The angular momentum evolution of very low mass stars

We present theoretical models of the angular momentum evolution of very low mass stars (0.1-0.5 M⊙). We also present models of solar analogs (0.6-1.1 M⊙) for comparison with previous work. We investigate the effect of rotation on the effective temperature and luminosity of these stars. Rotation lowers the effective temperature and luminosity of the models relative to standard models of the same mass and composition. We find that the decrease in Teff and L can be significant at the higher end of our mass range but becomes small below 0.4 M⊙. The effects of different assumptions about internal angular momentum transport are discussed. Formulae for relating Teff to mass and vrot are presented. We demonstrate that the kinetic energy of rotation is not a significant contribution to the luminosity of low-mass stars. Previous studies of the angular momentum evolution of low-mass stars concentrated on solar analogs and were complicated by uncertainties related to the internal transport of angular momentum. In this paper we extend our theoretical models for the angular momentum evolution of stars down to 0.1 M⊙. We compare our models to rotational data from young open clusters of different ages to infer the rotational history of low-mass stars and the dependence of initial conditions and rotational evolution on mass. We find that the qualitative conclusions for stars below 0.6 M⊙ do not depend on the assumptions about internal angular momentum transport with the exception of a zero-point shift in the angular momentum loss saturation threshold. We argue that this makes these low-mass stars ideal candidates for the study of the angular momentum loss law and distribution of initial conditions. For stars with masses between 0.6 and 1.1 M⊙, scaling the saturation threshold by the Rossby number can reproduce the observed mass dependence of the stellar angular momentum evolution. We find that neither models with solid-body rotation nor differentially rotating models can simultaneously reproduce the observed stellar spin-down in the 0.6-1.1 M⊙ range and for stars between 0.1 and 0.6 M⊙. We argue that the most likely explanation is that the saturation threshold drops more steeply at low masses than would be predicted with a simple Rossby scaling. In young clusters there is a systematic increase in the mean rotation rate with decreased temperature below 3500 K (0.4 M⊙). This suggests either inefficient angular momentum loss or mass-dependent initial conditions for stars near the fully convective boundary.