Regular oscillation sub-spectrum of rapidly rotating stars

¹ CNRS, IRAP, 14 avenue Edouard Belin, 31400 Toulouse, France
e-mail: pasek@irsamc.ups-tlse.fr
² Université de Toulouse, UPS-OMP, IRAP, Toulouse, France
³ CNRS, LPT (IRSAMC), 31062 Toulouse, France
⁴ Université de Toulouse, UPS, Laboratoire de Physique Théorique (IRSAMC), 31062 Toulouse, France
⁵ Institut d’Astrophysique et Géophysique de l’Université de Liège, Allée du 6 Août 17, 4000 Liège, Belgium

Received: 30 May 2012
Accepted: 17 August 2012

Abstract

Aims. We present an asymptotic theory that describes regular frequency spacings of pressure modes in rapidly rotating stars.

Methods. We use an asymptotic method based on an approximate solution of the pressure wave equation constructed from a stable periodic solution of the ray limit. The approximate solution has a Gaussian envelope around the stable ray, and its quantization yields the frequency spectrum.

Results. We construct semi-analytical formulas for regular frequency spacings and mode spatial distributions of a subclass of pressure modes in rapidly rotating stars. The results of these formulas are in good agreement with numerical data for oscillations in polytropic stellar models. The regular frequency spacings depend explicitly on internal properties of the star, and their computation for different rotation rates gives new insights on the evolution of mode frequencies with rotation.