Anisotropic turbulent transport in stably stratified rotating stellar radiation zones

S Mathis,C Charbonnel,A Palacios,P Eggenberger,L Amard,V Prat,N Lagarde

doi:10.1051/0004-6361/201629187

Abstract

Context. Rotation is one of the key physical mechanisms that deeply impact the evolution of stars. Helio- and asteroseismology reveal a strong extraction of angular momentum from stellar radiation zones over the whole Hertzsprung–Russell diagram. Aims. Turbulent transport in differentially rotating, stably stratified stellar radiation zones should be carefully modelled and its strength evaluated. Stratification and rotation imply that this turbulent transport is anisotropic. So far only phenomenological prescriptions have been proposed for the transport in the horizontal direction. This, however, constitutes a cornerstone in current theoretical formalisms for stellar hydrodynamics in evolution codes. We aim to improve its modelling. Methods. We derived a new theoretical prescription for the anisotropy of the turbulent transport in radiation zones using a spectral formalism for turbulence that takes simultaneously stable stratification, rotation, and a radial shear into account. Then, the horizontal turbulent transport resulting from 3D turbulent motions sustained by the instability of the radial differential rotation is derived. We implemented this framework in the stellar evolution code STAREVOL and quantified its impact on the rotational and structural evolution of solar metallicity low-mass stars from the pre-main-sequence to the red giant branch. Results. The anisotropy of the turbulent transport scales as N4τ2/(2Ω2), N and Ω being the buoyancy and rotation frequencies respectively and τ a time characterizing the source of turbulence. This leads to a horizontal turbulent transport of similar strength in average that those obtained with previously proposed prescriptions even if it can be locally larger below the convective envelope. Hence the models computed with the new formalism still build up too steep internal rotation gradients compared to helioseismic and asteroseismic constraints. As a consequence, a complementary transport mechanism such as internal gravity waves or magnetic fields is still needed to explain the observed strong transport of angular momentum along stellar evolution. Conclusions. The new prescription links for the first time the anisotropy of the turbulent transport in radiation zones to their stratification and rotation. This constitutes important theoretical progress and demonstrates how turbulent closure models should be improved to get firm conclusions on the potential importance of other processes that transport angular momentum and chemicals inside stars along their evolution.

Highlights

Rotation is one of the key physical mechanisms that deeply modify the dynamics and evolution of stars (e.g. Maeder 2009)
The angular velocity profile in the radiative interior derives from the redistribution of angular momentum by shear-induced turbulence and meridional flows, which are treated using the formalism derived by Zahn (1992), Maeder & Zahn (1998), and Mathis & Zahn (2004); uniform rotation is assumed in convective regions
Extending the theoretical formalism derived by Kitchatinov & Brandenburg (2012) to the case of rotating stably stratified flows with a vertical shear, we find that the ratio between the horizontal and the vertical turbulent transport scales as N4τ2/ 2Ω2, where we recall that N and Ω are the buoyancy and rotation frequencies, respectively, and τ is the time characterizing the source of the turbulence

Summary

Introduction

Rotation is one of the key physical mechanisms that deeply modify the dynamics and evolution of stars (e.g. Maeder 2009). Rotation modifies the evolutionary path of stars in the Hertzsprung–Russell diagram (hereafter HRD), their lifetime, their nucleosynthesis, chemical stratification and yields, and their magnetism. In this context, helio- and astero-seismology provide key information through the insight they give on the internal rotation profiles of the Sun and stars. Weak differential rotation rates are found in the radiative envelope of intermediate-mass and massive stars (Kurtz et al 2014; Saio et al 2015; Triana et al 2015; Murphy et al 2016; Aerts et al 2017). A strong extraction of angular momentum is required to explain the rotation rates of white dwarfs (e.g. Suijs et al 2008; Hermes et al 2017) and neutron stars (e.g. Heger et al 2005; Hirschi & Maeder 2010)

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Conclusion