When does a star cluster become a multiple star system? – I. Lifetimes of equal-mass small-Nsystems

Abstract

What is the difference between a long-lived unstable (or quasi-stable) multiple star system and a bona fide star cluster? In this paper, we present a possible framework to address this question, by studying the distributions of disruption times for chaotic gravitational encounters as a function of the number of interacting particles. To this end, we perform a series of numerical scattering experiments with the FEWBODY code, to calculate the distributions of disruption times as a function of both the particle number N and the virial coefficient k. The subsequent distributions are fit with a physically-motivated function, consisting of an initial exponential decay followed by a very slowly decreasing tail at long encounter times due to long-lived quasi-stable encounters. We find three primary features characteristic of the calculated distributions of disruption times. These are: (1) the system half-life increases with increasing particle number, (2) the fraction of long-lived quasi-stable encounters increases with increasing particle number and (3) both the system half-life and the fraction of quasistable encounters increase with decreasing virial coefficient. We discuss the significance of our results for collisional dynamics, and consider the extrapolation of our results to larger-N systems. We suggest that this could potentially offer a clear and unambiguous distinction between star clusters and (unstable or quasi-stable) multiple star systems. Although we are limited by very small-number statistics, our results tentatively suggest that (for our assumptions) this transition occurs at a critical particle number of order 100.

A statistical solution to the chaotic, non-hierarchical three-body problem

“…Here, v crit is the critical velocity, defined as the relative velocity at infinity required for a total encounter energy of zero. The motivation for these choices is that, as found in previous studies 39,40 , lower relative velocities at infinity and smaller impact parameters maximize the probability of long-lived resonant interactions occurring, which is probably needed to uphold the assumption of ergodicity. All angles defining the relative configurations of the binary orbital planes and phases are sampled to ensure isotropic scattering.…”

Illustrating chaos: a schematic discretization of the general three-body problem in Newtonian gravity

“…In this section, we introduce our formalism for constructing schematic diagrams of the general three-body problem, adapted from Leigh & Geller (2012) and Leigh et al (2016). We further present the numerical scattering experiments used to study the time evolution of the chaotic three-body problem, from which we construct an illustrative example of our schematic diagram formalism.…”

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

“…Mikkola 1983Mikkola , 1984Leonard 1989;Mikkola & Valtonen 1990;Leigh, Shara & Geller 2016). These studies typically adopted numerical approaches.…”

“…Following the procedure first outlined in Leigh, Shara & Geller (2016), consider a small star cluster of N = NA+ NB finite-sized particles. We consider two different types of particles, with masses mA and mB and radii RA and RB.…”

“…For this study, we adopt a tidal tolerance parameter δ = 10 −7 for all simulations. 4 This choice for δ, while computationally expensive, is needed to maximize the accuracy of our simulations while also minimizing the computational expense, and ensures that we have converged on the correct encounter outcome, particularly at low virial ratios (see Geller 2016 for more details).…”