Acceleration of cosmic rays at the post-adiabatic shocks of supernova remnants

¹ INAF – Osservatorio Astronomico di Palermo, Piazza del Parlamento 1, 90134 Palermo, Italy
² Institute for Applied Problems in Mechanics and Mathematics, National Academy of Sciences of Ukraine, Naukova St. 3-b, 79060 Lviv, Ukraine
³ INAF – Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
⁴ Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
⁵ INAF – Osservatorio Astrofisico di Catania, Via Santa Sofia 78, 95123 Catania, Italy

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 18 September 2025
Accepted: 21 March 2026

Abstract

When a supernova remnant (SNR) interacts with the dense material of an interstellar cloud, its shock wave decelerates rapidly, and the post-shock temperature drops to levels that permit efficient cooling of the shocked plasma. At this stage, the shock enters the post-adiabatic phase of its evolution. During this phase, the internal structure of the SNR undergoes significant changes, particularly in the immediate post-shock region, at spatial scales relevant to cosmic ray acceleration. Once the shock enters the post-adiabatic regime, the efficiency of diffusive shock acceleration increases due to a higher plasma compression, to a change in the direction of the advection velocity, and to an increased rate of momentum gain. As a result, the momentum spectrum of relativistic particles hardens, deviating from a pure power law at high energies. Particles could reach higher maximum values compared to classical predictions. We highlight the dynamics of post-adiabatic flows in SNRs, study their impact on particle acceleration, and present supporting observational evidence in the radio band.