume filling factors. 
Richard Ignace
astro-ph.SR