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.
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Background
Current theories of planetary formation do not allow for the accretion of Uranus and Neptune in their present positions. The protoplanetary disk was too diffuse and the time scales too long 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. 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.
It is now widely accepted that the Solar System was initially more compact and that the outer planets migrated outward to their current positions. The planetesimal-driven migration of the outer planets was first described in 1984 by Fernandez and Ip. This process is driven by the exchange of angular momentum between the planets and planetesimals originating from an outer disk. Early dynamical models assumed that this migration was smooth. In addition to reproducing the current positions of the outer planets, these models offered explanations for: the populations of resonant objects in the Kuiper belt, the eccentricity of Pluto's orbit, the inclinations of the hot classical Kuiper belt objects and the retention of a scattered disk, and the low mass of Kuiper belt and the location of its outer edge near the 2:1 resonance with Neptune. However, these models failed to reproduce the eccentricities of the outer planets, leaving them with very small eccentricities at the end of the migration.
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, the original Nice model provided for the origin of: the Jupiter trojans, the Neptune trojans; the irregular satellites of Saturn, Uranus, and Neptune; the various populations of trans-Neptunian objects; the magnitude of, and with the right initial conditions, the timing of the Late Heavy Bombardment.
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. 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. 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.
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. As a solution to this problem, theorists propose that the divergent migration of Jupiter and Saturn was dominated by planet–planet scattering while their period ratio was increasing from less than 2.1 to greater than 2.3. 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. 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.
Ejected planet
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. 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. 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.
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. 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. 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. 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.
A later study by Nathan Kaib and John Chambers found that the orbits of the terrestrial planets are reproduced in only a few percent of the numerical simulations when one or more ice giants are ejected with only 1% reproducing the orbits of both the terrestrial and the giant planets. This is in part due to Jupiter's and Saturn's period ratio jumping to a range of 2.3 to 2.5 in a small fraction (8.7%) of their simulations. The excitement of the terrestrial planets eccentricities also occurs while Jupiter's eccentricity is large following its encounters with an ice giant. This low success rate implies that the instability occurred before the formation of the terrestrial planets. However, the need for a rapid increase of Jupiter's and Saturn's period ratio to beyond 2.3 to reproduce the current asteroid belt significantly reduces the advantage of an early instability. 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 five-planet model selected from the 5% that reproduced the outer Solar System, a numerically similar result.
A five-planet Nice model
During the early Solar System the five giant planets are captured into a series of mean-motion resonances due to gas-driven migration. A disk of planetesimals orbits beyond these planets, extending to 30 AU. The planetesimal disk is stirred by gravitational interactions with Pluto-massed objects exciting eccentricities and inclinations. After several hundred million years these interactions cause the resonance chain of the giant planets to be broken. The planets then begin to migrate, driven by transfers of angular momentum as they scatter planetesimals. A net inward transfer of planetesimals causes Neptune to migrate outward as most planetesimals it scatters outward return to be scattered again while some of the planetesimals it scatters inward encounter Uranus and are prevented from returning. 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. Neptune migrates outward several AU and the orbits of the other planets diverge during this planetesimal-driven migration. The divergent migration of the planets leads to resonance crossings, exciting the eccentricities of the planets and destabilizing the planetary system. 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 and Saturn's orbits leading to a rapid increase of their period ratio until it is greater than 2.3. 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. After 10,000–100,000 years, the ice giant is ejected from the Solar System following an encounter with Jupiter, making it a rogue planet. 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.
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. 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. These encounters can also disturb the orbits of the regular satellites and may be responsible for the inclination of Iapetus's orbit. Saturn's rotational axis is tilted when it slowly crosses a spin-orbit resonance with Neptune. 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. 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. As Neptune slowly approaches its current orbit objects are left in fossilized high-perihelion orbits in the scattered disk. 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. Modest changes in the asteroids orbits also occur, shifting the distribution of eccentricities from that of the Grand Tack model toward the current distribution. Asteroid collisional families can be dispersed as the ice giant crosses the asteroid belt, and planetesimals from the outer belt are embedded in the asteroid belt as P- and D-type asteroids. 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.
Proposed names
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.