2022MNRAS.515.2256V

We critically assess limits on the maximum energy of protons accelerated within superbubbles around massive stellar clusters, considering a number of different scenarios. In particular, we derive under which circumstances acceleration of protons above peta-electronvolt (PeV) energies can be expected. While the external forward shock of the superbubble may account for acceleration of particles up to 100 TeV, internal primary shocks such as supernova remnants expanding in the low density medium or the collective wind termination shock which forms around a young compact cluster provide more favourable channels to accelerate protons up to 1 PeV, and possibly beyond. Under reasonable conditions, clustered supernovae launching powerful shocks into the magnetized wind of a young and compact massive star cluster are found to be the most promising systems to accelerate protons above 10 PeV. On the other hand, stochastic re-acceleration in the strongly turbulent plasma is found to be much less effective than claimed in previous works, with a maximum proton energy of at most a few hundred TeV.