Topological modes in stellar oscillations

TL;DR

This paper uncovers topological properties of stellar oscillations by linking them to topological insulators, revealing the existence of topological modes that are common across various stars and behave as gravity or pressure modes depending on conditions.

Contribution

It introduces a novel topological framework for understanding stellar oscillations, establishing a deep analogy with topological insulators and deriving conditions for topological modes in stars.

Findings

Topological modes are ubiquitous in stars across the Hertzsprung-Russell diagram.

Sign changes in the acoustic-buoyant frequency relate to the existence of Lamb-like waves.

Topological modes can be trapped in regions with strong internal structural variations.

Abstract

Stellar oscillations can be of topological origin. We reveal this deep and so-far hidden property of stars by establishing a novel parallel between stars and topological insulators. We construct an hermitian problem to derive the expression of the stellar $\mathrm{\textit{acoustic-buoyant}}$ frequency $S$ of non-radial adiabatic pulsations. A topological analysis then connects the changes of sign of the acoustic-buoyant frequency to the existence of Lamb-like waves within the star. These topological modes cross the frequency gap and behave as gravity modes at low harmonic degree $\ell$ and as pressure modes at high $\ell$. $S$ is found to change sign at least once in the bulk of most stellar objects, making topological modes ubiquitous across the Hertzsprung-Russel diagram. Some topological modes are also expected to be trapped in regions where the internal structure varies strongly locally.