Grand Tack Hypothesis

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 after capturing Saturn in a 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]

Description

In the Grand Tack model Jupiter undergoes a two-phase migration after its formation, migrating inward to 1.5 AU before reversing course and migrating outward. Jupiter's formation takes place near the ice line, at roughly 3.5 AU. After clearing a gap in the gas disk Jupiter undergoes 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 migrates toward the Sun, but being smaller undergoes type I migration, moving faster through the gas disk.^[6] Saturn is captured in a 2:3 mean-motion resonance with Jupiter during this migration. An overlapping gap in the gas disk then forms between Jupiter and Saturn,^[7] altering the balance of forces on these planets which are now migrating together. Jupiter having a greater mass is pushed outward more by the inner disk than Saturn is inward by the outer disk. This, along with a transfer of angular momentum from gas streaming through the gap,^[8] reverses their migration when Jupiter is at 1.5 AU.^[6] Their outward migration continues until the gas disk dissipates and it is supposed to end with Jupiter near its current orbit.

Scope of the Grand Tack Hypothesis

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

Mars Problem

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,^[9] much larger than the actual mass of Mars, 0.107 Earth-mass. Jupiter's inward migration alters this distribution of material,^[10] driving planetesimals inward to form a narrow dense band with a mix of materials inside 1.0 AU,^[11] and leaving the Mars region largely empty.^[12] Planetary embryos quickly form in the narrow band. While most later collide and merge to form the larger terrestrial planets, 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.^[13]

Asteroid belt

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.^[14] Rocky asteroids dominated the inner region, while more primitive and icy asteroids dominated the outer region beyond the ice line.^[15] 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 Jupiter and Saturn migrate into the outer region, scattering 0.5% of the primitive asteroids 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.^[12] In some cases icy asteroids are left with orbits crossing the region where the terrestrial planets form, delivering water to these planets.^[16]

Lost super-Earths

Unlike many recently discovered planetary systems, the Solar System has no large planets inside the orbit of Mercury. These close orbiting super-Earths may have been lost during Jupiter's inward migration.^[17] As Jupiter migrated, it captured planetesimals in mean-motion resonances, causing their orbits to shrink and their eccentricities to grow. A collisional cascade followed as their relative velocities became large enough to produce catastrophic impacts. Drag from the gas disk caused the resulting debris to spiral inward toward the Sun. If there were super-Earths in the early Solar System, they would have caught much of this debris in resonances and would have been driven into the Sun ahead of it. The current terrestrial planets then formed from planetesimals left behind when Jupiter reversed course.^[18]

Later developments

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. Rather, the nebula conditions lead to capture in a 2:1 mean-motion resonance. This outcome is a result of the relatively slow migration velocity with which the two planets approach each other. 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.^[19]

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 in this scenario.^[20]

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. Titan's later formation, necessary to avoid its Type I migration into Saturn, allows its atmosphere in contrast to survive.^[21]

Advocates

At the 45th Lunar and Planetary Science Conference held in 2014, Seth A. Jacobson, Alessandro Morbidelli, D. C. Rubie, Kevin Walsh, David P. O'Brien, Sean Raymond, S. Steart and S. Lock published a paper titled "Planet Formation within the Grand Tack Model", stating conclusions from a great number of N-body simulations of the formation of terrestrial planets.^[22]

Alternatives

The Grand Tack may not be necessary for the formation of a small Mars and a low-mass asteroid belt. When a large number of simulations of the accretion of the terrestrial planets are conducted, a small Mars forms in a small, but non-zero, fraction of cases.^[23][24][25] 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.^[26] A more limited migration of Jupiter and Saturn may be sufficient for the formation of a small Mars.^[27] Pebble accretion becomes less efficient with increasing distance from the Sun due to the decreasing density of gas in the planetesimal disk, this slows the growth of more-distant objects, leading to a small Mars and a low-mass asteroid belt.^[28][29]

See also

• Formation and evolution of the Solar System
• Jumping-Jupiter scenario
• Nice model
• Planetary migration

References