The effects of dynamical interactions on planets in young substructured star clusters

Abstract

We present N-body simulations of young substructured star clusters undergoing various dynamical evolutionary scenarios and examine the direct effects of interactions in the cluster on planetary systems. We model clusters initially in cool collapse, in virial equilibrium and expanding, and place a 1-Jupiter-mass planet at either 5 or 30 au from their host stars, with zero eccentricity. We find that after 10 Myr ∼10 per cent of planets initially orbiting at 30 au have been liberated from their parent star and form a population of free-floating planets. A small number of these planets are captured by other stars. A further ∼10 per cent have their orbital eccentricity (and less often their semimajor axis) significantly altered. For planets originally at 5 au the fractions are a factor of 2 lower. The change in eccentricity is often accompanied by a change in orbital inclination which may lead to additional dynamical perturbations in planetary systems with multiple planets. The fraction of liberated and disrupted planetary systems is highest for subvirial clusters, but virial and supervirial clusters also dynamically process planetary systems, due to interactions in the substructure. Of the planets that become free-floating, those that remain observationally associated with the cluster (i.e. within two half-mass radii of the cluster centre) have a similar velocity distribution to the entire star cluster, irrespective of whether they were on a 5 or 30 au orbit, with median velocities typically ∼1 km s−1. Conversely, those planets that are no longer associated with the cluster have similar velocities to the non-associated stars if they were originally at 5 au (∼9 km s−1), whereas the planets originally at 30 au have much lower velocities (3.8 km s−1) than the non-associated stars (10.8 km s−1). These findings highlight potential pitfalls of concluding that (a) planets with similar velocities to the cluster stars represent the very low mass end of the initial mass function and (b) planets on the periphery of a cluster with very different observed velocities form through different mechanisms.