The effect of spiral arm passages on the evolution of stellar clusters

We study the effect of spiral arm passages on the evolution of star clusters on planar and circular orbits around the centres of galaxies. Individual passages with different relative velocity (V-drift) and arm width are studied using N-body simulations. When the ratio of the time it takes the cluster to cross the density wave to the crossing time of stars in the cluster is much smaller than one, the energy gain of stars can be predicted accurately in the impulsive approximation. When this. ratio is much larger than one, the cluster is heated adiabatically and the net effect of heating is largely damped. For a given duration of the perturbation, this ratio is smaller for stars in the outer parts of the cluster compared to stars in the inner part. The cluster energy gain due to perturbations of various duration as obtained from our N-body simulations is in good agreement with theoretical predictions taking into account the effect of adiabatic damping. Perturbations by the broad stellar component of the spiral arms on a cluster are in the adiabatic regime and, therefore, hardly contribute to the energy gain and mass loss of the cluster. We consider the effect of crossings through the high-density shocked gas in the spiral arms, which result in a more impulsive compression of the cluster. The energy injected during each spiral arm passage can exceed the total binding energy of a cluster, but, since most of the energy goes in high velocity escapers from the cluster halo, only relatively little mass is lost. A single perturbation that injects the same amount of energy as the initial (negative) cluster energy causes at most similar to 40 per cent of the stars to escape. We find that a perturbation that delivers similar to 10 times the initial cluster energy is needed to completely unbind a cluster in a single passage. The net effect of spiral arm perturbations on the evolution of low mass (less than or similar to 100 M-circle dot) star clusters is more profound than on more massive clusters (greater than or similar to 1000 M-circle dot). This is due to the fact that the crossing time of stars in the latter is shorter, causing a larger fraction of stars to be in the adiabatic regime. The time-scale of disruption by subsequent spiral arm perturbations depends strongly on position with respect to the radius of corotation (R-CR), where V-drift = 0. The time between successive encounters scales with V-drift as t(drift) proportional to V-drift(-1) and the energy gain per passage drift scales as Delta E proportional to V-drift(2). Exactly at R-CR passages do not occur, so the time-scale of disruption is infinite. The time-scale of disruption is shortest at similar to 0.8-0.9 R-CR, since there V-drift is low. This location can be applicable to the solar neighbourhood. In addition, the four-armed spiral pattern of the Milky Way makes spiral arms contribute more to the disruption of clusters than in a similar but two-armed galaxy. Still, the disruption time due to spiral arm perturbations there is about an order of magnitude higher than what is observed for the solar neighbourhood, making spiral arm perturbations a moderate contributor to the dissolution of open clusters.