Semi-analytic solutions for the triangular points of double white dwarfs in the ER3BP: Impact of the body’s oblateness and the orbital eccentricity

Using an analytic/numerical approach, we investigate the effects of oblateness and eccentricity of the primaries on the triangular points of compact double degenerate white dwarf binaries. AM CVs stars in which stable mass transfer occur from a Roche-lobe filling white dwarf to its more massive white dwarf companion and detached double white dwarfs (DWDs) which are candidate progenitors of Type Ia supernovae will be models of this problem. They provide an excellent and powerful tool for probing the physics of white dwarfs. The oblateness of the main bodies and their eccentricity affect the positions of the triangular equilibrium points as is shown for ten DWDs. The triangular points are generally stable for 0 < μ < μc; where μμ is the mass ratio (μ ⩽ 1/2). The size of the region of stability increases with decrease in oblateness. Our study shows that due to the nature of the masses of these binaries, the mass ratio does not fall in the range of stability: as a result, they are unstable.