Oscillations of 2D ESTER models. I. The adiabatic case

TL;DR

This study investigates how 2D models of rapidly rotating stars affect acoustic mode patterns and rotational splittings, using numerical simulations to assess the impact of discontinuities and gradients on asteroseismic diagnostics.

Contribution

It introduces a numerical framework combining the ESTER and TOP codes to analyze pulsations in 2D rotating stellar models with discontinuities, enhancing understanding of mode patterns and rotation profile probing.

Findings

Asymptotic frequency patterns are largely preserved despite discontinuities.

The integral formula accurately matches rotational splittings, except in avoided crossings.

Acoustic glitch theory can predict periodicity of frequency patterns in models.

Abstract

Recent numerical and theoretical considerations have shown that low-degree acoustic modes in rapidly rotating stars follow an asymptotic formula and recent observations of pulsations in rapidly rotating delta Scuti stars seem to match these expectations. However, a key question is whether strong gradients or discontinuities can adversely affect this pattern to the point of hindering its identification. Other important questions are how rotational splittings are affected by the 2D rotation profiles expected from baroclinic effects and whether it is possible to probe the rotation profile using these splittings. Accordingly, we numerically calculate pulsation modes in continuous and discontinuous rapidly rotating models produced by the 2D ESTER (Evolution STEllaire en Rotation) code. This spectral multi-domain code self-consistently calculates the rotation profile based on baroclinic effects and allows us to introduce discontinuities without loss of numerical accuracy. Pulsations are calculated using an adiabatic version of the Two-dimensional Oscillation Program (TOP) code. The variational principle is used to confirm the high accuracy of the pulsation frequencies and to derive an integral formula that closely matches the generalised rotational splittings, except when modes are involved in avoided crossings. This potentially allows us to probe the the rotation profile using inverse theory. Acoustic glitch theory, applied along the island mode orbit deduced from ray dynamics, can correctly predict the periodicity of the glitch frequency pattern produced by a discontinuity or the Gamma1 dip related to the He II ionisation zone in some of the models. The asymptotic frequency pattern remains sufficiently well preserved to potentially allow its detection in observed stars.