| Abstract : | Recent observations of ?-rays from star clusters have motivated the study of the dynamics of stellar wind from massive star clusters, as potential sites of Cosmic Rays (CRs) acceleration. These ideas need to be checked with detailed studies, with regard to the details of CR acceleration in star clusters. We focus on the origin and accelerations of CRs in the young massive star cluster Westerlund 1 (WD1) with the help of hydrodynamical simulation. The ?-ray observations in star clusters reported a radial distribution of the projected CR energy density with a 1/r profile. The wind termination shocks of stellar winds have been identified as an important acceleration site, although CRs can also be injected in the central region of the cluster. Using idealized two-fluid simulations, we study these different CR injection methods in WD1 to explain the observed projected ?-ray luminosity, mass, and inferred projected CR energy density. We investigate whether or not this profile can help to distinguish between (1) continuous CR acceleration in star clusters, stellar wind-driven shocks, and (2) discrete CR acceleration in multiple supernova shocks. We find that the inferred CR energy density profiles from observations of ?-ray luminosity and mass can be much different from the true radial profile. We cover a large range of diffusion co-efficient and CR injection fractions to explain the observation and determine the optimum values of these parameters in the close vicinity of clusters. CR acceleration at either the cluster core or the termination shock can explain the observation if the diffusion coefficient is ~10^27 cm^2 s^-1 and 10-20% of the total energy goes into CRs. We also studied the multiple discrete supernova explosion scenarios in the cluster with an appropriate supernova rate and find that this scenario can also explain the observed ?-ray profile. |
