Grand tack hypothesis

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Jupiter might have shaped the Solar System on its Grand Tack

In planetary astronomy, the grand tack hypothesis proposes that after its formation at 3.5 AU, Jupiter migrated inward to 1.5 AU, before reversing course due to capturing Saturn in an orbital resonance, eventually halting near its current orbit at 5.2 AU. The reversal of Jupiter's migration is likened to the path of a sailboat changing directions (tacking) as it travels against the wind.[1]

The planetesimal disk is truncated at 1.0 AU by Jupiter's migration, limiting the material available to form Mars.[2] Jupiter twice crosses the asteroid belt, scattering asteroids outward then inward. The resulting asteroid belt has a small mass, a wide range of inclinations and eccentricities, and a population originating from both inside and outside Jupiter's original orbit.[3] Debris produced by collisions among planetesimals swept ahead of Jupiter may have driven an early generation of planets into the Sun.[4]


In the grand tack hypothesis Jupiter underwent a two-phase migration after its formation, migrating inward to 1.5 AU before reversing course and migrating outward. Jupiter's formation took place near the ice line, at roughly 3.5 AU. After clearing a gap in the gas disk Jupiter underwent type II migration, moving slowly toward the Sun with the gas disk. If uninterrupted, this migration would have left Jupiter in a close orbit around the Sun like recently discovered hot Jupiters in other planetary systems.[5] Saturn also migrated toward the Sun, but being smaller it migrated faster, undergoing either type I migration or runaway migration.[6] Saturn converged on Jupiter and was captured in a 2:3 mean-motion resonance with Jupiter during this migration. An overlapping gap in the gas disk then formed around Jupiter and Saturn,[7] altering the balance of forces on these planets which began migrating together. Saturn partially cleared its part of the gap reducing the torque exerted on Jupiter by the outer disk. The net torque on the planets then became positive, with the torques generated by the inner Lindblad resonances exceeding those from the outer disk, and the planets began to migrate outward.[8] The outward migration was able to continue because interactions between the planets allowed gas to stream through the gap.[9] The gas exchanged angular momentum with the planets during its passage, adding to the positive balance of torques; and transferred mass from the outer disk to the inner disk, allowing the planets to migrate outward relative to the disk.[10] The transfer of gas to the inner disk also slowed the reduction of the inner disk's mass relative to the outer disk as it accreted onto the Sun, which otherwise would weaken the inner torque, ending the planets outward migration.[8][11] In the grand tack hypothesis this process is assumed to have reversed the inward migration of the planets when Jupiter is at 1.5 AU.[6] The outward migration of Jupiter and Saturn continued until they reached a stable equilibrium if the disk was flared,[12] or the gas disk dissipated, and is supposed to end with Jupiter near its current orbit.[6]

Scope of the grand tack hypothesis[edit]

The hypothesis can be applied to multiple phenomena in the Solar System.

Mars problem[edit]

Jupiter's grand tack resolves the Mars problem by limiting the material available to form Mars. The Mars problem is a conflict between some simulations of the formation of the terrestrial planets, which when begun with planetesimals distributed throughout the inner Solar System, end with a 0.5–1.0 Earth-mass planet in its region,[13] much larger than the actual mass of Mars, 0.107 Earth-mass. Jupiter's inward migration alters this distribution of material,[14] driving planetesimals inward to form a narrow dense band with a mix of materials inside 1.0 AU,[15] and leaving the Mars region largely empty.[16] Planetary embryos quickly form in the narrow band. While most later collide and merge to form the larger terrestrial planets (Venus and Earth), some are scattered outside the band.[6] These scattered embryos, deprived of additional material slowing their growth, form the lower mass terrestrial planets Mars and Mercury.[17]

Asteroid belt[edit]

Jupiter and Saturn drive most asteroids from their initial orbits during their migrations, leaving behind an excited remnant derived from both inside and outside Jupiter's original location. Before Jupiter's migrations the surrounding regions contained asteroids which varied in composition with their distance from the Sun.[18] Rocky asteroids dominated the inner region, while more primitive and icy asteroids dominated the outer region beyond the ice line.[19] As Jupiter and Saturn migrate inward, ~15% of the inner asteroids are scattered outward onto orbits beyond Saturn.[2] After reversing course, Jupiter and Saturn first encounter these objects, scattering about 0.5% of the original population back inward onto stable orbits.[6] Later, as Jupiter and Saturn migrate into the outer region, about 0.5% of the primitive asteroids are scattered onto orbits in the outer asteroid belt.[6] The encounters with Jupiter and Saturn leave many of the captured asteroids with large eccentricities and inclinations.[16] Some of the icy asteroids are also left in orbits crossing the region where the terrestrial planets later formed, allowing water to be delivered to the accreting planets as when the icy asteroids collide with them.[20][21]

Later developments[edit]

The absence of close orbiting super-Earths in the Solar System may be the result of Jupiter's inward migration.[22] As Jupiter migrates inward, planetesimals are captured in its mean-motion resonances, causing their orbits to shrink and their eccentricities to grow. A collisional cascade follows as their relative velocities became large enough to produce catastrophic impacts. The resulting debris then spirals inward toward the Sun due to drag from the gas disk. If there were super-Earths in the early Solar System, they would have caught much of this debris in resonances and could have been driven into the Sun ahead of it. The current terrestrial planets would then form from planetesimals left behind when Jupiter reversed course.[23] However, the migration of close orbiting super-Earths into the Sun could be avoided if the debris coalesced into larger objects, reducing gas drag; and if the protoplanetary disk had an inner cavity, their inward migration could be halted near its edge.[24]

The presence of a thick atmosphere around Titan and its absence around Ganymede and Callisto may be due to the timing of their formation relative to the grand tack. If Ganymede and Callisto formed before the grand tack their atmospheres would have been lost as Jupiter moved closer to the Sun. However, for Titan to avoid Type I migration into Saturn, and for Titan's atmosphere to survive, it must have formed after the grand tack.[25][26]

The migration of the giant planets through the asteroid belt creates a spike in impact velocities that could result in the formation of CB chondrites. CB chondrites are metal rich carbonaceous chondrites containing iron/nickel nodules that formed from the crystallization of impact melts 4.8 ±0.3 Myrs after the first solids. The vaporization of these metals requires impacts of greater that 18 km/s, well beyond the maximum of 12.2 km/s in standard accretion models. Jupiter's migration across the asteroid belt increases the eccentricities and inclinations of the asteroids, resulting in a 0.5 Myr period of impact velocities sufficient to vaporize metals. If the formation of CB chondrites was due to Jupiter's migration it would have occurred 4.5-5 Myrs after the formation of the Solar System.[27]

Following the grand tack, perturbations from the terrestrial planets and the Nice model instability alter the orbital distribution of the remaining asteroids. The resulting eccentricity and semi-major axis distributions resemble that of the current asteroid belt. Some low-inclination asteroids are removed, leaving the inclination distribution slightly over-excited compared to the current asteroid belt.[28]

Recent modeling of the formation of planets from a narrow annulus indicates that the quick formation of Mars, the size of the Moon-forming impact, and the mass accreted by Earth following the formation of the Moon are best reproduced if the oligarchic growth phase ended with most of the mass in Mars-sized embryos and a small fraction in planetesimals. The Moon-forming impact occurs between 60 and 130 million years after the formation of the first solids in this scenario.[29]

Encounters with other embryos could destabilize a disk orbiting Mars reducing the mass of moons that form around Mars. After Mars is scattered from the annulus by encounters with other planets it continues to have encounters with other objects until the planets clear material from the inner Solar System. While these encounters enable the orbit of Mars to become decoupled from the other planets and remain on a stable orbit, they can also perturb the disk of material from which the moons of Mars form. These perturbations cause material to escape from the orbit of Mars or to impact on its surface reducing the mass of the disk resulting in the formation of smaller moons.[30]

Simulations of the formation of the terrestrial planets using models of the protoplanetary disk that include viscous heating and the migration of the planetary embryos indicate that Jupiter's migration may have reversed at 2.0 AU. In simulations the eccentricities of the embryos are excited by perturbations from Jupiter. As these eccentricities are damped by the denser gas disk of recent models, the semi-major axes of the embryos shrink, shifting the peak density of solids inward. For simulations with Jupiter's migration reversing at 1.5 AU, this resulted in the largest terrestrial planet forming near Venus's orbit rather than at Earth's orbit. Simulations that instead reversed Jupiter's migration at 2.0 AU yielded a closer match to the current Solar System.[9][31]

Most of the accretion of Mars must have taken place outside the narrow annulus of material formed by the grand tack if Mars has a different composition than Earth and Venus. The planets that grow in the annulus created by the grand tack end with similar compositions. If the grand tack occurred early, while the embryo that became Mars was relatively small, a Mars with a differing composition could form if it was instead scattered outward then inward like the asteroids. The chance of this occurring is roughly 2%.[32]

Later studies have shown that the convergent orbital migration of Jupiter and Saturn in the fading solar nebula is unlikely to establish a 3:2 mean-motion resonance. Instead of supporting a faster runaway migration, nebula conditions lead to a slower migration of Saturn and its capture in a 2:1 mean-motion resonance.[11] Capture of Jupiter and Saturn in the 2:1 mean-motion resonance does not typically reverse the direction of migration, but particular nebula configurations have been identified that may drive outward migration.[33] These configurations, however, tend to excite Jupiter's and Saturn's orbital eccentricity to values between two and three times as large as their actual values.[33] Also, if the temperature and viscosity of the gas allow Saturn to produce a deeper gap, the resulting net torque can again become negative, resulting in the inward migration of the system.[11]

The grand tack scenario ignores the ongoing accretion of gas on both Jupiter and Saturn.[34] In fact, to drive outward migration and move the planets to the proximity of their current orbits, the solar nebula had to contain a sufficiently large reservoir of gas around the orbits of the two planets. However, this gas would provide a source for accretion, which would affect the growth of Jupiter and Saturn and their mass ratio.[11] The type of nebula density required for capture in the 3:2 mean-motion resonance is especially dangerous for the survival of the two planets, because it can lead to significant mass growth and ensuing planet-planet scattering. But conditions leading to 2:1 mean-motion resonant systems may also put the planets at danger.[35] Accretion of gas on both planets also tends to reduce the supply toward the inner disk, lowering the accretion rate toward the Sun. This process works to deplete somewhat the disk interior to Jupiter's orbit, weakening the torques on Jupiter arising from inner Lindblad resonances and potentially ending the planets' outward migration.[11]


A small Mars forms in a small but non-zero fraction of simulations of terrestrial planet accretion that begin with planetesimals distributed across the entire inner Solar System.[36][37][38] If the accretion of the terrestrial planets occurred with Jupiter and Saturn in their present orbits (i.e. after the instability in the Nice model) a local depletion of the planetesimal disk near Mars's current orbit is sufficient for the formation of a low-mass Mars.[39] An early instability can also result in a small Mars if the planetesimal disk contains large embryos.[40] A planetesimal disk with a steep surface density profile, due to the inward drift of solids before the formation of planetesimals, also results in a small Mars and a low mass asteroid belt.[41] If the gas disk is flared and the pebbles are large, pebble accretion by planetesimals and embryos becomes significantly less efficient with increasing distance from the Sun, preventing the growth of objects beyond the size of Mars at its distance and leaving the asteroid belt with a small mass.[42][43] Sweeping secular resonances can excite inclinations and eccentricities, resulting in fragmentation instead of accretion as collision velocities increase, inhibiting the growth of planets beyond 1 AU.[44]

The eccentricities and inclinations of a low mass asteroid belt could have been exited by secular resonances if the resonant orbits of Jupiter and Saturn became chaotic during the period between the gas phase era and the instability of the Nice model.[45][46] Secular resonances sweeping during the dissipation of the gas disk could also excite the orbits of the asteroids, and remove those outside a particular size range if they spiraled toward the Sun due to gas drag after their eccentricities were excited.[47] The asteroid belt could also be excited and depleted by embedded embryos, either scattered inward by Jupiter, or left over from terrestrial planet formation. The former leaves the outer asteroid belt more excited than the inner asteroid belt, however, and the latter requires an additional ~90% depletion via an additional mechanism, more than in recent versions of the Nice model.[48] If the region of the asteroid belt was initially empty it could have been populated by icy planetesimals that were scattered inward during Jupiter's and Saturn's gas accretion,[49][50] and by stony asteroids that were scattered outward by the forming terrestrial planets.[51][52] The inward scattered icy planetesimals could also deliver water to the terrestrial region.[50]

The absence of inner super-Earth and the small mass of Mercury may be due to the formation of Jupiter's core close to the Sun and its outward migration across the inner Solar System. During its outward migration this core could push material outward in its resonances leaving the region inside Venus's orbit depleted.[53][24] In a protoplanetary disk that is evolving via a disk wind planetary embryos may migrate outward in a leaving the Solar System without planets inside Mercury.[54] An instability that led to catastrophic collisions between an early generational of inner planets may have resulted in the debris being ground small enough to be lost due to Poynting-Robertson drag.[55][56] If planetesimal formation was limited to early in the gas disk epoch an inner edge of the planetesimal disk might be located at the silicate condensation line of this time.[57] The magnetic field of some stars may have been aligned with the rotation of the disk, causing the gas in the inner regions of their disks to be depleted faster. This would enable the solid to gas ratio to reach values high enough for the formation of planetesimals via streaming instabilities closer than Mercury's orbit only in these systems.[58][59]

See also[edit]


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