Five-planet Nice model

The five-planet Nice model is a numerical model of the early Solar System that is a revised variation of the Nice model. It begins with five giant planets, the four that exist today plus an additional ice giant between Saturn and Uranus in a chain of mean-motion resonances.
After the resonance chain is broken, the five giant planets undergo a period of planetesimal-driven migration, followed by a period of orbital instability with gravitational encounters between planets similar to that in the original Nice model. During the instability the additional giant planet is scattered inward onto a Jupiter-crossing orbit and is ejected from the Solar System following an encounter with Jupiter. The model was first formally proposed in 2011 after simulations indicated that it was more likely to reproduce the current Solar System than a four-planet Nice model.

A five-planet Nice model

The following is a version of the five-planet Nice model that results in an [|early] instability and reproduces a number of aspects of the current Solar System. Although in the past the giant planet instability has been linked to the Late Heavy Bombardment, a number of recent studies indicate that the giant planet instability occurred early. The Solar System may have [|begun] with the giant planets in another resonance chain.
The Solar System ends its nebula phase with Jupiter, Saturn, and the three ice giants in a 3:2, 3:2, 2:1, 3:2 resonance chain with semi-major axes ranging from 5.5 – 20 AU. A dense disk of planetesimals orbits beyond these planets, extending from 24 AU to 30 AU. The planetesimals in this disk are stirred due to gravitational interactions between them, increasing the eccentricities and inclinations of their orbits. The disk spreads as this occurs, pushing its inner edge toward the orbits of the giant planets. Collisions between planetesimals in the outer disk also produce debris that is ground to dust in a cascade of collisions. The dust spirals inward toward the planets due to Poynting-Robertson drag and eventually reaches Neptune's orbit. Gravitational interactions with the dust or with the inward scattered planetesimals allow the giant planets to escape from the resonance chain roughly ten million years after the dissipation of the gas disk.
The planets then undergo a planetesimal-driven migration as they encounter and exchange angular momentum with an increasing number of planetesimals. A net inward transfer of planetesimals and outward migration of Neptune occurs during these encounters as most of those scattered outward return to be encountered again while some of those scattered inward are prevented from returning after encountering Uranus. A similar process occurs for Uranus, the extra ice giant, and Saturn, resulting in their outward migration and a transfer of planetesimals inward from the outer belt to Jupiter. Jupiter, in contrast, ejects most of the planetesimals from the Solar System, and as a result migrates inward. After 10 million years the divergent migration of the planets leads to resonance crossings, exciting the eccentricities of the giant planets and destabilizing the planetary system when Neptune is near 28 AU.
The extra ice giant is ejected during this instability. The extra ice giant enters a Saturn-crossing orbit after its eccentricity increases and is scattered inward by Saturn onto a Jupiter-crossing orbit. Repeated gravitational encounters with the ice giant cause jumps in Jupiter's and Saturn's semi-major axes, driving a step-wise separation of their orbits, and leading to a rapid increase of the ratio of their periods until it is greater than 2.3. The ice giant also encounters Uranus and Neptune and crosses parts of the asteroid belt as these encounters increase the eccentricity and semi-major axis of its orbit. After 10,000–100,000 years, the ice giant is ejected from the Solar System following an encounter with Jupiter, becoming a rogue planet. The remaining planets then continue to migrate at a declining rate and slowly approach their final orbits as most of the remaining planetesimal disk is removed.

Solar System effects

The migrations of the giant planets and encounters between them have many effects in the outer Solar System. The gravitational encounters between the giant planets excite the eccentricities and inclinations of their orbits. The planetesimals scattered inward by Neptune enter planet-crossing orbits where they may impact the planets or their satellites The impacts of these planetesimals leave craters and impact basins on the moons of the outer planets, and may result in the disruption of their inner moons. Some of the planetesimals are jump-captured as Jupiter trojans when Jupiter's semi-major axis jumps during encounters with the ejected ice giant. One group of Jupiter trojans can be depleted relative to the other if the ice giant passes through it following the ice giant's last encounter with Jupiter. Later, when Jupiter and Saturn are near mean-motion resonances, other Jupiter trojans can be captured via the mechanism described in the original Nice model.
Other planetesimals are captured as irregular satellites of the giant planets via three-body interactions during encounters between the ejected ice giant and the other planets. The irregular satellites begin with wide range of inclinations including prograde, retrograde, and perpendicular orbits. The population is later reduced as those in perpendicular orbits are lost due to the Kozai mechanism, and others are broken up by collisions among them. The encounters between planets can also perturb the orbits of the regular satellites and may be responsible for the inclination of Iapetus's orbit. Saturn's rotational axis may have been tilted when it slowly crossed a spin-orbit resonance with Neptune.
Many of the planetesimals are also implanted in various orbits beyond Neptune's orbit during its migration. While Neptune migrates outward several AU, the hot classical Kuiper belt and the scattered disk are formed as some planetesimals scattered outward by Neptune are captured in resonances, undergo an exchange of eccentricity vs inclination via the Kozai mechanism, and are released onto higher perihelion, stable orbits. Planetesimals captured in Neptune's sweeping 2:1 resonance during this early migration are released when an encounter with the ice giant causes its semi-major axis to jump outward, leaving behind a group of low-inclination, low-eccentricity objects in the cold classical Kuiper belt with semi-major axes near 44 AU. This process avoids close encounters with Neptune allowing loosely bound binaries, including 'blue' binaries, to survive. An excess of low-inclination plutinos is avoided due to a similar release of objects from Neptune's 3:2 resonance during this encounter. Neptune's modest eccentricity following the encounter, or the rapid precession of its orbit, allows the primordial disk of cold classical Kuiper belt objects to survive. If Neptune's migration is slow enough following this encounter the eccentricity distribution of these objects can be truncated by a sweeping mean-motion resonances, leaving it with a step near Neptune's 7:4 resonance. As Neptune slowly approaches its current orbit, objects are left in fossilized high-perihelion orbits in the scattered disk. Others with perihelia beyond Neptune's orbit but not high enough to avoid interactions with Neptune remain as a scattering objects, and those that remain in resonance at the end of Neptune's migration form the various resonant populations beyond Neptune's orbit. Objects that are scattered to very large semi-major axis orbits can have their perihelia lifted beyond the influences of the giant planets by the galactic tide or perturbations from passing stars, depositing them in the Oort cloud. If the hypothetical Planet Nine was in its proposed orbit at the time of the instability a roughly spherical cloud of objects would be captured with semi-major axes ranging from a few hundred to a few thousand AU.
In the inner Solar System the impacts of the instability vary with its timing and duration. An early instability could have been responsible for the removal of most of the mass from the Mars region, leaving Mars smaller than Earth and Venus. An early instability could also result in the depletion of the asteroid belt, and if it extended for a few hundred thousand years, the excitement of its eccentricities and inclinations. Asteroid collisional families can be dispersed due to interactions with various resonances and by encounters with the ice giant as it crosses the asteroid belt. Planetesimals from the outer belt are embedded in the asteroid belt as P- and D-type asteroids when their aphelion are lowered below Jupiter's orbit while they are in a resonance or during encounters with the ice giant, with some reaching the inner asteroid belt due to encounters with the ice giant. A late instability would have to be brief, driving a rapid separation of the orbits of Jupiter and Saturn, to avoid the excitation of the eccentricities of the inner planets due to secular resonance sweeping. This would also lead to more modest changes in the asteroid's orbits if the asteroid belt had an initial low mass, or if it had been depleted and excited by the Grand Tack, possibly shifting the distribution of their eccentricities toward the current distribution. A late instability could also result in roughly half of the asteroids escaping from the core of a previously depleted asteroid belt leading to a smaller, but extended bombardment of the inner planets by rocky objects when an inner extension of the asteroid belt is disrupted when the planets reach their present positions.

Development of the Nice model

Four planet models

Current theories of planetary formation do not allow for the accretion of Uranus and Neptune in their present positions. The protoplanetary disk was too diffuse and the time scales too long for them to form via planetesimal accretion before the gas disk dissipated, and numerical models indicate that later accretion would be halted once Pluto-sized planetesimals formed. Although more recent models including pebble accretion allow for faster growth the inward migration of the planets due to interactions with the gas disk leave them in closer orbits.
It is now widely accepted that the Solar System was initially more compact and that the outer planets migrated outward to their current positions. The planetesimal-driven migration of the outer planets was first described in 1984 by Fernandez and Ip. This process is driven by the exchange of angular momentum between the planets and planetesimals originating from an outer disk. Early dynamical models assumed that this migration was smooth. In addition to reproducing the current positions of the outer planets, these models offered explanations for: the populations of resonant objects in the Kuiper belt, the eccentricity of Pluto's orbit, the inclinations of the hot classical Kuiper belt objects and the retention of a scattered disk, and the low mass of Kuiper belt and the location of its outer edge near the 2:1 resonance with Neptune. However, these models failed to reproduce the eccentricities of the outer planets, leaving them with very small eccentricities at the end of the migration.
In the original Nice model Jupiter and Saturn's eccentricities are excited when they cross their 2:1 resonance, destabilizing the outer Solar System. A series of gravitational encounters ensues during which Uranus and Neptune are scattered outward into the planetesimal disk. There they scatter a great number of planetesimals inward, accelerating the migration of the planets. The scattering of planetesimals and the sweeping of resonances through the asteroid belt produce a bombardment of the inner planets. In addition to reproducing the positions and eccentricities of the outer planets, the original Nice model provided for the origin of: the Jupiter trojans, and the Neptune trojans; the irregular satellites of Saturn, Uranus, and Neptune; the various populations of trans-Neptunian objects; the magnitude of, and with the right initial conditions, the timing of the Late Heavy Bombardment.
However, sweeping secular resonances would perturb the orbits of inner Solar System objects if Jupiter's migration was slow and smooth. The ν₅ secular resonance crosses the orbits of the terrestrial planets exciting their eccentricities. While Jupiter and Saturn slowly approach their 2:1 resonance the eccentricity of Mars reaches values that can result in collisions between planets or in Mars being ejected from the Solar System. Revised versions of the Nice model beginning with the planets in a chain of resonances avoid this slow approach to the 2:1 resonance. However, the eccentricities of Venus and Mercury are typically excited beyond their current values when the ν₅ secular resonance crosses their orbits. The orbits of the asteroids are also significantly altered: the ν₁₆ secular resonance excites inclinations and the ν₆ secular resonance excites eccentricities, removing low-inclination asteroids, as they sweep across the asteroid belt. As a result, the surviving asteroid belt is left with a larger fraction of high inclination objects than is currently observed.
The orbits of the inner planets and the orbital distribution of the asteroid belt can be reproduced if Jupiter encounters one of the ice giants, accelerating its migration. The slow resonance crossings that excite the eccentricities of Venus and Mercury and alter the orbital distribution of the asteroids occur when Saturn's period was between 2.1 and 2.3 times that of Jupiter's. Theorists propose that these were avoided because the divergent migration of Jupiter and Saturn was dominated by planet–planet scattering at that time. Specifically, one of the ice giants was scattered inward onto a Jupiter-crossing orbit by a gravitational encounter with Saturn, after which it was scattered outward by a gravitational encounter with Jupiter. As a result, Jupiter's and Saturn's orbits rapidly diverged, accelerating the sweeping of the secular resonances. This evolution of the orbits of the giant planets, similar to processes described by exoplanet researchers, is referred to as the jumping-Jupiter scenario.