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 the 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 redshifted and blueshifted emission from the back and front hemispheres, respectively. 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 kappa(eff) approximate to kappa/(1 + tau(c)), where, for a given atomic opacity kappa and mean density rho, the clump optical thickness scales as tau(c) = kappa rho l/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' greater than or similar to 1, implying large porosity lengths h greater than or similar to r. The associated wind structure must thus have either a relatively large scale l less than or similar to r, or a small volume filling factor f approximate to 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 the prospect of instead having to invoke a substantial (approximately a factor of 5) downward revision in the assumed mass- loss rates.