A statistical approach to more than two-parameter families of triple encounters in two-dimensional space

Abstract

This paper deals with the role of triple encounters with low initial velocities and equal masses in the framework of statistical escape theory in two-dimensional space. This system is described by allowing for both energy and angular momentum conservation in the phase space. The complete statistical solutions (i.e. the semi-major axis ‘$a$’, the distributions of eccentricity ‘$e$’, and energy $E_{b}$ of the final binary, escape energy $E_{s}$ of escaper and its escape velocity $v_{s}$) of the system are calculated. These are in good agreement with the numerical results of Chandra and Bhatnagar (1999) in the range of perturbing velocities $v_{i}$ ($10^{-1} \le v_{i} \le 10^{-10}$) in two-dimensional space. The double limit process has been applied to the system. It is observed that when $v_{i} \to 0^{ +}$, a $v_{s}^{2} \to 2 / 3$ for all directions in two-dimensional space.