The Total Number of Giant Planets in Debris Disks with Central Clearings

Infrared spectra from the Spitzer Space Telescope (SSC) of many debris disks are well fit with a single black body temperature which suggest clearings within the disk. We assume that inside the clearing orbital instability due to planets removes dust generating planetesimal belts and dust generated by the outer disk that is scattered or drifts into the clearing. From numerical integrations we estimate a minimum planet spacing required for orbital instability (and so planetesimal and dust removal) as a function of system age and planet mass. We estimate that a 10 year old debris disk with a dust disk edge at a radius of 50 AU hosted by an A star must contain approximately 5 Neptune mass planets between the clearing radius and the iceline in order to remove all primordial objects within it. We infer that known debris disk systems contain at least a fifth of a Jupiter mass in massive planets. The number of planets and spacing required is insensitive to the assumed planet mass. However an order of magnitude higher total mass in planets could reside in these systems if the planets are more massive.