Transport by gravito-inertial waves in differentially rotating stellar radiation zones

Abstract

Context. We examine the dynamics of low-frequency waves in differentially rotating stellar radiation zones, the angular velocity being taken as generally as possible depending both on radius and on latitude in stellar interiors. The associated induced transport of angular momentum, which plays a key role in the evolution of rotating stars, is derived. Aims. We focus on the wave-induced transport of angular momentum, taking into account the Coriolis acceleration in the case of strong radial and latitudinal differential rotation. We thus go beyond the "weak differential rotation" approximation, where rotation is almost a solid-body one plus a residual radial differential rotation. As has been shown in previous works, the Coriolis acceleration modifies such transport. Methods. We built analytically a complete formalism that allows the study of rotational transport in stellar radiation zones taking into account the wave action modified by a general strong differential rotation. Results. The different approximations possible for low-frequency waves in a differentially rotating stably stratified radiative region, namely the traditional and the JWKB approximations, are examined and discussed. The complete bidimensional structure of regular elliptic gravito-inertial waves, which verify these approximations, is derived and compared to those in the "weak differential rotation" case. Next, associated transport of energy and of angular momentum in the vertical and in the horizontal directions and the dynamical equations, respectively for the mean radial differential rotation and the latitudinal one, are obtained. Conclusions. The complete formalism, which takes into account low-frequency wave action, is derived and can be used for the study of secular hydrodynamics of radiative regions and of the associated mixing. The modification of waves due to general strong differential rotation and their feed-back on the angular momentum transport are treated rigourously. In a forthcoming paper (Paper II), this formalism will be applied to the case of solar differential rotation. However, the case of hyperbolic gravito-inertial waves should be carefully studied.

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

“…The greater the ratio l(l+1) m 2 , the stronger is the attenuation Att = e −π l(l+1) We have not yet discussed a latter point: the choice of the method of resolution. Most of the publications concerning IGW use another process to solve the equation of propagation (Press 1981;Zahn et al 1997;Mathis 2009). In fact, the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) theory is particularly adapted to the resolution of this equation.…”

Seismic modelling of the late Be stars HD 181231 and HD 175869 observed with CoRoT: a laboratory for mixing processes

“…The Coriolis acceleration (and the centrifugal one) therefore modifies the propagation of internal waves as soon as the 2Ω/ω c ratio increases (ω c is the frequency at which the internal wave is excited). The induced transport of angular momentum and mixing is modified in two ways: -First, internal waves are trapped in an equatorial belt when ω c < 2Ω because of the Coriolis acceleration action (Lee & Saio 1997;Mathis 2009;Ballot et al 2010). The convective kinetic energy is then transmitted less efficiently to the internal waves in the radiative envelope.…”

Low-frequency internal waves in magnetized rotating stellar radiation zones

“…B ϕ (r, θ) = √ μρr sin θ ω A (r, θ); see Mathis 2009, for the hydrodynamical case). Then, a more subtle treatment has to be adopted, which we will provide in Paper III.…”

“…This means that the impact of ΔΩ on θ c;m constitutes only a small correction that does not change its main behaviour (see Mathis et al 2008, in the hydrodynamical case). A general differential rotation in which the critical latitude explicitely depends on the angular rotation profile and on its vertical and latitudinal gradients has been studied in Mathis (2009) in the purely hydrodynamical case and will be studied in Paper III.…”

“…General differential rotations (Ω (r, θ); cf. Mathis 2009, in the purely hydrodynamical case) and axisymmetric toroidal fields will be treated in Paper III.…”