Stability analysis of triangular equilibrium points in restricted three-body problem under effects of circumbinary disc, radiation and drag forces

Abstract

This paper examines the linear stability analysis around triangular equilibrium points of a test body in the gravitational field of a low-mass post-AGB binary system, enclosed by circumbinary disc and radiating with effective Poynting–Robertson (P–R) drag force. The equations of motion are derived and positions of triangular equilibrium points are located. These points are determined by; the circumbinary disc, radiation and P–R drag. In particular, for our numerical computations of triangular equilibrium points and the linear stability analysis, we have taken a pulsating star, IRAS 11472-0800 as the first primary, with a young white dwarf star; G29-38 as the second primary. We observe that the disc does not change the positions of the triangular points significantly, except on the y-axis. However, radiation, P–R drag and the mass parameter $\mu$ contribute effectively in shifting the location of the triangular points. Regarding the stability analysis, it is seen that these points under the combined effects of radiation, P–R drag and the disc, are unstable in the linear sense due to at least a complex root having a positive real part. In order to discern the effects of the parameters on the stability outcome, we consider the range of the mass parameter to be in the region of the Routhonian critical mass (0.038520). It is seen that in the absence of radiation and the presence of the disc, when the mass parameter is less than the critical mass, all the roots are pure imaginary and the triangular point is stable. However, when $\mu =0.038521$, the four roots are complex, but become pure imaginary quantities when the disc is present. This proofs that the disc is a stabilizing force. On introducing the radiation force, all earlier purely imaginary roots became complex roots in the entire range of the mass parameter. Hence, the component of the radiation force is strongly a destabilizing force and induces instability at the triangular points making it an unstable equilibrium point.