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

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 $H\approx (f_{\mathrm{cl}}-1)a$, where $f_{\mathrm{cl}}\equiv ⟨{\rho }^2⟩/{⟨\rho ⟩}^2$ 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 $\sim 1/\sqrt{1+{\tau }_{\mathrm{H}}}$, where ${\tau }_{\mathrm{H}}\equiv \kappa \rho H$ 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, $H\approx 0.02R_{\ast }$. For continuum processes like bound-free absorption of X-rays that are only marginally optically thick throughout the full stellar wind, this implies ${\tau }_{\mathrm{H}}\ll 1$, 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.

9 pages, 5 figures, accepted for MNRAS

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• Simulations of the line-driven instability in magnetic hot star winds
• Testing the Reliability of X-rays as a Tool for Constraining Mass-loss Rates of Hot Stars
• Ultraviolet Spectropolarimetry with Polstar: Clumping and Mass-loss Rate Corrections
• Spherically symmetric model atmospheres using approximate lambda operators V. Static inhomogeneous atmospheres of hot dwarf stars
• Deriving X-ray Line Profiles for Massive-Star Winds from Momentum-Conserving Dynamical Working Surface Solutions