Theoretical values of convective turnover times and Rossby numbers for solar-like, pre-main sequence stars

Context. Magnetic fields are at the heart of the observed stellar activity in late-type stars, and they are presumably generated by a dynamo mechanism at the interface layer (tachocline) between the radiative core and the base of the convective envelope. Aims. Since dynamo models are based on the interaction between differential rotation and convective motions, the introduction of rotation in the ATON 2.3 stellar evolutionary code allows for explorations regarding a physically consistent treatment of magnetic effects in stellar structure and evolution, even though there are formidable mathematical and numerical challenges involved. Methods. As examples of such explorations, we present theoretical estimates for both the local convective turnover time (tau(c)), and global convective times (tau(g)) for rotating pre-main sequence solar-type stars, based on up-to-date input physics for stellar models. Our theoretical predictions are compared with the previous ones available in the literature. In addition, we investigate the dependence of the convective turnover time on convection regimes, the presence of rotation and atmospheric treatment. Results. Those estimates, as opposed to the use of empirically derived values of tau(c) for such matters, can be used to calculate the Rossby number Ro, which is related to the magnetic activity strength in dynamo theories and, at least for main-sequence stars, shows an observational correlation with stellar activity. More important, they can also contribute for testing stellar models against observations. Conclusions. Our theoretical values of tau(c), tau(g) and Ro qualitatively agree with those published by Kim & Demarque (1996, ApJ, 457, 340). By increasing the convection efficiency, tau(g) decreases for a given mass. FST models show still lower values. The presence of rotation shifts tau(g) towards slightly higher values when compared with non-rotating models. The use of non-gray boundary conditions in the models yields values of tau(g) smaller than in the gray approximation.