Pulsation modes in rapidly rotating stellar models based on the Self-Consistent Field method

TL;DR

This study characterizes pulsation modes in rapidly rotating stellar models using the Self-Consistent Field method, revealing mode behaviors, classifications, and the effects of differential rotation on mode visibility and frequencies.

Contribution

It applies the SCF method to model pulsation modes in rapidly rotating stars, extending asymptotic formulas and providing insights into mode classification and rotation effects.

Findings

Pulsation modes follow patterns similar to polytropic models under moderate differential rotation.

Modes are categorized into island, chaotic, and whispering gallery types, linked to azimuthal order.

High differential rotation complicates mode detection at low azimuthal orders.

Abstract

Context: New observational means such as the space missions CoRoT and Kepler and ground-based networks are and will be collecting stellar pulsation data with unprecedented accuracy. A significant fraction of the stars in which pulsations are observed are rotating rapidly. Aims: Our aim is to characterise pulsation modes in rapidly rotating stellar models so as to be able to interpret asteroseismic data from such stars. Methods: The pulsation code developed in Ligni\`eres et al. (2006) and Reese et al. (2006) is applied to stellar models based on the self-consistent field (SCF) method (Jackson et al. 2004, 2005, MacGregor et al. 2007). Results: Pulsation modes in SCF models follow a similar behaviour to those in uniformly rotating polytropic models, provided that the rotation profile is not too differential. Pulsation modes fall into different categories, the three main ones being island, chaotic, and whispering gallery modes, which are rotating counterparts to modes with low, medium, and high l-|m| values, respectively. The frequencies of the island modes follow an asymptotic pattern quite similar to what was found for polytropic models. Extending this asymptotic formula to higher azimuthal orders reveals more subtle behaviour as a function of m and provides a first estimate of the average advection of pulsation modes by rotation. Further calculations based on a variational principle confirm this estimate and provide rotation kernels that could be used in inversion methods. When the rotation profile becomes highly differential, it becomes more and more difficult to find island and whispering gallery modes at low azimuthal orders. At high azimuthal orders, whispering gallery modes, and in some cases island modes, reappear.