On the response of a star cluster to a tidal perturbation

TL;DR

This study uses N-body simulations to analyze how star clusters respond to different tidal perturbations, revealing the importance of geometric distortion and cluster density profiles in energy gain and mass loss.

Contribution

It demonstrates that geometric distortion significantly influences energy gain during slow perturbations, challenging the traditional view of adiabatic damping effects.

Findings

Energy gain matches impulsive predictions for fast shocks.

Slow perturbations by a point-mass can cause similar or greater energy gain than fast shocks.

Cluster size and mass loss depend non-linearly on energy gain and density profile.

Abstract

We study the response of star clusters to individual tidal perturbations using controlled $N$-body simulations. We consider perturbations by a moving point mass and by a disc, and vary the duration of the perturbation as well as the cluster density profile. For fast perturbations (i.e. `shocks'), the cluster gains energy in agreement with theoretical predictions in the impulsive limit. For slow disc perturbations, the energy gain is lower, and this has previously been attributed to adiabatic damping. However, the energy gain due to slow perturbations by a point-mass is similar to, or larger than that due to fast shocks, which is not expected because adiabatic damping should be almost independent of the nature of the tides. We show that the geometric distortion of the cluster during slow perturbations is of comparable importance for the energy gain as adiabatic damping, and that the combined effect can qualitatively explain the results. The half-mass radius of the bound stars after a shock increases up to $\sim$7\% for low-concentration clusters, and decreases $\sim$3\% for the most concentrated ones. The fractional mass loss is a non-linear function of the energy gain, and depends on the nature of the tides and most strongly on the cluster density profile, making semi-analytic model predictions for cluster lifetimes extremely sensitive to the adopted density profile.