Lifetimes of tidally limited star clusters with different radii

We study the escape rate of stars, (N)over dot, from clusters with different radii on circular orbits in a tidal field using analytical predictions and direct N-body simulations. We find that (N)over dot depends on the ratio R equivalent to r(h)/r(J), where r(h) is the half-mass radius and r(J) the radius of the zero-velocity surface around the cluster. For R greater than or similar to 0.05, the 'tidal regime', there is almost no dependence of (N)over dot on R. To first order this is because the fraction of escapers per half-mass relaxation time, t(rh), scales approximately as R(3/2), which cancels out the r(h)(3/2) term in t(rh). For R less than or similar to 0.05, the 'isolated regime', (N)over dot scales as R(-3/2). The dissolution time-scale, t(dis), falls in three regimes. Clusters that start with their initial R, R(i), in the tidal regime dissolve completely in this regime and their t(dis) is, therefore, insensitive to the initial r(h). Our model predicts that R(i) has to be 10(-20)-10(-10) for clusters to dissolve completely in the isolated regime. This means that realistic clusters that start with R(i) less than or similar to 0.05 always expand to the tidal regime before final dissolution. Their t(dis) has a shallower dependence on Ri than what would be expected when t(dis) is a constant times t(rh). For realistic values of R(i), the lifetime varies by less than a factor of 1.5 due to changes in R(i). This implies that the 'survival' or 'vital' diagram for globular clusters should allow for more small clusters to survive. We note that with our result it is impossible to explain the universal peaked mass function of globular cluster systems by dynamical evolution from a power-law initial mass function, since the peak will be at lower masses in the outer parts of galaxies. Our results finally show that in the tidal regime t(dis) scales as N(0.65)/omega, with omega the angular frequency of the cluster in the host galaxy.