Nice model

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The Nice (/ˈns/) model is a scenario for the dynamical evolution of the Solar System. It is named for the location of the Observatoire de la Côte d'Azur, where it was initially developed, in Nice, France.[1][2][3] It proposes the migration of the giant planets from an initial compact configuration into their present positions, long after the dissipation of the initial protoplanetary gas disk. In this way, it differs from earlier models of the Solar System's formation. This planetary migration is used in dynamical simulations of the Solar System to explain historical events including the Late Heavy Bombardment of the inner Solar System, the formation of the Oort cloud, and the existence of populations of small Solar System bodies including the Kuiper belt, the Neptune and Jupiter trojans, and the numerous resonant trans-Neptunian objects dominated by Neptune. Its success at reproducing many of the observed features of the Solar System means that it is widely accepted as the current most realistic model of the Solar System's early evolution,[3] although it is not universally favoured among planetary scientists. One of its limitations that it does not reproduce the outer-system satellites and the Kuiper belt (see below).

Simulation showing the outer planets and planetesimal belt: a) early configuration, before Jupiter and Saturn reach a 2:1 resonance; b) scattering of planetesimals into the inner Solar System after the orbital shift of Neptune (dark blue) and Uranus (light blue); c) after ejection of planetesimals by planets.[4]


The original core of the Nice model is a triplet of papers published in the general science journal Nature in 2005 by an international collaboration of scientists: Rodney Gomes, Hal Levison, Alessandro Morbidelli and Kleomenis Tsiganis.[4][5][6] In these publications, the four authors proposed that after the dissipation of the gas and dust of the primordial Solar System disk, the four giant planets (Jupiter, Saturn, Uranus and Neptune) were originally found on near-circular orbits between ~5.5 and ~17 astronomical units (AU), much more closely spaced and compact than in the present. A large, dense disk of small, rock and ice planetesimals, their total about 35 Earth masses, extended from the orbit of the outermost giant planet to some 35 AU.

Scientists understand so little about the formation of Uranus and Neptune that Levison states, "...the possibilities concerning the formation of Uranus and Neptune are almost endless."[7] However, it is suggested that this planetary system evolved in the following manner. Planetesimals at the disk's inner edge occasionally pass through gravitational encounters with the outermost giant planet, which change the planetesimals' orbits. The planets scatter the majority of the small icy bodies that they encounter inward, exchanging angular momentum with the scattered objects so that the planets move outwards in response, preserving the angular momentum of the system. These planetesimals then similarly scatter off the next planet they encounter, successively moving the orbits of Uranus, Neptune, and Saturn outwards.[7] Despite the minute movement each exchange of momentum can produce, cumulatively these planetesimal encounters shift (migrate) the orbits of the planets by significant amounts. This process continues until the planetesimals interact with the innermost and most massive giant planet, Jupiter, whose immense gravity sends them into highly elliptical orbits or even ejects them outright from the Solar System. This, in contrast, causes Jupiter to move slightly inward.

The low rate of orbital encounters governs the rate at which planetesimals are lost from the disk, and the corresponding rate of migration. After several hundreds of millions of years of slow, gradual migration, Jupiter and Saturn, the two inmost giant planets, cross their mutual 1:2 mean-motion resonance. This resonance increases their orbital eccentricities, destabilizing the entire planetary system. The arrangement of the giant planets alters quickly and dramatically.[8] Jupiter shifts Saturn out towards its present position, and this relocation causes mutual gravitational encounters between Saturn and the two ice giants, which propel Neptune and Uranus onto much more eccentric orbits. These ice giants then plough into the planetesimal disk, scattering tens of thousands of planetesimals from their formerly stable orbits in the outer Solar System. This disruption almost entirely scatters the primordial disk, removing 99% of its mass, a scenario which explains the modern-day absence of a dense trans-Neptunian population.[5] Some of the planetesimals are thrown into the inner Solar System, producing a sudden influx of impacts on the terrestrial planets: the Late Heavy Bombardment.[4]

Eventually, the giant planets reach their current orbital semi-major axes, and dynamical friction with the remaining planetesimal disc damps their eccentricities and makes the orbits of Uranus and Neptune circular again.[9]

In some 50% of the initial models of Tsiganis and colleagues, Neptune and Uranus also exchange places approximately a billion years (20%)[citation needed] into the existence of the Solar System.[5] However, the simulation results only correspond to an even mass distribution in the protoplanetary disk and match the masses of the planets in those cases where the switch does take place.[1]

Solar System features[edit]

Running dynamical models of the Solar System with different initial conditions for the simulated length of the history of the Solar System will produce the various populations of objects within the Solar System. As the initial conditions of the model are allowed to vary, each population will be more or less numerous, and will have particular orbital properties. Proving a model of the evolution of the early Solar System is difficult, since the evolution cannot be directly observed.[8] However, the success of any dynamical model can be judged by comparing the population predictions from the simulations to astronomical observations of these populations.[8] At the present time, computer models of the Solar System that are begun with the initial conditions of the Nice scenario best match many aspects of the observed Solar System.[10]

The Late Heavy Bombardment[edit]

The crater record on the Moon and on the terrestrial planets is part of the main evidence for the Late Heavy Bombardment (LHB): an intensification in the number of impactors, at about 600 million years after the Solar System's formation. The number of planetesimals that would reach the Moon in the Nice model is consistent with the crater record from the LHB.

Trojans and the asteroid belt[edit]

During the period of orbital disruption following Jupiter and Saturn reaching the 2:1 resonance, the combined gravitational influence of the migrating giant planets would have quickly destabilized any existing Trojan groups in the L4 and L5 Lagrange points of Jupiter and Neptune.[11] During this time, the Trojan co-orbital region is termed "dynamically open".[3] Under the Nice model, the planetesimals leaving the disrupted disk cross this region in large numbers, temporarily inhabiting it. After the period of orbital instability ends, the Trojan region is "dynamically closed", capturing planetesimals present at the time. The present Trojan populations are then these acquired scattered planetesimals of the primordial asteroid belt.[6] This simulated population matches the libration angle, eccentricity and the large inclinations of the orbits of the Jupiter Trojans.[6] Their inclinations had not previously been understood.[3]

This mechanism of the Nice model similarly generates the Neptune trojans.[3]

A large number of planetesimals would have also been captured in the outer asteroid belt, at distances greater than 2.6 AU, and in the region of the Hilda family.[12] These captured objects would then have undergone collisional erosion, grinding the population away into smaller fragments that can then be acted on by the solar wind and YORP effect; removing more than 90% of them according to Bottke and colleagues.[12] The size frequency distribution of this simulated population following this erosion are in excellent agreement with observations.[12] This suggests that the Jupiter Trojans, Hildas and some of the outer asteroid belt, all spectral D-type asteroids, are the remnant planetesimals from this capture and erosion process,[12] possibly also including the dwarf planet Ceres.[13]

Outer-system satellites[edit]

Any original populations of irregular satellites captured by traditional mechanisms, such as drag or impacts from the accretion disks,[14] would be lost during the interactions of the planets at the time of global system instability.[5] In the Nice model, large numbers of planetesimals interact with the outer planets at this time, and some are captured during three-way interactions with those planets. The probability for any planetesimal to be captured by an ice giant is relatively high, a few 10−7.[15] These new satellites could be captured at almost any angle, so unlike the regular satellites of Saturn, Uranus and Neptune, they do not necessarily orbit in the planets' equatorial planes. Triton, the largest moon of Neptune, can be explained if it was captured in a three-body interaction involving the disruption of a binary planetoid, of which Triton was the less massive member (Cuk & Gladman 2005). However, such binary disruption would not in general have supplied the large number of small irregulars.[16] Some irregulars may have even been exchanged between planets.

The resulting irregular orbits match well with the observed populations' semimajor axes, inclinations and eccentricities, but not with their size distribution.[15] Subsequent collisions between these captured satellites may have created the suspected collisional families seen today. These collisions are also required to erode the population to the present size distribution.

There would not have been enough interactions with Jupiter in the simulations to explain Jupiter's retinue of irregulars, suggesting either that a second mechanism was at work for that planet, or that the parameters of the Nice model need to be revised.[15]

Formation of the Kuiper belt[edit]

The migration of the outer planets is also necessary to account for the existence and properties of the Solar System's outermost regions.[9] Originally, the Kuiper belt was much denser and closer to the Sun, with an outer edge at approximately 30 AU. Its inner edge would have been just beyond the orbits of Uranus and Neptune, which were in turn far closer to the Sun when they formed (most likely in the range of 15–20 AU), and in opposite locations, with Uranus farther from the Sun than Neptune.[4][9]

Some of the scattered objects, including Pluto, became gravitationally tied to Neptune's orbit, forcing them into mean-motion resonances.[17] The Nice model is favoured for its ability to explain the occupancy of current orbital resonances in the Kuiper belt, particularly the 2:5 resonance. As Neptune migrated outward, it approached the objects in the proto-Kuiper belt, capturing some of them into resonances and sending others into chaotic orbits. The objects in the scattered disc are believed to have been placed in their current positions by interactions with Neptune's migrating resonances.[18]

However, the Nice model still fails to account for some of the characteristics of the distribution. While it is able to produce both the hot population objects in the Kuiper belt that have highly inclined orbits and the low-inclination cold population, it predicts a greater average eccentricity in classical Kuiper belt object orbits than is observed (0.10–0.13 versus 0.07).[19]

The two populations not only possess different orbits, but different colors; the cold population is markedly redder than the hot, suggesting it has a different composition and formed in a different region. The hot population is believed to have formed nearer to Jupiter, and to have been ejected outward by movements among the gas giants. The cold population, on the other hand, has been proposed to have formed more or less in its current position, although the Nice model can also explain it being swept outwards later by Neptune during its migration, given that Neptune's orbit would have temporarily become more eccentric.[19][20] The Nice model can partially explain the color difference in that the cold population would still have originated at a greater distance from the Sun than the hot population. However, it cannot explain the apparent complete absence of gray objects in the cold population; a suggestion that has been made is that color differences may arise at least in part from surface evolution processes rather than entirely from differences in primordial composition.[19]

It is also difficult for the model to explain the frequency of paired objects, many of which are far apart and loosely bound.[21]

Scattered disc and Oort cloud[edit]

Those objects scattered by Jupiter into highly elliptical orbits formed the Oort cloud;[9] those objects scattered to a lesser degree by the migrating Neptune formed the current Kuiper belt and scattered disc.[9]


Main article: Nice 2 model

The Nice model has undergone significant modification since its initial publication. The initial conditions of the model have been changed as a result of investigations of the behavior of planets orbiting in a gas disk to a quadruple resonant configuration with Jupiter and Saturn in their 3:2 resonance.[22] The gravitational stirring of the outer planetesimal disk by Pluto-sized objects has been shown to result in breaking of the quadruple resonance via a mechanism that is not sensitive to the distance between the outer planet and the planetesimal disk.[23] This mechanism for triggering the late instability of resonant planets similar to that in the original Nice model has been referred to as the Nice 2 model.[23]

The smooth divergent migration of Jupiter and Saturn has been shown to excite the eccentricities of the terrestrial planets beyond their current values[24] and to leave an asteroid belt with an excessive ratio of high- to low-inclination objects after the migration.[25] In the case of the original Nice model, the slow approach of Jupiter and Saturn to their mutual 2:1 resonance, necessary to match the timing of the Late Heavy Bombardment, can result in the ejection of Mars and the destabilization of the inner Solar System.[24] A step-wise separation of Jupiter's and Saturn's orbits due to gravitational encounters with one of the ice giants, called the jumping-Jupiter scenario, has been shown to be necessary to avoid these issues.[25]

Hypothetical fifth giant planet[edit]

The frequent ejection of the ice giant encountering Jupiter has led Nesvorný to hypothesize an early Solar System with five giant planets, one of which was ejected during the instability.[26][27] A study published in 2015 based on a large ensemble of n-body simulations suggests that the ejection of a hypothetical fifth giant planet is statistically unlikely to produce the observed orbits of the terrestrial planets.[28] The study concluded that, if there was a giant-planet instability leading to the ejection of one ore more additional ice giants, it had to occur prior to the formation of the terrestrial planets and that such an instability could not be the source of the Late Heavy Bombardment.


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