Re-acceleration of Nonthermal Particles at Weak Cosmological Shock Waves

TL;DR

This paper analyzes how weak cosmological shocks re-accelerate existing cosmic-ray particles, affecting their pressure, spectrum, and resulting synchrotron emission, with implications for observed radio relics.

Contribution

It provides analytic solutions and compares them with kinetic simulations to understand CR re-acceleration at weak shocks in large-scale structures.

Findings

CR pressure can reach 10% of shock ram pressure at M ≤ 3

Re-acceleration enhances synchrotron emission significantly

Pre-existing CRs dominate over injected CRs at weak shocks

Abstract

We examine diffusive shock acceleration (DSA) of the pre-exisiting as well as freshly injected populations of nonthermal, cosmic-ray (CR) particles at weak cosmological shocks. Assuming simple models for thermal leakage injection and Alfv\'enic drift, we derive analytic, time-dependent solutions for the two populations of CRs accelerated in the test-particle regime. We then compare them with the results from kinetic DSA simulations for shock waves that are expected to form in intracluster media and cluster outskirts in the course of large-scale structure formation. We show that the test-particle solutions provide a good approximation for the pressure and spectrum of CRs accelerated at these weak shocks. Since the injection is extremely inefficient at weak shocks, the pre-existing CR population dominates over the injected population. If the pressure due to pre-existing CR protons is about 5 % of the gas thermal pressure in the upstream flow, the downstream CR pressure can absorb typically a few to 10 % of the shock ram pressure at shocks with the Mach number $M \la 3$. Yet, the re-acceleration of CR electrons can result in a substantial synchrotron emission behind the shock. The enhancement in synchrotron radiation across the shock is estimated to be about a few to several for $M \sim 1.5$ and $10^2-10^3$ for $M \sim 3$, depending on the detail model parameters. The implication of our findings for observed bright radio relics is discussed.