Jumping Jupiter scenario

Original Nice model

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 outer 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 (if any) are dependent on the physical properties of the gas disk and on whether or not the planets continue to gain mass via accretion of gas. 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. Capture and outward migration of Jupiter and Saturn in the 2:1 mean-motion resonance can lead to substantial eccentricity growth during the disk-gas phase, that if preserved would leave fossil Kirkwood gaps in the asteroid belt.

Alternative instability trigger

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.

Solar System constraints

Ramon Brasser, Alessandro Morbidelli, Rodney Gomes, Kleomenis Tsiganis, and Harold Levison published a series of three papers analyzing the orbital evolution of the Solar System during giant planet migration. The impact this migration had on the eccentricities of Jupiter and Saturn, the orbits of the terrestrial planets, and the orbital distribution of the asteroid belt allowed them to identify several constraints on the evolution of the outer Solar System. A number of these were found to be incompatible with smooth planetesimal-driven migration of Jupiter after the 2:1 resonance crossing.

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 planets without resonance crossing results in very small eccentricities. Resonance crossings excites 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 the encounters of an ice giant with 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. 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 (or from) 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. However, Venus and Mercury reach higher eccentricities than are observed when ν5 resonance later crosses their orbits. The authors proposed that the last two resonance crossings were avoided, thereby preventing the excessive excitation of the eccentricities of Mercury and Venus. This would occur if gravitational encounters between an ice giant and both gas giants caused the Jupiter–Saturn period ratio to jump from below 2.1 to beyond 2.3. The authors named this alternative evolution the jumping-Jupiter scenario.

A smooth planetesimal-driven migration of the giant planets 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, removing many of them. The remaining asteroid belt is left with a ratio of high- to low-inclination asteroids that is too high. 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. A giant-planet migration in which the Jupiter–Saturn period ratio jumps to beyond 2.3, in contrast, does not significantly alter the inclination distribution, yielding an asteroid belt with a final orbital distribution that is similar to its initial distribution. The requirement of a jump beyond 2.3 is independent of both the timing of the giant-planet migration, and whether the eccentricity distribution was excited by the Grand Tack.

Description

The jumping-Jupiter scenario replaces the smooth separation of Jupiter and Saturn with a series of jumps, thereby avoiding the sweeping of secular resonances through the inner Solar System as their period ratio crosses from 2.1-2.3. In the jumping-Jupiter scenario an ice giant is scattered inward by Saturn onto a Jupiter-crossing orbit and then scattered outward by Jupiter. Saturn's semi-major axis is increased in the first gravitational encounter and Jupiter's reduced by the second with the net result being an increase in their period ratio. In numerical simulations the process can be much more complex: while the trend is for Jupiter's and Saturn's orbits to separate, depending on the geometry of the encounters, individual jumps of Jupiter's and Saturn's semi-major axes can be either up and down. In addition to numerous encounters with Jupiter and Saturn, the ice giant can encounter other ice giant(s) and in some cases cross significant parts of the asteroid belt. The gravitational encounters occur over a period of 10,000–100,000 years, and end when dynamical friction with the planetesimal disk dampens the ice giant's eccentricity, raising its perihelion beyond Saturn's orbit; or when the ice giant is ejected from the Solar System. A jumping-Jupiter scenario occurs in a subset of numerical simulations of the Nice model, including some done for the original Nice model paper. The chances of Saturn scattering an ice giant onto a Jupiter-crossing orbit increases when the initial Saturn–ice giant distance is less than 3 AU, and with the 35-Earth-mass planetesimal belt used in the original Nice model, typically results in the ejection of the ice giant.

Implications for the early Solar System

The jumping-Jupiter scenario results in a number of differences with the original Nice model.

The rapid separation of Jupiter's and Saturn's orbits causes the secular resonances to quickly cross the inner Solar System. The number of asteroids removed from the core of the asteroid belt is reduced, leaving an inner extension of the asteroid belt as the dominant source of rocky impactors. The likelihood of preserving the low eccentricities of the terrestrial planets increases to above 20% in a selected jumping-Jupiter model. Since the modification of orbits in the asteroid belt is limited, its depletion and the excitement of its orbits must have occurred earlier. However, asteroid orbits are modified enough to shift the orbital distribution produced by a grand tack toward that of the current asteroid belt, to disperse collisional families, and to remove fossil Kirkwood gaps. The ice giant crossing the asteroid belt allows some icy planetesimals to be implanted into the inner asteroid belt.

In the outer Solar System icy planetesimals are captured as Jupiter trojans when Jupiter's semi-major axis jumps during encounters with the ice giant. Jupiter also captures irregular satellites via three body interactions during these encounters. Jupiter's regular satellites are perturbed but in roughly half of simulations remain in orbits similar to those observed. Encounters between an ice giant and Saturn perturb the orbit of Iapetus and may be responsible for its inclination. The dynamical excitement of the outer disk by Pluto-massed objects and its lower mass reduces the bombardment of Saturn's moons. Saturn's tilt is acquired when it is captured in a spin-orbit resonance with Neptune. The Solar System likely began with an additional ice giant that is ejected following its encounters with Jupiter. Jupiter's eccentricity is maintained if Neptune first migrates a significant distance into the planetesimal disk before encounters begin. This migration leaves the Kuiper belt with a broad inclination distribution and results in a clump of low inclination objects with similar semi-major axes when captured objects are released from its 2:1 resonance after Neptune encounters the iced giant.

Late Heavy Bombardment

Most of the rocky impactors of the Late Heavy Bombardment originate from an inner extension of the asteroid belt yielding a smaller but longer lasting bombardment. The innermost region of the asteroid belt is currently sparsely populated due to the presence of the ν6 secular resonance. In the early Solar System, however, this resonance was located elsewhere and the asteroid belt extended farther inward, ending at Mars-crossing orbits. During the giant planet migration the ν6 secular resonance first rapidly traversed the asteroid belt removing roughly half of its mass, much less than in the original Nice model. When the planets reached their current positions the ν6 secular resonance destabilized the orbits of the innermost asteroids. Some of these quickly entered planet crossing orbit initiating the Late Heavy Bombardment. Others entered quasi-stable higher inclination orbits, later producing an extended tail of impacts, with a small remnant surviving as the Hungarias. The increase in the orbital eccentricities and inclinations of the destabilized objects also raised impact velocities, resulting in a change the size distribution of lunar craters, and in the production of impact melt in the asteroid belt. The innermost (or E-belt) asteroids are estimated to have produced nine basin-forming impacts on the Moon between 4.1 and 3.7 billion years ago with three more originating from the core of the asteroid belt. The pre-Nectarian basins, part of the LHB in the original Nice model, are thought to be due to the impacts of leftover planetesimals from the inner Solar System.

The magnitude of the cometary bombardment is also reduced. The giant planets outward migration disrupts the outer planetesimal disk causing icy planetesimals to enter planet crossing orbits. Some of them are then perturbed by Jupiter onto orbits similar to those of Jupiter-family comets. These spend a significant fraction of their orbits crossing the inner Solar System raising their likelihood of impacting the terrestrial planets and the moon. In the original Nice model this results in a cometary bombardment with a magnitude similar to the asteroid bombardment. However, while low levels of iridium detected from rocks dating from this era have been cited as evidence of a cometary bombardment, other evidence such as the mix of highly siderophile elements in lunar rocks, and oxygen isotope ratios in the fragments of impactors are not consistent with a cometary bombardment. The size distribution of lunar craters is also largely consistent with that of the asteroids leading to the conclusion the bombardment was dominated by asteroids. The bombardment by comets can be reduced by a number of factors. The stirring of the orbits by pluto-massed objects excites of the inclinations of the orbits of the icy planetimals reducing the fraction of objects entering Jupiter-family orbits from 1/3 to 1/10. The mass of the outer disk in the five-planet model is roughly half that of the original Nice model. The magnitude of the bombardment may have been reduced further due to the icy planetesimals undergoing significant mass loss or their having broken up as the entered the inner Solar System. The largest impact basin resulting from this reduced bombardment is estimated to be the size of Mare Crisium, roughly half the size of the Imbrium basin. Evidence of this bombardment may have been destroyed by later impacts by asteroids.

Other issues have been raised regarding the connection between the Nice model and the Late Heavy Bombardment. although a recent work has found that a bombardment by impactors with this size distribution would result in too many large impact-basins relative to craters. If the E-belt was the product of collisions among a small number of large asteroids, however, it may have had a size distribution that differed from that of the asteroid belt with a larger fraction of small bodies. A recent work has found that the bombardment originating from the inner band of asteroids would yield only two lunar basins and would be insufficient to explain ancient impact spherule beds. It suggests instead that debris from a massive impact was the source, noting that this would better match the size distribution of impact craters. A second work concurs, finding that the asteroid belt was probably not the source of the late heavy bombardment. Noting the lack of direct evidence of cometary impactors, it proposes that leftover planetesimals were the source of most impacts and that Nice model may have occurred early. The number of recent large impacts by asteroids predicted by this work were also lower than have been identified.

Terrestrial planets

A giant-planet migration in which Jupiter and Saturn quickly cross from a 2.1 to a 2.3 period ratio can leave the terrestrial planets with orbits similar to their current orbits. The current angular momentum deficit (AMD) of the terrestrial planets, a measure of their differences from circular coplanar orbits, has a reasonable chance (>20%) of being reproduced in a selected jumping-Jupiter model if the AMD was initially between 10% and 70% of the current value and Mars began with a more eccentric and inclined orbit than the other planets.

This selected jumping-Jupiter model may not be typical. When a large number of simulations starting with five giant planets in a resonance chain and Jupiter and Saturn in a 3:2 resonance are used, 85% result in the loss of a terrestrial planet, less than 5% reproduce the current AMD, and only 1% reproduce both the AMD and the giant planet orbits. In addition to the secular-resonance crossings, the jumps in Jupiter's eccentricity when it encounters an ice giant can also excite the orbits of the terrestrial planets. This has led some to propose that the Nice model migration occurred before the formation of the terrestrial planets and that the LHB had another cause. However, the advantage of an early migration is significantly reduced by the requirement that the Jupiter–Saturn period ratio jump to beyond 2.3 to reproduce the current asteroid belt.

The jumping-Jupiter model can reproduce the eccentricity and inclination of Mercury's orbit. Mercury's eccentricity is excited when it crosses a secular resonance with Jupiter. When relativistic effects are included, Mercury's precession rate is faster, which reduces the impact of this resonance crossing, and results in a smaller eccentricity similar to its current value. Mercury's inclination may be the result of it or Venus crossing a secular resonance with Uranus.

Asteroid belt

The rapid traverse of resonances through the asteroid belt leaves its population and the overall distribution of its orbital elements largely preserved. The asteroid belt's depletion, the mixing of its taxonomical classes, and the excitation of its orbits, yielding a distribution of inclinations peaked near 10° and eccentricities peaked near 0.1, therefore must have occurred earlier. These may be the product of Jupiter's Grand Tack, provided that a few hundred million years elapsed between it and the Nice model instability for interactions with the terrestrial planets to remove an excess of higher eccentricity asteroids. Gravitational stirring by planetary embryos embedded in the asteroid belt could also produce its depletion, mixing, and excitation. However, most if not all of the embryos must have been lost before the instability. An initially small mass asteroid belt could have its inclinations and eccentricities excited by secular resonances that hopped across the asteroid belt if Jupiter's and Saturn's orbits became chaotic while in resonance.

The sweeping of resonances and the penetration of the ice giant into the asteroid belt results in the dispersal of asteroid collisional families formed during or before the Late Heavy Bombardment. A collisional family's inclinations and eccentricities are dispersed due to the sweeping secular resonances, including those inside mean motion resonances, with the eccentricities being most affected. Perturbations by close encounters with the ice giant result in the spreading of a family's semi-major axes. Most collisional families would thus become unidentifiable by techniques such as the hierarchical clustering method, and V-type asteroids originating from impacts on Vesta could be scattered to the middle and outer asteroid belt. However, if the ice giant spent a short time crossing the asteroid belt, some collisional families may remain recognizable by identifying the V-shaped patterns in plots of semi-major axes vs absolute magnitude produced by the Yarkovsky effect. The survival of the Hilda collisional family, a subset of the Hilda group thought to have formed during the LHB because of the current low collision rate, may be due to its creation after Hilda's jump-capture in the 3:2 resonance as the ice giant was ejected. The stirring of semi-major axes by ice giant the may also remove fossil Kirkwood gaps formed before the instability.

Planetesimals from the outer disc are embedded in all parts of the asteroid belt, remaining as P- and D-type asteroids. While Jupiter's resonances sweep across the asteroid belt outer disk planetesimals are captured by its inner resonances, evolve to lower eccentricities via secular resonances with in these resonances, and are released onto stable orbits as Jupiter's resonances move on. Others planetesimals are implanted in the asteroid belt during encounters with the ice giant, either directly leaving them with aphelia higher than that of the ice giant's perihelia, or by removing them from a resonance. Jumps in Jupiter's semi-major axis during its encounters with the ice giant shift the locations of its resonances, releasing some objects and capturing others. Many of those remaining after its final jump, along with others captured by the sweeping resonances as Jupiter migrates to its current location, survive as parts of the resonant populations such as the Hildas, Thule, and those in the 2:1 resonance. Objects originating in the asteroid belt can also be captured in the 2:1 resonance, along with a few among the Hilda population. The excursions the ice giant makes into the asteroid belt allows the icy planetesimals to be implanted farther into the asteroid belt, with a few reaching the inner asteroid belt with semi-major axis less than 2.5 AU. Some objects later drift into unstable resonances due to diffusion or the Yarkovsky effect and enter Earth-crossing orbits, with the Tagish Lake meteorite representing a possible fragment of an object that originated in the outer planetesimal disk. Numerical simulations of this process can roughly reproduce the distribution of P- and D-type asteroids and the size of the largest bodies, with differences such as an excess of objects smaller than 10 km being attributed to losses from collisions or the Yarkovsky effect, and the specific evolution of the planets in the model.

Jupiter trojans

Most of the Jupiter trojans are jump-captured shortly after a gravitational encounters between Jupiter and an ice giant. During these encounters Jupiter's semi-major axis can jump by as much as 0.2 AU, displacing the L4 and L5 points radially, and releasing many existing Jupiter trojans. New Jupiter trojans are captured from the population of planetesimals with semi-major axes similar to Jupiter's new semi-major axis. The captured trojans have a wide range of inclinations and eccentricities, the result of their being scattered by the giant planets as they migrated from their original location in the outer disk. Some additional trojans are captured, and others lost, during weak-resonance crossings as the co-orbital regions becomes temporarily chaotic. Following its final encounters with Jupiter the ice giant may pass through one of Jupiter's trojan swarms, scattering many, and reducing its population. In simulations, the orbital distribution of Jupiter trojans captured and the asymmetry between the L4 and L5 populations is similar to that of the current Solar System and is largely independent of Jupiter's encounter history. The capture efficiency is sufficient for the current population to be captured from a planetesimal disk with a mass that reproduces other aspects of the outer Solar System.

Irregular satellites

Jupiter captures a population of irregular satellites and the relative size of Saturn's population is increased. During gravitational encounters between planets, the hyperbolic orbits of unbound planetesimals around one giant planet are perturbed by the presence of the other. If the geometry and velocities are right, these three-body interactions leave the planetesimal in a bound orbit when planets separate. Although this process is reversible, loosely bound satellites including possible primordial satellites can also escape during these encounters, tightly bound satellites remain and the number of irregular satellites increases over a series of encounters. Following the encounters, the satellites with inclinations between 60° and 130° are lost due the Kozai resonance and the more distant prograde satellites are lost to the evection resonance. Collisions among the satellites result in the formation of families, in a significant loss of mass, and in a shift of their size distribution. The populations and orbits of Jupiter's irregular satellites captured in simulations are largely consistent with observations. Himalia, which has a spectra similar to asteroids in the middle of the asteroid belt, is somewhat larger than the largest captured in simulations. If it was a primordial object its odds of surviving the series of gravitational encounters range from 0.01 - 0.3, with the odds falling as the number increases. Saturn has more frequent encounters with the ice giant in the jumping-Jupiter scenario, and Uranus and Neptune have a reduce number of encounters if that was a fifth giant planet. This increases the size of Saturn's population relative to Uranus and Neptune when compared to the original Nice model, producing a closer match with observations.

Regular satellites

The orbits of Jupiter's regular satellites can remain dynamically cold despite encounters between the giant planets. Gravitational encounters between planets perturb the orbits of their satellites, exciting inclinations and eccentricities, and altering semi-major axes. If these encounter would lead to results inconsistent with the observations, for example, collisions between or the ejections of satellites or the disruption of the Laplace resonance of Jupiter's moons Io, Europa and Ganymede, this could provide evidence against jumping-Jupiter models. In simulations collisions between or the ejection of satellites was found to be unlikely, requiring an ice giant to approach within 0.02 AU of Jupiter. More distant encounters that disrupted the Laplace resonance were more common, though tidal interactions often lead to their recapture. A sensitive test of jumping-Jupiter models is the inclination of Callisto's orbit, which isn't damped by tidal interactions. Callisto's inclination remained small in six out of ten 5-planet models tested in one study (including some where Jupiter acquired irregular satellites consistent with observations), and another found the likelihood of Jupiter ejecting a fifth giant planet while leaving Callisto's orbit dynamically cold at 42%. Callisto is also unlikely to have been part of the Laplace resonance, because encounters that raise it to its current orbit leave it with an excessive inclination.

The encounters between planets also perturb the orbits of the moons of the other outer planets. Saturn's moon Iapetus can be excited to its current inclination the ice giant's closest approach was away from Saturn's equator. If Saturn acquired its tilt before the encounters Iapetus's inclination could also be excited due to multiple changes of its semi-major axis because the inclination of Saturn's Laplace plane would vary with the distance from Saturn. In simulations Iapetus was excited to its current inclination in five of ten of the jumping-Jupiter models tested, though three left it with excessive eccentricity. The low inclination of Uranus's moon Oberon, 0.1°, was preserved in nine out of ten. The preservation of Oberon's inclination favors the 5-planet models, with only a few encounters between Uranus and an ice giant, over 4-planet models in which Uranus encounters Jupiter and Saturn. The encounters between planets may have also be responsible for the absence of regular satellites of Uranus beyond the orbit of Oberon.

The loss of ices from the inner satellites is reduced. Numerous impacts of planetesimals onto the satellites of the outer planets occur during the Late Heavy Bombardment. In the bombardment predicted by the original Nice model, these impacts generate enough heat to vaporize the ices of Mimas, Enceladus and Miranda. The smaller mass planetesimal belt in the five planet models reduces this bombardment. Furthermore, the gravitational stirring by Pluto-massed objects in the Nice 2 model excites the inclinations and eccentricities of planetesimals. This increases their velocities relative to the giant planets, decreasing the effectiveness of gravitational focusing, thereby reducing the fraction of planetesimals impacting the inner satellites. Combined these reduce the bombardment by an order of magnitude. Estimates of the impacts on Iapetus are also less than 20% of that of the original Nice model.

Some of the impacts are catastrophic, resulting in the disruption of the inner satellites. In the bombardment of the original Nice model this may result in the disruption of several of the satellites of Saturn and Uranus. An order of magnitude reduction in the bombardment avoids the destruction of Dione and Ariel; but Miranda, Mimas, Enceladus, and perhaps Tethys would still be disrupted. These may be second generation satellites formed from the re-accretion of disrupted satellites. In this case Mimas would not be expected to be differentiated and the low density of Tethys may be due to it forming primarily from the mantle of a disrupted progenitor. Alternatively they may have accreted later from a massive Saturnian ring, or even as recently as 100 Myr ago after the last generation of moons were destroyed in an orbital instability.

Giant planet tilts

Jupiter's and Saturn's tilts can be produced by spin-orbit resonances. A spin-orbit resonance occurs when the precession frequency of a planet's spin-axis matches the precession frequency of another planet's ascending node. These frequencies vary during the planetary migration with the semi-major axes of the planets and the mass of the planetesimal disk. Jupiter's small tilt may be due to a quick crossing of a spin-orbit resonance with Neptune while Neptune's inclination was small, for example, during Neptune's initial migration before planetary encounters began. Alternatively, if that crossing occurred when Jupiter's semi-major axis jumped, it may be due to its current proximity to spin-orbit resonance with Uranus. Saturn's large tilt can be acquired if it is captured in a spin-orbit resonance with Neptune as Neptune slowly approached its current orbit at the end of the migration. The final tilts of Jupiter and Saturn are very sensitive to the final positions of the planets: Jupiter's tilt would be much larger if Uranus migrated beyond its current orbit, Saturn's would be much smaller if Neptune's migration ended earlier or if the resonance crossing was more rapid. Even in simulations where the final position of the giant planets are similar to the current Solar System, Jupiter's and Saturn's tilt are reproduced less than 10% of the time.

Fifth giant planet

The early Solar System may have begun with five giant planets. In numerical simulations of the jumping-Jupiter scenario the ice giant is often ejected following its gravitational encounters with Jupiter and Saturn, leaving planetary systems that begin with four giant planets with only three. Although beginning with a higher-mass planetesimal disk was found to stabilize four-planet systems, the massive disk either resulted in excess migration of Jupiter and Saturn after the encounters between an ice giant and Jupiter or prevented these encounters by damping eccentricities. This problem led David Nesvorný to investigate planetary systems beginning with five giant planets. After conducting thousands of simulations he reported that simulations beginning with five giant planets were 10 times as likely to reproduce the current orbits of the outer planets. A follow-up study by David Nesvorny and Alessandro Morbidelli sought initial resonant configurations that would reproduce the semi-major axis of the four outer planets, Jupiter's eccentricity, and a jump from <2.1 to >2.3 in Jupiter's and Saturn's period ratio. While less than 1% of the best four-planet models met these criteria roughly 5% of the best five-planet models were judged successful, with Jupiter's eccentricity being the most difficult to reproduce. A separate study by Konstantin Batygin and Michael Brown found similar probabilities (4% vs 3%) of reproducing the current outer Solar System beginning with four or five giant planets using the best initial conditions. Their simulations differed in that the planetesimal disk was placed close to the outer planet resulting in a period of migration before planetary encounters began. Criteria included reproducing the oscillations of Jupiter's and Saturn's eccentricities, a period when Neptune's eccentricity exceeded 0.2 during which hot classical Kuiper belt objects were captured, and the retention of a primordial cold classical Kuiper belt, but not the jump in Jupiter's and Saturn's period ratio. Their results also indicate that if Neptune's eccentricity exceeded 0.2, preserving a cold classical belt may require the ice giant to be ejected in as little as 10,000 years.

Neptune's migration into the planetesimal disk before planetary encounters begin allows allows Jupiter to retain a significant eccentricity and limits migration after the ejection of the fifth ice giant. Jupiter's eccentricity is excited by resonance crossings and gravitational encounters with the ice giant and is damped due to secular friction with the planetesimal disk. Secular friction occurs when the orbit of a planet suddenly changes and results in the excitation of the planetesimals' orbits and the reduction of the planet's eccentricity and inclination as the system relaxes. If gravitational encounters begin shortly after the planets leave their multi-resonant configuration, this leaves Jupiter with a small eccentricity. However, if Neptune first migrates outward disrupting the planetesimal disk, its mass is reduced and the eccentricities and inclinations of the planetesimals are excited. When planetary encounters are later triggered by a resonance crossing this lessens the impact of secular friction allowing Jupiter's eccentricity to be maintained. The smaller mass of the disk also reduces the divergent migration of Jupiter and Saturn following the ejection of the fifth planet. This can allow Jupiter's and Saturn's period ratio to jump beyond 2.3 during the planetary encounters without exceeding the current value once the planetesimal disk is removed. Although this evolution of the outer planet's orbits can reproduce the current Solar System, it is not the typical result in simulations that begin with a significant distance between the outer planet and the planetesimal disk as in the Nice 2 model. An extended migration of Neptune into the planetesimal disk before planetary encounters begin can occur if the disk's inner edge was within 2 AU of Neptune's orbit. This migration begins soon after the protoplanetary disk dissipates, resulting in an early instability, and is most likely if the giant planets began in a 3:2, 3:2, 2:1, 3:2 resonance chain.

A late instability can occur if Neptune first underwent a slow dust-driven migration towards a more distant planetesimal disk. For a five planet system to remain stable for 400 million years the inner edge of the planetesimal disk must be several AU beyond Neptune's initial orbit. Collisions between planetesimals in this disk creates debris that is ground down to dust in a collisional cascade. The dust drifts inward due to Poynting–Robertson drag, eventually reaching the orbits of the giant planets. Gravitational interactions with the dust causes the giant planets to escape from their resonance chain roughly 10 million years after the dissipation of the gas disk. The gravitational interactions then result in a slow dust-driven migration of the planets until Neptune approaches the inner edge of the disk. A more rapid planetesimal-driven migration of Neptune into the disk then ensues until the orbits of the planets are destabilized following a resonance crossing. The dust driven migration requires 7 - 22 Earth-masses of dust, depending on the initial distance between Neptune's orbit and the inner edge of the dust disk. The rate of the dust-driven migration slows with time as the amount of dust the planets encounters declines. As a result the timing of the instability is sensitive to the factors that control the rate of dust generation such as the size distribution and the strength of the planetesimals.

Kuiper belt

A slow migration of Neptune covering several AU results in a Kuiper belt with a broad inclination distribution. As Neptune migrates outward it scatters many objects from the planetesimal disk onto orbits with larger semi-major axes. Some of these planetesimals are then captured in mean-motion resonances with Neptune. While in a mean-motion resonance, their orbits can evolve via processes such as the Kozai mechanism, reducing their eccentricities and increasing their inclinations; or via apsidal and nodal resonances, which alter eccentricities and inclinations respectively. Objects that reach low-eccentricity high-perihelion orbits can escape from the mean-motion resonance and are left behind in stable orbits as Neptune's migration continues. The inclination distribution of the hot classical Kuiper belt objects is best reproduced in numerical simulations where Neptune migrated smoothly from 24 AU to 28 AU with an exponential timescale of 10 million years before jumping outward when it encounters with a fifth giant planet and with a 30 million years exponential timescale thereafter. The slow pace and extended distance of this migration provides sufficient time for inclinations to be excited before the resonances reach the region of Kuiper belt where the hot classical objects are captured and later deposited. The objects that remain in the mean-motion resonances at the end of Neptune's migration form the resonant populations such as the plutinos. The slow migration allows these objects to reach large inclinations before capture and to evolve to lower eccentricities without escaping from resonance. Few low inclination objects resembling the cold classical objects remain among the plutinos at the end of the Neptune's migration. The outward jump in Neptune's semi-major axes releases the low-inclination low-eccentricity objects captured as Neptune's 3:2 resonance initially swept outward. Afterwards, their captures are largely prevented due to the excitation of inclinations and eccentricities as secular resonances slowly sweep ahead of it. The number of planetesimals with initial semi-major axes beyond 30 AU must have been small to avoid an excess of objects in Neptune's 5:4 and 4:3 resonances. Additional hot classical Kuiper belt objects can be captured due to secular forcing if Neptune reaches a significant eccentricity, e > 0.12, following its encounter with the fifth giant planet.

Encounters between Neptune and Pluto-massed objects reduce the fraction of Kuiper belt objects in resonances. Velocity changes during the gravitational encounters with planetesimals that drive Neptune's migration cause small jumps in its semi-major axis, yielding a migration that is grainy instead of smooth. The shifting locations of the resonances produced by this rough migration increases the libration amplitudes of resonant objects, causing many to become unstable and escape from resonances. The observed ratio of hot classical objects to plutinos is best reproduced in simulations that include 1000–4000 Pluto-massed objects (i.e. large dwarf planets) or about 1000 bodies twice as massive as Pluto, making up 10–40% of the 20-Earth-mass planetesimal disk, with roughly 0.1% of this initial disk remaining in various parts of the Kuiper belt. The grainy migration also reduces the number of plutinos relative to objects in the 2:1 and 5:2 resonances with Neptune, and results in a population of plutinos with a narrower distribution of libration amplitudes. A large number of Pluto-massed objects requires the Kuiper belt's size distribution to deviate to a shallower slope at large diameters. Although for small diameters a knee, or a divot, was identified below a diameter of ~140 km, there is no evidence for a second deviation between this and ~1000 km.

The kernel of the cold classical Kuiper belt objects is left behind when Neptune encounters the fifth giant planet. The kernel is a concentration of Kuiper belt objects with small eccentricities and inclinations, and with semi-major axes of 44–44.5 AU identified by the Canada–France Ecliptic Plane Survey. As Neptune migrates outward low-inclination low-eccentricity objects are captured by its 2:1 mean-motion resonance. These objects are carried outward in this resonance until Neptune reaches 28 AU. At this time Neptune encounters the fifth ice giant, which has been scattered outward by Jupiter. The gravitational encounter causes Neptune's semi-major axis to jump outward. The objects that were in the 2:1 resonance, however, remain in their previous orbits and are left behind as Neptune's migration continues. To preserve the low eccentricities and inclinations of the cold classical belt objects the eccentricity and inclination of Neptune resulting from the jump must have been small, e < 0.12 and i < 6°. This constraint may be relaxed somewhat if Neptune's precession is rapid due to strong interactions with Uranus or a high surface density disk. If Neptune's rapid precession rate drops temporarily, a 'wedge' of missing low eccentricity objects can form beyond 44 AU. The appearance of this wedge can also be reproduced if the size of objects initially beyond 45 AU declined with distance. A slow sweeping of resonances, with an exponential timescale of 100 million years, while Neptune has a modest eccentricity can remove the higher-eccentricity low-inclination objects, truncating the eccentricity distribution of the cold classical belt objects and leaving a step near the current position of Neptune's 7:4 resonance.

Scattered Disk

In the scattered disk, a slow and grainy migration of Neptune leaves detached objects with perihelia greater than 40 AU clustered near its resonances. Planetesimals scattered outward by Neptune are captured in resonances, evolve onto lower-eccentricity higher-inclination orbits, and are released onto stable higher perihelion orbits. Beyond 50 AU this process requires a slower migration of Neptune for the perihelia to be raised above 40 AU. As a result, in the scattered disk fossilized high-perihelion objects are left behind only during the latter parts of Neptune's migration, yielding short trails (or fingers) on a plot of eccentricity vs. semi-major axis, near but just inside the current locations of Neptune's resonances. The extent of these trails is dependent on the timescale of Neptune's migration and extends farther inward if the timescale is longer. The release of these objects from resonance is aided by a grainy migration of Neptune which may be necessary for an object like 2004 XR190 to have escaped from Neptune's 8:3 resonance.