Planetesimal-driven Migration Research Articles

Self-consistent N-body simulation of planetesimal-driven migration. I. The trajectories of single planets in the uniform background

Abstract Recent exoplanet observations have revealed a diversity of exoplanetary systems, which suggests the ubiquity of radial planetary migration. One powerful known mechanism of planetary migration is planetesimal-driven migration (PDM), which can let planets undergo significant migration through gravitational scattering with planetesimals. In this series of papers, we present the results of our high-resolution, self-consistent N-body simulations of PDM, in which gravitational interactions among planetesimals, the gas drag, and Type I migration are all taken into account. In this first paper (Paper I), we investigate the migration of a single planet through PDM within the framework of the classical standard disk model (the minimum-mass solar nebula model). Paper I aims to improve our understanding of planetary migration through PDM, addressing previously unexplored aspects of both the gravitational interactions among planetesimals and the interactions with disk gas. Our results show that even small protoplanets can actively migrate through PDM. Such active migration can act as a rapid radial diffusion mechanism for protoplanets and significantly influence the early stages of planetary formation (i.e., during the runaway growth phase). Moreover, a fair fraction of planets migrate outward. This outward migration may offer a potential solution for the “planet migration problem” caused by Type I migration and gives a natural mechanism for outward migration assumed in many recent scenarios for the formation of outer planets.

Randomness and retention: using weak mean motion resonances to constrain Neptune’s late-stage migration

ABSTRACT Planet–planetesimal interactions cause a planet to migrate, manifesting as a random walk in semimajor axis. In models for Neptune’s migration involving a gravitational upheaval, this planetesimal-driven migration is a side-effect of the dynamical friction required to damp Neptune’s orbital eccentricity. This migration is noisy, potentially causing Trans-Neptunian Objects (TNOs) in mean motion resonance to be lost. With N-body simulations, we validate a previously derived analytic model for resonance retention and determine unknown coefficients. We identify the impact of random-walk (noisy) migration on resonance retention for resonances up to fourth order lying between 39 and 75 au. Using a population estimate for the weak 7:3 resonance from the well-characterized Outer Solar System Origins Survey (OSSOS), we rule out two cases: (1) a planetesimal disc distributed between 13.3 and 39.9 au with ≳ 30 Earth masses in today’s size distribution and Tmig ≳ 40 Myr and (2) a top-heavy size distribution with ≳2000 Pluto-sized TNOs and Tmig ≳10 Myr, where Tmig is Neptune’s migration time-scale. We find that low-eccentricity TNOs in the heavily populated 5:2 resonance are easily lost due to noisy migration. Improved observations of the low-eccentricity region of the 5:2 resonance and of weak mean motion resonances with Rubin Observatory’s Legacy Survey of Space and Time will provide better population estimates, allowing for comparison with our model’s retention fractions and providing strong evidence for or against Neptune’s random interactions with planetesimals.

How the formation of Neptune shapes the Kuiper belt

Hydrodynamical simulations predict the inward migration of giant planets during the gas phase of the protoplanetary disc. This phenomenon is also invoked to explain resonant and near-resonant exoplanetary system structures. The early inward migration may also have affected our Solar System and sculpted its different minor planet reservoirs. In this study we explore how the early inward migration of the giant planets shapes the Kuiper belt. We test different scenarios with only Neptune and Uranus and with all the four giant planets, also including some models with the subsequent outward planetesimal-driven migration of Neptune after the gas dispersal. We find objects populating mean motion resonances even when Neptune and Uranus do not migrate at all or only migrate inwards. When the planets are fixed, planetesimals stick only temporarily to the mean motion resonances, while inwards migration yields a new channel to populate the resonances without invoking convergent migration. However, in these cases, it is hard to populate mean motion resonances that do not cross the planetesimal disc (such as 2:1 and 5:2) and there is a lack of resonant Kuiper belt objects (KBOs) crossing Neptune’s orbit. These Neptune crossers are an unambiguous signature of the outward migration of Neptune. The starting position and the growth rate of Neptune have consequences for the contamination of the classical Kuiper belt region from neighbouring regions. The eccentricity and inclination space of the hot classical Kuiper belt objects and the scattered disc region become much more populated when all the giant planets are included. The 5:2 resonance with Neptune becomes increasingly populated with deeper inward migrations of Neptune. However, the overall inclination distribution is still narrower than suggested by observations, as is generally the case for Kuiper belt population models.

Effects of protoplanetary nebula on orbital dynamics of planetesimals in the outer Solar system

Massive gaseous nebula has been a key element to formation of large solid objects (planetesimals, giant planet cores) in the early phase of the Solar system evolution. Here, we focus on its effects during the stage when giant planets have already fully formed. Dynamical effects of the nebula on motion of planetesimals stirred by planets were twofold: (i) global gravitational acceleration, and (ii) local aerodynamic drag. Thanks to decreasing gas density with radial distance, in the outer Solar system the effect of the drag was deemed to be important only for small planetesimals (sizes $$\lesssim 10$$ km). However, we find that it was possibly important up to the sizes of $$\simeq 100$$ km as well. The gravitational field of the nebula produces secular oscillations of the orbital eccentricity and inclination of planetesimals. Eventually, their pericenter may be lifted away from strong planetary influence, exhibited during close encounters, even for small bodies born in the planetary heliocentric zone. It has been previously suggested that such pathway may, in some nebula models, launch planetesimals onto large-inclination and small-eccentricity orbits in the trans-Neptunian region. These orbits would be dynamically stable to present epoch. Our simulations generally do not support such extreme cases, but we find that, after the nebula disperses, some planetesimals may indeed reach low-inclination and low-eccentricity orbits exterior to Neptune. These bodies may have been implanted into the Kuiper belt during subsequent planetesimal-driven migration of planets. This raises a possibility that some present-day KBOs may have formed in the giant-planet zone (5–20 au).

Gap formation in planetesimal discs via divergently migrating planets

While many observed debris disks are thought to have gaps suggestive of the presence of planets, direct imaging surveys do not find many high mass planets in these systems. We investigate if divergent migration is a viable mechanism for forming gaps in young debris disks with planets of low enough mass to currently elude detection. We perform numerical integrations of planet pairs embedded in planetesimal disks to assess the conditions for which divergent, planetesimal-driven migration occurs and gaps form within the disk. Gap widths and the migration rate of planets within a pair depend on both disk mass and the degree to which the planets share disk material. We find that planet pairs with planets more massive than Neptune can produce gaps with widths similar to their orbit distance within 10 Myr at orbit separations probed by direct imaging campaigns. Pairs of migrating super-Earths likely cannot form observable gaps on the same time and distance scales, however. Inferring the responsible planet masses from these gaps while neglecting migration could overestimate the mass of planets by more than an order of magnitude.

Dynamical Evolution of the Early Solar System

Several properties of the Solar System, including the wide radial spacing of the giant planets, can be explained if planets radially migrated by exchanging orbital energy and momentum with outer disk planetesimals. Neptune's planetesimal-driven migration, in particular, has a strong advocate in the dynamical structure of the Kuiper belt. A dynamical instability is thought to have occurred during the early stages with Jupiter having close encounters with a Neptune-class planet. As a result of the encounters, Jupiter acquired its current orbital eccentricity and jumped inward by a fraction of an astronomical unit, as required for the survival of the terrestrial planets and from asteroid belt constraints. Planetary encounters also contributed to capture of Jupiter Trojans and irregular satellites of the giant planets. Here we discuss the dynamical evolution of the early Solar System with an eye to determining how models of planetary migration/instability can be constrained from its present architecture. Specifically, we review arguments suggesting that the Solar System may have originally contained a third ice giant on a resonant orbit between Saturn and Uranus. This hypothesized planet was presumably ejected into interstellar space during the instability. The Kuiper belt kernel and other dynamical structures in the trans-Neptunian region may provide evidence for the ejected planet. We favor the early version of the instability where Neptune migrated into the outer planetesimal disk within a few tens of millions of years after the dispersal of the protosolar nebula. If so, the planetary migration/instability was not the cause of the Late Heavy Bombardment. Mercury's orbit may have been excited during the instability.

Constraining the Giant Planets’ Initial Configuration from Their Evolution: Implications for the Timing of the Planetary Instability

Abstract Recent works on planetary migration show that the orbital structure of the Kuiper Belt can be very well reproduced if, before the onset of planetary instability, Neptune underwent a long-range planetesimal-driven migration up to ∼28 au. However, considering that all giant planets should have been captured in mean motion resonances among themselves during the gas-disk phase, it is not clear whether such a very specific evolution for Neptune is possible, or whether the instability could have happened at late times. Here, we first investigate which initial resonant configuration of the giant planets can be compatible with Neptune being extracted from the resonant chain and migrating to ∼28 au before planetary instability. We address the late instability issue by investigating the conditions where the planets can stay in resonance for about 400 Myr. Our results indicate that this can happen only in the case where the planetesimal disk is beyond a specific minimum distance δ stab from Neptune. Then, if there is a sufficient amount of dust produced in the planetesimal disk, which drifts inwards, Neptune can enter a slow dust-driven migration phase for hundreds of Myr until it reaches a critical distance from the disk. From that point, faster planetesimal-driven migration takes over and Neptune continues migrating outward until the instability happens. We conclude that although an early instability more easily reproduces the evolution of Neptune required to explain the structure of the Kuiper Belt, such evolution is also compatible with a late instability.

GLOBAL HIGH-RESOLUTION N-BODY SIMULATION OF PLANET FORMATION. I. PLANETESIMAL-DRIVEN MIGRATION

ABSTRACT We investigated whether outward planetesimal-driven migration (PDM) takes place or not in simulations when the self-gravity of planetesimals is included. We performed N-body simulations of planetesimal disks with a large width (0.7–4 au) that ranges over the ice line. The simulations consisted of two stages. The first-stage simulations were carried out to see the runaway growth phase using the planetesimals of initially the same mass. The runaway growth took place both at the inner edge of the disk and at the region just outside the ice line. This result was utilized for the initial setup of the second-stage simulations, in which the runaway bodies just outside the ice line were replaced by the protoplanets with about the isolation mass. In the second-stage simulations, the outward migration of the protoplanet was followed by the stopping of the migration due to the increase of the random velocity of the planetesimals. Owing to this increase of random velocities, one of the PDM criteria derived in Minton & Levison was broken. In the current simulations, the effect of the gas disk is not considered. It is likely that the gas disk plays an important role in PDM, and we plan to study its effect in future papers.

Planetesimal-driven migration as an explanation for observations of high levels of warm, exozodiacal dust

High levels of exozodiacal dust have been observed in the inner regions of a large fraction of main sequence stars. Given the short lifetime of the observed small dust grains, these 'exozodis' are difficult to explain, especially for old (>100 Myr) stars. The exozodiacal dust may be observed as excess emission in the mid-infrared, or using interferometry. We hypothesise that exozodi are sustained by planetesimals scattered by planets inwards from an outer planetesimal belt, where collision timescales are long. In this work, we use N-body simulations to show that the outwards migration of a planet into a belt, driven by the scattering of planetesimals, can increase, or sustain, the rate at which planetesimals are scattered from the outer belt to the exozodi region. We hypothesise that this increase is sufficient to sustain the observed exozodi on Gyr timescales. No correlation between observations of an outer belt and an exozodi is required for this scenario to work, as the outer belt may be too faint to detect. If planetesimal driven migration does explain the observed exozodi, this work suggests that the presence of an exozodi indicates the presence of outer planets and a planetesimal belt.

Planetesimal-driven migration of terrestrial planet embryos

We develop a model for planetesimal-driven migration (PDM) in the context of rocky planetary embryos in the terrestrial planet region during the runaway and oligarchic growth phases of inner planet formation. We develop this model by first showing that there are five necessary and sufficient criteria that must be simultaneously satisfied in order for a rocky inner Solar System embryo to migrate via PDM. To investigate which embryos within a given disk satisfy the five criteria, we have developed a Monte Carlo planetesimal merger code that simulates the growth of embryos from a planetesimal disk with nebular gas. The results of our Monte Carlo planetesimal merger code suggest that, for typical values of the minimum mass solar nebula for the inner Solar System, an average of 0.2 embryos capable of PDM emerge over the lifetime of the disk. Many disks in our simulations produce no migration candidates, but some produced as many as 3. The number of embryos that experience PDM in a disk increases with increasing disk mass and decreasing il planetesimal mass, although we were not able to simulate disks where the average initial planetesimal size was smaller than 50km. For disks 4× more massive than the standard minimum mass solar nebula, we estimate that an average of 1.5 embryos capable of PDM emerge, with some producing as many as 7.

TERRESTRIAL PLANET FORMATION DURING THE MIGRATION AND RESONANCE CROSSINGS OF THE GIANT PLANETS

The newly formed giant planets may have migrated and crossed a number of mutual mean motion resonances (MMRs) when smaller objects (embryos) were accreting to form the terrestrial planets. We investigated the effects of the planetesimal-driven migration of Jupiter and Saturn, and the influence of their mutual 1:2 MMR crossing on terrestrial planet formation for the first time, by performing N-body simulations. These simulations considered distinct timescales of MMR crossing and planet migration. In total, 68 high-resolution simulation runs using 2000 disk planetesimals were performed, which was a significant improvement on previously published results. Even when the effects of the 1:2 MMR crossing and planet migration were included in the system, Venus and Earth analogs (considering both orbits and masses) successfully formed in several runs. In addition, we found that the orbits of planetesimals beyond a ~1.5-2 AU were dynamically depleted by the strengthened sweeping secular resonances associated with Jupiter's and Saturn's more eccentric orbits (relative to present-day) during planet migration. However, this depletion did not prevent the formation of massive Mars analogs (planets with more than 1.5 times Mars' mass). Although late MMR crossings (at t > 30 Myr) could remove such planets, Mars-like small mass planets survived on overly excited orbits (high e and/or i), or were completely lost in these systems. We conclude that the orbital migration and crossing of the mutual 1:2 MMR of Jupiter and Saturn are unlikely to provide suitable orbital conditions for the formation of solar system terrestrial planets. This suggests that to explain Mars' small mass and the absence of other planets between Mars and Jupiter, the outer asteroid belt must have suffered a severe depletion due to interactions with Jupiter/Saturn, or by an alternative mechanism (e.g., rogue super-Earths).

Planetary Systems Dynamics Eccentric patterns in debris disks & Planetary migration in binary systems

AbstractWe present some highlights of two ongoing investigations that deal with the dynamics of planetary systems. Firstly, until recently, observed eccentric patterns in debris disks were found in young systems. However recent observations of Gyr-old eccentric debris disks leads to question the survival timescale of this type of asymmetry. One such disk was recently observed in the far-IR by the Herschel Space Observatory around ζ2 Reticuli. Secondly, as a binary companion orbits a circumprimary disk, it creates regions where planet formation is strongly handicapped. However, some planets were detected in this zone in tight binary systems (γ Cep, HD 196885). We aim to determine whether a binary companion can affect migration such that planets are brought in these regions and focus in particular on the planetesimal-driven migration mechanism.

MIGRATION RATES OF PLANETS DUE TO SCATTERING OF PLANETESIMALS

Planets migrate due to the recoil they experience from scattering solid (planetesimal) bodies. To first order, the torques exerted by the interior and exterior disks will cancel, analogous to the cancellation of the torques from the gravitational interaction with the gas (Type-I migration). Assuming the dispersion-dominated regime and power laws characterized by indices α and β for the surface density and eccentricity profiles, we calculate the net torque on the planet. We consider both distant encounters and close (orbit-crossing) encounters. We find that the close and distant encounter torques have opposite signs with respect to α and β; and that the torque is especially sensitive to the eccentricity gradient β. Compared to Type-I migration due to excitation of density waves, the planetesimal-driven migration rate is generally lower due to the lower surface density of solids in gas-rich disk, although this may be partially or fully offset when their eccentricity and inclinaton are small. Allowing for the feedback of the planet on the planetesimal disk through viscous stirring, we find that under certain conditions a self-regulated migration scenario emerges, in which the planet migrates at a steady pace that approaches the rate corresponding to the one-sided torque. If the ratio of the local disk mass in planetesimals to planet mass is low, however, migration will stall. We quantify the boundaries separating the three accretion regimes.

NEPTUNE ON TIPTOES: DYNAMICAL HISTORIES THAT PRESERVE THE COLD CLASSICAL KUIPER BELT

The current dynamical structure of the Kuiper belt was shaped by the orbital evolution of the giant planets, especially Neptune, during the era following planet formation, when the giant planets may have undergone planet-planet scattering and/or planetesimal-driven migration. Numerical simulations of this process, while reproducing many properties of the belt, fail to generate the high inclinations and eccentricities observed for some objects while maintaining the observed dynamically "cold" population. We present the first of a three-part parameter study of how different dynamical histories of Neptune sculpt the planetesimal disk. Here we identify which dynamical histories allow an in situ planetesimal disk to remain dynamically cold, becoming today's cold Kuiper belt population. We find that if Neptune undergoes a period of elevated eccentricity and/or inclination, it secularly excites the eccentricities and inclinations of the planetesimal disk. We demonstrate that there are several well-defined regimes for this secular excitation, depending on the relative timescales of Neptune's migration, the damping of Neptune's orbital inclination and/or eccentricity, and the secular evolution of the planetesimals. We model this secular excitation analytically in each regime, allowing for a thorough exploration of parameter space. Neptune's eccentricity and inclination can remain high for a limited amount of time without disrupting the cold classical belt. In the regime of slow damping and slow migration, if Neptune is located (for example) at 20 AU, then its eccentricity must stay below 0.18 and its inclination below 6{\deg}.

ON THE MIGRATION OF JUPITER AND SATURN: CONSTRAINTS FROM LINEAR MODELS OF SECULAR RESONANT COUPLING WITH THE TERRESTRIAL PLANETS

We examine how the late divergent migration of Jupiter and Saturn may have perturbed the terrestrial planets. We identify six secular resonances between the nu_5 apsidal eigenfrequency of Jupiter and Saturn and the four eigenfrequencies of the terrestrial planets (g_{1-4}). We derive analytic upper limits on the eccentricity and orbital migration timescale of Jupiter and Saturn when these resonances were encountered to avoid perturbing the eccentricities of the terrestrial planets to values larger than the observed ones. If Jupiter and Saturn migrated with eccentricities comparable to their present day values, smooth migration with exponential timescales characteristic of planetesimal-driven migration (\tau~5-10 Myr) would have perturbed the eccentricities of the terrestrial planets to values greatly exceeding the observed ones. This excitation may be mitigated if the eccentricity of Jupiter was small during the migration epoch, migration was very rapid (e.g. \tau<~ 0.5 Myr perhaps via planet-planet scattering or instability-driven migration) or the observed small eccentricity amplitudes of the j=2,3 terrestrial modes result from low probability cancellation of several large amplitude contributions. Further, results of orbital integrations show that very short migration timescales (\tau<0.5 Myr), characteristic of instability-driven migration, may also perturb the terrestrial planets' eccentricities by amounts comparable to their observed values. We discuss the implications of these constraints for the relative timing of terrestrial planet formation, giant planet migration, and the origin of the so-called Late Heavy Bombardment of the Moon 3.9+/-0.1 Ga ago. We suggest that the simplest way to satisfy these dynamical constraints may be for the bulk of any giant planet migration to be complete in the first 30-100 Myr of solar system history.

USING KUIPER BELT BINARIES TO CONSTRAIN NEPTUNE'S MIGRATION HISTORY

Approximately 10-20% of all Kuiper belt objects (KBOs) occupy mean-motion resonances with Neptune. This dynamical configuration likely resulted from resonance capture as Neptune migrated outward during the late stages of planet formation. The details of Neptune's planetesimal-driven migration, including its radial extent and the concurrent eccentricity evolution of the planet, are the subject of considerable debate. Two qualitatively different proposals for resonance capture have been proposed--migration-induced capture driven by smooth outward evolution of Neptune's orbit and chaotic capture driven by damping of the planet's eccentricity near its current semi-major axis. We demonstrate that the distribution of comparable-mass, wide-separation binaries occupying resonant orbits can differentiate between these two scenarios. If migration-induced capture occurred, this fraction records information about the formation locations of different populations of KBOs. Chaotic capture, in contrast, randomizes the orbits of bodies as they are placed in resonance. In particular, migration-induced capture produces the following signatures. The 2:1 resonance should contain a dynamically cold component, with inclinations less than 5-10 degrees, having a binary fraction comparable to that among cold classical KBOs. If the 3:2 resonance also hosts a cold component, its binary fraction should be 20-30% lower than in the cold classical belt. Among cold 2:1 (and if present 3:2) KBOs, objects with eccentricities e < 0.2 should have a binary fraction ~20% larger than those with e > 0.2. Searches for cold components in the binary fractions of resonant KBOs are currently practical. The additional migration-generated trends described here may be distinguished with objects discovered by LSST. (Abstract abridged.)

The effect of an early planetesimal-driven migration of the giant planets on terrestrial planet formation

The migration of the giant planets due to the scattering of planetesimals causes powerful resonances to move through the asteroid belt and the terrestrial planet region. Exactly when and how the giant planets migrated is not well known. In this paper we present results of an investigation of the formation of the terrestrial planets during and after the migration of the giant planets. The latter is assumed to have occurred immediately after the dissipation of the nebular disk -- i.e. "early" with respect to the timing of the Late Heavy Bombardment (LHB). The presumed cause of our modeled early migration of the giant planets is angular mometum transfer between the planets and scattered planetesimals.

EVIDENCE FROM THE ASTEROID BELT FOR A VIOLENT PAST EVOLUTION OF JUPITER'S ORBIT

We use the current orbital structure of large (>50km) asteroids in the main asteroid belt to constrain the evolution of the giant planets when they migrated from their primordial orbits to their current ones. Minton & Malhotra (2009) showed that the orbital distribution of large asteroids in the main belt can be reproduced by an exponentially-decaying migration of the giant planets on a time scale of tau ~ 0.5My. However, self-consistent numerical simulations show that the planetesimal-driven migration of the giant planets is inconsistent with an exponential change in their semi major axes on such a short time scale (Hahn & Malhotra, 1999). In fact, the typical time scale is tau > 5My. When giant planet migration on this time scale is applied to the asteroid belt, the resulting orbital distribution is incompatible with the observed one. However, the planet migration can be significantly sped up by planet-planet encounters. Consider an evolution where both Jupiter and Saturn have close encounters with a Neptune-mass planet (presumably Uranus or Neptune themselves) and where this third planet, after being scattered inwards by Saturn, is scattered outwards by Jupiter. This scenario leads to a very rapid increase in the orbital separation between Jupiter and Saturn that we show here to have only mild effects on the structure of asteroid belt. This type of evolution is called a jumping-Jupiter case. Our results suggest that the total mass and dynamical excitation of the asteroid belt before migration were comparable to those currently observed. Moreover, they imply that, before migration, the orbits of Jupiter and Saturn were much less eccentric than the current ones.

Planetesimal-driven planet migration in the presence of a gas disk

We report here on an extension of a previous study by Kirsh et al. (Kirsh, D.R., Duncan, M., Brasser, R., Levison, H.F. [2009]. Icarus 199, 197–209) of planetesimal-driven migration using our N-body code SyMBA (Duncan, M.J., Levison, H.F., Lee, M.H. [1998]. Astron. J. 116, 2067–2077). The previous work focused on the case of a single planet of mass M em, immersed in a planetesimal disk with a power-law surface density distribution and Rayleigh distributed eccentricities and inclinations. Typically 10 4–10 5 equal-mass planetesimals were used, where the gravitational force (and the back-reaction) on each planetesimal by the Sun and planet were included, while planetesimal–planetesimal interactions were neglected. The runs reported on here incorporate the dynamical effects of a gas disk, where the Adachi et al. (Adachi, I., Hayashi, C., Nakazawa, K. [1976]. Prog. Theor. Phys. 56, 1756–1771) prescription of aerodynamic gas drag is implemented for all bodies. In some cases the Papaloizou and Larwood (Papaloizou, J.C.B., Larwood, J.D. [2000]. Mon. Not. R. Astron. Soc. 315, 823–833) prescription of Type-I migration for the planet are implemented, as well as a mass distribution. In the gas-free cases, rapid planet migration was observed – at a rate independent of the planet’s mass – provided the planet’s mass was not large compared to the mass in planetesimals capable of entering its Hill sphere. In such cases, both inward and outward migrations can be self-sustaining, but there is a strong propensity for inward migration. When a gas disk is present, aerodynamic drag can substantially modify the dynamics of scattered planetesimals. For sufficiently large or small mono-dispersed planetesimals, the planet typically migrates inward. However, for a range of plausible planetesimal sizes (i.e. 0.5–5.0 km at 5.0 AU in a minimum mass Hayashi disk) outward migration is usually triggered, often accompanied by substantial planetary mass accretion. The origins of this behaviour are explained in terms of a toy model. The effects of including a size distribution and torques associated with Type-I migration are also discussed.

MODELING THE FORMATION OF GIANT PLANET CORES. I. EVALUATING KEY PROCESSES

One of the most challenging problems we face in our understanding of planet formation is how Jupiter and Saturn could have formed before the the solar nebula dispersed. The most popular model of giant planet formation is the so-called 'core accretion' model. In this model a large planetary embryo formed first, mainly by two-body accretion. This is then followed by a period of inflow of nebular gas directly onto the growing planet. The core accretion model has an Achilles heel, namely the very first step. We have undertaken the most comprehensive study of this process to date. In this study we numerically integrate the orbits of a number of planetary embryos embedded in a swarm of planetesimals. In these experiments we have included: 1) aerodynamic gas drag, 2) collisional damping between planetesimals, 3) enhanced embryo cross-sections due to their atmospheres, 4) planetesimal fragmentation, and 5) planetesimal driven migration. We find that the gravitational interaction between the embryos and the planetesimals lead to the wholesale redistribution of material - regions are cleared of material and gaps open near the embryos. Indeed, in 90% of our simulations without fragmentation, the region near that embryos is cleared of planetesimals before much growth can occur. The remaining 10%, however, the embryos undergo a burst of outward migration that significantly increases growth. On timescales of ~100,000 years, the outer embryo can migrate ~6 AU and grow to roughly 30 Earth-masses. We also find that the inclusion of planetesimal fragmentation tends to inhibit growth.