Small-N collisional dynamics – V. From N ≲ 10 to N ≳ 103

Abstract

ABSTRACT Direct collisions between finite-sized particles occur commonly in many areas of astrophysics. Such collisions are typically mediated by chaotic, bound gravitational interactions involving small numbers of particles. An important application is stellar collisions, which occur commonly in dense star clusters, and their relevance for the formation of various types of stellar exotica. In this paper, we return to our study of the collision rates and probabilities during small-number chaotic gravitational interactions ($N\, \lesssim$ 10), moving beyond the small-number particle limit and into the realm of larger particle numbers ($N\, \gtrsim$ 103) to test the extent of validity of our analytic model as a function of the particle properties and the number of interacting particles. This is done using direct N-body simulations of stellar collisions in dense star clusters, by varying the relative numbers of particles with different particle masses and radii. We compute the predicted rate of collisions using the mean free path approximation, adopting the point-particle limit and using the sticky-star approximation as our collision criterion. We evaluate its efficacy in the regime where gravitational focusing is important by comparing the theoretical rates to numerical simulations. Using the tools developed in previous papers in this series, in particular Collision Rate Diagrams, we illustrate that our predicted and simulated rates are in excellent agreement, typically consistent with each other to within 1 standard deviation.