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) encounters first Saturn and then 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 allows these resonances to quickly cross the inner Solar System without altering orbits excessively.[1] The jumping-Jupiter scenario also results in a number of other differences with the original Nice model. The fraction of lunar impactors from the asteroid belt during the Late Heavy Bombardment is significantly reduced,[2] most of the Jupiter trojans are captured via an alternative mechanism,[3] and Jupiter acquires its population of irregular satellites via the same process as the other planets.[2] The frequent ejection of an ice giant during simulations of the jumping-Jupiter scenario has led some to propose an additional giant planet in the early Solar System.[4][5]


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 the slow divergent migration of the giant planets. This planetesimal-driven migration of the giant planets continues until Jupiter and Saturn cross their mutual 2:1 resonance. The resonance crossing excites the eccentricity of Jupiter and Saturn. The increased eccentricity creates perturbations on Uranus and Neptune, increasing their eccentricities until the system becomes chaotic and orbits begin to intersect. Gravitational encounters between the planets 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. Dynamic 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.[6]

Resonant planetary orbits[edit]

Later versions of the Nice model begin with the giant planets in a series of resonances. This change reflects hydrodynamic models of the early Solar System. In these models, interactions between the giant planets and the gas disk results in the giant planets migrating toward the central star, in some cases becoming hot Jupiters.[7] 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.[8] The Grand Tack hypothesis,[9] with Jupiter's migration being reversed at 1.5 AU following the capture of Saturn in a 3:2 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,[10][11] and the extent of the outward migration (if any) are dependent on the physical properties of the gas disk.[11][12] The capture of Uranus and Neptune into further resonances during this outward migration results in a quadruply resonant system,[13] with several stable combinations having been identified.[14] Following the dissipation of the gas disk, the quadruple resonance is eventually broken due to interactions with planetesimals from the outer disk.[15] Numerical simulations from this point resembling the original Nice model with an instability beginning shortly after the quadruple resonance is broken[15] or following a period of planetesimal-driven migration when planets cross a different resonance.[14] However, they differ in that there is no slow approach to the 2:1 resonance as Jupiter and Saturn begin in this resonance[11][12] or cross it rapidly during the instability.[13] There are still some open questions about the damping of the orbital eccentricity (via interactions with planetesimals) of Jupiter and Saturn after the dispersal of disk's gas. In fact, capture of these two planets into the 2:1 mean-motion resonance is far more likely than capture into the 3:2 resonance and evolution in the 2:1 resonance can lead to substantial eccentricity growth during the disk-gas phase.[12]

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.[15] 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.[15] 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.[15] In combination with the updated initial conditions, this alternative mechanism for triggering a late instability has been called the Nice 2 model.[15]

Solar System constraints[edit]

Ramon Brasser, Alessandro Morbidelli, Rodney Gomes, Kleomenis Tsiganis, and Harold Levison published a series of three papers[1][2][16] 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.[16] 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.[16] 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.[16]

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][17] 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 ν6 secular resonance removes low-inclination asteroids and the ν16 secular resonance excites asteroid inclinations, 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 that includes a jumping-Jupiter scenario, 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 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.[3] 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.[18] 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.[19]

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 main 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. Other entered quasi-stable higher inclination orbits, later producing an extended tail of impacts, with a small remnant surviving as the Hunagrias. 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 main asteroid belt.[20] The pre-Nectarian basins, part of the LHB in the original Nice model,[21] are thought to be due to the impacts of leftover planetesimals from the inner Solar System.

Asteroid belt[edit]

The distribution of the orbital elements and the population of the asteroid belt is largely preserved during the planetary migration in the jumping-Jupiter scenario.[2][18] This places a number of constraints on models of the early Solar System. The excitation and depletion of the asteroid belt and the partial mixing of its taxonomical classes must have occurred during the planetary formation era.[18] If this was the result of gravitational encounters with planetary embryos,[22] bodies larger than Ceres, few if any could have remained in the asteroid belt at the end of that era.[2] Furthermore, because fossil Kirkwood gaps formed while Jupiter was on its initial orbit are not observed, Jupiter must have ended that era on a low-eccentricity orbit.[2] Simulations conducted by Fernando Roig and David Nesvorny indicated that the inclination distribution at the end of the planetary formation era resembled that of the Grand Tack model, but that the eccentricity distribution was less excited. The difference may indicate that higher-eccentricity asteroids left by the Grand Tack were depleted over time by the terrestrial planets, which were not included in their simulation.[18] The rapid migration in the jumping-Jupiter scenario also favors the survival of asteroid collisional families formed during the Late Heavy Bombardment.[23] One example of these is the Hilda collisional family, a subset of the Hilda group, which some researches have suggested was formed at that time because of the current low collision rate.[24] Asteroids in mean-motion resonance with Jupiter, such as those in the 2:1 resonance, can be jump-captured as the semi-major axis of the resonance jumps during Jupiter's encounters.[25] A few asteroids from the asteroid belt may be captured as Hildas, but most originate from the outer Solar System.[18]

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.[3] 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.[3][26] Following its final encounters with Jupiter the ice giant may pass through one of Jupiter's trojan swarms, scattering many, and reducing its population.[3] 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.[3]

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.[27] 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.[27] 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.[28]

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 other. If the geometry and velocities are right, these three-body interactions leave the planetesimal in a bound orbit when planets separate.[29] Although loosely bound satellites can be ejected in subsequent encounters, tightly bound satellites remain, and over a series of encounters the number of irregular satellites tends to increase.[30] After adjusting for losses from collisions, the population and orbits of the irregular satellites captured by Jupiter in simulations are largely consistent with its current population. However, the largest satellite expected to be captured was smaller than Himalia. Himalia also has a relatively tightly bound orbit and an spectral type similar to asteroids from the middle of the asteroid belt,[31] which may indicate that it is a survivor from a primordial population.[30] In simulations the more frequent encounters between Saturn and the ice giant, and the reduced number of encounters of Uranus and Neptune if that is a fifth ice giant, 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.[30][32]

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.[4][5] 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.[4] 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.[33]

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.[34] The simulations with the best results began with a significant migration of Neptune into the planetesimal disk.[34] 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.[34]

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.[5] This is in part due to using different criteria to judge success, such as retaining a primordial cold classical Kuiper belt.[34] Their results suggest that preserving a cold classical belt would require the ice giant to be ejected in 10,000 years.[5]

Kuiper belt[edit]

The slow outward migration of Neptune into the planetesimal disk seen in the simulations that best reproduce Jupiter's eccentricity also reproduces the large range of inclinations of objects in the Kuiper belt. Numerical simulations conducted by David Nesvorný using a variety of starting points and timescales revealed that the inclination distribution of the plutinos and of the hot classical Kuiper belt objects were best produced when Neptune migrated smoothly from 24 AU to 30 AU over a timescale of 30 million years.[35] This slow migration provides time for encounters with Neptune to excite the eccentricities and inclinations of the planetesimals. It is also needed for a fraction of these objects to be captured onto stable orbits with sizable inclinations in a three-step process first described by Rodney Gomes.[36] The objects are first scattered from the planetesimal disk onto orbits with larger semi-major axes. After some of these objects are captured in mean-motion resonances with Neptune, their inclinations and eccentricities evolve through processes such as the Kozai mechanism, reducing their eccentricities and increasing their eccentricities. At those lower eccentricities some objects then escape from the mean-motion resonance onto stable orbits while Neptune is migrating. The simulations conducted by Nesvorný ended with an excess of objects in mean-motion resonances when compared to observation. Nesvorný speculated that including the encounters between Neptune and a fifth giant planet, which would cause objects previously captured into the resonances to be released, would resolve this issue.[35]

An outward jump in the semi-major axis of Neptune caused by a gravitational encounter with another planet after Neptune migrated several AU may be responsible for the kernel of the cold classical Kuiper belt objects. The kernel is a concentration of Kuiper belt objects with small eccentricities and inclinations, and semi-major axes of 44–44.5 AU identified by the Canada-France Ecliptic Plane Survey.[37] In numerical simulations conducted by David Nesvorny planetesimals were captured by Neptune's 2:1 mean-motion resonance as Neptune migration out to 28 AU. These object then escaped from this resonance when Neptune's semi-major axis was made to jump, as it would if Neptune had a gravitational encounter with another ice giant, leaving a clump of objects with a semi-major axes near 44 AU. If the jump in Neptune's semi-major axis was outward these object remained in these orbits as the resonance moved away.[38]

See also[edit]


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