Instability of Triangular Equilibrium Points in the Restricted Three-Body Problem Under Effects of Circumbinary Disc, Radiation Pressure and P–R Drag

The paper examines instability of triangular equilibrium points of a test particle in the gravitational field of two primaries radiating with effective Poynting–Robertson (P–R) drag, enclosed by circumbinary disc. The equations of motion are derived and positions of triangular equilibrium points are located. It is seen that the locations are affected by the disc, radiation pressure and P–R drag of the primaries. In particular, for our numerical computations of the locations of the triangular equilibrium points and the linear stability analysis, we consider a low-mass pulsating star, IRAS 11472-0800 as the bigger primary, with a young white dwarf star; G29-38 as the smaller primary. We observe that the disc does not change the x-coordinates of the triangular points while their y-coordinates are been altered. However, radiation pressure, P–R drag and the mass parameter µ mainly contribute in shifting the location of the triangular points. As regards the stability analysis, these points are in general unstable under the combine effects of radiation, P–R drag and disc, in the entire range of the mass parameter due to complex roots with positive real parts. Further, in order to discern the effects of the parameters on the instability outcome, we broaden the range of the mass parameter to accommodate small values of the mass parameters. We observe that in the absence of radiation and the presence of 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 turn pure imaginary quantities when the disc is present. This proves that the disc is a stabilizing force while the radiation pressure and P–R drag induces instability around the triangular equilibrium points in the entire range of the mass parameter due to the presence of complex roots with positive real parts.