The unseen planets of double belt debris disc systems

The gap between two component debris discs is often taken to be carved by intervening planets scattering away the remnant planetesimals. We employ N-body simulations to determine how the time needed to clear the gap depends on the location of the gap and the mass of the planets. We invert this relation, and provide an equation for the minimum planet mass, and another for the expected number of such planets, that must be present to produce an observed gap for a star of a given age. We show how this can be combined with upper limits on the planetary system from direct imaging non-detections (such as with GPI or SPHERE) to produce approximate knowledge of the planetary system.