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

We study the reaction of a globular star cluster to a time-varying tidalperturbation (gravitational shock) using self-consistent N-body simulations andaddress two questions. First, to what extent is the cluster interior protectedby adiabatic invariants. Second, how much further energy change does thepostshock evolution of the cluster potential produce and how much does itaffect the dispersion of stellar energies. We introduce the adiabaticcorrection} as ratio of the energy change, , to its value in the impulseapproximation. When the potential is kept fixed, the numerical results for theadiabatic correction for stars with orbital frequency \omega can beapproximated as (1 + \omega^2 \tau^2)^{-\gamma}. For shocks with thecharacteristic duration of the order the half-mass dynamical time of thecluster, \tau < t_{dyn,h}, the exponent \gamma = 5/2. For more prolongedshocks, \tau > 4 t_{dyn,h}, the adiabatic correction is shallower, \gamma =3/2. When we allow for self-gravity and potential oscillations which follow theshock, the energy of stars in the core changes significantly, while the totalenergy of the system is conserved. Paradoxically, the postshock potentialfluctuations reduce the total amount of energy dispersion, . The effectis small but real and is due to the postshock energy change being statisticallyanti-correlated with the shock induced heating. These results are to be appliedto Fokker-Planck models of the evolution of globular clusters.Comment: 20 pages; ApJ 513 (in press