Grand Tack Hypothesis

The Grand Tack Hypothesis is a gas-disk-era hydrodynamic model of early Solar System evolution formulated in 2011 by Kevin J. Walsh, Alessandro Morbidelli, Sean N. Raymond, David P. O'Brien, and Avi M. Mandell (Nature, 2011). Named by analogy with the nautical maneuver in which a sailboat turns ("tacks") around a buoy against the wind, the hypothesis proposes that during the first 3 to 5 million years (Myr) after the condensation of calcium–aluminum-rich inclusions—while the gaseous protoplanetary disk was still present—newly formed Jupiter underwent a two-stage radial planetary migration. First, Jupiter migrated inward via Type II gas-disk migration from its birth region near ~3.5 astronomical units (AU) down to a turnaround point at ~1.5 AU (near the present-day orbit of Mars). Second, the rapid inward migration of Saturn trapped the two gas giants into a mutual 2:3 mean-motion orbital resonance, reversing the net gravitational disk torque and driving both planets outward until the solar gas disk dissipated with Jupiter near ~5.2–5.4 AU and Saturn near ~7.0 AU.

Prior to the Grand Tack Hypothesis, early Solar System dynamics treated terrestrial planet accretion (at 0.4–2.0 AU), giant-planet gas accretion (at 5–10 AU), and the compositional structure of the Asteroid Belt (at 2.1–3.3 AU) as separate problems. By coupling two-planet hydrodynamical migration directly to N-body terrestrial accretion simulations, Walsh et al. simultaneously resolved two long-standing puzzles of planetary science: the small-Mars problem and the radial mixing and mass depletion of the Asteroid Belt.

Classical N-body computer simulations of terrestrial planet formation starting from a continuous disk of planetesimals and planetary embryos spanning 0.5 AU to 4.0 AU (following Hayashi's Minimum Mass Solar Nebula, Σ_solid ∝ r^−3/2) consistently succeeded in forming Earth- and Venus-mass planets near 0.7 and 1.0 AU, yet systematically failed at 1.52 AU. Because the Hill sphere radius of an embryo increases linearly with heliocentric distance (R_H ∝ r), embryos in a continuous disk at 1.5 AU have a wider feeding zone and grow to 0.5 to 1.0 Earth masses (M_⊕)—roughly five to ten times larger than actual Mars (0.107 M_⊕), while leaving 1 to 2 M_⊕ of unwanted planets inside the Asteroid Belt.

In 2009, Brad Hansen demonstrated numerically that if solid building blocks for the terrestrial planets are initially confined to a narrow radial annulus between 0.7 AU and 1.0 AU with a sharp outer edge at 1.0 AU, subsequent gravitational scattering reproduces the mass distribution of the inner Solar System: two large planets (Venus, 0.815 M_⊕, and Earth, 1.00 M_⊕) form inside the high-density annulus, whereas Mercury (0.055 M_⊕) and Mars (0.107 M_⊕) represent small planetary embryos scattered out of the inner and outer edges of the annulus into starved, solid-depleted zones where their growth stalls early. Rapid isolation of Mars as a stranded planetary embryo is confirmed by short-lived ¹⁸²Hf–¹⁸²W (t_1/2 = 8.9 Myr) chronometry of Martian SNC meteorites, which shows that Mars accreted ~90% of its mass and differentiated its core within 2 to 4 Myr after Solar System birth (Dauphas & Pourmand, 2011), compared to 50–100 Myr for Earth and the Moon.

The Grand Tack Hypothesis provided the physical mechanism that carved Hansen's 1.0 AU outer edge: as Jupiter migrated inward to its 1.5 AU tack point, its moving 2:1 and 3:2 interior mean-motion resonances acted like a gravitational snowplow, shepherding inner rocky planetesimals inward into the 0.7–1.0 AU annulus while scattering remaining material near 1.5 AU outward, leaving behind a truncated inner disk edge at 1.0 AU.

The physical engine enabling Jupiter to "tack" at 1.5 AU rather than continuing into the Sun as a hot Jupiter relies on the Masset–Snellgrove (2001) two-planet resonance mechanism, whose key requirement is a mass ratio of M_Saturn / M_Jupiter ≈ 0.25 to 0.35 (matching the Solar System value of 95.16 / 317.83 = 0.299):

1. While Jupiter (~300 M_⊕) is locked in slow Type II inward migration at ~2.0–1.5 AU, Saturn's core at ~4.5–6.0 AU completes runaway gas accretion to ~60–95 M_⊕. Because Saturn is roughly one-third as large by mass as Jupiter, it opens only a partial density depression, triggering rapid inward Type III (runaway corotation) migration that traverses several AU in less than 10,000 years.
2. As Saturn converges onto Jupiter from the outside, it becomes captured in the 2:3 mean-motion orbital resonance (a_Sat / a_Jup = 1.310). At this compact spacing, the outer edge of Jupiter's gap merges with the inner edge of Saturn's gap, evacuating the gas between the two planets into a common cavity.
3. Inside this shared gap, the torque balance flips: high-mass Jupiter sits at the inner edge where it feels a strong positive inner Lindblad torque from the inner disk, whereas lower-mass Saturn sits at the outer edge where the negative outer Lindblad torque scales down by (M_Sat / M_Jup)² ≈ 0.09, driving Jupiter and Saturn outward in lockstep until the gas disk photoevaporates at ~5 Myr.

Without giant-planet migration, the primordial Asteroid Belt between 2.1 AU and 3.3 AU would have contained 1 to 2 Earth masses of rock on circular, coplanar orbits. Today, the Asteroid Belt contains only ~4.5 × 10⁻⁴ M_⊕ (with a third locked in Ceres), exhibits excited eccentricities (e = 0.05–0.30) and inclinations (i = 5°–20°), and displays an intermixed radial transition between anhydrous inner-disk S-type asteroids (ordinary chondrite parents) and hydrated outer-disk C-type asteroids (carbonaceous chondrite parents).

During the Grand Tack, Jupiter crosses the Asteroid Belt region twice: first scattering >99% of the inner S-type belt away during its inward leg (storing ~15% beyond 3.5 AU), and then—during its outward leg with Saturn—scattering ~0.5% of the S-type bodies and ~0.5% of outer icy C-type planetesimals (formed between 4 and 12 AU) back into stable orbits between 2.1 and 3.3 AU while injecting a companion wave of water-bearing C-type planetesimals across the 1.0 AU terrestrial zone to hydrate proto-Earth.

Why did Jupiter stop migrating inward at specifically ~1.5 AU?

In the Grand Tack model, the turnaround radius of Jupiter (~1.5 AU) is set by the relative timing between Jupiter's inward Type II drift and Saturn's runaway gas accretion. Placing the tack at 1.5 AU truncates the inner planetesimal disk at 1.0 AU, which reproduces the mass of Mars (0.107 M_⊕) at 1.52 AU and the inner edge of the Asteroid Belt at 2.1 AU.

How does the Grand Tack connect to the later Nice Model?

The Grand Tack occurs during the first 3 to 5 Myr while the gas disk is still present. When photoevaporation clears the gas disk at ~5 Myr, the Grand Tack leaves Jupiter, Saturn, Uranus, and Neptune parked in a compact, near-circular, coplanar chain of mutual mean-motion resonances (3:2, 3:2, 4:3) between 5.4 AU and ~15 AU—providing the initial boundary conditions required for the post-gas planetesimal-driven Nice Model instability.

What are the main alternative explanations for the small-Mars problem besides the Grand Tack?

Three major complementary or alternative mechanisms have been developed since 2011: (1) Early Clement–Kaib–Raymond Nice-Model Instability (2018), where secular resonances from an early giant-planet instability deplete the Mars/Asteroid Belt zone before Mars finishes accreting; (2) Drifting Pebble Accretion and Viscous Ring Models (Levison et al., 2015; Izidoro et al., 2015), where a pressure bump near 1.0 AU concentrates silicate planetesimals in a narrow ring; and (3) Convergent Type I Migration of Terrestrial Embryos.

1. Masset, F., & Snellgrove, M. (2001). "Reversing type II migration: Resonance trapping of a lighter giant protoplanet." Monthly Notices of the Royal Astronomical Society, 320(4), L55–L59. https://doi.org/10.1046/j.1365-8711.2001.04159.x
2. Hansen, B. M. S. (2009). "Formation of the terrestrial planets from a narrow annulus." The Astrophysical Journal, 703(1), 1131–1140. https://doi.org/10.1088/0004-637X/703/1/1131
3. Walsh, K. J., Morbidelli, A., Raymond, S. N., O'Brien, D. P., & Mandell, A. M. (2011). "A low mass for Mars from Jupiter's early gas-driven migration." Nature, 475(7355), 206–209. https://doi.org/10.1038/nature10201
4. Dauphas, N., & Pourmand, A. (2011). "Hf–W–Th evidence for rapid growth of Mars and its status as a planetary embryo." Nature, 473(7348), 489–492. https://doi.org/10.1038/nature10077
5. O'Brien, D. P., Walsh, K. J., Morbidelli, A., Raymond, S. N., & Mandell, A. M. (2014). "Water delivery and giant impacts in the 'Grand Tack' scenario." Icarus, 239, 74–84. https://doi.org/10.1016/j.icarus.2014.05.009