On the self-consistent response of stellar systems to gravitational shocks

We study the reaction of a globular star cluster to a time-varying tidal perturbation (gravitational shock) using self-consistent N-body simulations and address two questions. First, to what extent is the cluster interior protected by adiabatic invariants? Second, bow much further energy change does the postshock evolution of the cluster potential produce and how much does it affect the dispersion of stellar energies? We introduce the "adiabatic correction'" as ratio of the energy change, [Delta E], to its value in the impulse approximation. When the potential is kept fixed, the numerical results for the adiabatic correction for stars with orbital frequency omega can be approximated as (1 + omega(2)tau(2))(-y). For shocks with the characteristic duration of the order of the half-mass dynamical time of the cluster, tau less than or similar to t(dyn.h), the exponent gamma = 5/2. For more prolonged shocks, tau greater than or similar to 4t(dyn.h), the adiabatic correction is shallower, gamma = 3/2. When we allow for self-gravity and potential oscillations that follow the shock, the energy of stars in the core changes significantly while the total energy of the system is conserved. Paradoxically, the postshock potential fluctuations reduce the total amount of energy dispersion, [Delta E-2]. The effect is small but real and is due to the postshock energy change being statistically anticorrelated with the shock-induced heating. These results are to be applied to Fokker-Planck models of the evolution of globular clusters.