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-rayemission lines seen in Chandra spectra of early-type supergiant starscould be explained by the possibly porous nature of their spatiallystructured stellar winds. Such porosity could effectively reduce thebound-free absorption of X-rays emitted by embedded wind shocks, andthus allow a more similar transmission of redshifted and blueshiftedemission from the back and front hemispheres, respectively. To obtainthe localized self-shielding that is central to this porosity effect, itis necessary that the individual clumps be optically thick. In a mediumconsisting of clumps of size l and volume filling factor f, we arguethat the general modification in effective opacity should scaleapproximately as {κ}_{eff}~{κ}/(1+{τ}_{c}),where, for a given atomic opacity {κ} and mean density {ρ}, theclump optical thickness scales as {τ}_{c}={κ}{ρ}l/f. Fora simple wind structure parameterization in which the ``porositylength'' h{\equiv}l/f increases with local radius r as h=h^{'}r,we find that a substantial reduction in wind absorption requires a quitelarge porosity scale factor, h^{'}{\gt}~1, implying largeporosity lengths h{\gt}~r. The associated wind structure must thus haveeither a relatively large scale l{\lt}~r, or a small volume fillingfactor f~l/r{\lt}{\lt}1, or some combination of these. We argue that therelatively small-scale, moderate compressions generated by intrinsicinstabilities in line driving are unlikely to give such large porositylengths. This raises questions about whether porosity effects could playa 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-lossrates.