Angular momentum redistribution by mixed modes in evolved low-mass stars^⋆

I. Theoretical formalism

¹ LESIA, Observatoire de Paris, PSL Research University, CNRS, Université Pierre et Marie Curie, Université Denis Diderot, 92195 Meudon, France
e-mail: kevin.belkacem@obspm.fr
² Institut d’Astrophysique Spatiale, CNRS, Université Paris XI, 91405 Orsay Cedex, France
³ Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C, Denmark
⁴ Institut d’Astrophysique et de Géophysique, Université de Liège, Allée du 6 Août 17, 4000 Liège, Belgium
⁵ Laboratoire AIM Paris-Saclay, CEA/DSM-CNRS-Université Paris Diderot, IRFU /SAp, Centre de Saclay, 91191 Gif-sur-Yvette Cedex, France

Received: 6 March 2015
Accepted: 15 May 2015

Abstract

Seismic observations by the space-borne mission Kepler have shown that the core of red giant stars slows down while evolving, requiring an efficient physical mechanism to extract angular momentum from the inner layers. Current stellar evolution codes fail to reproduce the observed rotation rates by several orders of magnitude and instead predict a drastic spin-up of red giant cores. New efficient mechanisms of angular momentum transport are thus required. In this framework, our aim is to investigate the possibility that mixed modes extract angular momentum from the inner radiative regions of evolved low-mass stars. To this end, we consider the transformed Eulerian mean (TEM) formalism, which allows us to consider the combined effect of both the wave momentum flux in the mean angular momentum equation and the wave heat flux in the mean entropy equation as well as their interplay with the meridional circulation. In radiative layers of evolved low-mass stars, the quasi-adiabatic approximation, the limit of slow rotation, and the asymptotic regime can be applied for mixed modes and enable us to establish a prescription for the wave fluxes in the mean equations. The formalism is finally applied to a 1.3 M_⊙ benchmark model, representative of observed CoRoT and Kepler oscillating evolved stars. We show that the influence of the wave heat flux on the mean angular momentum is not negligible and that the overall effect of mixed modes is to extract angular momentum from the innermost region of the star. A quantitative and accurate estimate requires realistic values of mode amplitudes. This is provided in a companion paper.