X-ray shocks and radio relics detected in the cluster outskirts are commonly interpreted as shocks induced by mergers of sub-clumps. We study the properties of merger shocks in merging galaxy clusters, using a set of cosmological simulations for the large-scale structure formation of the universe. As a representative case, we here focus on the simulated clusters that undergo almost head-on collisions with mass ratio ∼ 2. Due to the turbulent nature of the intracluster medium, shock surfaces are not smooth, but composed of shocks with different Mach numbers. As the merger shocks expand outward from the core to the outskirts, the average Mach number, M s , increases in time. We suggest that the shocks propagating along the merger axis could be manifested as X-ray shocks and/or radio relics. The kinetic energy through the shocks, F φ , peaks at ∼ 1 Gyr after their initial launching, or at ∼ 1 − 2 Mpc from the core. Because of the Mach number dependent model adopted here for the cosmic ray (CR) acceleration efficiency, their CR-energy-weighted Mach number is higher with M s CR ∼ 3 − 4, compared to the kinetic-energy-weighted Mach number, M s φ ∼ 2 − 3. Most energetic shocks are to be found ahead of the lighter dark matter (DM) clump, while the heavier DM clump is located in the opposite side of clusters. Although our study is limited to the merger case considered, the results such as the means and variations of shock properties and their time evolution could be compared with the observed characteristics of merger shocks, constraining interpretations of relevant observations.

Collisionless shocks with low sonic Mach numbers, M s 4, are expected to accelerate cosmic ray (CR) protons via diffusive shock acceleration (DSA) in the intracluster medium (ICM). However, observational evidence for CR protons in the ICM has yet to be established. Performing particle-incell simulations, we study the injection of protons into DSA and the early development of a nonthermal particle population in weak shocks in high β (≈ 100) plasmas. Reflection of incident protons, selfexcitation of plasma waves via CR-driven instabilities, and multiple cycles of shock drift acceleration are essential to the early acceleration of CR protons in supercritical quasi-parallel shocks. We find that only in ICM shocks with M s M * s ≈ 2.25, a sufficient fraction of incoming protons are reflected by the overshoot in the shock electric potential and magnetic mirror at locally perpendicular magnetic fields, leading to efficient excitation of magnetic waves via CR streaming instabilities and the injection into the DSA process. Since a significant fraction of ICM shocks have M s < M * s , CR proton acceleration in the ICM might be less efficient than previously expected. This may explain why the diffuse gamma-ray emission from galaxy clusters due to proton-proton collisions has not been detected so far.

Giant radio relics in the outskirts of galaxy clusters are known to be lit up by the relativistic electrons produced via diffusive shock acceleration (DSA) in shocks with low sonic Mach numbers, M s 3. The particle acceleration at these collisionless shocks critically depends on the kinetic plasma processes that govern the injection to DSA. Here, we study the preacceleration of suprathermal electrons in weak, quasi-perpendicular (Q ⊥ ) shocks in the hot, high-β (β = P gas /P B ) intracluster medium (ICM) through two-dimensional particle-in-cell simulations. Guo et al. (2014a,b) showed that in high-β Q ⊥ -shocks, some of incoming electrons could be reflected upstream and gain energy via shock drift acceleration (SDA). The temperature anisotropy due to the SDA-energized electrons then induces the electron firehose instability (EFI), and oblique waves are generated, leading to a Fermi-like process and multiple cycles of SDA in the preshock region. We find that such electron preacceleration is effective only in shocks above a critical Mach number M * ef ≈ 2.3. This means that in ICM plasmas, Q ⊥ -shocks with M s 2.3 may not efficiently accelerate electrons. We also find that even in Q ⊥ -shocks with M s 2.3, electrons may not reach high enough energies to be injected to the full Fermi-I process of DSA, because long-wavelength waves are not developed via the EFI alone. Our results indicate that additional electron preaccelerations are required for DSA in ICM shocks, and the presence of fossil relativistic electrons in the shock upstream region may be necessary to explain observed radio relics.

Low sonic Mach number shocks form in the intracluster medium (ICM) during the formation of the large scale structure of the universe. Although observational evidence for γ-ray emission of hadronic origin from galaxy clusters has yet to be established, nonthermal cosmic ray (CR) protons are expected to be accelerated via diffusive shock acceleration (DSA) in those ICM shocks. Considering the results obtained from plasma simulations, we propose an analytic model that emulates the energy spectrum of CR protons accelerated in weak quasi-parallel (Q ) shocks in the test-particle regime. The transition from the postshock thermal to CR spectra occurs at the injection momentum, p inj , above which protons can undergo the full DSA process. While a fraction of the shock energy is transferred to CR protons during DSA, the gas thermal energy should decrease accordingly, and hence the postshock thermal distribution is expected to shift to lower temperatures. In our model the CR spectrum is anchored to the self-consistent, postshock thermal distribution at p inj . With this spectrum, the CR acceleration efficiency ranges η ∼ 10 −3 −0.02 for supercritical, Q ICM shocks with sonic Mach number 2.25 M s 5. Based on Ha et al. (2018), on the other hand, we argue that proton acceleration would be negligible in subcritical shocks with M s < 2.25.

Radio relics associated with merging galaxy clusters indicate the acceleration of relativistic electrons in merger-driven shocks with low sonic Mach numbers (M s ≲ 3) in the intracluster medium (ICM). Recent studies have suggested that electron injection to diffusive shock acceleration (DSA) could take place through the so-called Fermi-like acceleration in the shock foot of β = P gas/P B ≈ 20–100 shocks and the stochastic shock drift acceleration (SSDA) in the shock transition of β ≈ 1–5 shocks. Here, we explore how the SSDA can facilitate electron preacceleration in weak quasi-perpendicular (Q ⊥) shocks in β ≈ 20–100 plasmas by performing particle-in-cell simulations in a two-dimensional domain large enough to properly encompass ion-scale waves. We find that in supercritical shocks with M s ≳ M AIC * ∼ 2.3 , multiscale waves are excited by the ion and electron temperature anisotropies in the downstream of the shock ramp, and that through stochastic pitch-angle scattering off the induced waves, electrons are confined in the shock transition for an extended period. Gaining energy through the gradient-drift along the motional electric field, electrons could be preaccelerated all the way to injection to DSA at such ICM shocks. Our findings imply that the electron DSA process at weak ICM shocks could explain the origin of radio relics. However, a further investigation of electron acceleration at subcritical shocks with M s < 2.3 is called for, since the Mach numbers of some observed radio relic shocks derived from radio or X-ray observations are as low as M s ∼ 1.5.