Is There a Planet around β Pictoris? Perturbations of a Planet on a Circumstellar Dust Disk: 2. The Analytical Model

Abstract The β Pictoris circumstellar disk, like others, seems to exhibit an inner clearing zone, at typical distances of 1-50 AU from the star. We investigate the possibility that this void is caused by a planet embedded in the disk. We have implemented on a Connection Machine a code which simultaneously integrates the motions of 8192 particles. These are submitted to Poynting-Robertson (PR) drag, while being perturbed by a planet orbiting at 20 AU from the star. The free parameters are the planetary mass, the planetary orbital eccentricity, and the particle size. Above a critical planet mass of ∼10 -5 stellar masses (∼5 Earth masses, or 1 3 Uranian masses), the planet is able to trap particles in outer mean motion resonances, for time scales comparable to, or larger than, the PR decay time. No permament trapping is observed, however. Once they escape the resonances, the particles rapidly decay onto the star, on highly eccentric orbits. A moderate planetary orbital eccentricity (10 -2 ) can create large arclike structures in the disk. A depleted region corotating with the planet, and just outside it, is also observed. We show finally that these processes can create a steady state clearing zone extending inside the planet orbit. We emphasize that the structures excited on the disk by a planet could be a way to reveal bodies otherwise invisible by direct imagery.