The 2D dynamics of radiative zones of low-mass stars

¹ Laboratoire AIM Paris-Saclay, CEA/DRF - CNRS - Université Paris-Saclay, IRFU/DAp Centre de Saclay, 91191 Gif-sur-Yvette Cedex, France
e-mail: hypolite.delphine@gmail.com
² Institut de Recherche en Astrophysique et Planétologie, Observatoire Midi-Pyrénées, Université de Toulouse, 14 avenue Edouard Belin, 31400 Toulouse, France

Received: 15 June 2017
Accepted: 22 November 2017

Abstract

Context. Helioseismology and asteroseismology allow us to probe the differential rotation deep within low-mass stars. In the solar convective envelope, the rotation varies with latitude with an equator rotating faster than the pole, which results in a shear applied on the radiative zone below. However, a polar acceleration of the convective envelope can be obtained through 3D numerical simulations in other low-mass stars and the dynamical interaction of the surface convective envelope with the radiative core needs to be investigated in the general case.

Aim. In the context of secular evolution, we aim to describe the dynamics of the radiative core of low-mass stars to get a deeper understanding of the internal transport of angular momentum in such stars, which results in a solid rotation in the Sun from 0.7R_⊙ to 0.2R_⊙ and a weak radial core-envelope differential rotation in solar-type stars. This study requires at least a 2D description to capture the latitudinal variations of the differential rotation.

Methods. We build 2D numerical models of a radiative core on the top of which we impose a latitudinal shear so as to reproduce a conical or cylindrical differential rotation in a convective envelope. We perform a systematic study over the Rossby number R_o = ΔΩ/2Ω⁰ measuring the latitudinal differential rotation at the radiative–;convective interface. We provide a 2D description of the differential rotation and the associated meridional circulation in the incompressible and stably stratified cases using the Boussinesq approximation.

Results. The imposed shear generates a geostrophic flow implying a cylindrical differential rotation in the case of an isotropic viscosity. When compared to the baroclinic flow that arises from the stable stratification, we find that the geostrophic flow is dominant when the Rossby number is high enough (R_o ≥ 1) with a cylindrical rotation profile. For low Rossby numbers (R_o < 1), the baroclinic solution dominates with a quasi-shellular rotation profile. Using scaling laws from 3D simulations, we show that slow rotators (Ω₀ < 30Ω_⊙) are expected to have a cylindrical rotation profile. Fast rotators (Ω₀ > 30Ω_⊙) may have a shellular profile at the beginning of the main sequence in stellar radiative zones.

Conclusions. This study enables us to predict different types of differential rotation and emphasizes the need for a new generation of 2D rotating stellar models developed in synergy with 3D numerical simulations. The shear induced by a surface convective zone has a strong impact on the dynamics of the underlying radiative zone in low-mass stars. However, it cannot produce a flat internal rotation profile in a solar configuration calling for additional processes for the transport of angular momentum in both radial and latitudinal directions.