Disruption of exo-asteroids around white dwarfs and the release of dust particles in debris rings in co-orbital motion

Context. Close to the Roche radius of a white dwarf (WD), an asteroid on a circular orbit sheds material that then adopts a very similar orbit. Observations of the resulting debris show a periodic behaviour and changes in flux on short timescales, implying ongoing dynamical activity. Additional encounters from other minor planets may then yield co-orbital rings of debris at different inclinations. The structure, dynamics, and lifetime of these debris discs remains highly uncertain, but is important for understanding WD planetary systems. Aims. We aim to identify and quantify the locations of co-orbitals in WD–asteroid–dust particle three-body systems by exploring the influence of 1:1 resonant periodic orbits. We begin this exploration with co-planar and inclined orbits in the circular restricted three- body problem (CRTBP) and model the dynamical evolution of these exosystems over observable timescales. The mass ratio parameter for this class of systems (≈2 × 10−11) is one of the lowest ever explored in this dynamical configuration. Methods. We computed the periodic orbits, deduced their linear stability, and suitably seeded the dynamical stability (DS) maps. We carried out a limited suite of N-body simulations to provide direct comparisons with the DS maps. Results. We derive novel results for this extreme mass ratio in the CRTBP, including new unstable 3D families. We illustrate through the maps and N-body simulations where dust can exist in a stable configuration over observable timescales across a wide expanse of parameter space in the absence of strong external forces. Conclusions. Over a timescale of 10 years, the maximum orbital period deviations of stable debris due to the co-orbital perturbations of the asteroid is about a few seconds. Unstable debris in a close encounter with the asteroid typically deviates from the co-orbital configuration by more than about 20 km and is on a near-circular orbit with an eccentricity lower than ≈0.01.