Long-Wavelength, Free-Free Spectral Energy Distributions from Porous Stellar Winds

TL;DR

This paper investigates how macroclumping in stellar winds affects free-free spectral energy distributions, finding that shell-like clumps do not alter fluxes while spherical clumps can reduce fluxes under extreme conditions.

Contribution

It provides analytic and semi-analytic models comparing microclumping and macroclumping effects on SEDs, highlighting the impact of different clump geometries.

Findings

Shell fragment macroclumping does not affect mass-loss rate estimates.

Spherical macroclumps can significantly reduce long-wavelength fluxes.

Microclumping effects are geometry-independent, unlike macroclumping.

Abstract

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.