Orbital Evolution of a Particle Interacting with a Single Planet in a Protoplanetary Disk

We investigate the motion of a particle around a low mass planet embedded in a non-turbulent gaseous disk. We take into account the effect of the gas structure that is modified by the gravitational interaction between the planet. We derive an analytic formula that describes the change of the semi-major axis of the particle due to the encounter with the planet using local approximation in distant encounter regime. Our final formula includes the effects of steady, axisymmetric radial gas flow, the global gas pressure gradient in the disk, planet gravity, and the structure of the gas flow modified by the planet's gravity. We compare the analytic results with numerical calculations, and indicate that our formula well describes the secular evolution of the dust particles' semi-major axes well, especially for small particles with large drag coefficient. We discuss the conditions for dust gap opening around a low mass planet and radial distribution of dust particles. Our formula may provide a useful tool for calculating radial distribution of particles in a disk around the planet.