Cosmic ray-modified shocks: appearance of an isothermal jump

TL;DR

The paper demonstrates that strong cosmic ray-modified shocks with Mach number above 1.34 develop an isothermal jump due to cosmic ray energy diffusion, affecting shock structure and cosmic ray spectra.

Contribution

It reveals the formation of an isothermal jump in super-critical cosmic ray-modified shocks, a phenomenon not previously characterized, independent of feedback mechanisms.

Findings

Isothermal jump appears at Mach number > 1.34

Compression ratio at the jump is 3

CR spectrum slope is steeper than 2, at 2.5

Abstract

We point out that for sufficiently strong shocks, with Mach number $ M_1 > \sqrt{\frac{3 \gamma -1}{(3-\gamma ) \gamma }}= 1.34$ ($\gamma=5/3$), the solutions for cosmic ray-modified shocks experiences a bifurcation. As a result, for super-critical flows an isothermal jump forms (which is not a shock). The isothermal jump forms due to the energy diffusion of fast, but energetically subdominant cosmic rays. For super-critical flows the isothermal jump appears regardless of a particular feed-back mechanism from the CRs. The compression ratio at the isothermal jump is $2/ (\gamma-1)=3$, so that in the test particle regime the expected spectrum of low energy CRs experiencing first-order Fermi process is $p = 2\gamma/(3- \gamma) = 5/2$, steeper than conventional $p=2$.