Particle acceleration at recollimation shocks in sub-relativistic jets A model for jets in Seyfert Galaxies, Microquasars and Protostellar Systems

TL;DR

This paper develops a versatile semi-analytic model to study particle acceleration at recollimation shocks in sub-relativistic jets across various astrophysical systems, predicting maximum particle energies and potential observational signatures.

Contribution

It extends an existing jet hydrodynamics model to the sub-relativistic regime and formulates a semi-analytic particle acceleration framework applicable to multiple source classes.

Findings

Recollimation shocks can accelerate particles up to PeV and EeV energies.

Maximum particle energies vary with source class and jet properties.

Protons may escape and produce hadronic signatures in surrounding media.

Abstract

Context: Growing observational evidence suggests that sub-relativistic astrophysical jets may accelerate particles at slowly evolving standing shocks. Recollimation shocks are expected to develop when jets expand in dense environments; their formation may be mediated by the pressure of the cocoon surrounding the jet, while remaining compatible with a quasi-stationary behavior. Despite their high inclination relative to the jet axis, such shocks can be strong and enable efficient particle acceleration. Aims: The aim of this work is to improve the general understanding of particle acceleration via diffusive shock acceleration at recollimation shocks by developing a versatile modeling framework applicable to different classes of astrophysical jets, including Seyfert galaxies, microquasars, and protostellar systems. Methods: We extend an analytic jet hydrodynamics model previously introduced in the literature to the sub-relativistic regime and use it to identify the expected locations of the recollimation shock and the jet head. Within this framework, we formulate a semi-analytic acceleration and transport model for particles injected at the recollimation shock via diffusive shock acceleration. Results: By solving the space-dependent transport equation, we obtain particle distributions and spectra along the jet, as well as robust predictions for the maximum energies achievable as a function of the intrinsic properties of the system and the source class. Conclusions: Our results indicate that recollimation shocks may play a central role in particle acceleration in sub-relativistic jets. In Seyfert galaxies, such shocks may accelerate particles from PeV up to EeV energies, while in microquasars and protostellar jets maximum energies of tens of PeV and up to TeV are expected, respectively. Protons escaping the jets may diffuse through the cocoon, leading to possible hadronic signatures.