How dust particles orbiting white dwarfs can reveal undetected co-orbiting exoplanets II. Exoplanets on elliptic orbits

Abstract

Abridged. We aim to extend Paper I to the eccentric secondary orbit case and now analyse the elliptic restricted three-body problem (ERTBP). Our secondary masses include Ceres, Mercury, Earth, and Neptune so that we can help infer the presence of both large asteroids and planets through our analysis. We study dust particles on both planar (2D-ERTBP) and non-coplanar (3D-ERTBP) orbits. We computed families of 1/1 resonant symmetric and asymmetric periodic orbits in the 2D-ERTBP and 3D-ERTBP. Doing so produces novel results in their own right and diagnostic tools for precise guidance for our next steps. Based on them, we generated detailed phase portraits. Finally, we run suitably seeded $N$-body simulations to compare with the periodic orbits, and to provide observational links with debris close to WDs. New families of asymmetric periodic orbits, called $E^A_{41}$, $E^A_{42}$, and $E^A_{43}$ in the high-eccentricity 2D-ERTBP regime were discovered. They are generated by the new bifurcation point, $B_T^4$, along the new $A_2$ family, showcased in Paper I. Moreover, new isolated families of asymmetric periodic orbits, namely $E^A_{44}$, $E^A_{45}$, and $E^A_{46}$ were discovered. Families of short- and long- period asymmetric orbits starting from $L_4$, called $E^A_S$ and $E^A_L$, were also computed. In both the 2D- and 3D-ERTBP regimes, highly eccentric motion is exhibited for the dust particles in the majority of the families of either symmetric or asymmetric periodic orbits. The $N$-body simulations reveal that over ten years, the orbital period deviations of the dust are higher than in the circular restricted three-body problem (Paper I); in some architectures, Mercury-mass planets can regularly generate deviations exceeding $\sim$100 s, which potentially aids observational inferences of hidden asteroids or planets orbiting WDs.