A Steady, Radiative-Shock Method for Computing X-Ray Emission from Colliding Stellar Winds in Close, Massive-Star Binaries

We present a practical, efficient, semianalytic formalism for computing steady state X-ray emission from radiative shocks between colliding stellar winds in relatively close (orbital period up to order tens of days) massive-star, binary systems. Our simplified approach idealizes the individual wind flows as smooth and steady, ignoring the intrinsic instabilities and associated structure thought to occur in such flows. By also suppressing thin-shell instabilities for wind-collision radiative shocks, our steady state approach avoids the extensive structure and mixing that has thus far precluded reliable computation of X-ray emission spectra from time-dependent hydrodynamical simulations of close-binary, wind-collision systems; but in ignoring the unknown physical level of such mixing, the luminosity and hardness of X-ray spectra derived here represent upper limits to what is possible for a given set of wind and binary parameters. A key feature of our approach is the separation of calculations for the small-scale shock-emission from the ram-pressure-balance model for determining the large-scale, geometric form of the wind-wind interaction front. Integrating the localized shock emission over the full interaction surface and using a warm-absorber opacity to take account of attenuation by both the smooth wind and the compressed, cooled material in the interaction front, the method can predict spectra for a distant observer at any arbitrary orbital inclination and phase. We illustrate results for a sample selection of wind, stellar, and binary parameters, providing both full X-ray light curves and detailed spectra at selected orbital phases. The derived spectra typically have a broad characteristic form, and by synthetic processing with the standard XSPEC package, we demonstrate that they simply cannot be satisfactorily fitted with the usual attenuated single- or two-temperature thermal-emission models. We conclude with a summary of the advantages and limitations of our approach and outline its potential application for interpreting detailed X-ray observations from close, massive-star binary systems.