Jumping-Jupiter scenario
The jumping-Jupiter scenario specifies an evolution of giant-planet migration described by the Nice model, in which an ice giant is scattered inward by Saturn and then ejected by Jupiter, causing their semi-major axes to jump, and thereby quickly separating their orbits. The jumping-Jupiter scenario was proposed by Ramon Brasser, Alessandro Morbidelli, Rodney Gomes, Kleomenis Tsiganis, and Harold Levison after their studies revealed that the smooth divergent migration of Jupiter and Saturn resulted in an inner Solar System significantly different from the current Solar System. During this migration secular resonances swept through the inner Solar System exciting the orbits of the terrestrial planets and the asteroids, leaving the planets' orbits too eccentric, and the asteroid belt with too many high-inclination objects. The jumps in the semi-major axes of Jupiter and Saturn described in the jumping-Jupiter scenario can allow these resonances to quickly cross the inner Solar System without altering orbits excessively, although the terrestrial planets remain sensitive to its passage.
The jumping-Jupiter scenario also results in a number of other differences with the original Nice model. The fraction of lunar impactors from the core of the asteroid belt during the Late Heavy Bombardment is significantly reduced, most of the Jupiter trojans are captured during Jupiter's encounters with the ice giant, as are Jupiter's irregular satellites. In the jumping-Jupiter scenario, the likelihood of preserving four giant planets on orbits resembling their current ones appears to increase if the early Solar System originally contained an additional ice giant, which was later ejected by Jupiter into interstellar space. However, this remains an atypical result, as is the preservation of the current orbits of the terrestrial planets.
Background
Original Nice model
In the original Nice model a resonance crossing results in a dynamical instability that rapidly alters the orbits of the giant planets. The original Nice model begins with the giant planets in a compact configuration with nearly circular orbits. Initially, interactions with planetesimals originating in an outer disk drive a slow divergent migration of the giant planets. This planetesimal-driven migration continues until Jupiter and Saturn cross their mutual 2:1 resonance. The resonance crossing excites the eccentricities of Jupiter and Saturn. The increased eccentricities create perturbations on Uranus and Neptune, increasing their eccentricities until the system becomes chaotic and orbits begin to intersect. Gravitational encounters between the planets then scatter Uranus and Neptune outward into the planetesimal disk. The disk is disrupted, scattering many of the planetesimals onto planet-crossing orbits. A rapid phase of divergent migration of the giant planets is initiated and continues until the disk is depleted. Dynamical friction during this phase dampens the eccentricities of Uranus and Neptune stabilizing the system. In numerical simulations of the original Nice model the final orbits of the giant planets are similar to the current Solar System.Resonant planetary orbits
Later versions of the Nice model begin with the giant planets in a series of resonances. This change reflects some hydrodynamic models of the early Solar System. In these models, interactions between the giant planets and the gas disk result in the giant planets migrating toward the central star, in some cases becoming hot Jupiters. However, in a multiple-planet system, this inward migration may be halted or reversed if a more rapidly migrating smaller planet is captured in an outer orbital resonance. The Grand Tack hypothesis, which posits that Jupiter's migration is reversed at 1.5 AU following the capture of Saturn in a resonance, is an example of this type of orbital evolution. The resonance in which Saturn is captured, a 3:2 or a 2:1 resonance, and the extent of the outward migration depends on the physical properties of the gas disk and the amount of gas accreted by the planets. The capture of Uranus and Neptune into further resonances during or following this outward migration results in a quadruply resonant system, with several stable combinations having been identified. Following the dissipation of the gas disk, the quadruple resonance is eventually broken due to interactions with planetesimals from the outer disk. Evolution from this point resembles the original Nice model with an instability beginning either shortly after the quadruple resonance is broken or after a delay during which planetesimal-driven migration drives the planets across a different resonance. However, there is no slow approach to the 2:1 resonance as Jupiter and Saturn either begin in this resonance or cross it rapidly during the instability.Late escape from resonance
The stirring of the outer disk by massive planetesimals can trigger a late instability in a multi-resonant planetary system. As the eccentricities of the planetesimals are excited by gravitational encounters with Pluto-mass objects, an inward migration of the giant planets occurs. The migration, which occurs even if there are no encounters between planetesimals and planets, is driven by a coupling between the average eccentricity of the planetesimal disk and the semi-major axes of the outer planets. Because the planets are locked in resonance, the migration also results in an increase in the eccentricity of the inner ice giant. The increased eccentricity changes the precession frequency of the inner ice giant, leading to the crossing of secular resonances. The quadruple resonance of the outer planets can be broken during one of these secular-resonance crossings. Gravitational encounters begin shortly afterward due to the close proximity of the planets in the previously resonant configuration. The timing of the instability caused by this mechanism, typically occurring several hundred million years after the dispersal of the gas disk, is fairly independent of the distance between the outer planet and the planetesimal disk. In combination with the updated initial conditions, this alternative mechanism for triggering a late instability has been called the Nice 2 model.Planetary encounters with Jupiter
Encounters between Jupiter and an ice giant during the giant planet migration are required to reproduce the current Solar System. In a series of three articles Ramon Brasser, Alessandro Morbidelli, Rodney Gomes, Kleomenis Tsiganis, and Harold Levison analyzed the orbital evolution of the Solar System during giant planet migration. The first article demonstrated that encounters between an ice giant and at least one gas giant were required to reproduce the oscillations of the eccentricities of the gas giants. The other two demonstrated that if Jupiter and Saturn underwent a smooth planetesimal-driven separation of their orbits the terrestrial planets would have orbits that are too eccentric and too many of the asteroids would have orbits with large inclinations. They proposed that the ice giant encountered both Jupiter and Saturn, causing the rapid separation of their orbits, thereby avoiding the secular resonance sweeping responsible for the excitation of orbits in the inner Solar System.Exciting the oscillations of the eccentricities of the giant planets requires encounters between planets. Jupiter and Saturn have modest eccentricities that oscillate out of phase, with Jupiter reaching maximum eccentricity when Saturn reaches its minimum and vice versa. A smooth migration of the giant planets without resonance crossings results in very small eccentricities. Resonance crossings excite their mean eccentricities, with the 2:1 resonance crossing reproducing Jupiter's current eccentricity, but these do not generate the oscillations in their eccentricities. Recreating both requires either a combination of resonance crossings and an encounter between Saturn and an ice giant, or multiple encounters of an ice giant with one or both gas giants.
During the smooth migration of the giant planets the ν5 secular resonance sweeps through the inner Solar System, exciting the eccentricities of the terrestrial planets. When planets are in a secular resonance the precessions of their orbits are synchronized, keeping their relative orientations and the average torques exerted between them fixed. The torques transfer angular momentum between the planets causing changes in their eccentricities and, if the orbits are inclined relative to one another, their inclinations. If the planets remain in or near secular resonances these changes can accumulate resulting in significant changes in eccentricity and inclination. During a ν5 secular resonance crossing this can result in the excitation of the terrestrial planet's eccentricity, with the magnitude of the increase depending on the eccentricity of Jupiter and the time spent in the secular resonance. For the original Nice model the slow approach to Jupiter's and Saturn's 2:1 resonance results in an extended interaction of the ν5 secular resonance with Mars, driving its eccentricity to levels that can destabilize the inner Solar System, potentially leading to collisions between planets or the ejection of Mars. In later versions of the Nice model Jupiter's and Saturn's divergent migration across the 2:1 resonance is more rapid and the nearby ν5 resonance crossings of Earth and Mars are brief, thus avoiding the excessive excitation of their eccentricities in some cases. Venus and Mercury, however, reach significantly higher eccentricities than are observed when the ν5 resonance later crosses their orbits.
A smooth planetesimal-driven migration of the giant planets also results in an asteroid belt orbital distribution unlike that of the current asteroid belt. As it sweeps across the asteroid belt the ν16 secular resonance excites asteroid inclinations. It is followed by the ν6 secular resonance which excites the eccentricities of low-inclination asteroids. If the secular resonance sweeping occurs during a planetesimal driven migration, which has a timescale of 5 million years or longer, the remaining asteroid belt is left with a significant fraction of asteroids with inclinations greater than 20°, which are relatively rare in the current asteroid belt. The interaction of the ν6 secular resonance with the 3:1 mean-motion resonance also leaves a prominent clump in the semi-major-axis distribution that is not observed. The secular resonance sweeping would also leave too many high inclination asteroids if the giant planet migration occurred early, with all of the asteroids initially in low eccentricity and inclination orbits, and also if the orbits of the asteroids were excited by Jupiter's passage during the Grand Tack.
Encounters between an ice giant and both Jupiter and Saturn accelerate the separation of their orbits, limiting the effects of secular resonance sweeping on the orbits of the terrestrial planets and the asteroids. To prevent the excitation of orbits of the terrestrial planets and asteroids the secular resonances must sweep rapidly through the inner Solar System. The small eccentricity of Venus indicates that this occurred on a timescale of less than 150,000 years, much shorter than in a planetesimal driven migration. The secular resonance sweeping can be largely avoided, however, if the separation of Jupiter and Saturn was driven by gravitational encounters with an ice giant. These encounters must drive the Jupiter–Saturn period ratio quickly from below 2.1 to beyond 2.3, the range where the secular resonance crossings occur. This evolution of the giant planets orbits has been named the jumping-Jupiter scenario after a similar process proposed to explain the eccentric orbits of some exoplanets.