Angular momentum conservation and torsional oscillations in the Sun and solar-like stars

Context. The solar torsional oscillations, i.e., the perturbations of the angular velocity of rotation associated with the eleven-year activity cycle, are a manifestation of the interaction among the interior magnetic fields, amplified and modulated by the solar dynamo, and rotation, meridional flow and turbulent thermal transport. Therefore, they can be used, at least in principle, to put constraints on this interaction. Similar phenomena are expected to be observed in solar-like stars and can be modelled to shed light on analogous interactions in different environments. Aims. The source of torsional oscillations is investigated by means of a model for the angular momentum transport within the convection zone. Methods. A description of the torsional oscillations is introduced, based on an analytical solution of the angular momentum equation in the mean-field approach. It provides information on the intensity and location of the torques producing the redistribution of the angular momentum within the convection zone of the Sun along the activity cycle. The method can be extended to solar-like stars for which some information on the time-dependence of the differential rotation is becoming available. Results. Illustrative applications to the Sun and solar-like stars are presented. Under the hypothesis that the solar torsional oscillations are due to the mean-field Lorentz force, an amplitude of the Maxwell stresses vertical bar BrB phi vertical bar greater than or similar to 8 x 10(3) G(2) at a depth of similar to 0.85 R-circle dot at low latitude is estimated. Moreover, the phase relationship between Br and B-phi can be estimated, suggesting that BrB phi > 0 below similar to 0.85 R-circle dot and BrB phi < 0 above. Conclusions. Such preliminary results show the capability of the proposed approach to constrain the amplitude, phase and location of the perturbations leading to the observed torsional oscillations.