Questions: Planetary Accretion Timescales and Disk Lifetime Constraints

Question 1

Classical core accretion models estimate that forming a Jupiter-mass planet takes 5–10 Myr. Why does this create a problem, and what mechanism was proposed to address it?

• A. 5–10 Myr often exceeds disk lifetimes of 1–10 Myr; pebble accretion was proposed to build 10-Earth-mass cores in under 1 Myr by sweeping up aerodynamically slowed centimeter-scale pebbles
• B. 5–10 Myr often exceeds disk lifetimes; gravitational instability was proposed as the universal solution because it forms planets in thousands of years
• C. 5–10 Myr is too fast for envelope capture; gravitational instability was proposed to slow the assembly process
• D. There is no timescale problem — 5–10 Myr falls within the typical disk lifetime range

Answer: (A)

The timescale problem arises because a gas giant's core must reach ~10 Earth masses before it can gravitationally capture an envelope, and this must happen before the disk disperses. Classical estimates for reaching that mass (5–10 Myr) push against or exceed typical disk lifetimes (3–10 Myr). Pebble accretion — not gravitational instability — is the leading proposed solution: centimeter-scale pebbles are aerodynamically coupled to the disk gas and drift into the core's gravitational reach far more efficiently than rare planetesimal collisions, accelerating core growth by orders of magnitude. Gravitational instability (option B) can form planets quickly but requires unusually massive, cool disks and is likely rare.

Question 2

Astronomers find that disks in a young stellar cluster have lost nearly all their gas by age 4 Myr. What does this most directly constrain?

• A. The maximum size rocky planets can reach in those systems
• B. Whether gas giants could have formed via core accretion, since gas capture requires a disk still present when the core reaches ~10 Earth masses
• C. Whether pebble accretion ever operated, since pebbles require gas drag to drift
• D. The bulk composition of any rocky planets that formed, since disk gas affects rock chemistry

Answer: (B)

Gas giant formation via core accretion requires the gas disk to persist until a growing core (~10 Earth masses) can capture a massive envelope. If the disk is gone by 4 Myr, cores that did not reach critical mass in time cannot become gas giants. Options C and D identify real effects of disk dispersal but are not the most direct constraint — the central question is whether gas giants could form at all, which depends entirely on the timing of disk dispersal relative to core growth.

Question 3

Gravitational instability is the dominant gas giant formation pathway in most planetary systems because it operates on timescales thousands of times faster than core accretion.

• T. True
• F. False

Answer: False

While gravitational instability can form planets in thousands of years, it requires unusually massive and cool protoplanetary disks, which appear to be rare. Core accretion — accelerated by pebble accretion — is believed to be the dominant pathway in most systems. Speed alone does not make a mechanism dominant; it must also operate under realistic disk conditions. Most observed planetary systems are better explained by core accretion than by gravitational instability.

Question 4

The disk lifetime of 1–10 Myr sets a hard upper bound on how long any formation pathway has to complete the assembly of a gas giant.

• T. True
• F. False

Answer: True

Once a protoplanetary disk disperses through photoevaporation, viscous accretion, or dynamical clearing, the gas a growing core would need to capture is permanently gone. This makes disk lifetime a genuine deadline for gas giant formation, not merely a rough timescale. Any formation pathway that exceeds this deadline cannot produce gas giants, regardless of core size — which is precisely why pebble accretion, dramatically speeding core growth, is considered such an important theoretical advance.

Question 5

Why does disk dispersal set a hard constraint specifically on gas giant formation but not on rocky planet formation?

Model answer: Rocky planets are built from solid material — dust, pebbles, planetesimals, protoplanets — and do not require gas to complete their assembly. Gas giants, by contrast, need a gas-rich disk still present when their core reaches ~10 Earth masses so they can gravitationally capture a massive envelope. Once the disk disperses, that gas is gone permanently. Rocky planet formation can in principle continue from leftover solids even after disk dispersal, just more slowly and without gas-drag-assisted dynamics.

This distinction explains why a stellar system can host both gas giants (which must form quickly, before disk dispersal) and rocky planets (which can continue assembling afterward). It also explains why systems with short-lived disks tend to be gas-giant-poor: the gas vanished before any cores became massive enough to capture it.