Shear mixing in stellar radiative zones

Abstract

Context. Turbulent transport of chemical elements in radiative zones of stars is considered in current stellar evolution codes thanks to phenomenologically derived diffusion coefficients. Recent local numerical simulations suggest that the coefficient for radial turbulent diffusion due to radial differential rotation satisfies D t 0.058κ/Ri, in qualitative agreement with the model of Zahn (1992, A&A, 265, 115). However, this model does not apply (i) when differential rotation is strong with respect to stable thermal stratification or (ii) when chemical stratification has a significant dynamical effect, a situation encountered at the outer boundary of nuclear-burning convective cores. Aims. We extend our numerical study to consider the effects of chemical stratification and of strong shear, and compare the results with prescriptions used in stellar evolution codes. Methods. We performed local, direct numerical simulations of stably stratified, homogeneous, sheared turbulence in the Boussinesq approximation. The regime of high thermal diffusivities, typical of stellar radiative zones, is reached thanks to the so-called smallPéclet-number approximation, which is an asymptotic development of the Boussinesq equations in this regime. The dependence of the diffusion coefficient on chemical stratification was explored in this approximation. Results. Maeder's extension of Zahn's model in the strong-shear regime (Maeder 1995, A&A, 299, 84) is not supported by our results, which are better described by a model found in the geophysical literature. As regards the effect of chemical stratification, our quantitative estimate of the diffusion coefficient as a function of the mean gradient of mean molecular weight leads to the formula D t 0.45κ(0.12 − Ri µ )/Ri, which is compatible in the weak-shear regime with the model of Maeder & Meynet (1996, A&A, 313, 140) but not with Maeder's (1997, A&A, 321, 134).

New prescriptions of turbulent transport from local numerical simulations

“…In the small-Péclet-number regime, we showed (Prat & Lignières 2013) (Prat & Lignières 2014) as the Péclet number decreases, that is sensibly the same as in the SPNA. We can thus write…”

“…In the large-Péclet-number regime (see Prat & Lignières 2014), the generalisation of Zahn's model proposed by Maeder (1995), intended to be also valid in this regime, turned to be incompatible with our simulations. In the opposite, we found a good agreement with the model of Lindborg & Brethouwer (2008), proposed in the geophysical literature, in which the diffusion coefficient is given by…”

“…Our SPNA simulations performed with different values of the chemical Richardson number Ri μ (also presented in Prat & Lignières 2014) show that the quantity D t /(κRi −1 ) is well represented by an affine function of Ri μ , as represented in Fig. 2.…”

Modelling transport processes in stellar radiative interiors

“…The choice of the prescriptions for ν v and ν h can strongly affect the models outcomes [44] but is poorly constrained by observations. It can only be tested by numerical simulations, a work that [45] have undertaken with promising results.…”

Concluding remarks

“…Prat & Lignières [129] discuss turbulent mixing in stellar radiative zones, pointing out that turbulent motions involved in rotating stars are full 3D motions, and cannot be easily resolved in models having fewer dimensions. Kitiashvili et al [130] use numerical radiation transfer simulations in 3D to study convective and oscillation properties of MS stars observed by Kepler and having masses of 1M and above; they find supersonic granular-type convection significantly larger than solar granulation, with strong overshooting plumes penetrating the stable radiative zone, potentially affecting oscillation properties.…”