Low-frequency internal waves in magnetized rotating stellar radiation zones

II. Angular momentum transport with a toroidal field

¹ Laboratoire AIM Paris-Saclay, CEA/DSM-CNRS-Université Paris Diderot, IRFU/SAp Centre de Saclay, 91191 Gif-sur-Yvette, France
e-mail: stephane.mathis@cea.fr
² LESIA, Observatoire de Paris, CNRS, UPMC, Université Paris Diderot, Place Jules Janssen, 92195 Meudon, France
³ Departamento de Astronomía y Astrofísica, Universidad de Valencia, 46100 Burjassot (Valencia), Spain

Received: 22 October 2011
Accepted: 11 January 2012

Abstract

Context. With the progress of observational constraints on dynamical processes in stars, it becomes necessary to understand the angular momentum and the rotation profile history. In this context, internal waves constitute an efficient transport mechanism over long distances in stellar radiation zones. Indeed, they could be one of the mechanisms responsible for the quasi-flat rotation profile of the solar radiative region up to 0.2 R_⊙.

Aims. Angular momentum transport induced by internal waves depends on the properties of their excitation regions and of their dissipation during propagation. Then, the bottom of convective envelopes (the top of convective cores, respectively) are differentially rotating magnetic layers while radiation zones may host fossil magnetic fields. It is therefore necessary to understand the modification of internal wave mechanisms by both rotation and magnetic fields.

Methods. We continue our previous work by proceeding step by step. We analytically built a complete formalism that treats the angular momentum transport by internal waves while taking into account both the Coriolis acceleration and the Lorentz force in a non-perturbative way for an axisymmetric toroidal field. We assumed a uniform Alfvén frequency and a weak differential rotation to isolate the transport properties as a function of the Rossby and Elsasser numbers.

Results. We examined the different possible approximations to describe low-frequency internal waves modified by the Coriolis acceleration and the Lorentz force in a deep spherical shell. The complete structure of these waves, which become magneto-gravito-inertial waves, is given assuming the quasi-linear approximation first in the adiabatic case and then in the dissipative one. Vertical and equatorial trapping phenomena appear that favor retrograde waves. The efficiency of the induced transport as a function of the Rossby and Elsasser numbers is then obtained.

Conclusions. A complete study of the transport of angular momentum induced by magneto-gravito-inertial waves in stellar radiative regions is achieved for an axisymmetric toroidal magnetic field for a uniform Alfvén frequency and a weak differential rotation. General differential rotation, complex azimuthal magnetic fields, and poloidal and mixed fields will be examined in follow-up studies.