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 can be explained by the 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 tranmission of redand blue-shifted wind emission from the back and front hemispheres. Here we characterize this porosity in terms of a typical scale l and volume filling factor f required to make individual clumps optically thick, as required for the effective self-shielding of material that is central to the porosity effect. For a simple 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 length gradient, h ∼ 1, implying large porosity lengths h ≈ r. The associated wind structure must thus either 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