Temporal signatures of leptohadronic feedback mechanisms in compact sources

TL;DR

This paper explores how feedback mechanisms in leptohadronic models of compact astrophysical sources can lead to complex temporal behaviors, including oscillations and steady states, impacting the interpretation of high-energy emissions.

Contribution

It introduces an analytical and numerical study of feedback-induced temporal behaviors in leptohadronic systems, highlighting the role of supercriticality in source variability.

Findings

Supercritical systems can exhibit periodic or damped oscillatory behaviors.

Feedback loops can lead to steady states or oscillations depending on parameters.

Implications for modeling and interpreting blazar emissions, such as in 3C 279.

Abstract

The hadronic model of Active Galactic Nuclei and other compact high energy astrophysical sources assumes that ultra-relativistic protons, electron-positron pairs and photons interact via various hadronic and electromagnetic processes inside a magnetized volume, producing the multiwavelength spectra observed from these sources. A less studied property of such systems is that they can exhibit a variety of temporal behaviours due to the operation of different feedback mechanisms. We investigate the effects of one possible feedback loop, where \gamma-rays produced by photopion processes are being quenched whenever their compactness increases above a critical level. This causes a spontaneous creation of soft photons in the system that result in further proton cooling and more production of \gamma-rays, thus making the loop operate. We perform an analytical study of a simplified set of equations describing the system, in order to investigate the connection of its temporal behaviour with key physical parameters. We also perform numerical integration of the full set of kinetic equations verifying not only our analytical results but also those of previous numerical studies. We find that once the system becomes `supercritical', it can exhibit either a periodic behaviour or a damped oscillatory one leading to a steady state. We briefly point out possible implications of such a supercriticality on the parameter values used in Active Galactic Nuclei spectral modelling, through an indicative fitting of the VHE emission of blazar 3C 279.