Abstract
Context. Stellar interiors are the seat of efficient transport of angular momentum all along their evolution. In this context, understanding the dependence of the turbulent transport triggered by the instabilities of the vertical and horizontal shears of the differential rotation in stellar radiation zones as a function of their rotation, stratification, and thermal diffusivity 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. Aims. We investigate horizontal shear instabilities in rotating stellar radiation zones by considering the full Coriolis acceleration with both the dimensionless horizontal Coriolis component f̃ and the vertical component f. Methods. We performed a linear stability analysis using linearized equations derived from the Navier-Stokes and heat transport equations in the rotating nontraditional f-plane. We considered a horizontal shear flow with a hyperbolic tangent profile as the base flow. The linear stability was analyzed numerically in wide ranges of parameters, and we performed an asymptotic analysis for large vertical wavenumbers using the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximation for nondiffusive and highly-diffusive fluids. Results. As in the traditional f-plane approximation, we identify two types of instabilities: the inflectional and inertial instabilities. The inflectional instability is destabilized as f̃ 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 also extended in the nondiffusive limit as 0 < f < 1 + f̃ 2/N2, where N is the dimensionless Brunt-Väisälä frequency. More strikingly, in the high thermal diffusivity limit, it is always inertially unstable at any colatitude θ except at the poles (i.e., 0° < θ < 180°). We also derived the critical Reynolds numbers for the inertial instability using the asymptotic dispersion relations obtained from the WKBJ analysis. Using the asymptotic and numerical results, we propose a prescription for the effective turbulent viscosities induced by the inertial and inflectional instabilities that can be possibly used in stellar evolution models. The characteristic time of this turbulence is short enough so that it is efficient to redistribute angular momentum and to mix chemicals in stellar radiation zones.
Highlights
Stellar rotation is one of the key physical processes to build a modern picture of stellar evolution (e.g., Maeder 2009, and references therein)
Stellar interiors are the seat of efficient mechanisms that transport angular momentum all along their evolution. These mechanisms have not been identified yet even if several candidates have been proposed, such as stable and unstable magnetic fields (e.g., Moss 1992; Charbonneau & MacGregor 1993; Spruit 1999, 2002; Fuller et al 2019), stochastically-excited internal gravity waves (e.g., Talon & Charbonnel 2005; Rogers 2015; Pinçon et al 2017), and mixed gravito-acoustic modes (Belkacem et al 2015a,b). In this framework, improving our knowledge of the hydrodynamical turbulent transport induced by the instabilities of the stellar differential rotation is mandatory since it has been recently proposed as another potential efficient mechanism to transport angular momentum (Barker et al 2020; Garaud 2020) while it constitutes one of the cornerstones of the theory of the rotational transport and mixing along the evolution of stars (Zahn 1992)
If the turbulence triggered by the horizontal shear acts to damp its source, the horizontal differential rotation, as proposed by Zahn (1992) we predict a very efficient transport of angular momentum that can lead to the so-called shellular rotation where horizontal gradients of the angular velocity are weak
Summary
Stellar rotation is one of the key physical processes to build a modern picture of stellar evolution (e.g., Maeder 2009, and references therein). Nontraditional effects can be important for stellar structure configurations where the Coriolis acceleration can compete with the Archimedean force in the direction of both entropy and chemical stratification, for instance during the formation of the radiative core of pre-main-sequence, lowmass stars or in the radiative envelope of rapidly rotating upper main-sequence stars These regimes should be treated properly to build robust one- or two-dimensional (1D or 2D) secular models of the evolution of rotating stars (e.g., Ekström et al 2012; Amard et al 2019; Gagnier et al 2019). We, continue our previous work that examined the effect of thermal diffusion on horizontal shear instabilities in stably stratified rotating stellar radiative zones (Park et al 2020), but we consider the full Coriolis acceleration.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
