On the Self‐consistent Response of Stellar Systems to Gravitational Shocks

Abstract

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, how much further energy change does the postshock evolution of the cluster potential produce and how much does it a †ect the dispersion of stellar energies ? We introduce the "" adiabatic correction ÏÏ as ratio of the energy change, S*ET, to its value in the impulse approximation. When the potential is kept Ðxed, the numerical results for the adiabatic correction for stars with orbital frequency u can be approximated as (1 ] u2q2)~c. For shocks with the characteristic duration of the order of the half-mass dynamical time of the cluster, the expo-q [ t dyn,h , nent c \ 5/2. For more prolonged shocks, the adiabatic correction is shallower, c \ 3/2. q Z 4t dyn,h , When we allow for self-gravity and potential oscillations that follow the shock, the energy of stars in the core changes signiÐcantly while the total energy of the system is conserved. Paradoxically, the postshock potential Ñuctuations reduce the total amount of energy dispersion, S*E2T. The e †ect 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.