Horizontal shear instabilities in rotating stellar radiation zones: II. Effects of the full Coriolis acceleration

Abstract: Stellar interiors are the seat of efficient transport of angular momentum all along their evolution. Understanding the dependence of the turbulent transport triggered by the shear instabilities due to the differential rotation in stellar radiation zones is mandatory. Indeed, it constitutes one of the cornerstones of the rotational transport and mixing theory which is implemented in stellar evolution codes to predict the rotational and chemical evolutions of stars. We investigate horizontal shear instabilities in stellar radiation zones by considering the full Coriolis acceleration with both the dimensionless horizontal component $\tilde{f}$ and the vertical component $f$. We performed a linear stability analysis for a horizontal shear flow with a hyperbolic tangent profile, both numerically and asymptotically using the WKBJ approximation. As in the traditional approximation, we identified the inflectional and inertial instabilities. The inflectional instability is destabilized as $\tilde{f}$ increases and its maximum growth rate increases significantly, while the thermal diffusivity stabilizes the inflectional instability similarly to the traditional case. The inertial instability is also strongly affected; for instance, the inertially unstable regime is extended in the non-diffusive limit as $0<f<1+\tilde{f}^{2}/N^{2}$, where $N$ is the dimensionless Brunt-V\"ais\"al\"a frequency. More strikingly, in the high-thermal-diffusivity limit, it is always inertially unstable at any colatitude $\theta$ except at the poles (i.e., $0^{\circ}<\theta<180^{\circ}$). Using the asymptotic and numerical results, we propose a prescription for the effective turbulent viscosities induced by the instabilities to be possibly used in stellar evolution models. The characteristic time of this turbulence is short enough to redistribute efficiently angular momentum and mix chemicals in the radiation zones.