Rotational evolution of slow--rotator sequence stars II. Modeling the wind braking and rotational coupling in the entire mass range of solar-like stars

In recent years, ground- and space-based photometric surveys have characterized the rotational evolution of solar-like stars to an unprecedented level of detail. In this work we focus on the slow--rotator sequence, an emergent feature recognizable in the color--period diagram of Galactic open clusters. Understanding the evolution of this sequence is a promising avenue for formulating a robust rotation period--mass--age relation, which can be used to estimate stellar ages. Our model of the rotational evolution of stars on the slow--rotator sequence takes into account magnetized wind braking and rotational decoupling between the radiative interior and the convective envelope. This decoupling naturally develops as the internal redistribution of angular momentum lags behind the loss of angular momentum at the stellar surface, and is parameterized in the model by a rotational coupling timescale. Using data from the literature on rotation and membership of stars in a selection of open clusters, aged between 100 Myr and 4 Gyr, we constrain the mass dependence of the two competing processes of wind braking at the surface and angular momentum transport in the interior. Consistent with our previous findings, our best-fitting model requires a mass-dependent coupling timescale; this result is insensitive to the details of the wind braking model used. We show that the mass dependence of the coupling timescale follows a broken power law in the entire solar-like mass range (0. 4--1. 25, M_⊙), with the exponent change occurring at ≈ 0. 6, M_⊙. At the same time, our approach can be used to infer semi-empirically the mass dependence of the wind braking model that best fits the observational constraints. Based on our findings, we propose a novel wind braking law with a particularly simple mass term, directly proportional to the moment of inertia of the convective envelope of the star.