The Heating of Thermal Electrons in Fast Collisionless Shocks: The Integral Role of Cosmic Rays

TL;DR

This paper investigates how cosmic ray-induced lower hybrid waves heat electrons in collisionless shocks, revealing the kinetic wave growth as a key mechanism influencing shock structure and electron-proton temperature ratios.

Contribution

It provides a detailed analysis of lower hybrid wave growth modes, identifying the kinetic case as the only one with a growing mode, impacting understanding of electron heating in shocks.

Findings

Kinetic lower hybrid waves exhibit a growing mode.

Wave growth can outpace magnetic field amplification at low Alfvén Mach numbers.

Electron heating mechanisms are linked to cosmic ray precursors.

Abstract

Understanding the heating of electrons to quasi-thermal energies at collisionless shocks has broad implications for plasma astrophysics. It directly impacts the interpretation of X-ray spectra from shocks, is important for understanding how energy is partitioned between the thermal and cosmic ray populations, and provides insight into the structure of the shock itself. In Ghavamian, Laming & Rakowski (2007) we presented observational evidence for an inverse square relation between the electron-to-proton temperature ratio and the shock speed at the outer blast waves of supernova remnants in partially neutral interstellar gas. There we outlined how lower hybrid waves generated in the cosmic ray precursor could produce such a relationship by heating the electrons to a common temperature independent of both shock speed and the strength of the ambient magnetic field. Here we explore the mechanism of lower hybrid wave heating of electrons in more detail. Specifically we examine the growth rate of the lower hybrid waves for both the kinetic (resonant) and reactive cases. We find that only the kinetic case exhibits a growing mode. At low Alfv\'en Mach numbers (~15) the growth of lower hybrid waves can be faster than the magnetic field amplification by modified Alfv\'en waves.