The Effect of Porosity on X-ray Emission Line Profiles from Hot-star Winds

We investigate the degree to which the nearly symmetric form of X-ray emission lines seen in Chandra spectra of early-type supergiant stars could be explained by a possibly porous nature of their spatially structured stellar winds. Such porosity could effectively reduce the bound-free absorption of X-rays emitted by embedded wind shocks, and thus allow a more similar transmission of redvs. blue-shifted emission from the back vs. front hemispheres. To obtain the localized self-shielding that is central to this porosity effect, it is necessary that the individual clumps be optically thick. In a medium consisting of clumps of size l and volume filling factor f , we argue that the general modification in effective opacity should scale approximately as κeff ≈ κ/(1 + τc), where, for a given atomic opacity κ and mean density ρ, the clump optical thickness scales as τc = κρl/f . For a simple wind structure parameterization in which the ‘porosity length’ h ≡ l/f increases with local radius r as h = h r, we find that a substantial reduction in wind absorption requires a quite large porosity scale factor, h ∼ 1, implying large porosity lengths h ∼ r. The associated wind structure must thus have either a relatively large scale l ∼ r, or a small volume filling factor f ≈ l/r ≪ 1, or some combination of these. We argue that the relatively small-scale, moderate compressions generated by intrinsic instabilities in line-driving are unlikely to give such large porosity lengths. This raises questions about whether porosity effects could play a significant role in explaining nearly symmetric X-ray line profiles, leaving again the prospect of instead having to invoke a substantial (ca. factor 5) downward revision in the assumed mass-loss rates. Subject headings: line: profiles — stars: early-type — stars: mass loss — stars: winds, outflow — X-rays: stars