Questions: Planetary Formation II: Gravitational Instability and Direct Collapse

Question 1

A massive giant planet is observed orbiting at 60 AU from its host star. Core accretion struggles to explain this planet's formation. What is the primary reason core accretion fails at such distances?

• A. At 60 AU, the protoplanetary disk is too hot for planetesimals to stick together
• B. Stellar radiation at 60 AU prevents gas from accumulating around rocky cores
• C. At large orbital distances, orbital periods are long and disk material is sparse, making core growth too slow — the gas disk dissipates before a core can capture a hydrogen envelope
• D. The Toomre Q parameter is always greater than 1 at large distances, preventing any planet formation

Answer: (C)

Core accretion is a bottom-up process requiring millions of years to build a rocky core large enough to capture gas. At large orbital distances (50–100 AU), the physical timescale problem is severe: orbital periods are long (objects move slowly relative to one another), the surface density of solids is low, and collisional growth is extremely slow. Protoplanetary disks typically disperse within a few million years. Core accretion simply cannot build a massive core quickly enough at these distances before the gas disk disappears. Disk instability, which can form a massive planet in thousands of years, provides the only plausible mechanism for observed planets at wide separations.

Question 2

A protoplanetary disk has Toomre Q < 1, meaning it is gravitationally unstable. Under what additional condition will the disk actually fragment into bound objects rather than simply developing spiral density waves?

• A. The disk must be rotating faster than the local orbital velocity
• B. The disk must be closer than 10 AU to the host star
• C. The cooling timescale must be short enough for collapsing regions to radiate away heat before thermal pressure halts contraction
• D. The disk mass must exceed the mass of the host star

Answer: (C)

Gravitational instability is a necessary but not sufficient condition for fragmentation. When a disk region collapses, compression heats the gas. If this heat cannot be radiated away quickly (slow cooling), the pressure buildup halts the collapse and the perturbation instead develops into a spiral arm that redistributes angular momentum without forming a bound object. Only if cooling is rapid enough — the cooling timescale is short compared to the dynamical timescale — can a collapsing clump lose its pressure support and continue contracting into a planet. This cooling criterion is why fragmentation preferentially occurs in the outer, cooler regions of disks.

Question 3

Disk instability can form giant planets on timescales of hundreds to thousands of years — orders of magnitude faster than core accretion.

• T. True
• F. False

Answer: True

This is one of the most striking features of the disk instability mechanism. Because it works by direct gravitational collapse of the disk itself — rather than the incremental bottom-up process of core accretion — it can produce a giant planet in as little as hundreds to thousands of years. Core accretion typically requires millions of years to form a giant planet. This dramatic timescale difference is precisely why disk instability is invoked for planets at large orbital separations where core accretion cannot operate fast enough before the disk disperses.

Question 4

A protoplanetary disk with Toomre Q < 1 will typically fragment directly into planetary-mass objects, regardless of other disk properties.

• T. True
• F. False

Answer: False

Q < 1 is necessary but not sufficient for fragmentation. Even a gravitationally unstable disk (Q < 1) may not fragment if its cooling timescale is too long. In that case, the disk develops spiral density waves — a non-fragmenting response that redistributes angular momentum and mass without forming bound clumps. The disk may also heat up due to the energy released by these waves, raising Q back above 1 and suppressing fragmentation. True fragmentation into bound objects requires Q < 1 AND rapid enough cooling, typically expressed as the cooling timescale being less than a few times the orbital period.

Question 5

Why does disk instability preferentially operate in the outer regions of protoplanetary disks, and why is this complementary to core accretion rather than competing with it?

Model answer: Disk instability requires a disk that is massive enough for self-gravity to overcome thermal pressure and rotational shear (Q < 1) and cool enough for the cooling timescale to be short. The outer disk naturally meets both conditions: it is cooler (lower temperatures give less thermal pressure support) and — in massive disks — can accumulate enough surface density relative to the reduced stellar tidal forces at large radii. Core accretion, by contrast, is most effective in the inner and middle disk where orbital timescales are short and solid density is higher, but it cannot form giant planets at large separations before the disk dissipates. The two mechanisms together explain the full range of observed planetary architectures: core accretion in the inner disk for terrestrial and gas giant planets at moderate distances, disk instability in the outer disk for directly-imaged super-Jupiters at tens to hundreds of AU.

The HR 8799 system, with four giant planets at 15–70 AU, is a key example that is very difficult to explain by core accretion alone and strongly suggests disk instability operated in that system's outer disk. Recognizing that the two mechanisms occupy different niches in parameter space (distance from star, disk mass, cooling efficiency) resolves what initially seems like a competition into a complementary picture.