Five-planet Nice model

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The five-planet Nice model is a recent variation of the Nice model that begins with five giant planets, the current four plus an additional ice giant, in a chain of mean-motion resonances. After the resonance chain is broken, the five giant planets undergo a period of planetesimal-driven migration, followed by a gravitational instability similar to that in the original Nice model. During the instability the additional giant planet is scattered inward onto a Jupiter-crossing orbit and is ejected from the Solar System following an encounter with Jupiter. An early Solar System with five giant planets was proposed in 2011 after numerical models indicated that this is more likely to reproduce the current Solar System.[1]

Background[edit]

Current theories of planetary formation do not allow for the accretion of Uranus and Neptune in their present positions.[2] The protoplanetary disk was too diffuse and the time scales too long[3] for them to form via planetesimal accretion before the gas disk dissipated, and numerical models indicate that later accretion would be halted once Pluto-sized planetesimals formed.[4] Although more recent models including pebble accretion allow for faster growth the inward migration of the planets due to interactions with the gas disk leave them in closer orbits.[5]

It is now widely accepted that the Solar System was initially more compact and that the outer planets migrated outward to their current positions.[6] The planetesimal-driven migration of the outer planets was first described in 1984 by Fernandez and Ip.[7] This process is driven by the exchange of angular momentum between the planets and planetesimals originating from an outer disk.[8] Early dynamical models assumed that this migration was smooth. In addition to reproducing the current positions of the outer planets,[9] these models offered explanations for: the populations of resonant objects in the Kuiper belt,[10] the eccentricity of Pluto's orbit,[11] the inclinations of the hot classical Kuiper belt objects and the retention of a scattered disk,[12] and the low mass of Kuiper belt and the location of its outer edge near the 2:1 resonance with Neptune.[13] However, these models failed to reproduce the eccentricities of the outer planets, leaving them with very small eccentricities at the end of the migration.[14]

The original Nice model resolved this problem by beginning with the Jupiter and Saturn inside their 2:1 resonance. Jupiter's and Saturn's eccentricities are excited when, after a period of slow divergent migration, they cross the 2:1 resonance. This destabilizes the outer Solar System and a series of gravitational encounters ensues during which Uranus and Neptune are scattered outward into the planetesimal disk. There they scatter a great number of planetesimals inward accelerating the migration of the planets. The scattering of planetesimals and the sweeping of resonances through the asteroid belt produce a bombardment of the inner planets. In addition to reproducing the positions and eccentricities of the outer planets,[15] the original Nice model provided for the origin of: the Jupiter trojans,[16] the Neptune trojans;[17] the irregular satellites of Saturn, Uranus, and Neptune;[18] the various populations of trans-Neptunian objects;[19] the magnitude of, and with the right initial conditions, the timing of the Late Heavy Bombardment.[20]

The original Nice model was not without its own problems, however. During Jupiter's and Saturn's divergent migration secular resonances sweep through the inner Solar System. The ν5 secular resonance crosses the orbits of the terrestrial planets exciting their eccentricities.[21] While Jupiter and Saturn slowly approach their 2:1 resonance the eccentricity of Mars reaches values that can result in collisions between planets or in Mars being ejected from the Solar System. Revised versions of the Nice model beginning with the planets in a chain of resonance avoid this slow approach to the 2:1 resonance. However, the eccentricities of Venus and Mercury are typically excited beyond their current values when the ν5 secular resonance crosses their orbits.[22] The orbits of the asteroids are also significantly altered: the ν16 secular resonance excites inclinations and the ν6 secular resonance excites eccentricities removing low-inclination asteroids as they sweep across the asteroid belt. As a result, the surviving asteroid belt is left with a larger fraction of high inclination objects than is currently observed.[23]

Reproducing the orbits of the inner planets and the orbital distribution of the asteroid belt requires a giant planet migration more rapid than that produced in models of planetesimal-driven migration.[23] The slow resonance crossings that excite the eccentricities of Venus and Mercury and alter the orbital distribution of the asteroid occur when Saturn's period was between 2.1 and 2.3 times that of Jupiter's. Theorists propose that these were avoided because the divergent migration of Jupiter and Saturn was dominated by planet–planet scattering at that time. Specifically, one of the ice giants was scattered inward onto a Jupiter-crossing orbit by a gravitational encounter with Saturn, after which it was scattered outward by a gravitational encounter with Jupiter.[22] As a result, Jupiter's and Saturn's orbits rapidly diverged, accelerating the sweeping of the secular resonances. This evolution of the orbits of the giant planets, similar to processes described by exoplanet researchers, is referred to as the jumping-Jupiter scenario.[24]

Ejected planet[edit]

The encounters between the ice giant and Jupiter in the jumping-Jupiter scenario often lead to the ejection of the ice giant. For this ice giant to be retained its eccentricity must be damped by dynamical friction with the planetesimal disk, raising its perihelion beyond Saturn's orbit. The planetesimal disk masses typically used in the Nice model are often insufficient for this, leaving systems beginning with four giant planets with only three at the end of the instability. The ejection of the ice giant can be avoided if the disk mass is larger, but the separation of Jupiter and Saturn often grows too large and their eccentricities become too small as the larger disk is cleared. These problems led David Nesvorný of the Southwest Research Institute to propose that the Solar System began with five giant planets, with an additional Neptune-mass planet between Saturn and Uranus.[1] Using thousands of simulations with a variety of initial conditions he found that the simulations beginning with five giant planets were ten times more likely to reproduce the orbits of the outer planets.[25] A follow-up study by David Nesvorný and Alessandro Morbidelli found that the required jump in Jupiter's and Saturn's period ratio occurred and the orbits of the outer planets were reproduced in 5% of simulations for one five-planet system vs less than 1% for four-planet systems. The most successful began with a significant migration of Neptune, disrupting the planetesimal disk, before planetary encounters were triggered by resonance crossing. This reduces secular friction, allowing Jupiter's eccentricity to be preserved after it is excited by resonance crossings and planetary encounters.[26]

Konstantin Batygin, Michael E. Brown, and Hayden Betts, in contrast, found four- and five-planet systems had a similar likelihoods (4% vs 3%) of reproducing the orbits of the outer planets, including the oscillations of Jupiter's and Saturn's eccentricities, and the hot and cold populations of Kuiper belt.[27][28] In their investigations Neptune's orbit was required to have a high eccentricity phase during which the hot population was implanted. A rapid precession of Neptune's orbit during this period due to interactions with Uranus was also necessary for the preservation a primordial belt of cold classical objects.[27] For a five-planet system they found that the low eccentricities of the cold classical belt were best preserved if the fifth giant planet was ejected in 10,000 years.[28] Since their study examined only the outer Solar System, it did not include a requirement that Jupiter's and Saturn's orbits diverged rapidly as would be necessary to reproduce the current inner Solar System, however.[26]

Initial conditions[edit]

The giant planets begin in a chain of resonances. During their formation in the protoplanetary disk interactions between the giant planets and the gas disk caused them to migrate inward toward the Sun. Jupiter's inward migration continued until it was halted, or reversed, as in the Grand Tack model, when it captured a faster migrating Saturn in a mean-motion resonance.[29] The resonance chain was extended as the three ice giants also migrated inward and were captured in further resonances.[26] A long-range migration of Neptune outward into the planetesimal disk before planetary encounters begins is most likely if the planets were captured in a 3:2, 3:2, 2:1, 3:2 resonance chain, occurring in 65% of simulations when the inner edge was within 2 AU. While this resonance chain has the highest likelihood of reproducing Neptune's migration other resonance chains are also possible if the instability occurred early.

A late instability may have followed an extended period of slow dust-driven migration. The late escape from a resonance chain, as described in the Nice 2 model, and a long-range migration of Neptune is unlikely. If the inner edge of the planetesimal disk is close an early escape from resonance occurs, if it is distant an instability typically triggered before a significant migration of Neptune occurs. This gap may be bridged if an early escape from resonance is followed by an extended period of slow dust-driven migration. Resonance chains other than the 3:2, 3:2, 2:1, 3:2 are unlikely in this case. Instabilities occur during the slow migration for tighter resonance chains and the distant disk is unrealistically narrow for more relaxed resonance chains. The rate of dust-driven migration slows with time as the rate of dust generation declines. As a result, the timing of the instability is sensitive to factors that determine the rate of dust generation such as the size distribution and the strength of the planetesimals.[30]

A five-planet Nice model[edit]

The Solar System ends its nebula phase with Jupiter, Saturn, and the three ice giants in a 3:2, 3:2, 2:1, 3:2 resonance chain with semi-major axis ranging from 5.5 – 20 AU. A disk of planetesimals orbits beyond these planets extend from several AU beyond Neptune's orbit out to 30 AU. Collisions between planetesimals in the outer disk produce debris that is ground to dust in a cascade of collisions. The dust spirals inward toward the planets due to Poynting-Robertson drag and eventually reaches Neptune's orbit. Gravitational interactions with the dust allow the giant planets to escape from the resonance chain roughly ten million years after the dissipation of the gas disk. After a series of distant planetary encounters the planets settle into an extended period of slow dust-driven migration. Their orbits slowly diverge over four hundred million years until Neptune approaches the inner edge of the planetesimal disk. The migration of the planets then accelerates and transitions to a planetesimal-driven migration as Neptune encounters and exchanges angular momentum with an increasing number of planetesimals.[30] A net inward transfer of planetesimals and outward migration of Neptune occur during these encounters as most of those scattered outward return to be encountered again while some of those scattered inward are prevented from returning after encountering Uranus. A similar process occurs for Uranus, the extra ice giant, and Saturn resulting in their outward migration and a transfer of planetesimals inward from the outer belt to Jupiter. Jupiter, in contrast, ejects most of the planetesimals from the Solar System, and as a result migrates inward.[15] The divergent migration of the planets leads to resonance crossings, exciting the eccentricities of the giant planets and destabilizing the planetary system when Neptune is near 28 AU.[31] During this instability the extra ice giant enters a Saturn-crossing orbit and is scattered inward by Saturn onto a Jupiter-crossing orbit. Repeated gravitational encounters with the ice giant drive a step-wise separation of Jupiter's and Saturn's orbits leading to a rapid increase of their period ratio until it is greater than 2.3.[22] The ice giant also encounters Uranus and Neptune and crosses parts of the asteroid belt as these encounters increase the eccentricity and semi-major axis of its orbit.[32] After 10,000–100,000 years, the ice giant is ejected from the Solar System following an encounter with Jupiter, becoming a rogue planet.[1] The remaining planets then continue to migrate at a declining rate and slowly approach their final orbits as most of the remaining planetesimal disk is removed.[33]

The migrations of the giant planets have many impacts throughout the Solar System. The planetesimals scattered inward by Neptune enter planet-crossing orbits, initiating the Late Heavy Bombardment. Some of these planetesimals are jump-captured as Jupiter trojans during encounters between Jupiter and the ejected ice giant as Jupiter's semi-major axis changes.[34] Others are captured as irregular satellites of the giant planets via three-body interactions during encounters between the ejected ice giant and the other planets.[35] These encounters can also disturb the orbits of the regular satellites and may be responsible for the inclination of Iapetus's orbit.[36] Saturn's rotational axis is tilted when it slowly crosses a spin-orbit resonance with Neptune.[37][38] While Neptune migrates outward several AU, the hot classical Kuiper disk is formed as some planetesimals scattered outward by Neptune are captured in resonances, undergo an exchange of eccentricity vs inclination via the Kozai mechanism, and are released onto higher perihelion, stable orbits.[31] Planetesimals captured in Neptune's 2:1 resonance during this early migration are released when an encounter with the ice giant causes its semi-major axis to jump outward, leaving behind a group of low-inclination, low-eccentricity objects with semi-major axes near 44 AU.[39] As Neptune slowly approaches its current orbit objects are left in fossilized high-perihelion orbits in the scattered disk.[40][33] In the inner Solar System, the rapid separation of the orbits of Jupiter and Saturn reduces the excitation of the eccentricities of the inner planets due to resonance sweeping.[41] Modest changes in the asteroids orbits also occur,[32] shifting the distribution of eccentricities from that of the Grand Tack model toward the current distribution.[42] Asteroid collisional families can be dispersed as the ice giant crosses the asteroid belt,[43] and planetesimals from the outer belt are embedded in the asteroid belt as P- and D-type asteroids.[44] When the planets reach their present position the innermost part of the asteroid belt is disrupted leading to an extended Late Heavy Bombardment of the inner planets by rocky objects.[45]

Timing of the instability[edit]

The timing of the instability in the Nice model was initially proposed to have coincided with the Late Heavy Bombardment, a spike in the impact rate thought to have occurred several million years after the formation of the Solar System. However, recently a number of issues have been raised regarding the timing of the Nice model instability, whether it was the cause of the Late Heavy Bombardment, and if an alternative would better explain the associated craters and impact basins.

A five-planet Nice model with a late instability has a low probability of reproducing the Solar System. Jupiter's and Saturn's period ratio makes the required jump in a small fraction of simulations (7%–8.7%)[26][46] and the eccentricities of the terrestrial planets can also be excited when Jupiter encounters the ice giant.[21] In a study by Nathan Kaib and John Chambers this resulted in the orbits of the terrestrial planets being reproduced in a few percent of simulation with only 1% reproducing both the terrestrial and giant planets orbits. This led Kaib and Chambers to propose that the instability occurred early, before the formation of the terrestrial planets.[46] However, a jump in the ratio of the orbital periods of Jupiter and Saturn is still required to reproduce the asteroid belt, reducing the advantage of an early instability.[47][48] A previous study by Ramon Brasser, Kevin Walsh, and David Nesvorny found a reasonable chance (greater than 20%) of reproducing the inner Solar System using a selected five-planet model.[41] The shapes of the impact basins on Iapetus are also consistent with a late bombardment.[49][50]

The bombardment produced by the Nice model may not match the Late Heavy Bombardment. An impactor size distribution similar to the asteroids would result in too many large impact basins relative to smaller craters.[51] The innermost asteroid belt would need a different size distribution, perhaps due to its small asteroids being the result of collision between a small number of large asteroids, to match this constraint.[52] While the Nice model predicts a bombardment by both asteroids and comets,[20] most evidence (although not all)[53] points toward a bombardment dominated by asteroids.[54][55][56] This may reflect the reduced cometary bombardment in the five-planet Nice model and the significant mass loss or the break-up of comets after entering the inner Solar System,[57] potentially allowing the evidence of cometary bombardment to have been lost.[58] However, two recent estimates of the asteroid bombardment find it is also insufficient to explain the Late Heavy Bombardment.[59][60] Reproducing the lunar craters and impact basins identified with the Late Heavy Bombardment, about 1/6 of the craters larger than 150 km in diameter, and the craters on Mars may be possible if a different crater-scaling law is used. The remaining lunar craters would then be the result of another population of impactors with a different size distribution, possibly planetesimals left over from the formation of the planets.[61] This crater-scaling law also reproduces more recently formed large craters.[62][60]

The craters and impact basins identified with the Late Heavy Bombardment may have another cause. Some recently offered alternative include debris from the impact that formed the Borealis Basin on Mars,[63] and catastrophic collisions among lost planets once orbiting inside Mercury.[64] These explanations have their own potential problems, for example, the timing of the formation of the Borealis basin,[65] and whether objects should remain on orbits inside Mercury's.[66] A monotonically declining bombardment by planetesimals leftover from the formation of the terrestrial planets has also been proposed. This hypothesis requires the lunar mantle to have crystallized relatively late which may explain the differing concentrations of highly siderophile elements in the Earth and Moon.[67] A previous work, however, found that this population would become depleted due to its dynamical and collisional evolution, making the formation of several or even the last two impact basins unlikely.[68]

Proposed names[edit]

According to Nesvorný, colleagues have suggested several names for the hypothetical fifth giant planet—Hades, after the Greek god of the underworld; Liber, after the Roman god of wine and a cognate of Dionysus and Bacchus; and Mephitis, after the Roman goddess of toxic gases. Another suggestion is "Thing 1" from Dr. Seuss's Cat in the Hat children's book.[69]

Notes on Planet Nine[edit]

In January 2016, Batygin and Brown proposed that a distant massive ninth planet is responsible for the alignment of the perihelia of several trans-Neptunian objects with semi-major axes greater than 250 AU.[70] Although the mechanism for the ejection of the fifth giant planet in the five-planet Nice model is reminiscent of the origin of Planet Nine, with a gravitational instability including an encounter with Jupiter, it is unlikely to be the same planet. The estimated timing of the capture of Planet Nine onto its distant orbit, three to ten million years after the formation of the Solar System, when the Sun was still in its birth cluster, is inconsistent with a giant-planet instability that was responsible for the Late Heavy Bombardment.[71] A nearby star close enough to aid in Planet Nine's capture would also result in the capture of the Oort cloud objects on orbits much closer than has been estimated from the orbits of comets.[72] However, Batygin and Brown remarked that there is possibility of retaining the ejected giant just by interactions with primordial planetesimals.[70][73]

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