Winds from clu\sters with non-uniform stellar distributions

TL;DR

This paper models the complex wind interactions in dense stellar clusters with non-uniform distributions, revealing how the radial density profile influences the flow dynamics and X-ray emission, combining analytic and numerical approaches.

Contribution

It introduces a combined analytic and 3D numerical framework to study cluster winds with non-uniform stellar distributions, highlighting differences from homogeneous models.

Findings

Steep radial stellar distributions lead to high central densities and supersonic flows.

Cluster wind properties vary significantly with the stellar density profile.

Predicted X-ray emissions can be compared with observations to validate models.

Abstract

We present analytic and numerical models of the `cluster wind' resulting from the multiple interactions of the winds ejected by the stars of a dense cluster of massive stars. We consider the case in which the distribution of stars (i.e., the number of stars per unit volume) within the cluster is spherically symmetric, has a power-law radial dependence, and drops discontinuously to zero at the outer radius of the cluster. We carry out comparisons between an analytic model (in which the stars are considered in terms of a spatially continuous injection of mass and energy) and 3D gasdynamic simulations (in which we include 100 stars with identical winds, located in 3D space by statistically sampling the stellar distribution function). From the analytic model, we find that for stellar distributions with steep enough radial dependencies the cluster wind flow develops a very high central density and a non-zero central velocity, and for steeper dependencies it becomes fully supersonic throughout the volume of the cluster (these properties are partially reproduced by the 3D numerical simulations). Therefore, the wind solutions obtained for stratified clusters can differ dramatically from the case of a homogeneous stellar distribution (which produces a cluster wind with zero central velocity, and a fully subsonic flow within the cluster radius). Finally, from our numerical simulations we compute predictions of X-ray emission maps and luminosities, which can be directly compared with observations of cluster wind flows.