Acceleration of cosmic rays by double shock waves in galaxy clusters: application to radio relics

Abstract

Context. Radio relics in galaxy clusters are known to be good laboratories for verification of the applicability of the diffusive shock acceleration (DSA) model in its canonical version. The need for such verification stems from the inconsistencies in the shock properties resulting from radio observations compared to X-ray observations. Aims. In this article we aim to explore how the presence of a second shock in the vicinity of a relic modifies the spectrum of accelerated electrons and decipher which of the involved parameters can have a significant impact on their shape. Methods. We analytically studied DSA of cosmic rays in two stationary shocks aiming to investigate the change of the distribution function. The latter eventually leads to spectrum slope deviations visible in different observations and simulations that do not appear to be explained by the case wherein cosmic rays interact with a single shock wave. Results. We obtain a complex distribution function $f(x,p)$ depending on many parameters (distance between two shocks, compression ratios, spatial diffusion coefficients, injection value, etc.). This function reveals modifications that occur because of the coupled acceleration in both shocks. Apparently, deviations in the particle spectrum from the pure power law depend on a few parameters such as $Q_1/Q_2$, ${\kappa }_1/{\kappa }_2$, $r_1/r_2$, and $L$. Although we do not verify this idea by taking a particular cluster as an example, we demonstrate a potential cause of spectral disturbances in radio relics. In general terms, our findings appear to correlate with results from the literature when the distance between the shocks is of the order of the width of a radio relic and ${\kappa }_1/{\kappa }_2\propto 3$.

8 pages, 7 figures

References in corpus (15)

• Diffuse Radio Emission from Galaxy Clusters
• Shock Waves in Eulerian Cosmological Simulations: Main Properties and Acceleration of Cosmic Rays
• Non linear particle acceleration at non-relativistic shock waves in the presence of self-generated turbulence
• Cosmological Shocks in Adaptive Mesh Refinement Simulations and the Acceleration of Cosmic Rays
• Deep LOFAR observations of the merging galaxy cluster CIZA J2242.8+5301
• Spectral age modelling of the `Sausage' cluster radio relic
• Relics in galaxy clusters at high radio frequencies
• The radio relic in Abell 2256: overall spectrum and implications for electron acceleration
• Shocks and non-thermal particles in clusters of galaxies
• The highest-frequency detection of a radio relic: 16-GHz AMI observations of the `Sausage' cluster
• MC${}^2$: Dynamical Analysis of the Merging Galaxy Cluster MACS J1149.5+2223
• Analytical model for cluster radio relics
• Collision of Merger and Accretion Shocks: Formation of Mpc-scale Contact Discontinuity in the Perseus Cluster
• First detection at 5.5 and 9 GHz of the radio relics in bullet cluster with ATCA
• Gamma-ray emission from galaxy cluster outskirts versus radio relics

Cited by in corpus (1)

• A multishock scenario for the formation of radio relics