Chaos in Stellar Dynamics - Outcomes of Binary-Single interactions in Globular Clusters

Abstract: Gravitational encounters between a single star and a binary system can frequently occur in the cores of dense stellar systems like globular clusters. These three-body scattering encounters can lead to a variety of outcomes since the energy of the binary components can be exchanged with the interacting single star. The outcome of these interactions strongly depend on the initial conditions of the interactions and can result in stellar collisions, exchange encounters and dissolution of binary systems. From an astrophysical point of view, these interactions can lead to the formation of exotic stellar objects and binary systems that include gravitational wave sources, X-ray binaries and blue stragglers. Such interactions involving binary systems also play an important role in preventing the core collapse of globular clusters and can influence their dynamical evolution. The classical three-body gravitational problem has challenged researchers for many centuries and no general closed-form solution has been found. Therefore, numerical experiments are carried out to compute the outcome of these interactions. The time evolution of such a system is chaotic, this means that even small changes in the initial setup can lead to a completely different outcome. In this study, we explore how the outcome of binary-single encounters can change with the numerical method that is used to solve them. We do this by carrying out a large number of numerical scattering experiments involving combinations of stars and black holes with existing codes designed for small-N gravitational dynamics. We specifically investigate the differences in outcome that can arise from using different regularization schemes and numerical accuracies. We also briefly explore how the outcomes may be influenced by inclusion of additional physical processes such as gravitational wave radiation and tides. Such processes can dissipate energy and angular momentum during these binary-single interactions and their effects are studied in interactions involving black holes and stars. We find that while there are differences in outcomes of individual interactions, the statistical outcome of an ensemble of these interactions is not significantly influenced by the regularization scheme. We do find that using relatively high numerical accuracy do influence the statistical outcome of the interactions and increases their computational time. However, using too low of a numerical accuracy produces larger differences and can give incorrect results. For our runs with interactions involving black holes, the inclusion of post-Newtonian terms do not result in more mergers or produce more binaries that would merge within a Hubble time. We also find that the binary black holes that do merge within a Hubble time after an encounter have properties similar to the binary black hole mergers that have been detected by gravitational wave observatories. Additionally, we find that the inclusion of tidal effects reduce the number of mergers and increase the number of temporary bound triples and the effect becomes more notable when more stars are included in the interaction.