A roadmap to hadronic supercriticalities: a comprehensive study of the parameter space for high-energy astrophysical sources

Hadronic supercriticalities are radiative instabilities that appear when large amounts of energy are stored in relativistic protons. When the proton energy density exceeds some critical value, a runaway process is initiated resulting in the explosive transfer of the proton energy into electron-positron pairs and radiation. The runaway also leads to an increase of the radiative efficiency, namely the ratio of the photon luminosity to the injected proton luminosity. We perform a comprehensive study of the parameter space by investigating the onset of hadronic supercriticalities for a wide range of source parameters (i.e. magnetic field strengths of 1 G-100 kG and radii of 10(11)-10(16) cm) and maximum proton Lorentz factors (10(3)-10(9)). We show that supercriticalities are possible for the whole range of source parameters related to compact astrophysical sources, like gamma-ray bursts and cores and jets of active galactic nuclei. We also provide an in-depth look at the physical mechanisms of hadronic supercriticalities and show that magnetized relativistic plasmas are excellent examples of non-linear dynamical systems in high-energy astrophysics.