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 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]

Updated initial conditions[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 addition of the gravitational interactions between planetesimals to the models revealed another mechanism for triggering a late instability in the outer Solar System. During numerical simulations which included these interactions a transfer of energy between the planetesimals and the giant planets was observed.[15] 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.[15] Because the planets are locked in resonance the inward migration also resulted 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 during this migration. Eventually, the breaking of the quadruple resonance of the outer planets occurs 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. 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.[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]

The jumping-Jupiter scenario yields a much smaller flux of impactors from the 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.[2] For comparison, 90% of the asteroids were removed during planetary migration in the original Nice model.[20] 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.[2] This conclusion, however, conflicts with evidence indicating that the impactors that created the lunar basins were not comets.[21][22] A recent paper that 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.[23] 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.[23]

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, 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.[24] 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.[25] 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.[26] A few asteroids from the asteroid belt may be captured as Hildas, but most originate from the outer Solar System.[18]

Jupiter trojans[edit]

In the jumping-Jupiter scenario, most of the Jupiter trojans are captured shortly after a gravitational encounter between Jupiter and an ice giant via a process called jump-capture. 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 any existing Jupiter trojans. New Jupiter trojans are captured from the population of planetesimals with semi-major axes matching Jupiter's new semi-major axis.[3] Following its final encounter with Jupiter the ice giant may pass through one of Jupiter's trojan swarms, scattering the captured bodies and reducing its population, potentially explaining the asymmetry of the L4 and L5 groups.[3] Later, some of the trojans are lost and others captured during weak-resonance crossings as the co-orbital region becomes temporarily chaotic.[3][27] In numerical simulations the orbital distribution of Jupiter trojans captured was similar to that of the current Solar System and independent of the particular history of the jumping-Jupiter scenario. The capture efficiency was such that the current population could be reproduced starting with a planetesimal belt consistent with models reproducing other aspects of the outer Solar System.[3]

Galilean satellites[edit]

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. Although 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.[28] The Laplace resonance of the inner satellites was disrupted in some simulations but was often restored by tidal interactions.[28] 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.[28]

Irregular satellites[edit]

Jupiter and Saturn undergo many gravitational encounters with an ice giant in the jumping-Jupiter scenario, allowing Jupiter to capture a population of irregular satellites and increasing the relative size of Saturn's population. During these encounters, the hyperbolic orbits of planetesimals around a gas giant are perturbed by the presence of the ice giant. If the geometry and velocities are right, these three-body interactions leave the planetesimal in a bound orbit when the ice giant recedes.[29] Although loosely bound satellites can also be ejected, tightly bound satellites remain, and over a series of encounters the number of irregular satellites tends to increase.[30] The population and orbits of the irregular satellites captured by Jupiter in the simulations are consistent with its current population.[30] The more-frequent encounters between Saturn and the ice giant increase the size of its population relative to Uranus and Neptune when compared to the original Nice model, producing a closer match with observations.[30][31]

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.[32]

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.[33] The simulations with the best results began with a significant migration of Neptune into the planetesimal disk.[33] 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.[33]

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.[33] 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.[34] 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.[35] 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.[34]

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.[36] 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.[37]

See also[edit]


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