A one-dimensional toy model of globular clusters

We introduce a one-dimensional toy model of globular clusters. The model is a version of the well-known gravitational sheets system, where we also take into account mass and energy loss by evaporation of stars at the boundaries. Numerical integration by the ‘‘exact’’ event-driven dynamics is performed, for initial uniform density and Gaussian random velocities. Two distinct quasistationary asymptotic regimes are attained, depending on the initial energy of the system. We guess the forms of the density and velocity profiles that fit numerical data extremely well and allow us to perform an independent calculation of the self-consistent gravitational potential. Some power laws for the asymptotic number of stars and for the collision times are suggested.