On the orbital period modulation of RS CVn binary systems

The Applegate hypothesis proposed to explain the orbital period modulation of RS Canum Venaticorum (RS CVn) close binaries (Applegate 1992) is considered in the framework of a general model to treat the angular momentum exchanges within the convective envelope of a magnetically active star. This model assumes that the convection zone is strictly adiabatic and that the Taylor-Proudman balance holds, leading to an internal angular velocity constant over cylindrical surfaces co-axial with the rotation axis. It turns out that the angular velocity perturbations, whatever their origin, can be expressed in terms of the eigenfunctions of the equation of angular momentum conservation with stress-free boundary conditions. Moreover, a lower limit for the energy dissipation rate in a turbulent convection zone can be set, thanks to the extremal properties of the eigenfunctions. This approach allows to apply precise constraints on the amplitude and the radial profile of the angular velocity variations that are required to explain the observed orbital period changes in classical RS CVn binaries (i.e. with orbital period longer than 1-2 d and a subgiant secondary component). It is found that an angular velocity change as large as 10 per cent of the unperturbed angular velocity at the base of the stellar convection zone is needed. Such a large change is not compatible with the observations. Moreover, it would produce an energy dissipation rate much larger than the typical luminosities of the active components of RS CVn systems, except in the case that fast rotation and internal magnetic fields reduce the turbulent viscosity by at least 2 orders of magnitude with respect to the value given by the mixing-length theory. Therefore, the model proposed by Applegate should be rejected, at least in the case of classical RS CVn close binaries. Possible alternative models are briefly discussed, emphasizing the effects of intense magnetic fields (similar to 10 T) on the internal structure of magnetically active stars and the dynamics of close binary systems.