Electron Heating in Low Mach Number Perpendicular Shocks. II. Dependence on the Pre-shock Conditions

Abstract

Recent X-ray observations of merger shocks in galaxy clusters have shown that the post-shock plasma is two-temperature, with the protons being hotter than the electrons. In this work, the second of a series, we investigate by means of two-dimensional particle-in-cell simulations the efficiency of electron irreversible heating in perpendicular low Mach number shocks. We consider values of plasma beta (ratio of thermal and magnetic pressures) in the range 4 β p0 32 and sonic Mach number (ratio of shock speed to pre-shock sound speed) in the range 2 M s 5, as appropriate for galaxy cluster shocks. As shown in Paper I, magnetic field amplification -induced by shock compression of the preshock field, or by strong proton cyclotron and mirror modes accompanying the relaxation of proton temperature anisotropy -can drive the electron temperature anisotropy beyond the threshold of the electron whistler instability. The growth of whistler waves breaks the electron adiabatic invariance, and allows for efficient entropy production. We find that the post-shock electron temperature T e2 exceeds the adiabatic expectation T e2,ad by an amount (T e2 − T e2,ad )/T e0 0.044 M s (M s − 1) (here, T e0 is the pre-shock temperature), which depends only weakly on the plasma beta, over the range 4 β p0 32 which we have explored, and on the proton-to-electron mass ratio (the coefficient of 0.044 is measured for our fiducial m i /m e = 49, and we estimate that it will decrease to 0.03 for the realistic mass ratio). Our results have important implications for current and future observations of galaxy cluster shocks in the radio band (synchrotron emission and Sunyaev-Zel'dovich effect) and at X-ray frequencies.

Density jump as a function of magnetic field strength for parallel collisionless shocks in pair plasmas

“…The reason for this is that there is heating at the shock front, due to both compression and entropy generation. Both processes could affect electrons and ions differently, resulting in a downstream plasma with different electron and ion temperatures (Guo, Sironi & Narayan 2017, 2018). In a pair plasma, electrons and positrons will undergo identical heating, so we can speak of a single perpendicular temperature and a single parallel temperature.…”

Kinetic Simulations of Strongly-Magnetized Parallel Shocks: Deviations from MHD Jump Conditions

“…This choice was motivated by two reasons: the temperature of the two species would have the same value downstream of the shock and the instabilities, relevant for this problem, are unchanged in the electron-positron limit (Gary & Karimabadi 2009;Schlickeiser 2010). In the ion-electron limit, the temperature of the two species is not necessarily equal (Guo et al 2017(Guo et al , 2018Tran & Sironi 2020), however, examining this problem in this framework would require a description of the ion/electron energy partition. While this is an important step in understanding the physics of non-relativistic collisionless shocks, it is beyond the scope of this work The setup of the shock simulations are similar to those described in Spitkovsky (2008b); Sironi & Spitkovsky (2011b); Sironi et al (2013), where the shock is formed by initializing the plasma with a supersonic flow towards a reflecting wall (in the negative 𝑥 direction) on the left hand side of the simulation.…”

Two-temperature magnetohydrodynamic simulations for sub-relativistic active galactic nucleus jets: dependence on the fraction of the electron heating

“…However, some theoretical studies of collisionless shocks showed that shocks primarily heat ions. Guo et al (2018) carried out two-dimensional kinetic particle-in-cell simulations of low-Mach-number shocks, assuming galactic shocks, and showed T e /T i ∼ 0.24 at M = 5, independent of the plasma beta ranging 4 < β < 32. In addition, Matsukiyo (2010) found that the post-shock temperature ratio is proportional to the magnetosonic Mach number and T e /T i = 0.01 when the shock parameters are β = 10 and M = 14.…”