Runaway Gas Accretion Research Articles

On the formation of planetary systems via oligarchic growth in thermally evolving viscous discs

We present N-body simulations of planetary system formation in thermally-evolving, viscous disc models. The simulations incorporate type I migration (including corotation torques and their saturation), gap formation, type II migration, gas accretion onto planetary cores, and gas disc dispersal through photoevaporation. The aim is to examine whether or not the oligarchic growth scenario, when combined with self-consistent disc models and up-to-date prescriptions for disc-driven migration, can produce planetary systems similar to those that have been observed. The results correlate with the initial disc mass. Low mass discs form close-packed systems of terrestrial-mass planets and super-Earths. Higher mass discs form multiple generations of planets, with masses in the range 10 < mp < 45M_Earth. These planets generally type I migrate into the inner disc, because of corotation torque saturation, where they open gaps and type II migrate into the central star. Occasionally, a final generation of low-to-intermediate mass planets forms and survives due to gas disc dispersal. No surviving gas giants were formed in our simulations. Analysis shows that these planets can only survive migration if a core forms and experiences runaway gas accretion at orbital radii r > 10 au prior to the onset of type II migration. We conclude that planet growth above masses mp > 10M_Earth during the gas disc life time leads to corotation torque saturation and rapid inward migration, preventing the formation and survival of gas giants. This result is in contrast to the success in forming gas giant planets displayed by some population synthesis models. This discrepancy arises, in part, because the type II migration prescription adopted in the population synthesis models causes too large a reduction in the migration speed when in the planet dominated regime.

PLANET TRAPS AND PLANETARY CORES: ORIGINS OF THE PLANET-METALLICITY CORRELATION

Massive exoplanets are observed preferentially around high metallicity ([Fe/H]) stars while low-mass exoplanets do not show such an effect. This so-called planet-metallicity correlation generally favors the idea that most observed gas giants at $r<10$ AU are formed via a core accretion process. We investigate the origin of this phenomenon using a semi-analystical model, wherein the standard core accretion takes place at planet traps in protostellar disks where rapid type I migrators are halted. We focus on the three major exoplanetary populations - hot-Jupiters, exo-Jupiters located at $r \simeq 1$ AU, and the low-mass planets. We show using a statistical approach that the planet-metallicity correlations are well reproduced in these models. We find that there are specific transition metallicities with values [Fe/H]$=-0.2$ to $-0.4$, below which the low-mass population dominates, and above which the Jovian populations take over. The exo-Jupiters significantly exceed the hot-Jupiter population at all observed metallicities. The low-mass planets formed via the core accretion are insensitive to metallicity, which may account for a large fraction of the observed super-Earths and hot-Neptunes. Finally, a controlling factor in building massive planets is the critical mass of planetary cores ($M_{c,crit}$) that regulates the onset of runaway gas accretion. Assuming the current data is roughly complete at [Fe/H]$>-0.6$, our models predict that the most likely value of the "mean" critical core mass of Jovian planets is $\braket{M_{c,crit}} \simeq 5 M_{\oplus}$ rather than $10 M_{\oplus}$. This implies that grain opacities in accreting envelopes should play an important role in lowering $M_{c,crit}$.

ACCRETION OF JUPITER-MASS PLANETS IN THE LIMIT OF VANISHING VISCOSITY

In the core-accretion model the nominal runaway gas-accretion phase brings most planets to multiple Jupiter masses. However, known giant planets are predominantly Jupiter-mass bodies. Obtaining longer timescales for gas accretion may require using realistic equations of states, or accounting for the dynamics of the circumplanetary disk (CPD) in low-viscosity regime, or both. Here we explore the second way using global, three-dimensional isothermal hydrodynamical simulations with 8 levels of nested grids around the planet. In our simulations the vertical inflow from the circumstellar disk (CSD) to the CPD determines the shape of the CPD and its accretion rate. Even without prescribed viscosity Jupiter's mass-doubling time is $\sim 10^4$ years, assuming the planet at 5.2 AU and a Minimum Mass Solar Nebula. However, we show that this high accretion rate is due to resolution-dependent numerical viscosity. Furthermore, we consider the scenario of a layered CSD, viscous only in its surface layer, and an inviscid CPD. We identify two planet-accretion mechanisms that are independent of the viscosity in the CPD: (i) the polar inflow -- defined as a part of the vertical inflow with a centrifugal radius smaller than 2 Jupiter-radii and (ii) the torque exerted by the star on the CPD. In the limit of zero effective viscosity, these two mechanisms would produce an accretion rate 40 times smaller than in the simulation.

Meridional circulation of gas into gaps opened by giant planets in three-dimensional low-viscosity disks

We examine the gas circulation near a gap opened by a giant planet in a protoplanetary disk. We show with high resolution 3D simulations that the gas flows into the gap at high altitude over the mid-plane, at a rate dependent on viscosity. We explain this observation with a simple conceptual model. From this model we derive an estimate of the amount of gas flowing into a gap opened by a planet with Hill radius comparable to the scale-height of a layered disk (i.e. a disk with viscous upper layer and inviscid midplane). Our estimate agrees with modern MRI simulations (Gressel, O., Nelson, R.P., Turner, N.J., Ziegler, U. [2013]. arXiv:1309.2871). We conclude that gap opening in a layered disk cannot slow down significantly the runaway gas accretion of Saturn to Jupiter-mass planets.

Photophoresis boosts giant planet formation

In the core accretion model of giant planet formation, a solid protoplanetary core begins to accrete gas directly from the nebula when its mass reaches about 5 earth masses. The protoplanet has at most a few million years to reach runaway gas accretion, as young stars lose their gas disks after 10 million years at the latest. Yet gas accretion also brings small dust grains entrained in the gas into the planetary atmosphere. Dust accretion creates an optically thick protoplanetary atmosphere that cannot efficiently radiate away the kinetic energy deposited by incoming planetesimals. A dust-rich atmosphere severely slows down atmospheric cooling, contraction, and inflow of new gas, in contradiction to the observed timescales of planet formation. Here we show that photophoresis is a strong mechanism for pushing dust out of the planetary atmosphere due to the momentum exchange between gas and dust grains. The thermal radiation from the heated inner atmosphere and core is sufficient to levitate dust grains and to push them outward. Photophoresis can significantly accelerate the formation of giant planets.

Trapping of giant-planet cores – I. Vortex aided trapping at the outer dead zone edge

In this paper the migration of a 10 M⊕ planetary core is investigated at the outer boundary of the ‘dead zone’ of a protoplanetary disc by means of 2D hydrodynamic simulations done with the graphics processor unit version of the fargo code. In the dead zone, the effective viscosity is greatly reduced due to the disc self-shielding against stellar UV radiation, X-rays from the stellar magnetosphere and interstellar cosmic rays. As a consequence, mass accumulation occurs near the outer dead zone edge, which is assumed to trap planetary cores enhancing the efficiency of the core-accretion scenario to form giant planets. Contrary to the perfect trapping of planetary cores in 1D models, our 2D numerical simulations show that the trapping effect is greatly dependent on the width of the region where viscosity reduction is taking place. Planet trapping happens exclusively if the viscosity reduction is sharp enough to allow the development of large-scale vortices due to the Rossby wave instability. The trapping is only temporarily, and its duration is inversely proportional to the width of the viscosity transition. However, if the Rossby wave instability is not excited, a ring-like axisymmetric density jump forms, which cannot trap the 10 M⊕ planetary cores. We revealed that the stellar torque exerted on the planet plays an important role in the migration history as the barycentre of the system significantly shifts away from the star due to highly non-axisymmetric density distribution of the disc. Our results still support the idea of planet formation at density/pressure maximum, since the migration of cores is considerably slowed down enabling them further growth and runaway gas accretion in the vicinity of an overdense region.

LIPAD Simulations of Giant Planet Core Formation

AbstractWe present some preliminary results from our investigation of giant planetary core formation using numerical simulations with the Lagrangian Integrator for Planetary Accretion and Dynamics (LIPAD) by Levison et al. (2012). LIPAD couples dynamics with collisional evolution, including fragmentation. We start with a cold planetesimal disk using particles of a few kilometres in size. Our simulations show growth from kilometre-sized planetesimals to several Earth-mass sized embryos (tens of thousands of kilometers) can occur. However, these embryos may not be large enough to start runaway gas accretion necessary to build the envelopes of gas giant planets.

THE STRUCTURE OF GAS-ACCRETING PROTOPLANETS AND THE CONDITION OF THE CRITICAL CORE MASS

In the core accretion model for the formation of gas giant planets, runaway gas accretion onto a core is the primary requisite, triggered when the core mass reaches a critical value. The recently revealed wide diversity of the extrasolar giant planets suggests the necessity to further the understanding of the conditions resulting in the critical core mass that initiates runaway accretion. We study the internal structure of protoplanets under hydrostatic and thermal equilibria represented in terms of a polytropic equation of state to investigate what factors determine and affect the critical core mass. We find that the protoplanets, embedded in protoplanetary disks, have the same configuration as red giants, characterized by the envelope of the centrally-condensed type solution. Applying the theory of stellar structure with homology invariants, we demonstrate that there are three types of criteria for the critical core mass depending on the stiffness of polytrope and the nature of outer boundary condition. For the stiff polytropes of index $N \le 3$ with the Bondi radius as the outer boundary, the criterion governing the critical core mass occurs at the surface. For stiff polytropes with the Hill outer boundary and for soft polytropes of $N>3$, this criterion acts at the bottom of gaseous envelope. Further, we elucidate the roles and effects of coexistent radiative and convective zones in the envelope of critical core mass. Based on the results, we discuss the relevance of Bondi and Hill surface conditions and explore the parameter dependences of critical core mass.

RAPID FORMATION OF SATURN AFTER JUPITER COMPLETION

We have investigated Saturn's core formation at a radial pressure maximum in a protoplanetary disk, which is created by gap opening by Jupiter. A core formed via planetesimal accretion induces the fragmentation of surrounding planetesimals, which generally inhibits further growth of the core by removal of the resulting fragments due to radial drift caused by gas drag. However, the emergence of the pressure maximum halts the drift of the fragments, while their orbital eccentricities and inclinations are efficiently damped by gas drag. As a result, the core of Saturn rapidly grows via accretion of the fragments near the pressure maximum. We have found that in the minimum-mass solar nebula, kilometer sized planetesimals can produce a core exceeding 10 Earth masses within two million years. Since Jupiter may not have undergone significant type II inward migration, it is likely that Jupiter's formation was completed when the local disk mass has already decayed to a value comparable to or less than Jovian mass. The expected rapid growth of Saturn's core on a timescale comparable to or shorter than observationally inferred disk lifetime enables Saturn to acquire the current amount of envelope gas before the disk gas is completely depleted. The high heat energy release rate onto the core surface due to the rapid accretion of the fragments delays onset of runaway gas accretion until the core mass becomes somewhat larger than that of Jupiter, which is consistent with the estimate based on interior modeling. Therefore, the rapid formation of Saturn induced by gap opening of Jupiter can account for the formation of multiple gas giants (Jupiter and Saturn) without significant inward migration and larger core mass of Saturn than that of Jupiter.

SUBMILLIMETER ARRAY OBSERVATIONS OF THE RX J1633.9-2442 TRANSITION DISK: EVIDENCE FOR MULTIPLE PLANETS IN THE MAKING

We present continuum high resolution Submillimeter Array (SMA) observations of the transition disk object RX J1633.9-2442, which is located in the Ophiuchus molecular cloud and has recently been identified as a likely site of ongoing giant planet formation. The observations were taken at 340 GHz (880 micron) with the SMA in its most extended configuration, resulting in an angular resolution of 0.3" (35 AU at the distance of the target). We find that the disk is highly inclined (i ~50 deg) and has an inner cavity ~25 AU in radius, which is clearly resolved by our observations. We simultaneously model the entire optical to millimeter wavelength spectral energy distribution (SED) and SMA visibilities of RX J1633.9-2442 in order to constrain the structure of its disk. We find that an empty cavity ~25 AU in radius is inconsistent with the excess emission observed at 12, 22, and 24 micron. Instead, the mid-IR excess can be modeled by either a narrow, optically thick ring at ~10 AU or an optically thin region extending from ~7 AU to ~25 AU. The inner disk (r < 5 AU) is mostly depleted of small dust grains as attested by the lack of detectable near-IR excess. We also present deep Keck aperture masking observations in the near-IR, which rule out the presence of a companion up to 500 times fainter than the primary star (in K-band) for projected separations in the 5-20 AU range. We argue that the complex structure of the RX J1633.9-2442 disk is best explained by multiple planets embedded within the disk. We also suggest that the properties and incidence of objects such as RX J1633.9-2442, T Cha, and LkCa 15 (and those of the companions recently identified to these two latter objects) are most consistent with the runaway gas accretion phase of the core accretion model, when giant planets gain their envelopes and suddenly become massive enough to open wide gaps in the disk.

Gas giant formation with small cores triggered by envelope pollution by icy planetesimals

We have investigated how envelope pollution by icy planetesimals affects the critical core mass for gas giant formation and the gas accretion time-scales. In the core-accretion model, runaway gas accretion is triggered after a core reaches a critical core mass. All the previous studies on the core-accretion model assumed that the envelope has the solar composition uniformly. In fact, the envelope is likely polluted by evaporated materials of icy planetesimals because icy planetesimals going through the envelope experience mass loss via strong ablation and most of their masses are deposited in the deep envelope. In this paper, we have demonstrated that envelope pollution in general lowers the critical core masses and hastens gas accretion on to the protoplanet because of the increase in the molecular weight and reduction of adiabatic temperature gradient. Widely- and highly-polluted envelopes allow smaller cores to form massive envelopes before disc dissipation. Our results suggest that envelope pollution in the course of planetary accretion has the potential to trigger gas giant formation with small cores. We propose that it is necessary to take into account envelope pollution by icy planetesimals when we discuss gas giant formation based on the core-accretion model.

Planet formation from planetesimals and diversity of planetary systems

Here, gravitational scattering of planetesimals (viscous stirring and dynamical friction) and their growth through pairwise collisions (runaway/oligarchic growth) are explained in detail. The masses of accreted protoplanets depend on initial disk surface density and semimajor axis. When the mass of a protoplanet becomes larger than a critical value that is a few to ten earth masses, runaway gas accretion from the disk onto the planet starts. The dependence of the protoplanet masses is responsible for the diversity of extrasolar planetary systems, although orbital migrations of planets are also important drivers to produce the diversity.

The formation of Uranus and Neptune in solid-rich feeding zones: Connecting chemistry and dynamics

The core accretion theory of planet formation has at least two fundamental problems explaining the origins of Uranus and Neptune: (1) dynamical times in the trans-saturnian solar nebula are so long that core growth can take >15 Myr and (2) the onset of runaway gas accretion that begins when cores reach ∼10 M ⊕ necessitates a sudden gas accretion cutoff just as Uranus and Neptune’s cores reach critical mass. Both problems may be resolved by allowing the ice giants to migrate outward after their formation in solid-rich feeding zones with planetesimal surface densities well above the minimum-mass solar nebula. We present new simulations of the formation of Uranus and Neptune in the solid-rich disk of Dodson-Robinson et al. (Dodson-Robinson, S.E., Willacy, K., Bodenheimer, P., Turner, N.J., Beichman, C.A. [2009]. Icarus 200, 672–693) using the initial semimajor axis distribution of the Nice model (Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A. [2005]. Nature 435, 466–469; Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R. [2005]. Nature 435, 462–465; Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F. [2005]. Nature 435, 459–461), with one ice giant forming at 12 AU and the other at 15 AU. The innermost ice giant reaches its present mass after 3.8–4.0 Myr and the outermost after 5.3–6 Myr, a considerable time decrease from previous one-dimensional simulations (e.g. Pollack, J.B., Hubickyj, O., Bodenheimer, P., Lissauer, J.J., Podolak, M., Greenzweig, Y. [1996]. Icarus 124, 62–85). The core masses stay subcritical, eliminating the need for a sudden gas accretion cutoff. Our calculated carbon mass fractions of 22% are in excellent agreement with the ice giant interior models of Podolak et al. (Podolak, M., Weizman, A., Marley, M. [1995]. Planet. Space Sci. 43, 1517–1522) and Marley et al. (Marley, M.S., Gómez, P., Podolak, M. [1995]. J. Geophys. Res. 100, 23349–23354). Based on the requirement that the ice giant-forming planetesimals contain >10% mass fractions of methane ice, we can reject any Solar System formation model that initially places Uranus and Neptune inside of Saturn’s orbit. We also demonstrate that a large population of planetesimals must be present in both ice giant feeding zones throughout the lifetime of the gaseous nebula. This research marks a substantial step forward in connecting both the dynamical and chemical aspects of planet formation. Although we cannot say that the solid-rich solar nebula model of Dodson-Robinson et al. (Dodson-Robinson, S.E., Willacy, K., Bodenheimer, P., Turner, N.J., Beichman, C.A. [2009]. Icarus 200, 672–693) gives exactly the appropriate initial conditions for planet formation, rigorous chemical and dynamical tests have at least revealed it to be a viable model of the early Solar System.

Evolution of Migrating Planets Undergoing Gas Accretion

We analyze the orbital and mass evolution of planets that undergo run-away gas accretion by means of 2D and 3D hydrodynamic simulations. The disk torque distribution per unit disk mass as a function of radius provides an important diagnostic for the nature of the disk-planet interactions. We first consider torque distributions for nonmigrating planets of fixed mass and show that there is general agreement with the expectations of resonance theory. We then present results of simulations for mass-gaining, migrating planets. For planets with an initial mass of 5 Earth masses, which are embedded in disks with standard parameters and which undergo run-away gas accretion to one Jupiter mass (Mjup), the torque distributions per unit disk mass are largely unaffected by migration and accretion for a given planet mass. The migration rates for these planets are in agreement with the predictions of the standard theory for planet migration (Type I and Type II migration). The planet mass growth occurs through gas capture within the planet's Bondi radius at lower planet masses, the Hill radius at intermediate planet masses, and through reduced accretion at higher planet masses due to gap formation. During run-away mass growth, a planet migrates inwards by only about 20% in radius before achieving a mass of ~1 Mjup. For the above models, we find no evidence of fast migration driven by coorbital torques, known as Type III migration. We do find evidence of Type III migration for a fixed mass planet of Saturn's mass that is immersed in a cold and massive disk. In this case the planet migration is assumed to begin before gap formation completes. The migration is understood through a model in which the torque is due to an asymmetry in density between trapped gas on the leading side of the planet and ambient gas on the trailing side of the planet.

Infall of Planetesimals onto Growing Giant Planets: Onset of Runaway Gas Accretion and Metallicity of Their Gas Envelopes

We have investigated the planetesimal accretion rate onto giant planets that are growing through gas accretion, using numerical simulations and analytical arguments. We derived the condition for the opening of a gap in the planetesimal disk, which is determined by a competition between the expansion of the planet's Hill radius due to the planet's growth and the damping of planetesimal eccentricity due to gas drag. We also derived the semianalytical formula for the planetesimal accretion rate as a function of the ratios of the rates of the Hill radius expansion, the damping, and planetesimal scattering by the planet. The predicted low planetesimal accretion rate due to the opening of the gap in early gas accretion stages quantitatively shows that 2, which is a long (more than a Myr), slow gas accretion phase before the onset of runaway gas accretion, is not likely to occur. In late stages, rapid Hill radius expansion fills the gap, resulting in significant planetesimal accretion, which is as large as several M⊕ for Jupiter and Saturn. The efficient onset of runaway gas accretion and the late pollution may reconcile the ubiquity of extrasolar giant planets with the metal-rich envelopes of Jupiter and Saturn inferred from interior structure models. These formulae will give deep insights into the formation of extrasolar gas giants and the diversity in the metallicities of transiting gas giants.

Orbital evolution and accretion of protoplanets tidally interacting with a gas disk: II. Solid surface density evolution with type-I migration

This paper investigates the surface density evolution of a planetesimal disk due to the effect of type-I migration by carrying out N-body simulation and through analytical method, focusing on terrestrial planet formation. The coagulation and the growth of the planetesimals take place in the abundant gas disk except for a final stage. A protoplanet excites density waves in the gas disk, which causes the torque on the protoplanet. The torque imbalance makes the protoplanet suffer radial migration, which is known as type-I migration. Type-I migration time scale derived by the linear theory may be too short for the terrestrial planets to survive, which is one of the major problems in the planet formation scenario. Although the linear theory assumes a protoplanet being in a gas disk alone, Kominami et al. [Kominami, J., Tanaka, H., Ida, S., 2005. Icarus 167, 231–243] showed that the effect of the interaction with the planetesimal disk and the neighboring protoplanets on type-I migration is negligible. The migration becomes pronounced before the planet's mass reaches the isolation mass, and decreases the solid component in the disk. Runaway protoplanets form again in the planetesimal disk with decreased surface density. In this paper, we present the analytical formulas that describe the evolution of the solid surface density of the disk as a function of gas-to-dust ratio, gas depletion time scale and semimajor axis, which agree well with our results of N-body simulations. In general, significant depletion of solid material is likely to take place in inner regions of disks. This might be responsible for the fact that there is no planet inside Mercury's orbit in our Solar System. Our most important result is that the final surface density of solid components ( Σ d ) and mass of surviving planets depend on gas surface density ( Σ g ) and its depletion time scale ( τ dep ) but not on initial Σ d ; they decrease with increase in Σ g and τ dep . For a fixed gas-to-dust ratio and τ dep , larger initial Σ d results in smaller final Σ d and smaller surviving planets, because of larger Σ g . To retain a specific amount of Σ d , the efficient disk condition is not an initially large Σ d but the initial Σ d as small as the specified final one and a smaller gas-to-dust ratio. To retain Σ d comparable to that of the minimum mass solar nebula (MMSN), a disk must have the same Σ d and a gas-to-dust ratio that is smaller than that of MMSN by a factor of 1.3 × ( τ dep / 1 Myr ) at ∼1 AU. (Equivalently, type-I migration speed is slower than that predicted by the linear theory by the same factor.) The surviving planets are Mars-sized ones in this case; in order to form Earth-sized planets, their eccentricities must be pumped up to start orbit crossing and coagulation among them. At ∼5 AU, Σ d of MMSN is retained under the same condition, but to form a core massive enough to start runaway gas accretion, a gas-to-dust ratio must be smaller than that of MMSN by a factor of 3 × τ dep / 1 Myr .

Accretion of the gaseous envelope of Jupiter around a 5–10 Earth-mass core

New numerical simulations of the formation and evolution of Jupiter are presented. The formation model assumes that first a solid core of several M ⊕ accretes from the planetesimals in the protoplanetary disk, and then the core captures a massive gaseous envelope from the protoplanetary disk. Earlier studies of the core accretion–gas capture model [Pollack, J.B., Hubickyj, O., Bodenheimer, P., Lissauer, J.J., Podolak, M., Greenzweig, Y., 1996. Icarus 124, 62–85] demonstrated that it was possible for Jupiter to accrete with a solid core of 10–30 M ⊕ in a total formation time comparable to the observed lifetime of protoplanetary disks. Recent interior models of Jupiter and Saturn that agree with all observational constraints suggest that Jupiter's core mass is 0–11 M ⊕ and Saturn's is 9–22 M ⊕ [Saumon, G., Guillot, T., 2004. Astrophys. J. 609, 1170–1180]. We have computed simulations of the growth of Jupiter using various values for the opacity produced by grains in the protoplanet's atmosphere and for the initial planetesimal surface density, σ init , Z , in the protoplanetary disk. We also explore the implications of halting the solid accretion at selected core mass values during the protoplanet's growth. Halting planetesimal accretion at low core mass simulates the presence of a competing embryo, and decreasing the atmospheric opacity due to grains emulates the settling and coagulation of grains within the protoplanet's atmosphere. We examine the effects of adjusting these parameters to determine whether or not gas runaway can occur for small mass cores on a reasonable timescale. We compute four series of simulations with the latest version of our code, which contains updated equation of state and opacity tables as well as other improvements. Each series consists of a run without a cutoff in planetesimal accretion, plus up to three runs with a cutoff at a particular core mass. The first series of runs is computed with an atmospheric opacity due to grains (hereafter referred to as ‘grain opacity’) that is 2% of the interstellar value and σ init , Z = 10 g / cm 2 . Cutoff runs are computed for core masses of 10, 5, and 3 M ⊕ . The second series of Jupiter models is computed with the grain opacity at the full interstellar value and σ init , Z = 10 g / cm 2 . Cutoff runs are computed for core masses of 10 and 5 M ⊕ . The third series of runs is computed with the grain opacity at 2% of the interstellar value and σ init , Z = 6 g / cm 2 . One cutoff run is computed with a core mass of 5 M ⊕ . The final series consists of one run, without a cutoff, which is computed with a temperature dependent grain opacity (i.e., 2% of the interstellar value for T < 350 K ramping up to the full interstellar value for T > 500 K ) and σ init , Z = 10 g / cm 2 . Our results demonstrate that reducing grain opacities results in formation times less than half of those for models computed with full interstellar grain opacity values. The reduction of opacity due to grains in the upper portion of the envelope with T ⩽ 500 K has the largest effect on the lowering of the formation time. If the accretion of planetesimals is not cut off prior to the accretion of gas, then decreasing the surface density of planetesimals lowers the final core mass of the protoplanet, but increases the formation timescale considerably. Finally, a core mass cutoff results in a reduction of the time needed for a protoplanet to evolve to the stage of runaway gas accretion, provided the cutoff mass is sufficiently large. The overall results indicate that, with reasonable parameters, it is possible that Jupiter formed at 5 AU via the core accretion process in 1 Myr with a core of 10 M ⊕ or in 5 Myr with a core of 5 M ⊕ .

Migration and giant planet formation

We extend the core-accretion model of giant gaseous planets by Pollack et al. ([CITE]) to include migration, disc evolution and gap formation. Starting with a core of a fraction of an Earth's mass located at 8 AU, we end our simulation with the onset of runaway gas accretion when the planet is at 5.5 AU 1 Myr later. This timescale is about a factor ten shorter than the one found by Pollack et al. ([CITE]) even though the disc was less massive initially and viscously evolving. Other initial conditions can lead to even shorter timescales. The reason for this speed-up is found to result from the fact that a moving planet does not deplete its feeding zone to the extend of a static planet. Thus, the uncomfortably long formation timescale associated with the core-accretion scenario can be considerably reduced and brought in much better agreement with the typical disc lifetimes inferred from observations of young circumstellar discs.

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.

On the Formation Timescale and Core Masses of Gas Giant Planets

Numerical simulations show that the migration of growing planetary cores may be dominated by turbulent fluctuations in the protoplanetary disk, rather than by any mean property of the flow. We quantify the impact of this stochastic core migration on the formation timescale and core mass of giant planets at the onset of runaway gas accretion. For standard solar nebula conditions, the formation of Jupiter can be accelerated by almost an order of magnitude if the growing core executes a random walk with an amplitude of a few tenths of an AU. A modestly reduced surface density of planetesimals allows Jupiter to form within 10 Myr, with an initial core mass below 10 , in better agreement with observational constraints. For extrasolar planetary systems, the M results suggest that core accretion could form massive planets in disks with lower metallicities, and shorter lifetimes, than the solar nebula. Subject headings: accretion, accretion disks — planetary systems: formation — planets and satellites: formation — planets and satellites: individual (Jupiter) — solar system: formation