Between the Cosmic-Ray "Knee" and the "Ankle": Contribution from Star Clusters

We show that massive, young star clusters may be possible candidates that can accelerate Galactic cosmic rays (CRs) in the range of 107-109 GeV (between the "knee" and "ankle"). Various plausible scenarios, such as acceleration at the wind termination shock and supernova shocks inside these young star clusters, have been proposed, since it is difficult to accelerate particles up to the 107-109 GeV range in the standard paradigm of CR acceleration in supernova remnants. We consider a model for the production of different nuclei in CRs from massive stellar winds using the observed distribution of young star clusters in the Galactic plane. We present a detailed calculation of CR transport in the Galaxy, taking into account the effect of diffusion, interaction losses during propagation, and particle reacceleration by old supernova remnants to determine the all-particle CR spectrum. Using the maximum energy estimate from the Hillas criterion, we argue that a young, massive star cluster can accelerate protons up to a few tens of PeV. Upon comparison with the observed data, our model requires a CR source spectrum with an exponential cutoff of 5 x 107 Z GeV (50 Z PeV) from these clusters, together with a CR injection fraction of similar to 5% of the wind kinetic energy. We discuss the possibility of achieving these requirements in star clusters, as well as the associated uncertainties, in the context of considering star clusters as the natural accelerator of the "second component" of Galactic CRs.