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

Abstract

Growing observational evidence suggests that subrelativistic (SR) astrophysical jets may accelerate particles at slowly evolving standing shocks. Recollimation shocks (RCS) 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. Such shocks can be strong and can enable efficient particle acceleration. The aim of this work is to improve the general understanding of particle acceleration via diffusive shock acceleration at RCS by developing a versatile modeling framework applicable to different classes of astrophysical jets, including Seyfert galaxies (SEY), microquasars (MQ), and protostellar systems (PS). We extended an analytic jet hydrodynamics model previously introduced in the literature to the SR regime and used it to identify the expected locations of the RCS and the jet head. Within this framework, we formulated a semi-analytic acceleration and transport model for particles injected at the RCS via diffusive shock acceleration. By solving the space-dependent transport equation, we obtained 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. Our results indicate that RCS may play a central role in particle acceleration in SR jets. In SEY such shocks may accelerate particles from PeV up to EeV energies, while in MQ and PS maximum energies of respectively tens of PeV and up to TeV energies are expected. While leptonic emission may be associated with bright knots along the jet, accelerated protons are expected to escape the jet and interact with the surrounding cocoon. Depending on the properties of the system, proton interactions can give rise to extended hadronic emission morphologies.