Angular momentum relaxation in models of rotating early-type stars

¹ IRAP, Université de Toulouse, CNRS, CNES, 14, avenue Édouard Belin, F-31400 Toulouse, France
² ISAE-SUPAERO, Université de Toulouse, F-31400 Toulouse, France
³ Université Paris-Saclay, Université de Paris, Sorbonne Paris Cité, CEA, CNRS, AIM, F-91191 Gif-sur-Yvette, France

^⋆ Corresponding authors: Michel.Rieutord@irap.omp.eu; Enzo.Brossier-Secher@student.isae-supaero.fr; Joey.Mombarg@cea.fr

Received: 2 April 2025
Accepted: 14 May 2025

Abstract

Context. The rotational evolution of stars remains an open question in stellar physics because numerous phenomena contribute to the distribution of angular momentum.

Aims. This paper aims to determine the timescale over which a rotating early-type star relaxes to a steady baroclinic state or, equivalently, the conditions under which its nuclear evolution is slow enough to allow the star's evolution to be modelled as a series of quasi-steady states.

Methods. We investigate the damping timescale of baroclinic and viscous eigenmodes that are potentially excited by the continuous forcing of nuclear evolution. We first examine this with a spherical Boussinesq model. Since much of the dynamics is concentrated in the radiative envelope of the star, we then improve the realism of the modelling by using a polytropic model of the envelope that incorporates a realistic density profile.

Results. The polytropic model of the envelope highlights the key role of the region at the core-envelope interface. The results of evolutionary models recently obtained with two-dimensional axisymmetric ESTER models appear to arise from the slow damping of viscous modes. Using a vanishing Prandtl number appears to be too strong an approximation to explain the models’ dynamics. Baroclinic modes, previously thought to be good candidates for this relaxation process, are found to be too rapidly damped.

Conclusions. The dynamical response of rotating stars to the slow forcing of their nuclear evolution appears as a complex combination of non-oscillating eigenmodes. Simple Boussinesq approaches are not sufficiently realistic to explain this reality. This study underlines the key role of layers near the core-envelope interface in early-type stars as well as the importance of angular momentum transport mechanisms-here represented by viscosity-for early-type stars to reach critical rotation, which is presumably associated with the Be phenomenon.