Jon O. Sundqvist, Stanley P. Owocki, David H. Cohen, Maurice A. Leutenegger, Richard H. D. Townsend
We present a generalised formalism for treating the porosity-associated
reduction in continuum opacity that occurs when individual clumps in a
stochastic medium become optically thick. We consider geometries resulting in
either isotropic or anisotropic effective opacity, and, in addition to an
idealised model in which all clumps have the same local overdensity and scale,
we also treat an ensemble of clumps with optical depths set by Markovian
statistics. This formalism is then applied to the specific case of bound-free
absorption of X-rays in hot star winds, a process not directly affected by
clumping in the optically thin limit. We find that the Markov model gives
surprisingly similar results to those found previously for the single clump
model, suggesting that porous opacity is not very sensitive to details of the
assumed clump distribution function. Further, an anisotropic effective opacity
favours escape of X-rays emitted in the tangential direction (the `venetian
blind' effect), resulting in a 'bump' of higher flux close to line centre as
compared to profiles computed from isotropic porosity models. We demonstrate
how this characteristic line shape may be used to diagnose the clump geometry,
and we confirm previous results that for optically thick clumping to
significantly influence X-ray line profiles, very large porosity lengths,
defined as the mean free path between clumps, are required. Moreover, we
present the first X-ray line profiles computed directly from line-driven
instability simulations using a 3-D patch method, and find that porosity
effects from such models also are very small. This further supports the view
that porosity has, at most, a marginal effect on X-ray line diagnostics in O
stars, and therefore that these diagnostics do indeed provide a good `clumping
insensitive' method for deriving O star mass-loss rates.
View original:
http://arxiv.org/abs/1111.1762
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