The dynamical fate of planetary systems in young star clusters

We carry out N-body simulations to examine the effects of dynamical interactions on planetary systems in young open star clusters. We explore how the planetary populations in these star clusters evolve, and how this evolution depends on the initial amount of substructure, the virial ratio, the cluster mass and density, and the initial semi-major axis of the planetary systems. The fraction of planetary systems that remains intact as a cluster member, f_BPS, is generally well-described by the functional form f_BPS = f₀(1 + [a/a₀]^c)^-1, where (1-f₀) is the fraction of stars that escapes from the cluster, a₀ the critical semi-major axis for survival, and c a measure for the width of the transition region. The effect of the initial amount of substructure over time t can be quantified as f_BPS = A(t) + B(D), where A(t) decreases nearly linearly with time, and B(D) decreases when the clusters are initially more substructured. Provided that the orbital separation of planetary systems is smaller than the critical value a₀, those in clusters with a higher initial stellar density (but identical mass) have a larger probability of escaping the cluster intact. These results help us to obtain a better understanding of the difference between the observed fractions of exoplanets-hosting stars in star clusters and in the Galactic field. It also allows us to make predictions about the free-floating planet population over time in different stellar environments.