Edward Wolfgang Thommes

The formation of Uranus and Neptune in the Jupiter–Saturn region of the Solar System

Planets are believed to have formed through the accumulation of a large number of small bodies. In the case of the gas-giant planets Jupiter and Saturn, they accreted a significant amount of gas directly from the protosolar nebula after accumulating solid cores of about 5–15 Earth masses. Such models, however, have been unable to produce the smaller ice giants Uranus and Neptune at their present locations, because in that region of the Solar System the small planetary bodies will have been more widely spaced, and less tightly bound gravitationally to the Sun. When applied to the current Jupiter–Saturn zone, a recent theory predicts that, in addition to the solid cores of Jupiter and Saturn, two or three other solid bodies of comparable mass are likely to have formed. Here we report the results of model calculations that demonstrate that such cores will have been gravitationally scattered outwards as Jupiter, and perhaps Saturn, accreted nebular gas. The orbits of these cores then evolve into orbits that resemble those of Uranus and Neptune, as a result of gravitational interactions with the small bodies in the outer disk of the protosolar nebula.

Oligarchic growth of giant planets

Runaway growth ends when the largest protoplanets dominate the dynamics of the planetesimal disk; the subsequent self-limiting accretion mode is referred to as “oligarchic growth.” Here, we begin by expanding on the existing analytic model of the oligarchic growth regime. From this, we derive global estimates of the planet formation rate throughout a protoplanetary disk. We find that a relatively high-mass protoplanetary disk (∼10 × minimum-mass) is required to produce giant planet core-sized bodies (∼10 M⊕) within the lifetime of the nebular gas (≲10 million years). However, an implausibly massive disk is needed to produce even an Earth mass at the orbit of Uranus by 10 Myrs. Subsequent accretion without the dissipational effect of gas is even slower and less efficient. In the limit of noninteracting planetesimals, a reasonable-mass disk is unable to produce bodies the size of the Solar System’s two outer giant planets at their current locations on any timescale; if collisional damping of planetesimal random velocities is sufficiently effective, though, it may be possible for a Uranus/Neptune to form in situ in less than the age of the Solar System. We perform numerical simulations of oligarchic growth with gas and find that protoplanet growth rates agree reasonably well with the analytic model as long as protoplanet masses are well below their estimated final masses. However, accretion stalls earlier than predicted, so that the largest final protoplanet masses are smaller than those given by the model. Thus the oligarchic growth model, in the form developed here, appears to provide an upper limit for the efficiency of giant planet formation.

THE FORMATION OF URANUS AND NEPTUNE AMONG JUPITER AND SATURN

The outer giant planets, Uranus and Neptune, pose a challenge to theories of planet formation. They exist in a region of the solar system where long dynamical timescales and a low primordial density of material would have conspired to make the formation of such large bodies (~15 and 17 times as massive as Earth, respectively) very difficult. Previously, we proposed a model that addressed this problem: Instead of forming in the trans-Saturnian region, Uranus and Neptune underwent most of their growth among proto-Jupiter and proto-Saturn, were scattered outward when Jupiter acquired its massive gas envelope, and subsequently evolved toward their present orbits. We present the results of additional numerical simulations, which further demonstrate that the model readily produces analogs to our solar system for a wide range of initial conditions. We also find that this mechanism may partly account for the high orbital inclinations observed in the Kuiper belt.

Excitation of Orbital Eccentricities of Extrasolar Planets by Repeated Resonance Crossings

Orbits of known extrasolar planets that are located outside the tidal circularization regions of their parent stars are often substantially eccentric. By contrast, planetary orbits in our solar system are approximately circular, reflecting planet formation within a nearly axisymmetric, circumsolar disk. We propose that orbital eccentricities may be generated by the divergent orbital migration of two planets in a viscously accreting circumstellar disk. The migration is divergent in the sense that the ratio of the orbital period of the outer planet to that of the inner planet grows. As the period ratio diverges, the planets traverse, but are not captured into, a series of mean motion resonances that amplify their orbital eccentricities in rough inverse proportion to their masses. Strong viscosity gradients in protoplanetary disks offer a way to reconcile the circular orbits of solar system gas giants with the eccentric orbits of currently known extrasolar planets.

Intermediate-Mass Black Hole(s) and Stellar Orbits in the Galactic Center

Many young stars reside within the central half-parsec from Sgr A*, the supermassive black hole in the Galactic center. The origin of these stars remains a puzzle. Recently, Hansen & Milosavljevic (HM) have argued that an intermediate-mass black hole (IMBH) could have delivered the young stars to the immediate vicinity of Sgr A*. Here we focus on the final stages of the HM scenario. Namely, we integrate numerically the orbits of stars that are initially bound to the IMBH but are stripped from it by the tidal field of Sgr A*. Our numerical algorithm is a symplectic integrator designed specifically for the problem at hand; however, we have checked our results with SYMBA, a version of the widely available SWIFT code. We find that the distribution of the postinspiral orbital parameters is sensitive to the eccentricity of the inspiraling IMBH. If the IMBH is on a circular orbit, then the inclinations of numerically computed orbits relative to the inspiral plane are almost always smaller than 10°, and therefore (1) the simulations are in good agreement with the observed motions of stars in a clockwise-moving stellar disk; and (2) the simulations never reproduce the orbits of stars outside this disk, which include those in the second thick ring of stars and the randomly oriented unrelaxed orbits of some of the S stars. If the IMBHs orbital eccentricity is e = 0.6, then approximately half of the stars end up with orbital inclinations below 10°, and another half have inclinations anywhere between 0° and 180°; this is somewhat closer to what is observed. We also show that if the IRS 13 cluster is bound by an IMBH, as has been argued by Maillard et al., then the same IMBH could not have delivered all of the young stars to their present location.

A scattered Uranus and Neptune, and implications for the asteroid belt

It has been proposed that Uranus and Neptune originated interior to ∽ 10 AU , as potential gas giant cores which were scattered outward when Jupiter won the race to reach runaway gas accretion. We present further numerical simulations of this scenario, which show that it reproduces the present configuration of the outer Solar System with a high degree of success for a wide range of initial conditions. Also, we show that this mechanism may have simultaneously ejected planets from the asteroid belt.