Flow Generation via Catastrophic Loss of Equilibrium in Weakly-Rotating Self-Gravitating Fluids: A Minimal Idealized Model

TL;DR

This paper models how catastrophic loss of equilibrium in weakly rotating self-gravitating fluids leads to energy conversion from gravity to flow, enhancing understanding of astrophysical phenomena like galaxy dynamics and accretion discs.

Contribution

It introduces an exact minimal idealized model for catastrophic energy transformations in self-gravitating fluids, paralleling stellar plasma relaxation studies.

Findings

Energy from gravity converts into kinetic flow during catastrophe.

The model explains flow generation in astrophysical systems.

Insights into stability and dynamics of rotating stars and accretion disks.

Abstract

This paper explores the catastrophic energy transformations, in particular the ones leading to the generation of a flow in a weakly rotating self-gravitating fluid/gas found, for instance, in the vicinity of a massive compact object. Because of the similarity in the governing equations, the system dynamics is worked out exactly in parallel to the methods developed for investigating catastrophic relaxation in stellar plasmas [1-3]. In the latter a more ``complex" equilibrium state, on slow changes in the environment, can lose its equilibrium (catastrophe), and transform to a less complex state with a very different energy mix from the original. It is shown that a similar transformation in the weakly rotating self-gravitating fluid/gas will convert much of its gravitation energy into kinetic energy in the flow. Since flows are a perennial ingredient of high-energy astrophysical systems, the energy transformation processes revealed in present study, can advance our understanding of a variety of them. Some particularly relevant examples are: macro-scale flows / structures in galaxies, accretion discs, and the dynamics and stability of a rotating star / its atmosphere.