Tidal Shocking by Extended Mass Distributions

We derive expressions for the tidal field exerted by a spherically symmetric galaxy having an extended mass distribution and use our analysis to calculate tidal heating of stars in a globular cluster or a satellite galaxy. We integrate the tidal force over accurate orbits in various models for the primary by using the impulse approximation, coupled with adiabatic corrections that allow for time variation of the perturbation. We verify the results with direct N -body simulations, and we also compare them with the conventional straight-path approximation. Heating on highly eccentric orbits dominates, since adiabatic corrections strictly prohibit energy changes on low-eccentricity orbits. The results are illustrated for globular cluster NGC 6712. For the orbital eccentricities higher than 0.9, the future lifetime of NGC 6712 is less than 10 10 yr. Our analysis can be used to study tidal interactions of star clusters andgalaxies in a semianalytical manner.