The impact of disk-locking on convective turnover times of low-mass pre-main sequence and main sequence stars

The impact of disk-locking on the stellar properties related to magnetic activity from the theoretical point of view is investigated. We use the ATON stellar evolution code to calculate theoretical values of convective turnover times ($\tau_{\rm c}$) and Rossby numbers ($Ro$, the ratio between rotation periods and $\tau_{\rm c}$) for pre-main sequence (pre-MS) and main sequence (MS) stars. We investigate how $\tau_{\rm c}$ varies with the initial rotation period and with the disk lifetime, using angular momentum conserving models and models simulating the disk-locking mechanism. In the latter case, the angular velocity is kept constant, during a given locking time, to mimic the magnetic locking effects of a circumstellar disk. The local convective turnover times generated with disk-locking models are shorter than those obtained with angular momentum conserving models. The differences are smaller in the early pre-MS, increase with stellar age and become more accentuated for stars with $M$$\geq$$1 {\rm M}_{\odot}$ and ages greater than 100 Myr. Our new values of $\tau_{\rm c}$ were used to estimate $Ro$ for a sample of stars selected from the literature in order to investigate the rotation-activity relationship. We fit the data with a two-part power-law function and find the best fitting parameters of this relation. The differences we found between both sets of models suggest that the star's disk-locking phase properties affect its Rossby number and its position in the rotation-activity diagram. Our results indicate that the dynamo efficiency is lower for stars that had undergone longer disk-locking phases.