PT and anti-PT symmetries for astrophysical waves

TL;DR

This paper explores how PT and anti-PT symmetries influence the behavior of linear perturbations in various astrophysical fluid problems, revealing their role in stability, wave propagation, and the location of exceptional points.

Contribution

It demonstrates the presence and significance of PT and anti-PT symmetries in astrophysical fluid dynamics, linking symmetry breaking to instabilities and wave propagation regions.

Findings

Discrete symmetries are present despite non-Hermitian processes.

Symmetry breaking correlates with certain instabilities and non-propagation regions.

Locations and orders of Exceptional Points are calculated using a resultant method.

Abstract

Context: Discrete symmetries have found numerous applications in photonics and quantum mechanics, but remain little studied in fluid mechanics, particularly in astrophysics. Aims: We aim to show how PT and anti-PT symmetries determine the behaviour of linear perturbations in a wide class of astrophysical problems. They set the location of Exceptional Points in the parameter space and the associated transitions to instability, and are associated to the conservation of quadratic quantities that can be determined explicitly. Methods: We study several classical local problems: the gravitational instability of isothermal spheres and thin discs, the Schwarzschild instability, the Rayleigh-B\'enard instability and acoustic waves in dust-gas mixtures. We calculate the locations and the order of the Exceptional Points with a method of resultant, as well as the conserved quantities in the different regions of the parameter space using Krein theory. Results: All problems studied here exhibit discrete symmetries, even though Hermiticity is broken by different physical processes (self-gravity, buoyancy, diffusion, drag). This analysis provides genuine explanations for certain instabilities, and for the existence of regions in the parameter space where waves do not propagate. Those correspond to breaking of PT and anti-PT symmetries respectively. Not all instabilities are associated to symmetry breaking (e.g. the Rayleigh-Benard instability).