@article{3068713,
    title = "A roadmap to hadronic supercriticalities: A comprehensive study of the parameter space for high-energy astrophysical sources",
    author = "Mastichiadis, A. and Florou, I. and Kefala, E. and Boula, S.S. and Petropoulou, M.",
    journal = "Monthly Notices of the Royal Astronomical Society",
    year = "2020",
    volume = "495",
    number = "2",
    pages = "2458-2474",
    publisher = "Oxford University Press",
    issn = "0035-8711, 1365-2966",
    doi = "10.1093/mnras/staa1308",
    abstract = "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 1011−1016 cm) and maximum proton Lorentz factors (103−109). 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. © 2020 The Author(s)."
}