Small-N collisional dynamics – IV. Order in the realm of not-so-small-N

Abstract

In this paper, the fourth in the series, we continue our study of combinatorics in chaotic Newtonian dynamics. We focus once again on the chaotic four-body problem in Newtonian gravity assuming finite-sized particles, and interactions that produce direct collisions between any two particles. Our long-term goal is to predict the probability of a given collision event occurring over the course of an interaction, as a function of the numbers and properties of the particles. In previous papers, we varied the number of interacting particles, as well as the distributions of particle radii and masses. Here, we refine the methods developed in these preceding studies, and arrive at a final and robust methodology that can be used to study collisional dynamics in a variety of astrophysical contexts, ranging from stars in star clusters, galaxies in galaxy groups and clusters and even the collisional growth of planetesimals in protoplanetary disks. We further present and refine the concept of a Collision Rate Diagram (CRD), the primary tool we use to quantify the relative rates for different collision scenarios to occur. The agreement between our final theoretical model and the results of numerical scattering simulations is excellent.

White dwarf - main sequence star collisions from wide triples in the field

“…It was found the combined rate for all the possible channels that lead to a SN is 3 order of magnitude lower than the observed rate. In Leigh et al (2018) it was shown that gravitational scattering is dominated by triple-single scattering events, similar to paper I and this manuscript, rather than binary-binary or triple-binary scattering.…”

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

“…A pair of stars then remain bound in a binary while the third star is ejected, typically taking away more positive kinetic energy than it came in with. This sets the scene for subsequent single-binary interactions to occur, in which three stars undergo a chaotic gravitationally-bound interaction within a small volume with a correspondingly high probability of a collision occurring (see Leigh & Geller 2012Leigh et al 2016Leigh et al , 2018, for more details on the expected probabilities). If the collision occurs during an interaction with a third bound star, we classify it as a direct binary collision (see Sec.…”

“…the collision probability should be proportional to 𝑁 2 ). In subsequent studies and Leigh et al (2017Leigh et al ( , 2018 expanded the parameter space to consider particles having different masses and radii. Eventually, they were able to build from first principles, on a combinatorics-based back bone, analytic predictions for the relative probabilities of different collision scenarios occurring (e.g., multi-collision scenarios).…”

A New Method to Constrain the Origins of Dark-matter-free Galaxies and Their Unusual Globular Clusters

“…We adopt GC types A, B and C and (conservatively) assume that they adhere to a ratio in mass and size of 1:2:≥ 3, respectively (the units are not relevant for the relative rates, only the absolute rates). 5 We then follow the procedure described in Leigh et al (2017) and expanded upon in Leigh et al (2018) to calculate the relative collision rates for different particles types. Specifically, we calculate the relative collision rates using Equations 19 and 24 in Leigh et al (2017).…”