Statistical approach to triple systems in three-dimensional motion
Abstract
This paper considers disruption of triple close approaches with low initial velocities and equal masses in the framework of statistical escape theory in a three-dimensional space. The statistical escape theory is based on the assumption that the phase trajectory of a triple system is quasi-ergodic. This system is described by allowing for both energy and angular momentum conservation in the phase space. In this paper, "possibility of escape" is derived with the formation of a binary on the basis of relative distances of the participating bodies. The complete statistical solutions (i.e. the semi-major axis a, the distributions of eccentricity e of the binary, binary energy E_{b}, escape energy E_{s} of escaper, and its escape velocity v_{s}) of the system are derived from the allowable phase space volumes and are in good agreement with the numerical results in the range of perturbing velocities v_{i}(10^{-1} ≤ v_{i} ≤ 10^{-10}) and directions of v_{i}(0 ≤ α_{i},β_{i},γ_{i} ≤ π ), i = 1,2,3. In this paper, the double limit process has been applied to approximate the escape probability. Through this process, it is observed that the perturbing velocity v_{i} \to 0^{+} , as the product of the semi-major axis a of the final binary and the square of the escape velocity v_{s} approach 2/3, i.e. a v_{s}2 \to 2 / 3, whatever direction of v_{i} may be.
- Publication:
-
Astrophysics and Space Science
- Pub Date:
- July 2018
- DOI:
- 10.1007/s10509-018-3352-8
- Bibcode:
- 2018Ap&SS.363..147K
- Keywords:
-
- Astrophysics;
- Three-body problem;
- Triple close approaches;
- Statistical theory