Keele Research Repository

The introduction of the Rossby number (R0), which incorporates the convective turnover time (τ), in 1984 was a pioneering idea for understanding the correlation between stellar rotation and activity. The convective turnover time, which cannot be measured directly, is often inferred using existing τ–mass or τ–color relations, typically established based on an ensemble of different types of stars by assuming that τ is a function of mass. In this work, we use Gaia Early Data Release 3 to demonstrate that the masses used to establish one of the most cited τ-mass relations are overestimated for G-type dwarfs and significantly underestimated for late M dwarfs, offsets that affect studies using this τ–mass relation to draw conclusions. We discuss the challenges of creating such relations then and now. In the era of Gaia and other large data sets, stars used to establish these relations require characterization in a multidimensional space, rather than via the single-characteristic relations of the past. We propose that new multidimensional relations should be established based on updated theoretical models and all available stellar parameters for different interior structures from a set of carefully vetted single stars, so that the convective turnover time can be estimated more accurately.