Cosmic ray moderation of the thermal instability

Abstract

Abstract.We apply the Hermite-Bieler theorem in the analysis of the effect of cosmic rays on the thermal stability of an initially uniform, static background. The cosmic rays were treated in a fluid approximation and the diffusion coefficient was assumed to be constant in time and space. The inclusion of cosmic rays does not alter the criterion for the thermal stability of a medium subjected to isobaric perturbations. It does alter the criteria for the stability of a medium perturbed by small amplitude sound waves. In the limit of a high background cosmic ray pressure to thermal pressure ratio, the instability in response to high frequency sound waves is suppressed.

Two-fluid models of cosmic ray modified radiative shocks

“…This is directly related to our finding that the thermal overstability is suppressed even for weak shocks: the overstability is suppressed if the cold dense layer is absent and the presence of cosmic rays act to ensure its absence. Without a cold dense layer that reflects sound waves effectively , perturbations are not confined within the cooling region and are damped by the large postshock cosmic ray pressure (Wagner et al 2005).…”

“…A linear stability analysis of a two-fluid medium including radiative cooling has revealed that cosmic rays suppress the growth of small amplitude perturbations (Wagner et al 2005). To investigate whether they can damp the thermal overstability of radiative shocks, we performed time-dependent hydrodynamic simulations of a two-fluid medium with radiative cooling.…”

Thermal instability and the effects of cosmic-ray diffusion

“…Qualitative analysis of the roots of the algebraic polynomial equations is generally in the form of Hurwitz analysis. In the case without a magnetic field, Wagner et al (2005) derived conditions for the stability of the system when φ≫ 1 or φ≪ 1. However, we found it difficult to perform such an analysis analytically and present the stability criteria in a simplified closed form (except for ζ= 0) because of the complicated coefficients of the characteristic .…”

“…Fukue & Kamaya 2007). In another study,Wagner et al (2005) derived the stability condition of a non‐magnetized thermal system for a few simplified cases. However, the growth rate of the perturbations was not studied by Wagner et al (2005).…”

“…In another study,Wagner et al (2005) derived the stability condition of a non‐magnetized thermal system for a few simplified cases. However, the growth rate of the perturbations was not studied by Wagner et al (2005). In this study, we follow a similar approach but in a magnetized case, considering the net cooling function of the system and the dynamical effects of CRs.…”