On the inefficiency of particle re-acceleration mechanisms in the cores of massive stellar clusters

We consider scenarios for non-thermal particle acceleration and re-acceleration in the central cores of compact massive star clusters, aided by insights from high resolution hydrodynamic simulations. We show that i) particles are unlikely to interact with many shocks during their lifetimes in the core; ii) colliding flows do not produce hard spectra; iii) turbulent re-acceleration in the core is suppressed. Inefficient re-acceleration mechanisms are not expected to produce hard components nor to increase the maximum energy within the cores of massive star clusters. Models in which the observed ultra-high energy gamma rays originate in the core of massive stellar clusters are thus disfavoured.