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.