The influence of the irregular forces on the motions in the three-body problem

TL;DR

This paper investigates how irregular forces affect the stability and evolution of triple hierarchical stellar systems, showing that such forces can lead to instability over cosmological timescales.

Contribution

It introduces a detailed analysis of irregular forces in the three-body problem, highlighting their impact on the long-term stability of hierarchical stellar systems.

Findings

Mean motions experience secular accelerations due to perturbations.

Distant component's mean motion increases over time.

Hierarchical systems may become unstable and evolve into systems with comparable component distances.

Abstract

The influence of the irregular forces on the evolution of a triple hierarchical stellar system moving in the field of stars have been studied. Triple hierarchical stellar systems are stable in contrary to the stellar systems with comparable distances between all components. We considered the motion in the frame of the general tree-body problem using differential equations of the motion with the Hamiltonian without short-periodic terms. For isolated triple stellar systems, where we took into account the perturbations until the third order, we obtained the solution in which the mean motions of both components have the secular accelerations. Under the influence of perturbations of the distant component the mean motion in the near pair is slowed and vice versa. The mean motion of the distant star is constantly increasing. These changes are small, but on the cosmological time interval the hierarchical systems will convert into stellar systems, in which all components have comparable distances between each other. Such systems become unstable. In a general case, if we take into account the irregular forces, the angular momentum of this system and its summary energy might be either loss or gain. These changes may influence on the dynamical evolution and stability of the stellar system.