Realistic modeling of wind and supernovae shocks in star clusters: addressing ${}^{22}\mathrm{N}\mathrm{e}{\mathrm{/}}^{20}\mathrm{N}\mathrm{e}$ and other problems in Galactic cosmic rays

Cosmic ray (CR) sources leave signatures in the isotopic abundances of CRs. Current models of Galactic CRs that consider supernovae (SNe) shocks as the main sites of particle acceleration cannot satisfactorily explain the higher ${}^{22}\mathrm{N}\mathrm{e}{\mathrm{/}}^{20}\mathrm{N}\mathrm{e}$ ratio in CRs compared to the interstellar medium. Although stellar winds from massive stars have been invoked, their contribution relative to SNe ejecta has been taken as a free parameter. Here we present a theoretical calculation of the relative contributions of wind termination shocks (WTSs) and SNe shocks in superbubbles, based on the hydrodynamics of winds in clusters, the standard stellar mass function, and stellar evolution theory. We find that the contribution of WTSs towards the total CR production is at least $25\mathrm{\%}$, which rises to $\gtrsim 50\mathrm{\%}$ for young ($\lesssim 10$ Myr) clusters, and explains the observed ${}^{22}\mathrm{N}\mathrm{e}{\mathrm{/}}^{20}\mathrm{N}\mathrm{e}$ ratio. We argue that since the progenitors of apparently isolated supernovae remnants (SNRs) are born in massive star clusters, both WTS and SNe shocks can be integrated into a combined scenario of CRs being accelerated in massive clusters. This scenario is consistent with the observed ratio of SNRs to $\gamma$-ray bright ($L_{\gamma }\gtrsim {10}^{35}$ erg s${}^{-1}$) star clusters, as predicted by star cluster mass function. Moreover, WTSs can accelerate CRs to PeV energies, and solve other longstanding problems of the standard supernova paradigm of CR acceleration.