Characterizing the turbulent porosity of stellar-wind structure generated by the line-deshadowing instability

TL;DR

This paper investigates how turbulence-induced clumping in stellar winds affects continuum absorption and scattering, introducing a 'turbulent porosity length' that influences opacity reduction, with implications for stellar wind modeling.

Contribution

It introduces a new formalism linking turbulent porosity to clumping factors and autocorrelation lengths, providing a quantitative measure of porosity effects in stellar winds.

Findings

Porosity length scales with clumping factor and autocorrelation length.

Effective opacity reduction depends on local optical thickness of the porosity length.

Simulated porosity lengths are small, about 2% of stellar radius.

Abstract

We analyze recent 2D simulations of the nonlinear evolution of the line-deshadowing instability (LDI) in hot-star winds, to quantify how the associated highly clumped density structure can lead to a "turbulent porosity" reduction in continuum absorption and/or scattering. The basic method is to examine the statistical variations of mass column as a function of path length, and fit these to analytic forms that lead to simple statistical scalings for the associated mean extinction. A key result is that one can characterize porosity effects on continuum transport in terms of a single "turbulent porosity length", found here to scale as $H \approx (f_{\rm cl} - 1) a$, where $f_{\rm cl} \equiv \left < \rho^2 \right >/\left < \rho \right >^2$ is the clumping factor in density $\rho$, and $a$ is the density autocorrelation length. For continuum absorption or scattering in an optically thick layer, we find the associated effective reduction in opacity scales as $\sim 1/\sqrt{1+\tau_{\rm H}}$, where $\tau_{\rm H} \equiv \kappa \rho H$ is the local optical thickness of this porosity length. For these LDI simulations, the inferred porosity lengths are small, only about a couple percent of the stellar radius, $H \approx 0.02 R_\ast$. For continuum processes like bound-free absorption of X-rays that are only marginally optically thick throughout the full stellar wind, this implies $\tau_{\rm H} \ll 1$, and thus that LDI-generated porosity should have little effect on X-ray transport in such winds. The formalism developed here could however be important for understanding the porous regulation of continuum-driven, super-Eddington outflows from luminous blue variables.