Asymptotic theory of gravity modes in rotating stars II. Impact of general differential rotation

TL;DR

This paper develops a theoretical framework to understand how general differential rotation affects gravity wave propagation in stars, revealing new regimes including chaotic ray dynamics and implications for stellar oscillation spectra.

Contribution

It derives a local dispersion relation for gravito-inertial waves in differentially rotating stars and explores the resulting wave propagation regimes using a Hamiltonian ray model.

Findings

Differential rotation creates diverse resonant cavities for waves.

Identifies regimes where wave dynamics are similar to uniform rotation.

Discovers new chaotic wave regimes due to differential rotation.

Abstract

Context. Differential rotation has a strong influence on stellar internal dynamics and evolution, notably by triggering hydrodynamical instabilities, by interacting with the magnetic field, and more generally by inducing transport of angular momentum and chemical elements. Moreover, it modifies the way waves propagate in stellar interiors and thus the frequency spectrum of these waves, the regions they probe, and the transport they generate. Aims. We investigate the impact of a general differential rotation (both in radius and latitude) on the propagation of axisymmetric gravito-inertial waves. Methods. We use a small-wavelength approximation to obtain a local dispersion relation for these waves. We then describe the propagation of waves thanks to a ray model that follows a Hamiltonian formalism. Finally, we numerically probe the properties of these gravito-inertial rays for different regimes of radial and latitudinal differential rotation. Results. We derive a local dispersion relation that includes the effect of a general differential rotation. Subsequently, considering a polytropic stellar model, we observe that differential rotation allows for a large variety of resonant cavities that can be probed by gravito-inertial waves. We identify that for some regimes of frequency and differential rotation, the properties of gravito-inertial rays are similar to those found in the uniformly rotating case. Furthermore, we also find new regimes specific to differential rotation, where the dynamics of rays is chaotic. Conclusions. As a consequence, we expect modes to follow the same trend. Some parts of oscillation spectra corresponding to regimes similar to those of the uniformly rotating case would exhibit regular patterns, while parts corresponding to the new regimes would be mostly constituted of chaotic modes with a spectrum rather characterised by a generic statistical distribution.