Modelling the rotational evolution of solar-like stars: the rotational coupling time-scale

We investigate the rotational evolution of solar-like stars with a focus on the internal angular momentum transport processes. The double-zone model, in which the star's radiative core and convective envelope are assumed to rotate as solid bodies, is used to test simple relationships between the core-envelope coupling time-scale, tau(c), and rotational properties, like the envelope angular velocity or the differential rotation at the core-envelope interface. The trial relationships are tested by fitting the model parameters to available observations via a Markov chain Monte Carlo method. The synthetic distributions are tested for compatibility with their observational counterparts by means of the standard Kolmogorov-Smirnov (KS) test. A power-law dependence of tau(c) on the inner differential rotation leads to a more satisfactory agreement with observations than a two-valued prescription for tau(c), which would imply a dichotomy between the initially slow (P(rot) greater than or similar to 3 d) and fast (P(rot) less than or similar to 3 d) rotators. However, we find it impossible to reconcile the high fraction of fast rotators in alpha Per with the rotation period distributions in stellar systems at earlier and later evolutionary stages. This could be explained by local environmental effects (e.g. early removal of circumstellar discs due to ultraviolet radiation and winds from nearby high-mass stars) or by observational biases. The low KS probability that the synthetic and observed distributions are not incompatible, found in some cases, may be due to oversimplified assumptions of the double-zone model, but the large relative uncertainties in the age determination of very young clusters and associations are expected to play a relevant role. Other possible limitations and uncertainties are discussed.