Electron Injection in Weak high-beta ICM shocks

Abstract

From observations of the so-called radio relics, the electrons are inferred to be accelerated via diffusive shock acceleration (DSA) in low sonic Mach number shocks induced in the intracluster medium (ICM). Here we study the electron preacceleration and injection to DSA at weak quasi-perpendicular shocks in high beta ICM through 2D PIC simulations. We showed that some of incoming electrons are reflected upstream and gain energy via shock drift acceleration (SDA). The temperature anisotropy due to the SDA-energized backstreaming electrons then induces the electron firehose instability (EFI). Nonpropagating oblique waves are generated in the shock foot, which leads to a Fermi-like process and multiple cycles of SDA in the preshock region. Such electron preacceleration is effective only in shocks above a critical Mach number Mef > 2.3. However, electrons may not reach high enough energies to be injected to the full Fermi-I process of DSA, because long-wavelength waves are not self-developed via the EFI alone. Our results indicate that additional electron preaccelerations are required for DSA in ICM shocks, and that the presence of fossil relativistic electrons in the shock upstream region may be necessary to explain observed radio relics unless there are pre-existing turbulent waves longer than the EFI-driven waves.