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 pe rturbation (gravitational shock) using self-consistent N-body simulations a nd address two questions. First, to what extent is the cluster interior pro tected 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 resu lts for the adiabatic correction for stars with orbital frequency omega can be approximated as (1 + omega(2)tau(2))(-y). For shocks with the character istic 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 p rolonged shocks, tau greater than or similar to 4t(dyn.h), the adiabatic co rrection is shallower, gamma = 3/2. When we allow for self-gravity and pote ntial oscillations that follow the shock, the energy of stars in the core c hanges significantly while the total energy of the system is conserved. Par adoxically, 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 sh ock-induced heating. These results are to be applied to Fokker-Planck model s of the evolution of globular clusters.