Lifetimes of tidally limited star clusters with different radii

Abstract

We study the escape rate of stars, Ṅ, from clusters with different radii on circular orbits in a tidal field using analytical predictions and direct N-body simulations. We find that Ṅ depends on the ratio R ≡ rh/rJ, where rh is the half-mass radius and rJ the radius of the zero-velocity surface around the cluster. For R≳0.05, the 'tidal regime', there is almost no dependence of Ṅ on R. To first order this is because the fraction of escapers per half-mass relaxation time, trh, scales approximately as R3/2, which cancels out the r3/2h term in trh. For R≲ 0.05, the 'isolated regime', Ṅ scales as R-3/2. The dissolution time-scale, tdis, falls in three regimes. Clusters that start with their initial R, Ri; in the tidal regime dissolve completely in this regime and their tdis is, therefore, insensitive to the initial rh. Our model predicts that Ri 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≲0.05 always expand to the tidal regime before final dissolution. Their tdis has a shallower dependence on Ri than what would be expected when tdis is a constant times trh. For realistic values of Ri, the lifetime varies by less than a factor of 1.5 due to changes in Ri;. 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 tdis scales as N0.65/ω, with ω the angular frequency of the cluster in the host galaxy. © 2008 The Authors. Journal compilation © 2008 RAS.