Supplementary material from "Radiative loss and ion-neutral collisional effects in astrophysical plasmas"

In this paper, we study the role of radiative cooling (RC) in a two-fluid model consisting of coupled neutrals and charged particles. We first analyse the linearized two-fluid equations where we include radiative losses in the energy equation for the charged particles. In a one-dimensional geometry for parallel propagation and in the limiting cases of weak and strong coupling, it can be shown analytically that the instability conditions for the thermal mode and the sound waves, the isobaric and isentropic criteria, respectively, remain unchanged with respect to one-fluid radiative plasmas. For the parameters considered in this paper, representative for the solar corona, the RC produces growth of the thermal mode and damping of the sound waves. In the weak coupling limit, the growth of the thermal instability and the damping of the sound waves is as derived in Field (Field 1965 Astrophys. J. 142, 531) using the charged fluid properties. When neutrals are included and are sufficiently coupled to the charges, the thermal mode growth rate and the wave damping both reduce by the same factor, which depends on the ionization fraction only. For a heating function which is constant in time, we find that the growth of the thermal mode and the damping of the sound waves are slightly larger. The numerical calculation of the eigenvalues of the general system of equations in a three-dimensional geometry confirm the analytic results. We then run two-dimensional fully nonlinear simulations which give consistent results: a higher ionization fraction or lower coupling will increase the growth rate. The magnetic field contribution is negligible in the linear phase. Ionization-recombination effects might play an important role because the RC produces a large range of temperatures in the system. In the numerical simulation, after the first condensation phase, when the minimum temperature is reached, the fraction of neutrals increases four orders of magnitude because of the recombination.This article is part of the theme issue ‘Partially ionized plasma of the solar atmosphere: recent advances and future pathways’.