The Effect of Porosity on X‐Ray Emission‐Line Profiles from Hot‐Star Winds

Abstract

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 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 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/ , 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 scale factor, h' 1, implying large 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 lengths. This raises questions about whether 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.