Abstract
Context.Turbulent transport in stellar radiative zones is a key ingredient of stellar evolution theory, but the anisotropy of the transport due to the stable stratification and the rotation of these regions is poorly understood. The assumption of shellular rotation, which is a cornerstone of the so-called rotational mixing, relies on an efficient horizontal transport. However, this transport is included in many stellar evolution codes through phenomenological models that have never been tested.Aims.We investigate the impact of horizontal shear on the anisotropy of turbulent transport.Methods.We used a relaxation approximation (also known asτapproximation) to describe the anisotropising effect of stratification, rotation, and shear on a background turbulent flow by computing velocity correlations.Results.We obtain new theoretical scalings for velocity correlations that include the effect of horizontal shear. These scalings show an enhancement of turbulent motions, which would lead to a more efficient transport of chemicals and angular momentum, in better agreement with helio- and asteroseismic observations of rotation in the whole Hertzsprung-Russell diagram. Moreover, we propose a new choice for the non-linear time used in the relaxation approximation, which characterises the source of the turbulence.Conclusions.For the first time, we describe the effect of stratification, rotation, and vertical and horizontal shear on the anisotropy of turbulent transport in stellar radiative zones. The new prescriptions need to be implemented in stellar evolution calculations. To do so, it may be necessary to implement non-diffusive transport.
Highlights
The transport of angular momentum and chemical species plays a key role in stellar evolution
We investigated the impact of horizontal shear on the anisotropy of the transport in stably stratified, rotating stellar radiative zones
We were able to derive new scalings for mean velocity correlations that confirmed that the main effect is to significantly enhance turbulent motions
Summary
The transport of angular momentum and chemical species plays a key role in stellar evolution. The anisotropy of the transport is due to the combined effect of rotation and stable stratification, which limit horizontal and vertical motions through the buoyancy force and the Coriolis acceleration, respectively Those coefficients are based on phenomenological arguments and introduce large uncertainties in stellar evolution models. M+18 added a vertical shear (due to radial differential rotation) to the formalism of KB12 and show that it has no significant effect on the anisotropy of turbulence They used estimates of mean velocity correlations to propose new prescriptions for the horizontal turbulent diffusion coefficient of chemical elements. The implementation of these prescriptions in stellar evolution computations shows a slightly enhanced transport of angular momentum throughout the main sequence, but not enough to fit helio- and asteroseismic observations.
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