The time-dependent one-zone hadronic model - First principles

TL;DR

This paper introduces a comprehensive time-dependent one-zone hadronic model that self-consistently describes proton, electron, photon, neutron, and neutrino interactions, revealing new insights into the efficiency and variability of hadronic processes in astrophysical sources.

Contribution

It develops a coupled kinetic equations framework for a time-dependent hadronic model, incorporating Monte Carlo simulations, to analyze energy transfer, neutrino spectra, and variability effects in astrophysical environments.

Findings

Hadronic models can be efficient under certain conditions.

Temporal behavior can differ significantly from leptonic models.

Parameter regimes exist where hadronic processes dominate.

Abstract

We present a time-dependent approach to the one-zone hadronic model in the case where the photon spectrum is produced by ultrarelativistic protons interacting with soft photons that are produced from protons and low magnetic fields. Assuming that protons are injected at a certain rate in a homogeneous spherical volume containing a magnetic field, the evolution of the system can be described by five coupled kinetic equations, for protons, electrons, photons, neutrons, and neutrinos. Photopair and photopion interactions are modelled using the results of Monte-Carlo simulations and, in particular from the SOPHIA code for the latter. The coupling of energy losses and injection introduces a self-consistency in our approach and allows the study of the comparative relevancy of processes at various conditions, the efficiency of the conversion of proton luminosity to radiation, the resulting neutrino spectra, and the effects of time variability on proton injection, among other topics. We present some characteristic examples of the temporal behaviour of the system and show that this can be very different from the one exhibited by leptonic models. Furthermore, we argue that, contrary to the wide-held belief, there are parameter regimes where the hadronic models can become quite efficient. However, to keep the free parameters at a minimum and facilitate an in-depth study of the system, we have only concentrated on the case where protons are injected; i.e., we did not consider the effects of a co-accelerated leptonic component.