Reevaluating thermal instability in a uniform plasma: an extended analysis of instability domains

Thermal instability plays a crucial role in the dynamics of astrophysical plasmas. Building upon the foundational work of G. B. Field (1965) and the subsequent analysis by T. Waters & D. Proga (2019), this study revisits thermal instability in a uniform, non-magnetic medium. We aim to reevaluate and expand the understanding of instability domains, focusing on the classification and characteristics of thermal and acoustic modes in the presence of heating, radiative cooling, and thermal conduction. Except for Spitzer's expression for parallel thermal conductivity, heating and cooling processes are unspecified. Additionally, we investigate the existence of isobaric and isochoric thermal modes across the extreme limits of very short and very long wavelengths, as well as at intermediate wavelengths; we address a common misconception about the existence of purely adiabatic perturbations. We also perform an in-depth analysis of the dispersion relation for an infinite, uniform hydrodynamic medium, as derived by G. B. Field (1965). This enables the generation of growth rate and dispersion diagrams, providing insight into thermal instability across different wavelength ranges. With the inclusion of thermal conduction, our study refines the classification of the instability regions previously outlined by T. Waters & D. Proga (2019). Our findings confirm that their classification holds when the Field length is smaller than or comparable to the thermal wavelength. For larger Field lengths, a simplified classification becomes impractical. Furthermore, we discuss the potential implications of the catastrophic cooling instability (T. Waters & A. Stricklan 2025) in coronal rain formation.