Accretion of Mass and Spin Angular Momentum by a Planet on an Eccentric Orbit

Abstract

We have extended our previous calculations of planetary accretion rates (Y. Greenzweig and J. J. Lissauer 1990, Icarus87, 40–77, and 1992, Icarus100, 440–463) to the case of a planet on an eccentric orbit. We have found that the dependence of accretion rates on planetary and planetesimal eccentricities can be reduced to a single parameter and that the extent of a planet's single-pass feeding zones depends (in the limit of small planetary mass) only upon the sum of the eccentricities of the planet and the planetesimals and their mutual inclination. We have also addressed the problem of the origin of planetary rotation by calculating the spin angular momentum contributed by all particles which are accreted by a planet in a uniform particle disk. Previous authors (J. J. Lissauer and D. M. Kary 1991, Icarus94, 126–159; L. Dones and S. Tremaine 1993, Icarus103, 67–92) have obtained analytic solutions for nongravitating planets on circular orbits in two-dimensional disks. We have developed new techniques which allow us to extend these calculations to the cases in which the planet's orbit is eccentric and the disk is three-dimensional. Nongravitating planets on eccentric orbits accrete the same specific rotational angular momentum as planets on circular orbits in disks of planetesimals on eccentric orbits. Planetesimal inclinations reduce the specific angular momentum accreted by nongravitating planets by 25–65%. By performing a series of numerical three-body simulations, we have found that a gravitating planet on an orbit with eccentricity e 0⪡ in a disk of planetesimals on circular orbits obtains the same rotation rate as a planet on a circular orbit in a disk of planetesimals which have e= e 0. When the planet and the planetesimals are both on eccentric orbits with e⪡ 1, the spin angular momentum is determined by the distribution of relative eccentricity vectors. If the eccentricities of the planet and planetesimals differ significantly, inclination typically acts to reduce the magnitude of the rotation rate by a few tens of percent. However, in certain cases where the eccentricities of the planet and planetesimals are comparable, inclination can change slow retrograde rotation to slow prograde rotation. A planet which accretes material primarily from the extremities of its feeding zone during the latter stage of its growth attains rapid systematic prograde rotation only if the amplitude of its epicyclic motion is comparable to or smaller than the radius of its Hill sphere.