Non-perturbative effect of rotation on dipolar mixed modes in red giant stars

TL;DR

This paper investigates the impact of rotation on dipolar mixed modes in red giant stars using a non-perturbative approach, revealing limitations of perturbative methods and proposing spectral differences as diagnostics for core rotation.

Contribution

It introduces a non-perturbative method for analyzing rotational effects on stellar oscillations, extending beyond the perturbative approach for rapid core rotation scenarios.

Findings

Perturbative methods are valid only when rotational splitting is small compared to mode spacing.

Non-perturbative computations are necessary for rapid core rotation, with one spectral term sufficing under certain conditions.

Differences in period spacings among m-families can serve as seismic diagnostics for core rotation.

Abstract

The space missions CoRoT and Kepler provide high quality data that allow us to test the transport of angular momentum in stars by the seismic determination of the internal rotation profile. Our aim is to test the validity of the seismic diagnostics for red giants rotation that are based on a perturbative method and to investigate the oscillation spectra when the validity does not hold. We use a non-perturbative approach implemented in the ACOR code (Ouazzani et al. 2012) that accounts for the effect of rotation on pulsations, and solves the pulsation eigenproblem directly for dipolar oscillation modes. We find that the limit of the perturbation to first order can be expressed in terms of the rotational splitting compared to the frequency separation between consecutive dipolar modes. Above this limit, non-perturbative computations are necessary but only one term in the spectral expansion of modes is sufficient as long as the core rotation rate remains significantly smaller than the pulsation frequencies. Each family of modes with different azimuthal symmetry, m, has to be considered separately. In particular, in case of rapid core rotation, the density of the spectrum differs significantly from one m-family of modes to another, so that the differences between the period spacings associated with each m-family can constitute a promising guideline toward a proper seismic diagnostic for rotation.