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A unique and often overlooked property of a source loaded with relativisticprotons is that it can become supercritical, i.e. it can undergo an abrupttransition from a radiatively inefficient to a radiatively efficient state onceits proton energy density exceeds a certain threshold. In this paper, weinvestigate the temporal variability of hadronic systems in this hardlyexplored regime. We show that there exists a range of proton densities thatprevent the system from reaching a steady state, but drive it instead in aquasi-periodic mode. The escaping radiation then exhibits limit cycles, even ifall physical parameters are held constant in time. We extend our analysis tocases where the proton injection rate varies with time and explore thevariability patterns of escaping radiation as the system moves in and out fromthe supercritical regime. We examine the relevance of our results to thevariability of the prompt gamma-ray burst emission and show that, at least on aphenomenological level, some interesting analogies exist.

Patterns of variability in supercritical hadronic systems