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

Stan Owocki^1 and David Cohen^2

1) Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, Newark, DE 19716
2) Department of Physics and Astronomy, Swarthmore College, Swarthmore, PA 19081

We investigate the degree to which the nearly symmetric form of X-ray emission lines seen in {\it 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 red- vs. 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 $\ell$ and volume filling factor $f$, we argue that the general modification in effective opacity should scale approximately as $\kappa_{eff} \approx \kappa/(1+\tau_{c})$, where, for a given atomic opacity $\kappa$ and mean density $\rho$, the clump optical thickness scales as $\tau_c = \kappa \rho \ell/f$. For a simple wind structure parameterization in which the `porosity length' $h \equiv \ell/f$ 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 $ \ell \approx r$, or a small volume filling factor $f \approx \ell/r \ll 1$, 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.

Reference: ApJ
Status: Manuscript has been accepted