The Azimuthal Distribution of Dust Particles in an Eccentric Protoplanetary Disk with an Embedded Gas Giant Planet

We investigate the dust velocity and spatial distribution in an eccentric protoplanetary disk under the secular gravitational perturbation of an embedded planet of about 5 Jupiter masses. We first employ the FARGO code to obtain the two-dimensional density and velocity profiles of the gas disk with the embedded planet in the quasi-steady state. We then apply the secular perturbation theory and incorporate the gas drag to estimate the dust velocity on the secular timescale. The dust-to-gas ratio of the unperturbed disk is simply assumed to be 0.01. In our fiducial disk model with the planet at 5 AU, we find that for 0.01 cm- to 1 m-sized dust particles well coupled to the gas, the dust behaves similarly to the gas and exhibits non-axisymmetric dynamics as a result of eccentric orbits. However, for the case of a low-density gaseous disk (termed ``transition disk'' henceforth in this article) harboring the planet at 100 AU, the azimuthal distributions of dust of various sizes can deviate significantly.