Orbital Evolution of Planets Embedded in a Planetesimal Disk

Abstract

The existence of the Oort Comet Cloud, the Kuiper Belt, and plausible inefficiencies in planetary core formation, all suggest that there was once a residual planetesimal disk of mass 10-100 Earth-masses in the vicinity of the giant planets following their formation. Since removal of this disk requires an exchange of orbital energy and angular momentum with the planets, significant planetary migration can ensue. The planet migration phenomenon is examined numerically by evolving the orbits of the giant planets while they are embedded in a planetesimal disk having a mass of M_d=10 to 200 Earth-masses. We find that Saturn, Uranus, and Neptune evolve radially outwards as they scatter the planetesimals, while Jupiter's orbit shrinks as it ejects mass. Higher-mass disks result in more rapid and extensive planet migration. If orbit expansion and resonance trapping by Neptune is invoked to explain the eccentricities of Pluto and its cohort of Kuiper Belt Objects at Neptune's 3:2 mean-motion resonance, then our simulations suggest that a disk mass of order M_d~50 Earth-masses is required to expand Neptune's orbit by ~7 AU in order to pump up Plutino eccentricities to e~0.3. Such planet migration implies that the initial Solar System was more compact in the past, with the Jupiter-Neptune separation having been smaller by about 30%. The planetesimal disk is also the source of the Oort Cloud of comets. Using the results of our simulations together with a simple treatment of Oort Cloud dynamics, we estimate that ~12 Earth-masses of disk material was initially deposited in the Oort Cloud, of which ~4 Earth-masses will persist over the age of the Solar System. The majority of these comets originated from the Saturn-Neptune region of the solar nebula.