Particle acceleration at radiative supernova remnant shocks

Laboratoire d’étude de l’Univers et des phénomènes eXtrêmes, LUX, Observatoire de Paris, Université PSL, Sorbonne Université, CNRS, 92190 Meudon, France

^★ Corresponding author: pierre.cristofari@obspm.fr

Received: 5 April 2025
Accepted: 20 October 2025

Abstract

Context. Numerous astrophysical shock waves evolve in an environment where the radiative cooling behind the shock affects the hydrodynamical structure downstream, thereby influencing the potential for particle acceleration via diffusive shock acceleration (DSA).

Aims. We study the possibility for DSA to energize particles from the thermal pool and from preexisting cosmic rays at radiative shocks, focusing on the case of supernova remnants (SNRs).

Methods. We relied on a semi-analytical description of particle acceleration at collisionless shocks in the test-particle limit, estimating the particle spectrum, maximum energy, and total proton and electron content expected from SNRs throughout the radiative phase.

Results. Our results indicate that DSA at radiative shocks can lead to significant particle acceleration during the first few tens of kiloyears of the radiative phase. Although the associated multiwavelength emission from SNRs in the radiative phase may not be detectable with current observatories in most cases, the radiative phase is found to lead to substantial deviations from the canonical p⁻⁴ of the test-particle limit. The hardening and/or steepening is due to an interplay between a growing contribution of the reaccelerated term as the SNR volume expands and the effects of adiabatic and radiative losses on trapped particles as particles are confined for a longer time. The slope of the cumulative proton and electron spectra over the SNR lifetime thus depends on the environment in which the SNR shock propagates, and on the duration of the radiative phase during which DSA can take place. Overall, DSA in the radiative phase can lead to a total electron spectrum steeper than the proton spectrum, both at SNRs from thermonuclear and core–collapse SNe. Finally, we comment on the case of young radiative SNRs (in the first month to a few years after the explosion) for which the denser environments (with mass-loss rates of Ṁ ∼ 10⁻¹ − 1 M_⊙/yr) tend to inhibit DSA.