Small-N collisional dynamics III: The battle for the realm of not-so-small-N

Abstract

In this paper, the third in the series, we continue our study of combinatorics in chaotic Newtonian dynamics. We study the chaotic four-body problem in Newtonian gravity assuming finite-sized particles, and we focus on interactions that produce direct collisions between any two stars. Our long-term goal is to construct an equation that gives the probability of a given collision event occurring over the course of the interaction, as a function of the total encounter energy and angular momentum as well as the numbers and properties of the particles. In previous papers, we varied the number of interacting particles and the distribution of particle radii, for all equal mass particles. Here, we focus on the effects of different combinations of particle masses. We develop an analytic formalism for calculating the time-scales for different collision scenarios to occur. Our analytic time-scales reproduce the simulated time-scales when gravitational focusing is included. We present a method for calculating the relative rates for different types of collisions to occur, assuming two different limits for the particle orbits; radial and tangential. These limits yield relative collision probabilities that bracket the probabilities we obtain directly from numerical scattering experiments, and are designed to reveal important information about the (time-averaged) trajectories of the particles as a function of the interaction parameters. Finally, we present a Collision Rate Diagram (CRD), which directly compares the predictions of our analytic rates to the simulations and quantifies the quality of the agreement. The CRD will facilitate refining our analytic collision rates in future work, as we expand in to the remaining parameter space.

13 pages, 6 figures, 2 tables; accepted for publication in MNRAS

References in corpus (5)

• Dependency of dynamical ejections of O stars on the masses of very young star clusters
• Red giant stellar collisions in the Galactic Centre
• On the origins of enigmatic stellar populations in Local Group galactic nuclei
• Collisional Particle Disks
• Small-N collisional dynamics II: Roaming the realm of not-so-small-N

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• Searching for the extra-tidal stars of globular clusters using high-dimensional analysis and a core particle spray code
• The physical origin of super-competitive accretion during the formation of the first supermassive black holes
• The mean free path approximation and stellar collisions in star clusters: Numerical exploration of the analytic rates and the role of perturbations on binary star mergers
• Analytic Modelling of Binary-Single Encounters: Non-Thermal Eccentricity Distribution and Gravitational-Wave Source Formation
• Binary-binary scattering in the secular limit
• Formation of supermassive stars in the first stellar clusters: Dependence on the gas temperature
• Chaos in the vicinity of a singularity in the Three-Body Problem: The equilateral triangle experiment in the zero angular momentum limit