# Intuitive explanation of the source of energy that cause Jupiter and Saturn to migrate outward in the Grand Tack Hypothesis?

The Grand Tack Hypothesis states that Jupiter first migrate inward, but it was caught up by the faster inward migration of Saturn, and when the two planets reached 3:2 mean-motion resonance they migrated outward together.

As a student who only knows high-school physics, I can imagine that to make these massive gas giants to migrate outward, they should receive a tremendous amount of energy (like how we send satellite into the space). The Nature paper that proposes the Grand Tack Hypothesis (Walsh et.al., 2011) does not seem to explain why they migrate outward, but references another simulation study (Masset & Snellgrove, 2001), which is unfortunately to hard for me to understand now.

Is there an intuitive explanation of why Jupiter and Saturn can migrate outward? What is the energy source?

• excellent question! Key point is (without time to write full answer now): migration happens within a gaseous disk. Thus energy and angular momentum can be transfered from and to the gas as well, not just between the planets themselves. Commented Jul 8, 2021 at 10:23
• This is wonderful. I'd worked as a visualization person with data from a simulation of the Grand Tack, but didn't understand the mechanism of the phase where Jupiter and Saturn sweep back outward, except that it somehow depended on a resonance between them. This explanation, and the link to the recent review, are much appreciated! Commented Jul 13, 2021 at 5:04

First let's try to understand why planets migrate inwards. Planets are formed in a protoplanetary disk; a huge disk of gas and dust that accretes on to a newly forming star at the centre. Gravitational interactions between the planets and the gas in the disk play a very important role in planetary formation and evolution.

As planets orbits within the disk, they generate 'spiral density waves'. These are simply changes to the density of the gas in the region local to the planet, which move at a different speed compared to the rest of the material in the disk. The consequence is that the wave exterior to the planet exerts a negative torque and acts to slow the planet down. The wave interior to the planet exerts a positive torque and speeds it up. The net effect is that the negative torque wins, which causes the planet to lose angular momentum and migrate towards the star. On the timescales of planetary formation this is a relatively fast process, and typically affects lower mass planets.

When you have a planet as large as Jupiter, something else happens. The torques that the planet exerts on the disk are so strong that the repel the gas away from its orbital region entirely, opening up a 'gap' in the disk. The planet now migrates inwards following the natural evolution of the disk ie. the timescale that gas naturally migrates and accretes on to the star. The planet and the gap migrate inwards together as one. This is a much slower than the process than the one described for smaller planets, hence why Saturn was able to catch up with Jupiter.

So, why did Jupiter migrate outwards?

When Jupiter and Saturn became locked in an orbital resonance, they formed a common gap in the disk. Saturn essentially cleared the region exterior to Jupiter, reducing the torque exerted on Jupiter by the outer part of the disk. But the gas repelled away by Jupiter in the inner region became piled up at the inner edge of the disk, increasing in density and enhancing its own torques back on Jupiter. The net effect is now that the positive torques from the inner disk overcome the negative torques from the outer disk, and the planets migrate outwards.

For this to work, you need quite a specific scenario. Modelling suggests that outward migration can only occur when the inner planet is 2-4x larger that the outer planet. For further reading I would highly suggest this recent review by Raymond & Morbidelli (2020), which gives an excellent description of our best current models of the formation of the Solar System.

• Welcome to astronomy SE and thanks for the nice explanation! Commented Jul 8, 2021 at 11:49
• Thanks for the answer. Is the force that pushes Jupiter outwards similar to the tidal force that pushes the moon away from the Earth? Commented Jul 9, 2021 at 4:44
• In a kind of metaphorical sense yes, because both systems involve a body that exerts force on the system, with the system then proving a feedback that impacts the bodys motion. But the key thing is to always remember that planetary migration takes place in a gaseous disk. The interactions between the planet and the disk material are what drive migration. Once the gas in the disk disperses then orbital resonance chains can become unstable (the 'breaking-the-chains' scenario). Commented Jul 9, 2021 at 9:36
• Is the "negative torque" here, essentially a friction force against dust? Or something else (net tiny contribution of unequal gravity due to density waves?)? Can you clarify in your answer, it could help Commented Jul 9, 2021 at 10:44
• The torques are indeed a result of the unequal gravity due to the density waves. I must admit I find this quite amazing! Quoting from Raymond & Morbidelli (2020): "...The gravitational attraction that the wave exerts on the planet produces a negative torque that slows the planet down. The interior wave leads the planet and exerts a positive torque. The net effect on the planet depends on the balance between these two torques of opposite signs...." Commented Jul 9, 2021 at 16:34

In short: By the time all that migration happened there still was a large gas disc around the Sun. The energy that Jupiter and Saturn lost when migrating inwards or gained when migrating outwards, was exchanged with the disk. When Jupiter and Saturn migrated inwards, some gas in the disk got the energy they lost and migrated outwards. When both planets migrated outward, the energy came from some gas losing energy and migrating inwards.

That is, the energy source (and the energy sink) was the gas disc.