The relation between post-shock temperature, cosmic-ray pressure and cosmic-ray escape for non-relativistic shocks

TL;DR

This paper derives a relation between cosmic-ray pressure and post-shock temperature in supernova remnants, showing that high cosmic-ray pressure requires significant energy flux escape, supported by application to observations of RCW 86.

Contribution

It introduces a two-fluid thermodynamic model linking cosmic-ray pressure and temperature, and applies it to observational data to estimate cosmic-ray energy flux escape.

Findings

Post-shock cosmic-ray pressure is at least 50%.

Energy flux escape is at least 20%.

At least 5% of supernova energy accelerates cosmic rays.

Abstract

Supernova remnants are thought to be the dominant source of Galactic cosmic rays. This requires that at least 5% of the available energy is transferred to cosmic rays, implying a high cosmic-ray pressure downstream of supernova remnant shocks. Recently, it has been shown that the downstream temperature in some remnants is low compared to the measured shock velocities, implying that additional pressure support by accelerated particles is present. Here we use a two-fluid thermodynamic approach to derive the relation between post-shock fractional cosmic-ray pressure and post-shock temperature, assuming no additional heating beyond adiabatic heating in the shock precursor and with all non-adiabatic heating occurring at the subshock. The derived relations show that a high fractional cosmic-ray pressure is only possible, if a substantial fraction of the incoming energy flux escapes from the system. Recently a shock velocity and a downstream proton temperature were measured for a shock in the supernova remnant RCW 86. We apply the two-fluid solutions to these measurements and find that the the downstream fractional cosmic-ray pressure is at least 50% with a cosmic-ray energy flux escape of at least 20%. In general, in order to have 5% of the supernova energy go into accelerating cosmic rays, on average the post-shock cosmic-ray pressure needs to be 30% for an effective cosmic-ray adiabatic index of 4/3.