The jumping-Jupiter scenario specifies an evolution of the giant planet migration described by the Nice model in which an ice giant planet (Uranus, Neptune, or an additional Neptune-mass planet) encounters first Saturn and then Jupiter causing the step-wise separation of their orbits. The jumping-Jupiter scenario was proposed by Ramon Brasser, Alessandro Morbidelli, Rodney Gomes, Kleomenis Tsiganis, and Harold Levison after their studies revealed that the smooth divergent migration of Jupiter and Saturn resulted in an inner Solar System significantly different from the current Solar System. The sweeping of secular resonances through the inner Solar System during the migration excited the eccentricities of the terrestrial planets beyond current values and left an asteroid belt with an excessive ratio of high to low inclination objects. 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. The jumping-Jupiter scenario also results in a number of other differences with the original Nice model. The fraction of lunar impactors from main asteroid belt during the Late Heavy Bombardment is significantly reduced, most of the Jupiter Trojans are captured via an alternative mechanism, and Jupiter acquires its population of irregular satellites via the same process as the other planets. 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.
- 1 Background
- 2 Jumping-Jupiter Scenario
- 3 References
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 the slow divergent migration of the giant planets. The planetesimal driven migration of the giant planets progresses 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.
Updated Initial conditions
In later versions of the Nice model the initial conditions were modified to be consistent with models of the early Solar System when the giant planets formed in a gas disk. Numerical simulations of multiple giant planets orbiting in a gas disk revealed that the planets would migrate at differing rates resulting in their capture into resonances. Investigations by Pierens and Nelson focusing on Jupiter and Saturn demonstrated that they can be captured in their mutual 3:2 resonance. However, capture in this resonance does require special conditions. Once in the 3:2 resonance, Jupiter’s and Saturn’s inward migration is halted and outward migration may begin. The range of outward migration of the two planets depends on several physical properties of the solar nebula. The addition of more planets to the model results in their capture into further resonances. The end product is a system in quadruple resonance with each planet in resonance with its nearest neighbors. Several stable quadruple resonances have been identified. After the gas disk is lost the quadruple resonance may be broken due to interactions with planetesimals from an outer disk. Subsequent evolution resembles the original Nice model with gravitational encounters between planets beginning either shortly after the quadruple resonance is broken or after a period of planetesimal driven migration when Jupiter and Saturn cross their mutual 5:3 resonance. Both case differ from the original Nice model in that the instability begins with Jupiter and Saturn in closer proximity and that the 2:1 resonance crossing occurs during the rapid phase of divergent migration.
Alternative Instability Trigger
Including the gravitational interactions between the planetesimals revealed another mechanism for triggering the late instability of resonant giant planets. During numerical simulations which included the interactions between planetesimals a transfer of energy between the planetesimals and the giant planets was observed. This energy transfer led to the migration of the planets toward the Sun and occurred even when there were no encounters between planetesimals and the planets. Closer investigation indicated that the energy transfer was due to 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 inward migration also resulted in an increase in the eccentricity of the inner ice giant. Eventually crossing of secular resonances during this migration causes the resonance to be broken. Gravitational encounters begin shortly afterward due to the close proximity of the planets in the previously resonant configuration. Numerical simulations indicate that the timing of the instability caused by this mechanism is fairly independent of the distance between the outer planet and the planetesimal disk and typically occurs after several hundred million years. 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. Their research identified several constraints on the evolution of the outer Solar System. A number of these were found to be incompatible with the smooth planetesimal-driven migration of Jupiter after the 2:1 resonance crossing.
In the first paper the authors examined the secular architecture of the outer Solar System. Numerical simulations indicated that smooth migration of the outer planets would not result in their current eccentricities. Furthermore, while the Jupiter-Saturn 2:1 resonance crossing was shown to reproduce the mean eccentricities of Jupiter and Saturn it did not reproduce the oscillations of their eccentricities. The authors found that creating the secular architecture of the outer Solar System required a gravitational encounter between Saturn and one of the ice giants in addition to the resonance crossing. An alternative scenario involving encounters between an ice giant and both gas giants was also shown to be consistent with the current outer Solar System.
The second paper analyzed the dynamical evolution of the terrestrial planets. Numerical simulations conducted by the authors revealed that the eccentricities of the terrestrial planets were excited beyond their current values during the migration of the giant planets. The excitation of eccentricities was the result of the ν5 secular resonance sweeping through the inner Solar System. The authors determined that if Jupiter and Saturn crossed their mutual 2:1 resonance during the rapid phase of divergent migration some of the ν5 resonance crossings would be quick enough to avoid excessively altering the orbits of the terrestrial planets. Later versions of the Nice model, with Jupiter and Saturn beginning in the mutual 3:2 resonance, meet this constraint. However, the original Nice model, with a slow approach to the 2:1 resonance being necessary to match the timing of the Late Heavy Bombardment, does not. In numerical simulations this resulted in the eccentricity of Mars being excited to values sufficient to destabilize the inner Solar System. For the two other resonances the authors offered two alternatives. First, if particular initial conditions were met, the resonance crossings would dampen initially higher eccentricities. Second, the resonance crossings could be avoided 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 the latter alternative the jumping-Jupiter scenario.
The authors considered the orbital structure of the asteroid belt in the third paper. While a previous study had shown that the current asteroid belt was consistent with a giant planet migration having an exponential time scale of 0.5 million years, the authors found this rate to be unrealistic as previous numerical simulation of planetesimal-driven migration and the dynamical lifetimes of the Centaurs indicated that the time scale would be at least 5 My. Simulations of the asteroid belt during a giant planet migration with this minimum realistic time scale of 5 My yielded an orbital distribution which was not consistent with the current asteroid belt. The authors found that as they swept the belt the ν6 secular resonance removed low inclination asteroids and the ν16 secular resonance excited asteroid inclinations resulting in a ratio of high to low inclination asteroids which was too large. Numerical simulations using a jumping-Jupiter scenario, in contrast, did not significantly alter the inclination distribution, yielding an asteroid belt with a final orbital distribution similar to its initial distribution.
The jumping Jupiter scenario meets the constraint provided by the current Solar System by allowing ratio of Jupiter and Saturn’s periods to rapidly traverse the range 2.1 - 2.3. In the jumping-Jupiter scenario an ice giant planet 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. The net result is a rapid increase in the period ratio. In numerical simulations the process can be much more complex with the ice giant undergoing many encounters with Jupiter and Saturn on a time scale of 10,000-100,000 years. These gravitational encounters end when dynamic friction with the planetesimal disk raises the ice giant’s perihelion above Saturn’s orbit or when it 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. In this the authors noted that 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 that with a 35 Earth mass planetesimal belt it resulted in the ejection of the ice giant in all 14 cases. 
Implications for the Early Solar System
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
The jumping-Jupiter scenario yields a much smaller flux of impactors from the main asteroid belt during the Late Heavy Bombardment. Numerical simulations of the asteroid belt during a jumping-Jupiter scenario revealed that roughly 50% of the asteroids were removed. For comparison, 90% of the asteroids were removed during planetary migration in the original Nice model. The mass of asteroids impacting the inner planets is reduced by roughly an order of magnitude in the jumping-Jupiter scenario potentially leaving comets as the dominant source of the impactors. This conclusion, however, conflicts with evidence indicating that the lunar basin-forming impactors were not comets. A recent paper which offers asteroids from a primordial extension of the asteroid belt to Mars-crossing orbits as the primary source of the LHB of the Moon may resolve this issue. These E-belt asteroids were in stable orbits until the outer planets reached their current configuration at the end of the giant planet migration. Their orbits were then destabilized by the ν6 secular resonance driving them onto Earth-crossing orbits as part of the Late Heavy Bombardment.
The inclination distribution and population of the asteroid belt is mostly preserved during the planetary migration in the jumping-Jupiter scenario. This places a number of constraints on models of the early Solar System. The excitation and depletion of the asteroid belt must have occurred during the planetary formation era. Few, if any, bodies larger than Ceres (planetary embryos) could have remained in the asteroid belt at the end of that era. Furthermore, since 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. The rapid migration in the jumping-Jupiter scenario also favors the survival of asteroid collisional families formed during the Late Heavy Bombardment. 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.
Instead of being chaotically captured during resonance crossings as in the original Nice model most of the Jupiter Trojans are captured by an alternative mechanism called jump-capture in the jumping-Jupiter scenario. In the original Nice model the Trojans were captured shortly after Jupiter and Saturn crossed their mutual 2:1 resonance. At this time the divergent migration of Jupiter and Saturn caused the co-orbital region to transition from chaotic to stable locking the transient population of objects in that region onto long term orbits. The planetary encounters in the jumping-Jupiter scenario offer an alternative mechanism for capturing Jupiter Trojans. During the gravitational encounters between Jupiter and the ice giant Jupiter's semi-major axis can jump by as much as 0.2 AU. As a result the L4 and L5 points are displaced radially releasing any existing Trojans. New Jupiter Trojans are captured from the population of planetesimals with semi-major axes matching Jupiter’s new semi-major axis. This mechanism first described by David Nesvorný, David Vokrouhlický, and Alessandro Morbidelli, is referred to as jump-capture. Some additional Trojans are trapped via chaotic capture during the crossing of weak resonances near the end of planetary migration. Numerical simulations of a variety of jumping-Jupiter scenarios indicate that the orbital distribution of Trojans captured is independent of the particular history of the jumping-Jupiter scenario and is similar to that of the current Solar System. The size of the outer planetesimal belt required to reproduce the current population of Jupiter Trojans is also consistent with the mass necessary to produce the current Solar System orbits. The jumping-Jupiter scenario also offers a potential explanation for the L4/L5 asymmetry. After its final encounter with Jupiter the ice giant may pass through one of the Trojan swarms scattering the captured bodies and reducing its population.
The encounters between the ice giant and Jupiter dynamically perturb the orbits of the Galilean satellites. The perturbations excite the eccentricities and inclinations of the orbits and alter the semi-major axes potentially breaking the Laplace resonance of Io, Europa and Ganymede. These possibilities were investigated Rogerio Deienno, David Nesvorny, David Vokrouhlicky, and Tadashi Yokoyama using numerical simulations. While encounters beyond 0.05 AU had little effect those inside 0.02 AU were found to disrupt the orbits of the satellites, potentially leading to collisions between or the ejections of the satellites. The Laplace resonance of the inner satellites was disrupted in some simulations but was often restored by tidal interactions. The orbit of Callisto was the most affected by the encounters. Its inclination, which is not damped by tidal interactions, places the strongest constraints on the encounters limiting those between 0.02 AU and 0.03 AU to a few.
The jumping-Jupiter scenario enables Jupiter to capture irregular satellites from the planetesimal disk by three-body interactions during planetary encounters, the same process as the other giant planets. The capture of irregular satellites by Jupiter during a jumping-Jupiter scenario was examined by David Nesvorný, David Vokrouhlický and Rogerio Deienno using a selection of jumping-Jupiter models which successfully reproduced the current Solar System. In these numerical simulations Jupiter captured a population of irregular satellites consistent with its current population. A similar number of irregular satellites was captured by each giant planet in these simulations also yielding a good match with observations. This is in contrast to previous research using the original Nice model in which Jupiter captured few or no irregular satellites and Saturn captured significantly fewer than Uranus and Neptune. The number of irregular satellites captured was shown to be related to the number of encounters between planets, with more encounters a larger populations was produced. In the jumping-Jupiter models Jupiter and Saturn have numerous encounters with the ice giant, which was ejected in these simulations, and fewer encounters involving Uranus and Neptune occurred in comparison the original Nice model. The irregular satellites captured by Neptune were spread over a larger radius than in most runs of the original Nice model which may be due to the distance Neptune migrated before the encounters began.
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 beginning with four giant planets with only three. While beginning with a larger mass planetesimal disk was found to stabilize four planet systems these simulations end with Jupiter and Saturn too far apart. 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.
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. The simulations with the best results began with a significant migration of Neptune into the planetesimal disk. 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. While 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.
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. This is in part due to using different criteria to judge success such as retaining a primordial cold classical Kuiper belt. Their results suggest that preserving a cold classical belt would require the ice giant to be ejected in 10,000 years.
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