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.

Popular Abstract

Dynamics in astronomy is concerned with the causes of motion of objects in space. The dominating force which defines the motions of astronomical objects and governs their dynamical evolution is gravity. This is an attractive force that can act over a long range and influences everything that
has mass or energy. In dynamical astronomy, a wide range of scales is investigated, including: how planets orbit stars, how stars move around in multiple systems and star clusters, and how galaxies dynamically evolve and interact with each other. In this project, we study dynamical interactions
between stars and black holes in dense star clusters where stars are packed close together.

The magnitude of the gravitational force between two bodies depends strongly on their separation, the force becomes weaker over large distances. Therefore, relatively isolated stars like the Sun are not likely to experience strong dynamical interactions with other stars. However, in the
centre of dense clusters of stars such as globular clusters, hundreds of thousands of stars can be tightly packed together in the same volume of space as between the Sun and its nearest neighbour. In these dense environments, stars interact more frequently and are likely to experience close encounters
that are interesting as they can lead to the formation of exotic stellar objects like mass transferring binary systems, and it can also result in collisions between stars. These tightly packed
star clusters can also contain stellar remnants like black holes which can dynamically interact with each other or with surrounding stars, which can lead to the formation of black hole binaries. These objects may merge by emitting gravitational waves, ripples in the fabric of spacetime, that can now be directly detected with ground based detectors like LIGO and Virgo. Dynamical interactions are also important for the overall evolution of globular clusters where binary systems in the centre of the cluster frequently interact with nearby stars and act as an energy source to counteract gravitational collapse of the star cluster, similar to how nuclear reactions in a star generate energy to support it from collapsing.

This project focuses on investigating the outcome of hundreds of thousands of strong dynamical encounters between a binary system and a single object, involving both stars and black holes. Such interactions can result in diverse outcomes. For instance, the binary can be slightly perturbed by
the single, one of the binary components gets exchanged with the single or objects get close enough during the interaction that they merge. These 3-body interactions can be very chaotic which means that a small change in the initial parameters can affect the outcome drastically and numerical
simulation tools are required to predict the outcomes of these interactions. The problem with these simulation tools is that there are a wide variety of codes that seek to solve these problems and one can obtain different outcomes for the same interactions due to differences in the numerical
methods used in these codes as well as the chaotic nature of these interactions.

The primary goal of this project is to check how using different numerical methods and settings in simulation codes changes the outcome of a variety of binary-single interactions on a statistical scale. We also investigate how this may change specific properties of objects after the interaction.
We find that the distribution of outcomes differs slightly between settings, but statistically the differences are negligible. We also specifically investigated how computation of such interactions could influence merger times for binary black holes. We find that the problem is complicated and
whether an interaction will result in an increase or decrease in the binary merger time depends on the initial configuration, and does not strongly depend on the used simulation tools or settings.

• author: Hellström, Lucas
• supervisor: Abbas Askar
• organization: Lund Observatory - Undergoing reorganization; Department of Astronomy and Theoretical Physics - Undergoing reorganization
• course: ASTM31 20201
• year: 2020
• type: H2 - Master's Degree (Two Years)
• subject: Physics and Astronomy
• keywords: Stellar Dynamics, Binary-Single interactions, Dynamical encounters, Additional processes
• publication/series: Lund Observatory Examensarbeten
• report number: 2020-EXA157
• language: English
• id: 9021633
• date added to LUP: 2020-06-26 14:35:52
• date last changed: 2020-06-26 14:35:52