2007MNRAS.377.1287Q

Two-dimensional particle discs in proximity to a planet are numerically integrated to determine when a planet in a circular orbit can truncate a particle disc. Collisions are treated by giving each particle a series of velocity perturbations during the integration. We estimate the mass of a planet required to truncate a particle disc as a function of collision rate, related to the disc optical depth, and velocity perturbation size, related to the disc velocity dispersion. We find that for particle discs in the regime estimated for debris discs, a Neptune mass planet is sufficiently massive to truncate the disc. If both the velocity dispersion and the disc optical depth are low (dispersion less than approximately 0.02 in units of circular motion, and optical depth less than 10^–4) then an Earth mass planet suffices. We find that the disc is smooth and axisymmetric unless the velocity perturbation is small and the planet mass is of the order of or greater than a Neptune mass in which case azimuthal structure is seen near prominent mean motion resonances.