Rotating globular clusters .1. Onset of the gravothermal instability

Rotation in globular clusters can a priori influence their dynamical evolution prior to core collapse in two different ways. First, the rate of evaporation of stars is increased; second, the limit of stability of the cluster with respect to the gravothermal catastrophe can be displaced. We have investigated these two processes with the help of a simple cluster model, which generalizes the King distribution function to rotating clusters. We find that the critical concentration for the onset of the gravothermal instability is not much modified by the cluster rotation, as it is reduced by at most 15%. The effect of rotation on the total mass loss in the evaporation phase is much more noticeable, and amounts to a factor of similar to 1.5 to 2 for cluster models in which the rotational energy initially represents 15% to 20% of the total kinetic energy. Surprisingly, this increased mass loss is not accompanied by an increase of the evolution rate of the cluster concentration, which is found to be more or less insensitive to the cluster rotation.