How planetary growth outperforms migration

Planetary migration is a major challenge for planet formation theories. The speed of Type I migration is proportional to the mass of a protoplanet, while the final decade of growth of a pebble-accreting planetary core takes place at a rate that scales with the mass to the two-thirds power. This results in planetary growth tracks (i.e., the evolution of a protoplanet's mass versus its distance from the star) that become increasingly horizontal (migration-dominated) with rising mass of the protoplanet. It has been shown recently that the migration torque on a protoplanet is reduced proportional to the relative height of the gas gap carved by the growing planet. Here we show from 1-D simulations of planet-disc interaction that the mass at which a planet carves a 50% gap is approximately 2.3 times the pebble isolation mass. Our measurements of the pebble isolation mass from 1-D simulations match published 3-D results relatively well, except at very low viscosities where the 3-D pebble isolation mass is significantly higher, possibly due to gap edge instabilities not captured in 1-D. The pebble isolation mass demarks the transition from pebble accretion to gas accretion. Gas accretion to form gas-giant planets therefore takes place over a few astronomical units of migration after reaching first the pebble isolation mass and, shortly after, the 50% gap mass. Our results demonstrate how planetary growth can outperform migration, both during core accretion and during gas accretion, even when the Stokes number of the pebbles is small, St~0.01, and the pebble-to-gas flux ratio in the protoplanetary disc is in the nominal range of 0.01-0.02. We find that planetary growth is very rapid in the first million years of the protoplanetary disc and that the probability for forming gas-giant planets increases with the initial size of the protoplanetary disc and with decreasing turbulent diffusion.Comment: Accepted for publication in Astronomy & Astrophysic

<i>N</i>-body simulations of planet formation via pebble accretion:II. How various giant planets form

Aims. The connection between initial disc conditions and final orbital and physical properties of planets is not well-understood. In this paper, we numerically study the formation of planetary systems via pebble accretion and investigate the effects of disc properties such as masses, dissipation timescales, and metallicities on planet formation outcomes. Methods. We improved the N-body code SyMBA that was modified for our Paper I by taking account of new planet–disc interaction models and type II migration. We adopted the ‘two-α’ disc model to mimic the effects of both the standard disc turbulence and the mass accretion driven by the magnetic disc wind. Results. We successfully reproduced the overall distribution trends of semi-major axes, eccentricities, and planetary masses of extrasolar giant planets. There are two types of giant planet formation trends, depending on whether or not the disc’s dissipation timescales are comparable to the planet formation timescales. When planet formation happens fast enough, giant planets are fully grown (Jupiter mass or higher) and are distributed widely across the disc. On the other hand, when planet formation is limited by the disc’s dissipation, discs generally form low-mass cold Jupiters. Our simulations also naturally explain why hot Jupiters (HJs) tend to be alone and how the observed eccentricity-metallicity trends arise. The low-metallicity discs tend to form nearly circular and coplanar HJs in situ, because planet formation is slower than high-metallicity discs, and thus protoplanetary cores migrate significantly before gas accretion. The high-metallicity discs, on the other hand, generate HJs in situ or via tidal circularisation of eccentric orbits. Both pathways usually involve dynamical instabilities, and thus HJs tend to have broader eccentricity and inclination distributions. When giant planets with very wide orbits (“super-cold Jupiters”) are formed via pebble accretion followed by scattering, we predict that they belong to metal-rich stars, have eccentric orbits, and tend to have (~80%) companions interior to their orbits

Constructing the secular architecture of the solar system I: The giant planets

Using numerical simulations, we show that smooth migration of the giant planets through a planetesimal disk leads to an orbital architecture that is inconsistent with the current one: the resulting eccentricities and inclinations of their orbits are too small. The crossing of mutual mean motion resonances by the planets would excite their orbital eccentricities but not their orbital inclinations. Moreover, the amplitudes of the eigenmodes characterising the current secular evolution of the eccentricities of Jupiter and Saturn would not be reproduced correctly; only one eigenmode is excited by resonance-crossing. We show that, at the very least, encounters between Saturn and one of the ice giants (Uranus or Neptune) need to have occurred, in order to reproduce the current secular properties of the giant planets, in particular the amplitude of the two strongest eigenmodes in the eccentricities of Jupiter and Saturn.Comment: Astronomy & Astrophysics (2009) in pres

A Survey of Orbits of Co-orbitals of Jupiter

working version of a paper planned for Planetary and Space ScienceJupiter’s Trojan asteroids fulfill the prediction of Lagrange that orbits can be stable when a small body orbits in specific locations relative to its ‘parent’ planet and the Sun. The first such Trojan asteroid was discovered in 1906 and subsequently similar asteroids have been discovered associated with Mars and with Neptune. To date no Trojans have been discovered associated with Earth, but several horseshoe asteroids, co-orbital asteroids moving along a large range of the Earth’s orbit, have been found. Other planets also are not known to have Trojan-type asteroids associated with them. Since the number of detected Jupiter Trojans has increased dramatically in the last few years, we have conducted a numerical survey of their orbital motions to see whether any in fact move in horseshoe orbits. We find that none do, although there is some possibility that escaped Trojans have been detected. Here we also use the enlarged database of information about Trojans to summarize their orbital properties as now known

Onset of giant planet migration before 4480 million years ago

Immediately after their formation, the terrestrial planets experienced intense impact bombardment by comets, leftover planetesimals from primary accretion, and asteroids. This temporal interval in solar system evolution, termed late accretion, thermally and chemically modified solid planetary surfaces and may have impeded the emergence of life on the Hadean Earth. The sources and tempo of late accretion are, however, vague. Here, we present a timeline that relates variably retentive radiometric ages from asteroidal meteorites, to new dynamical models of late accretion that invokes giant planet migration. Reconciliation of the geochronological data with dynamical models shows that giant planet migration immediately leads to an intense 30 Myr influx of comets to the entire solar system. The absence of whole-sale crustal reset ages after 4450 Ma for the most resilient chronometers from Earth, Moon, Mars, Vesta and various meteorite parent bodies confines the onset of giant planet migration to no later than ca. 4480 Ma. Waning impacts from planetesimals, asteroids (and a minor cometary component) continue to strike the inner planets through a protracted monotonic decline in impactor flux; this is in agreement with predictions from crater chronology. Amended global 3-D thermal analytical bombardment models derived from our new impact mass-production functions show that persistent niches for prebiotic chemistry on the early Hadean Earth could endure late accretion for at least the last 4400 Myr.Comment: Main text: 46564 characters with spaces/7549 words Tables: 3 Figures:7 References: 11

Inner solar system dynamical analogs of plutinos

accepted by Icarus, November 2007By studying orbits of asteroids potentially in 3:2 exterior mean motion resonance with Earth, Venus, and Mars, we have found plutino analogs. We identify at least 27 objects in the inner solar system dynamically protected from encounter through this resonance. These are four objects associated with Venus, six with Earth, and seventeen with Mars. Bodies in the 3:2 exterior resonance (including those in the plutino resonance associated with Neptune) orbit the Sun twice for every three orbits of the associated planet, in such a way that with sufficiently low libration amplitude close approaches to the planet are impossible. As many as 15% of Kuiper Belt objects share the 3:2 resonance, but are poorly observed. One of several resonance sweeping mechanisms during planetary migration is likely needed to explain the origin and properties of 3:2 resonant Kuiper Belt objects. Such a mechanism likely did not operate in the inner solar system. We suggest that scattering by the next planet out allows entry to, and exit from, 3:2 resonance for objects associated with Venus or Earth. 3:2 resonators of Mars, on the other hand, do not cross the paths of other planets, and have a long lifetime. There may exist some objects trapped in the 3:2 Mars resonance which are primordial, with our tests on the most promising objects known to date indicating lifetimes of at least tens of millions of years. Identifying 3:2 resonant systems in the inner Solar System permits this resonance to be studied on shorter timescales and with better determined orbits than has been possible to date, and introduces new mechanisms for entry into the resonant configuration

A new and simple prescription for planet orbital migration and eccentricity damping by planet-disc interactions based on dynamical friction

During planet formation gravitational interaction between a planetary embryo and the protoplanetary gas disc causes orbital migration of the planetary embryo, which plays an important role in shaping the final planetary system. While migration sometimes occurs in the supersonic regime, wherein the relative velocity between the planetary embryo and the gas is higher than the sound speed, migration prescriptions proposed thus far describing the planet-disc interaction force and the timescales of orbital change in the supersonic regime are inconsistent with one another. Here we discuss the details of existing prescriptions in the literature and derive a new simple and intuitive formulation for planet-disc interactions based on dynamical friction that can be applied in both supersonic and subsonic cases. While the existing prescriptions assume particular disc models, ours include the explicit dependence on the disc parameters; hence it can be applied to discs with any radial surface density and temperature dependence (except for the local variations with radial scales less than the disc scale height). Our prescription will reduce the uncertainty originating from different literature formulations of planet migration and will be an important tool to study planet accretion processes, especially when studying the formation of close-in low-mass planets that are commonly found in exoplanetary systems.Comment: 10 pages, 1 figure, accepted for publication in MNRAS; typos corrected, the reference list was complete