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

摘要

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 vs) 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) <= v(i) <= 10(-10)) in two-dimensional space. The double limit process has been applied to the system. It is observed that when v(i) -> 0(+), a v(s)(2) -> 2/3 for all directions in two-dimensional space.