The Hot, Diffuse Gas in a Dense Cluster of Massive Stars

We present an analytic model describing the ““ cluster wind ÏÏ Ñow that results from the multiple interaction of the stellar winds produced by the stars of a dense cluster of massive stars. The analytic solution (obtained by matching an inner and an outer solution at the radius of the stellar cluster) can have asymptotically subsonic or supersonic behavior, the latter possibility being appropriate for the case of a cluster surrounded by a low-pressure environment. We also present a three-dimensional numerical simulation of such a cluster wind. We Ðnd that the behavior of the mean Ñow computed from the numerical simulation quite closely follows the Ñow properties deduced from the analytic model. Finally, we discuss the observational properties of the cluster wind produced by dense clusters such as the ““ Arches ÏÏ cluster close to the center of our Galaxy. In particular, we predict that the X-ray emission from the intracluster gas in this stellar cluster could be detectable. Subject headings : hydrodynamics È shock waves È stars : winds, outÑows