Questions: Planetary Formation I: Core Accretion and Migration

Question 1

Hot Jupiters are gas giant planets found orbiting within 0.1 AU of their stars — well inside the orbit of Mercury. According to core accretion theory with migration, how did they arrive there?

• A. They formed close to their stars from a dense inner disk region where gas and rocky material were both abundant enough for giant planet assembly
• B. They migrated inward from beyond the snow line, where ice augmented the solid material available for core growth and runaway gas accretion was possible before the disk dissipated
• C. They are failed stellar companions that condensed directly from gas by gravitational instability without requiring a solid core phase
• D. They were gravitationally captured from other solar systems during close stellar encounters in young star clusters

Answer: (B)

Hot Jupiters cannot have formed where we find them — the inner disk is too hot for ice to condense, providing insufficient solid material for a large core, and the limited gas there is not enough for runaway gas accretion. Core accretion requires forming beyond the snow line where ice approximately doubles the solid surface density. Once a gas giant formed there, Type II migration (the planet opens a gap in the disk and migrates inward locked to the disk's viscous evolution) carried it inward, sometimes all the way to a very short period orbit. Migration is the critical bridge between where planets form and where we find them.

Question 2

The 'meter-size barrier' in core accretion theory describes the challenge that:

• A. Meter-sized boulders are too massive for gas drag to affect, so they stall at that size and cannot grow further
• B. Objects around a meter across experience aerodynamic drag from disk gas that causes them to spiral inward toward the star faster than they can grow through further collisions
• C. At meter scales, electrostatic repulsion between silicate surfaces prevents sticking, so collisions become destructive
• D. Meter-sized rocks are fragmented by tidal forces from the protostar before they can accumulate into larger bodies

Answer: (B)

Objects in the centimeter-to-meter size range experience the worst of both worlds: they are large enough to feel significant aerodynamic drag from the surrounding gas (unlike tiny dust grains that are tightly coupled to the gas), but small enough that this drag is not negligible. The gas orbits slightly slower than Keplerian speed due to pressure support; meter-sized rocks orbit at full Keplerian speed and therefore feel a continuous headwind that saps their angular momentum, causing them to spiral inward. The timescale for a meter-sized rock to fall into the star can be only hundreds of years — far too fast for growth. Streaming instabilities solve this by concentrating particles directly into kilometer-scale planetesimals.

Question 3

Gas giant planets require a solid core of approximately 10 Earth masses before they can begin accreting hydrogen and helium from the surrounding disk.

• T. True
• F. False

Answer: True

This is the critical core mass threshold in core accretion theory. Below ~10 Earth masses, a growing core can hold only a thin gaseous envelope — any gas it attracts is in quasi-hydrostatic equilibrium and does not accrete rapidly. At approximately 10 Earth masses, the core's gravitational pull becomes strong enough to overcome the thermal pressure supporting the envelope, triggering runaway gas accretion: gas pours in rapidly, and the planet can grow from a 10 Earth-mass core to hundreds of Earth masses in as little as 100,000 years. The race is to reach this threshold before the protoplanetary disk dissipates (typically within 3–10 million years).

Question 4

According to core accretion theory, the difference between rocky terrestrial planets and gas giants is only one of distance from the star — gas giants simply form in a denser part of the inner disk, not through a fundamentally different process.

• T. True
• F. False

Answer: False

Gas giants form beyond the snow line (not closer to the star) and through an additional phase — runaway gas accretion — that has no analog in terrestrial planet formation. The snow line matters because water ice condenses beyond it, roughly doubling the surface density of solid material available for core growth and enabling cores to grow large enough to reach critical mass. Rocky terrestrial planets never reach critical core mass because the inner disk lacks this extra solid material. Gas giants also require runaway gas accretion as a distinct third phase after dust coagulation and core accretion; terrestrial planets form entirely from solid material without this gas-capture step.

Question 5

Why is the snow line important in the core accretion model, and what happens to a rocky core once it reaches approximately 10 Earth masses?

Model answer: The snow line is the distance from the star where water ice condenses (roughly 3 AU in our solar system). Beyond it, both silicate rock and water ice are available as solid building blocks, roughly doubling the surface density of solid material compared to the inner disk. This extra material allows rocky cores to grow larger than they could in the ice-free inner disk. When a core reaches approximately 10 Earth masses (the critical core mass), its gravitational attraction becomes sufficient to pull in and retain hydrogen and helium gas from the surrounding disk rather than just holding a thin hydrostatic envelope. At this point, runaway gas accretion begins: the envelope collapses and gas accretes rapidly, potentially growing the planet to Jupiter size within ~100,000 years — well before the disk dissipates.

The snow line acts as a boundary between where terrestrial and gas-giant formation are possible. Interior to it, solid surface densities are too low for cores to reach critical mass. Exterior to it, ice boosts solid density and cores can grow large enough to trigger the gas accretion phase that distinguishes gas giants from rocky planets.