Perturbations of a planet on the β Pictoris circumstellar dust disk 3. Time scale of collisional destruction versus resonance time scale

We have already shown that a planet orbiting β Pictoris is able to confine the circumstellar dust. Here we present new numerical simulations which improve this model. The new model takes into account destructive collisions between particles, and looks at the steady state between the collision and the dust replenishment. We show that there exists a critical value of the normal optical depth (τ_opc ∼ 4 × 10^-4) and if the optical depth is smaller than this critical value in the resonant region (20-50 AU), asymmetric structures are created by the planet and maintained in spite of collisions. Although these structures cannot explain the asymmetries now observed in the disk, they could be a way to reveal bodies otherwise invisible by direct imagery.