Five-planet Nice model
[1] 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.
[6] 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.
[6] 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.
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.
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.
[27] Neptune's modest eccentricity following the encounter,[29] or the rapid precession of its orbit,[30] allows the primordial disk of cold classical Kuiper belt objects to survive.
[34] 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.
[35] An early instability could also result in the depletion of the asteroid belt,[36] and if it extended for a few hundred thousand years, the excitement of its eccentricities and inclinations.
[39] 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.
[45] 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.
[14] In the original Nice model Jupiter and Saturn's eccentricities are excited when they cross their 2:1 resonance, destabilizing the outer Solar System.
[12] 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.
The planetesimal disk masses typically used in the Nice model are often insufficient for this, leaving systems beginning with four giant planets with only three at the end of the instability.
[60] Konstantin Batygin, Michael E. Brown, and Hayden Betts, in contrast, found four- and five-planet systems had a similar likelihoods (4% vs 3%) of reproducing the orbits of the outer planets, including the oscillations of Jupiter's and Saturn's eccentricities, and the hot and cold populations of Kuiper belt.
[63] A rapid precession of Neptune's orbit during this period due to interactions with Uranus was also necessary for the preservation of a primordial belt of cold classical objects.
[65] Ford and Chiang modeled systems of planets in a packed oligarchy, the result of their formation in a more massive dynamically cool disk.
[60] A long-range migration of Neptune outward into the planetesimal disk before planetary encounters begins is most likely if the planets were captured in a 3:2, 3:2, 2:1, 3:2 resonance chain, occurring in 65% of simulations when the inner edge was within 2 AU.
As a result, the timing of the instability is sensitive to factors that determine the rate of dust generation such as the size distribution and the strength of the planetesimals.
[6] The timing of the instability in the Nice model was initially proposed to have coincided with the Late Heavy Bombardment, a spike in the impact rate thought to have occurred several hundred million years after the formation of the Solar System.
However, recently a number of issues have been raised regarding the timing of the Nice model instability, whether it was the cause of the Late Heavy Bombardment, and if an alternative would better explain the associated craters and impact basins.
Most of the effects of the Nice model instability on the orbits of the giant planets and those of the various small body populations that originated in the outer planetesimal disk are independent of its timing, however.
[2] However, a jump in the ratio of the orbital periods of Jupiter and Saturn is still required to reproduce the asteroid belt, reducing the advantage of an early instability.
[69][70] A previous study by Ramon Brasser, Kevin Walsh, and David Nesvorny found a reasonable chance (greater than 20%) of reproducing the inner Solar System using a selected five-planet model.
The presence of Patroclus-Menoetius among the Jupiter Trojans requires that the giant planet instability occurred within 100 million years of the formation of the Solar System.
The remaining lunar craters would then be the result of another population of impactors with a different size distribution, possibly planetesimals left over from the formation of the planets.
Some recently offered alternatives include debris from the impact that formed the Borealis Basin on Mars,[85] and catastrophic collisions among lost planets once orbiting inside Mercury.
This hypothesis requires the lunar mantle to have crystallized relatively late which may explain the differing concentrations of highly siderophile elements in the Earth and Moon.
[89] A previous work, however, found that the most dynamically stable part of this population would become depleted due to its collisional evolution, making the formation of several or even the last two impact basins unlikely.
[91] In January 2016, Batygin and Brown proposed that a distant massive ninth planet is responsible for the alignment of the perihelia of several trans-Neptunian objects with semi-major axes greater than 250 AU.
