Testing cosmic ray acceleration with radio relics: a high-resolution study using MHD and tracers

Abstract

Weak shocks in the intracluster medium may accelerate cosmic-ray protons and cosmic-ray electrons differently depending on the angle between the upstream magnetic field and the shock normal. In this work, we investigate how shock obliquity affects the production of cosmic rays in high-resolution simulations of galaxy clusters. For this purpose, we performed a magneto-hydrodynamical simulation of a galaxy cluster using the mesh refinement code ENZO. We use Lagrangian tracers to follow the properties of the thermal gas, the cosmic rays and the magnetic fields over time. We tested a number of different acceleration scenarios by varying the obliquity-dependent acceleration efficiencies of protons and electrons, and by examining the resulting hadronic γ-ray and radio emission. We find that the radio emission does not change significantly if only quasi-perpendicular shocks are able to accelerate cosmic-ray electrons. Our analysis suggests that radio emitting electrons found in relics have been typically shocked many times before z = 0. On the other hand, the hadronic γ-ray emission from clusters is found to decrease significantly if only quasi-parallel shocks are allowed to accelerate cosmic-ray protons. This might reduce the tension with the low upper limits on γ-ray emission from clusters set by the Fermi-satellite.

On the Non-Thermal Energy Content of Cosmic Structures

“…Both these scenarios are probably underestimating the magnetic energy in the cluster centre, because the finite Reynolds number achieved in our run (R e ≤ 500, based on R e ∼ 0.5 N 4/3 , where N is the 1-dimensional size of the high-resolution domain of the simulations, in number of cells, e.g., [48]) likely causes a delayed start of the small-scale dynamo amplification, compared to reality (e.g., [37]). Limited to the single case of the Coma cluster, our primordial seeding run seems to be in better agreement with the observational results of Faraday Rotation (e.g., [49,50]), which suggests a distribution of magnetic energy that scales with the gas thermal energy, and a significant magnetisation in the outskirts (even if limited to a single narrow sector of Coma, e.g., [50]); • The cosmic-ray energy goes from the upper limit obtained with out post-processing modelling of tracers [39] to zero in case no CR-protons are accelerated by shocks within the cluster. The increasing trend with radius of the CR-energy follows from the sharp increase of the acceleration efficiency as a function of Mach number, which rapidly increase towards cluster outskirts (e.g., [38]).…”

“…Our AMR scheme is aggressive in order to allow the largest possible dynamical range in the gas flows, which is crucial to allow the growth of a small-scale dynamo (e.g., [37]): we refined all cells which are ≥10% denser then their surrounding, as well as whenever the 1-D velocity jump with their neighbours is ≥1.5 (e.g., [38]). More details on this cluster simulation are discussed in [39] and Wittor et al (this volume).…”

“…The dynamics of CRs is simulated in post-processing using tracer particles ( [39], see also Wittor et al this volume). This is a reasonable approximation, under the following assumptions: (a) the CRs are frozen into the gas because their spatial diffusion relative to the thermal gas is negligible on our resolution scale (∆x); (b) they represent a passive fluid with limited influence on the gas dynamics, which is justified by the low, ∼1% energy budget, allowed by γ-ray upper limits [27] and also based on our previous work using a self-consistent 2-fluid model for CRs [29,44].…”

“…The magnetic energy is computed as E mag = B 2 ∆x 3 /(8π), where B is the magnetic field strength in each cell. Finally, the CR-proton energy in the cell is computed as E cr = ∑ i e cr,i , where e cr,i is the CR-energy measured by each tracer particle ending up in the cell; e cr,i is the result of the injection and the reacceleration of CRs by shocks, and of the adiabatic compression/expansion experienced by each tracer, neglecting energy losses via Coulomb/hadronic collisions (see [39], for details).…”

“…The CRs are assumed to follow the ultra-relativistic equation of state (Γ cr = 4/3) and are injected in the simulation by shock waves with an acceleration efficiency that scales with the Mach number [46], rescaled by a factor ∼1/5 to take into account the results of our recent work, where only quasi-parallel shocks are assumed to injected CR-protons [39]. We are also taking into account the effect of re-accelerated CRs in case of pre-existing CRs in the upstream of shocks [29].…”