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

Abstract

We analyse recent 2D simulations of the non-linear 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 ≈ (fcl - 1)a, where fcl ≡ 〈ρ2〉/〈ρ〉2 is the clumping factor in density ρ, 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 ~1/√1 + τH, where τH ≡ κρH is the local optical thickness of this porosity length. For these LDI simulations, the inferred porosity lengths are small, only about a couple per cent of the stellar radius, H ≈ 0.02R*. For continuum processes like bound-free absorption of X-rays that are only marginally optically thick throughout the full stellar wind, this implies τH ≪ 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.