Coupling between internal waves and shear-induced turbulence in stellar radiation zones: the critical layers

Abstract

Context. Internal gravity waves (IGW) are known as one of the candidates for explaining the angular velocity profile in the Sun and in solar-type main-sequence and evolved stars due to their role in the transport of angular momentum. Our contribution deals with critical layers, which are defined as the locations where the Doppler-shifted frequency of the wave approaches zero (i.e., they correspond to corotation resonances). Aims. The IGW propagate through stably stratified radiative regions, where they extract or deposit angular momentum through two processes: radiative and viscous dampings and critical layers. Our goal is to obtain a complete picture of the effects of these processes. Methods. First, we expose a mathematical resolution of the equation of propagation for IGW in adiabatic and non-adiabatic cases near critical layers. Then, the use of a dynamical stellar evolution code, which treats the secular transport of angular momentum, allows us to apply these results to the case of a solar-like star. Results. The analysis reveals two cases depending on the value of the Richardson number at critical layers: a stable one, where IGW are attenuated as they pass through a critical level, and an unstable turbulent case, where they can be reflected/transmitted by the critical level with a coefficient larger than one. Such over-reflection/transmission can have strong implications on our vision of angular momentum transport in stellar interiors. Conclusions. This paper highlights the existence of two regimes defining the interaction between an IGW and a critical layer. An application exposes the effect of the first regime, showing a strengthening of the damping of the wave. Moreover, this work opens up new ways concerning the coupling between IGW and shear instabilities in stellar interiors.

Internal rotation of 13 low-mass low-luminosity red giants in theKeplerfield

“…It is then clear that a very effective mechanism for angular momentum transport is at work. Internal gravity waves are capable of transferring considerable amounts of angular momentum (Rogers 2015;Alvan et al 2013), which provides a suitable explanation for 'anomalous' rotation rates in other types of stars, such as those reported by Kurtz et al (2014); Saio et al (2015), and Triana et al (2015). However, Fuller et al (2014) showed that this mechanism falls short of explaining the observed rotation rate ratios in stars on the red giant branch.…”

Theoretical seismology in 3D: nonlinear simulations of internal gravity waves in solar-like stars

“…With the large-scale meridional circulation (Zahn 1992;Mathis & Zahn 2004), the different hydrodynamical shear and baroclinic instabilities (Zahn 1983), and the fossil magnetic field (Gough & McIntyre 1998;Brun & Zahn 2006;Garaud & Garaud 2008;Duez & Mathis 2010;Strugarek et al 2011b), IGWs constitute the fourth main process responsible for the angular momentum redistribution in radiative interiors. Indeed, when they propagate, IGWs are able to transport and deposit a net amount of angular momentum by radiative damping (Press 1981;Schatzman 1993;Zahn et al 1997) and corotation resonances (Booker & Bretherton 1967;Alvan et al 2013). Their action induces important changes in the internal rotation profiles of stars during their evolution (Talon & Charbonnel 2008;Charbonnel et al 2013;).…”

Asymptotic theory of gravity modes in rotating stars

“…Such amplitude equations are already used to investigate the driving of the atmospheric circulation by waves (Marks & Eckermann 1995). To conduct similar investigations in stars, it will be necessary to model energy deposition processes such as thermal dissipation and critical layers (Fritts et al 1998;Alvan et al 2013) and to take phase changes at caustics into account (Broutman et al 2004).…”