Existence and Stability of Equilibrium Points in the R3BP With Triaxial-Radiating Primaries and an Oblate Massless Body Under the Effect of the Circumbinary Disc - Vincent, A. E.; Perdiou, A. E.; Perdios, E. A. (Frontiers in Astronomy and Space Sciences, 2022)
The paper studies the existence, location and stability of equilibrium points in a generalized restricted three body problem (R3BP) that consists of an oblate infinitesimal body when the primaries are radiating sources with triaxiality of the two stars surrounded by a belt (circumbinary disc). The existence, number, location and stability of the collinear and triangular Lagrangian equilibrium points of the problem depend on the mass parameter and the perturbing forces involved in the equations of motion. We find numerically that four additional collinear equilibrium points $L_{ni},$ $i=1,2,3,4,$ exist, in addition to the three Eulerian points $L_i,$ $i=1,2,3,$ of the classical case, making up a total of up to seven collinear points. $L_{n1}$ and $L_{n2}$ result due to the potential from the belt while $L_{n3}$ and $L_{n4}$ arise from the effect of triaxiality. The positions of the equilibrium points are affected by the presence of perturbations since they are deviated from the classical R3BP on the x-axis and out of the x-axis, respectively. The stability of the equilibrium points, for a particular set of the parameters, is analysed and it is concluded that all the collinear points are unstable except $L_{n1}$ which is always linearly stable. The range of stability of the Lagrangian points $L_{4,5}$ is determined analytically and found that is stable for $0<μ<μ_{crit}$ and unstable for $μ_{crit}<μ<1/2$ where $μ_{crit}$ is the critical mass ratio which depends on the combined effects of the perturbing forces. It is noticed that the critical mass ratio decreases with the increase in the values of the radiation pressure, triaxiality and oblate infinitesimal body; however it increases with the increment in the value of mass of the disc. All three of the former and the latter one possess destabilizing and stabilizing behavior, respectively. The net effect is that the size of the region of stability decreases when the value of these parameters increases. In our model, the binary HD155876 system, it is found that there exists one stable collinear equilibrium point viz. $L_{n1}$.