Non-gray rotating stellar models and the evolutionary history of the Orion Nebular Cluster

Context. Rotational evolution in the pre-main sequence is described with new sets of pre-MS evolutionary tracks including rotation, non-gray boundary conditions (BCs) and either low (LCE) or high convection efficiency (HCE). Aims. Using observational data and our theoretical predictions, we aim at constraining (1) the differences obtained for the rotational evolution of stars within the ONC by means of these different sets of new models; (2) the initial angular momentum of low mass stars, by means of their templates in the ONC. Methods. We discuss the reliability of current stellar models for the pre-MS. While the 2D radiation hydrodynamic simulations predict HCE in pre-MS, semi-empirical calibrations either seem to require that convection is less efficient in pre-MS than in the following MS phase (lithium depletion) or are still contradictory (binary masses). We derive stellar masses and ages for the ONC by using both LCE and HCE. Results. The resulting mass distribution for the bulk of the ONC population is in the range 0.2-0.4 M circle dot for our new non-gray models and, as in previous analyse, in the range 0.1-0.3 M circle dot for models having gray BCs. In agreement with Herbst et al. (2002) we find that a large percentage (similar to 70%) of low-mass stars (M less than or similar to 0.5 M circle dot for LCE; M less than or similar to 0.35 M circle dot for HCE) in the ONC appears to be fast rotators (P < 4 days). Three possibilities are open: 1) similar to 70% of the ONC low mass stars lose their disk at early evolutionary phases; 2) their locking period is shorter; 3) the period evolution is linked to a different morphology of the magnetic fields of the two groups of stars. We also estimate the range of initial angular momentum consistent with the observed periods. Conclusions. The comparisons made indicate that a second parameter is needed to describe convection in the pre-MS, possibly related to the structural effect of a dynamo magnetic field.