Orbital Evolution of Planets Embedded in a Planetesimal Disk

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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 M⊕ 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 MD = 10–200 M⊕. We find that Saturn, Uranus, and Neptune evolve radially outward 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 orbital expansion and resonance trapping by Neptune are 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 MD ~ 50 M⊕ is required to expand Neptune's orbit by Δa ~ 7 AU, in order to pump up Plutino eccentricities to e ~ 0.3. Such planet migration implies that the solar system was more compact in the past, with the initial Jupiter-Neptune separation having been smaller by about 30%. We discuss the fate of the remnants of the primordial planetesimal disk. We point out that most of the planetesimal disk beyond Neptune's 2:1 resonance should reside in nearly circular, low-inclination orbits, unless there are (or were) additional, unseen, distant perturbers. 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 M⊕ of disk material was initially deposited in the Oort cloud, of which ~4 M⊕ will persist over the age of the solar system. The majority of these comets originated from the Saturn-Neptune region of the solar nebula.
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