A STATISTICAL APPROACH TO FAMILIES OF TRIPLE CLOSE APPROACHES OCCURING IN STELLAR SYSTEMS IN THREE DIMENSIONS (II)

Ranjeet Kumar; Navin Chandra; Surekha Tomar

Volume : III, Issue : VII, July - 2014

A STATISTICAL APPROACH TO FAMILIES OF TRIPLE CLOSE APPROACHES OCCURING IN STELLAR SYSTEMS IN THREE DIMENSIONS (II)

Ranjeet Kumar, Navin Chandra, Surekha Tomar

Abstract :

This is the second part of a series of papers dealing with the statistical approach to families of triple close approaches in three dimensional space. The three-dimensional case is completely different from the two dimensional case. In this paper, the complete statistical solutions (i.e. the distributions of eccentricity e of the binary, binary energy Eb and the escape velocity of escaper s v etc.) of the system are calculated and are in good agreement with the numerical results of dynamical evolution in the range of 1 10 0 10 v 10 − − ≤ ≤ and direction of 0 v (0 , ) ≤ ≤ αβ π . We have also applied double limit process as in two dimensional study of our previous paper (I) to the system in three dimensional space and observed that the perturbing velocity + 0 v 0 → , the product of the semi-major axis �a� of the final binary and the square of the escape velocity v∞ i.e. 2 av 2 3 ∞ → , whatever direction of 0 v may be.