Jumping-Jupiter scenario

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The jumping-Jupiter scenario specifies an evolution of giant-planet migration described by the Nice model, in which an ice giant (Uranus, Neptune, or an additional Neptune-mass planet) is scattered inward by Saturn and outward by Jupiter, causing the step-wise separation of their orbits.[1] 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.[1] The sweeping of secular resonances through the inner Solar System during the migration excited the eccentricities of the terrestrial planets beyond current values[1] and left an asteroid belt with an excessive ratio of high- to low-inclination objects.[2] The step-wise separation 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,[1] although the terrestrial planets remain sensitive to its passage.[3][4] 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,[5] most of the Jupiter trojans are captured during Jupiter's encounters with the ice giant,[6] as are Jupiter's irregular satellites.[7] 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.[8] However, this remains an atypical result,[9] as is the preservation of the current orbits of the terrestrial planets.[4]


Original Nice model[edit]

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.[10]

Resonant planetary orbits[edit]

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.[11] 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.[12] The Grand Tack hypothesis,[13] 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,[14][15] 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.[15][16][17] The capture of Uranus and Neptune into further resonances during or following this outward migration results in a quadruply resonant system,[18] with several stable combinations having been identified.[19] Following the dissipation of the gas disk, the quadruple resonance is eventually broken due to interactions with planetesimals from the outer disk.[20] Evolution from this point resembles the original Nice model with an instability beginning either shortly after the quadruple resonance is broken[20] or after a delay during which planetesimal-driven migration drives the planets across a different resonance.[19] However, there is no slow approach to the 2:1 resonance as Jupiter and Saturn either begin in this resonance[15][17] or cross it rapidly during the instability.[18] 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,[17] that if preserved can leave fossil Kirkwood gaps in the asteroid belt which are not observed.[21]

Alternative instability trigger[edit]

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.[20] 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.[20] 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.[20] In combination with the updated initial conditions, this alternative mechanism for triggering a late instability has been called the Nice 2 model.[20]

Solar System constraints[edit]

Ramon Brasser, Alessandro Morbidelli, Rodney Gomes, Kleomenis Tsiganis, and Harold Levison published a series of three papers[1][2][22] 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.[22] 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.[22] 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.[22]

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, these eccentricities can reach levels that destabilize the inner Solar System, leading to collisions between planets or the ejection of Mars, during the slow approach of Jupiter and Saturn to their 2:1 resonance.[1][23] 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 are brief, hence not resulting in the excessive excitation of the orbits of Earth and Mars.[1] The authors proposed that the last two resonance crossings were avoided, also 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.[1]

A smooth planetesimal-driven migration of the giant planets does not result in an orbital distribution that resembles that of the current asteroid belt.[2] The ν16 secular resonance excites asteroid inclinations and the ν6 secular resonance removes low-inclination asteroids, resulting in a ratio of high- to low-inclination asteroids that is too large.[2] 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. 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.[2] The requirement of a jump beyond 2.3 is independent of the timing of the giant-planet migration and whether the eccentricity distribution was excited by the Grand Tack.[24][25]


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.[1] In the jumping-Jupiter scenario an ice giant is scattered inward by Saturn onto a Jupiter-crossing orbit and then scattered outward by Jupiter.[2] 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.[2] 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.[6] 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.[26] 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.[1] 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.[27]

Implications for the early Solar System[edit]

In addition to preserving low eccentricities of the terrestrial planets and maintaining the pre-migration orbital distribution of the asteroid belt the jumping-Jupiter scenario results in a number of other differences with the original Nice model. These include the source regions for lunar impactors during the Late Heavy Bombardment, constraints on the formation of the asteroid belt, the capture mechanisms for Jupiter's irregular satellites and trojans, and the possibility of additional giant planets in the early Solar System.

Late Heavy Bombardment[edit]

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.[2] 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 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.[5] The pre-Nectarian basins, part of the LHB in the original Nice model,[28] are thought to be due to the impacts of leftover planetesimals from the inner Solar System. The increase in the orbital eccentricities and inclinations of the destabilized objects raised impact velocities, resulting in a change the size distribution of lunar craters,[29] and in the production of impact melt in the asteroid belt.[30]

Terrestrial planets[edit]

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.[3]

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.[4] 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.[23] 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.[4] 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.[25]

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.[31]

Asteroid belt[edit]

The rapid traverse of resonances through the asteroid belt leaves its population and the distribution of its orbital elements largely preserved.[2] 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.[26] 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.[26][21] If instead they were the result of gravitational stirring by planetary embryos embedded in the asteroid belt,[32] few if any of these could have remained when the planetary migration began.[2] The dispersal of asteroid collisional families formed during or before the Late Heavy Bombardment by resonance sweeping is also limited.[33] Their apparent absence may instead be due to the stirring of semi-major axes while an ice giant was crossing the asteroid belt.[34] 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,[35] may be due to its creation after Hilda's jump-capture in the 3:2 resonance as the ice giant was ejected.[26]

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.[36] The ice giant's encounters with Jupiter and with planetesimals provide additional pathways for outer belt planetesimals to enter stable orbits in the asteroid belt. Jumps in Jupiter's semi-major axis shift the locations of its resonances releasing some objects and capturing others, with many of those remaining after its final jump surviving as parts of the resonant populations such as the Hildas, Thule, and those in the 2:1 resonance.[37] Objects originating in the asteroid belt can also be captured in the 2:1 resonance,[38] along with a few among the Hilda population.[26] Encounters with the ice giant can directly implant planetesimals in the asteroid belt with orbits having aphelia higher than that of the ice giant. Encounters or close approaches between planetesimals and the ice giant can also remove planetesimals from resonances, leaving some on stable orbits. While the combination of these processes deposits planetesimals primarily in the middle and outer asteroid belt, the excursions the ice giant makes into the asteroid belt allows them 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.[37]

Giant planet tilts[edit]

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.[39] 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.[40]

Jupiter trojans[edit]

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.[6] 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.[6][41] Following its final encounters with Jupiter the ice giant may pass through one of Jupiter's trojan swarms, scattering many, and reducing its population.[6] 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.[6]

Regular satellites[edit]

The encounters between planets dynamically perturb the orbits of their satellites, exciting inclinations and eccentricities, and altering semi-major axes. If close enough, an ice giant approaching within 0.02 AU of Jupiter, the encounters can disrupt systems of satellites, leading to collisions between or the ejections of satellites. The Laplace resonance of Jupiter's moons Io, Europa and Ganymede can be disrupted during encounters but is often restored by tidal interactions.[42] Callisto is unlikely to have been part of the Laplace resonance, because encounters that remove it from a resonance to its current orbit leave it with an excessive inclination.[42] The outer satellites are most affected by the encounters, allowing their inclinations, which are not damped by tidal interactions to be used as a test of individual jumping-Jupiter models. For Jupiter, six out of ten 5-planet models tested left Callisto with an inclination near its current level. Saturn's moon Iapetus was excited to its current inclination in five of ten, though three left it with excessive eccentricity. The low inclination of Uranus's moon Oberon, 0.1°, is 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.[43] A separate study estimated the likelihood of Jupiter ejecting a fifth giant planet while leaving Callisto a dynamically cold orbit at 42%.[44]

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.[45] 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.[46] Estimates of the impacts on Iapetus are also less than 20% of that of the original Nice model.[47]

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.[48] Alternatively they may have accreted later from a massive Saturnian ring,[49] or even as recently as 100 Myr ago after the last generation of moons were destroyed in an orbital instability.[50]

Irregular satellites[edit]

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.[51] Collisions among the satellites result in the formation of families, in a significant loss of mass, and in a shift of their size distribution.[52] The populations and orbits of Jupiter's irregular satellites captured in simulations are largely consistent with observations. The more frequent encounters between the ice giant and Saturn in the jumping-Jupiter scenario, and a reduced number of encounters with Uranus and Neptune if that is a fifth giant planet, 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.[7][53] Himalia, which has a relatively tight orbit and a spectral type similar to asteroids from the middle of the asteroid belt,[54] is somewhat larger than the largest captured in simulations (though less so as measured by Cassini), raising the possibility that it is a survivor from a primordial population.[7]

Fifth giant planet[edit]

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.[8][55] Although beginning with a higher-mass planetesimal disk was found to stabilize four-planet systems, these simulations end with Jupiter and Saturn too far apart.[8] 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 Solar System.[56]

The most difficult aspect of the current Solar System to reproduce in simulations has been Jupiter's eccentricity. A follow-up study by David Nesvorný and Alessandro Morbidelli reported that even for the best combination of initial conditions this constraint was met in only 7% of simulations.[9] The simulations with the best results began with a significant migration of Neptune into the planetesimal disk.[9] This disrupted the planetesimal disk and drove the divergent migration of Jupiter and Saturn until an instability was triggered. The inner ice giant then began its encounters with Jupiter and Saturn. With a smaller mass of planetesimals remaining less dampening of Jupiter's eccentricity and post-encounter migration of Jupiter and Saturn occurred. Although this evolution yields a good match with the current Solar System the authors noted that a wide variety of outcomes were produced by the jumping-Jupiter scenario and that this case should be considered neither the typical nor the expected result.[9]

A separate study by Konstantin Batygin and Michael Brown also found a low probability of reproducing the current Solar System. However, their study yielded similar probabilities for planetary systems beginning with four and five giant planets.[55] This is in part due to using different criteria to judge success, such as retaining a primordial cold classical Kuiper belt.[9] Their results suggest that preserving a cold classical belt would require the ice giant to be ejected in 10,000 years.[55]

Kuiper belt[edit]

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.[57][58] Those that remain in the mean-motion resonances form the resonant populations such as the plutinos. The inclination distribution of the hot classical Kuiper belt objects and of the plutinos 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.[59] 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. It also allows for those objects that remained in resonance to have reached large inclinations before capture and to evolve to lower eccentricities without escaping from resonance.[60] 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.[61]

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 of the positions of 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, closer to observations.[59] The large number of Pluto-massed objects would result in a significant reduction in the slope of the size distribution of KBO objects at large diameters. Although for small diameters a knee, or a divot, was identified below a diameter of ~140 km,[62][63] there is no evidence for a second deviation of the size distribution onto a shallower slope at larger diameters between ~140 km and ~1000 km.[62]

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.[64] 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.[65] 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°.[66] If Neptune's precession is rapid (due to strong interactions with the other planets or a high surface density disk)[61] this constraint may be relaxed somewhat, and if the precession rate drops rapidly, a 'wedge' of missing low eccentricity objects can form beyond 44 AU.[67] 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.[68]

Scattered Disk[edit]

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.[69][70]

See also[edit]


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