Electron Preacceleration in Weak Quasi-perpendicular Shocks in High-beta Intracluster Medium

Abstract

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.

Microinstabilities in the Transition Region of Weak Quasi-perpendicular Intracluster Shocks

“…The electron preacceleration has been a key outstanding problem in understanding the production of CR electrons in weak ICM shocks. Previous studies have shown that, in low-M s , high-β Q ⊥ shocks, thermal electrons could be preaccelerated primarily through the Fermi-like acceleration in the shock foot (Matsukiyo et al 2011;Guo et al 2014aGuo et al , 2014bKang et al 2019) and the stochastic shock drift acceleration (SSDA) in the shock transition region (Katou & Amano 2019;Niemiec et al 2019;. Although it has been shown that the electron preacceleration would be enhanced by preexisting strong magnetic fluctuations in the low-β (∼1) regime (e.g., Guo & Giacalone 2015;Trotta et al 2020), the effect of such turbulence on high-β ICM shocks has yet to be investigated and will not be considered here.…”

Electron Acceleration at Rippled Low Mach Number Shocks in Merging Galaxy Clusters

“…In effect, electron spectra are formed in a wideenergy range, and the maximum Lorentz factor reaches γ max ≈ 60. This value is much larger than is needed for injection to DSA, γ inj ≈ 25, estimated under assumption that the injection momentum p inj ∼ 3p th,i [6]. The fraction of supra-thermal particles reaches 5%, and ∼ 40% of the energy…”

“…Total plasma beta β = 5 (β e = β i = 2.5). Although this value is lower than β assumed in simulations in which EFI is strongly excited [4,6], it is a necessary compromise to fit the ion-scale rippling modes in the simulation box and at the same time allow to follow the long-time development of the system under available computing resources. We apply a reduced ion-to-electron mass ratio m i /m e = 100.…”

“…However, such spectra were shown to be formed only in the upstream region of the shock, and downstream spectra were still close to thermal distributions. Most recent similar studies show that such electron preacceleration occurs only in shocks above a so-called "EFI critical Mach number", M * ef ≈ 2.3, and shocks with M s 2.3 cannot accelerate electrons [6]. On the other hand, at supercritical shocks with M s M * ef electrons may not reach a sufficiently high energy to be injected into DSA, because EFI was observed to saturate and did not generate long-wavelength modes.…”

“…With growing plasma beta, the temperature anisotropy becomes smaller, the growth rate of the AIC instability decreases and the rippling modes have larger wavelengths. It was estimated that for parameters used in [4,5,6] in simulations with β = 20 or higher, the ripple wavelength is much larger than the transverse box size they used, so that the modes could not be resolved. On the other hand, at plasma β close to that used in [7], a sustained Fermi-like process may be inhibited on account of the strong magnetic pressure that suppresses the growth of the EFI, even though electron reflection via SDA can be efficient.…”