Questions: Planetary Migration in Protoplanetary Disks

Question 1

A textbook on planet formation states that planets orbit where they formed. Based on migration theory, what is wrong with this assumption, and what evidence most directly contradicts it?

• A. Nothing is wrong — migration theory only applies to unstable multi-planet systems, not single planets
• B. The assumption ignores gravitational disk-planet torques; hot Jupiters — gas giants orbiting within 0.1 AU — could not have assembled there because insufficient gas existed at those distances, so they must have migrated inward
• C. The assumption applies only to rocky planets; gas giants always form in situ regardless of disk torques
• D. The assumption is wrong because planets migrate outward, not inward, placing them farther than their formation location

Answer: (B)

Hot Jupiters are the canonical evidence against in situ formation: gas giants require massive amounts of gas to accrete during formation, and the inner disk (close to the star) has too little gas to form them. They must have formed farther out where gas was abundant, then migrated inward through disk-planet gravitational interactions. This is a concrete, observationally confirmed case where assuming 'planets sit where they formed' leads to an impossible formation scenario. The broader lesson is that migration is a normal phase of planetary system evolution, not an exceptional event.

Question 2

A newly discovered exoplanet is a 2-Jupiter-mass gas giant orbiting at 0.04 AU from its star. Which migration mechanism most likely produced this configuration?

• A. Type I migration — low-mass planets migrate fastest due to asymmetric disk torques
• B. Type III (runaway) migration — it reached this orbit because positive feedback exponentially accelerated its inward movement
• C. Type II migration — it formed farther out where gas was abundant, opened a gap in the disk as it grew massive, then migrated inward locked to the disk's viscous evolution
• D. No migration occurred — Jupiter-mass planets are too heavy to be moved by disk torques

Answer: (C)

A 2-Jupiter-mass planet is massive enough to open a gap in the disk, placing it in the Type II regime. Type I applies to low-mass (roughly Earth-mass) planets that cannot disturb the disk structure. Type III applies to a narrow intermediate mass range with partial gap-opening. Once a planet opens a full gap, it becomes locked into the gap and migrates inward as the disk itself viscously evolves — the 'boat in a river' analogy. This slower, gap-locked migration is the standard explanation for hot Jupiters. Option A is wrong because a 2-Jupiter-mass planet is far too massive for Type I; option D is wrong because Type II migration is specifically the mechanism for massive planets.

Question 3

Type I migration can be fast enough to destroy a forming planet — an Earth-mass planet at 5 AU could spiral into its star in roughly 100,000 years, which is far shorter than the disk's multi-million-year lifetime.

• T. True
• F. False

Answer: True

This timescale problem is one of the central puzzles of planet formation theory: if Type I migration acts so quickly, how do terrestrial planets survive long enough to form at all? Theoretical responses include migration stalls at disk density transitions, outward migration in regions of certain disk temperature gradients, and the fact that formation itself is rapid. The short Type I timescale is not an artifact — it is a real challenge to standard formation models and motivates study of mechanisms that can slow or reverse inward migration.

Question 4

A planet undergoing Type II migration moves faster than a Type I migrating planet, because gap-opening releases additional gravitational energy that accelerates the inward drift.

• T. True
• F. False

Answer: False

Type II migration is significantly slower than Type I. In Type I, the planet is swept inward by the net torque imbalance between inner and outer disk spiral arms — this can be alarmingly fast. In Type II, the planet has opened a gap and becomes coupled to the disk's own viscous evolution timescale, which is typically 10⁵–10⁶ years — slower than Type I. Gap-opening does not release energy that accelerates migration; it instead decouples the planet from the fastest torque mechanisms by removing the local gas that was driving rapid Type I drift. The gap is a throttle, not an accelerator.

Question 5

What causes the net inward migration of low-mass planets in Type I migration, even though both the inner and outer disk exert gravitational torques on the planet?

Model answer: The outer disk's gravitational torque on the planet is slightly stronger than the inner disk's torque, creating a net angular momentum loss. When a planet loses angular momentum, it falls to a lower orbit (closer to the star). The asymmetry arises because the outer spiral wave the planet excites in the disk is typically stronger than the inner one due to disk density and temperature gradients.

Angular momentum conservation governs orbital mechanics: to move inward, a planet must lose angular momentum to the disk. The planet excites spiral density waves both inside and outside its orbit. The outer wave extracts angular momentum from the planet (negative torque on planet), while the inner wave deposits angular momentum into the planet (positive torque). When the outer torque exceeds the inner, the net effect is angular momentum loss and inward migration. This asymmetry is sensitive to disk structure, which is why migration rates depend so strongly on local disk density and temperature profiles — and why some disk conditions can produce outward migration or migration traps.