Rotation periods for very low mass stars in Praesepe

We investigate the rotation periods of fully convective very low mass (VLM, M < 0.3 M-circle dot) stars, with the aim to derive empirical constraints for the spin-down due to magnetically driven stellar winds. Our analysis is based on a new sample of rotation periods in the main-sequence cluster Praesepe (age 600 Myr). From photometric light curves obtained with the Isaac Newton Telescope, we measure rotation periods for 49 objects, among them 26 in the VLM domain. This enlarges the period sample in this mass and age regime by a factor of 6. Almost all VLM objects in our sample are fast rotators with periods < 2.5 d, in contrast to the stars with M > 0.6 M-circle dot in this cluster which have periods of 7-14 d. Thus, we confirm that the period-mass distribution in Praesepe exhibits a radical break at M similar to 0.3-0.6 M-circle dot. Our data indicate a positive period-mass trend in the VLM regime, similar to younger clusters. In addition, the scatter of the periods increases with mass. For the M > 0.3 M-circle dot objects in our sample, the period distribution is probably affected by binarity. By comparing the Praesepe periods with literature samples in the cluster NGC 2516 (age similar to 150 Myr) we constrain the spin-down in the VLM regime. An exponential rotational braking law P proportional to exp (t/tau) with a mass-dependent tau is required to reproduce the data. The spin-down time-scale tau increases steeply towards lower masses; we derive tau similar to 0.5 Gyr for 0.3 M-circle dot and > 1 Gyr for 0.1 M-circle dot. These constraints are consistent with the current paradigm of the spin-down due to wind braking. We discuss possible physical origins of this behaviour and prospects for future work.