Question

Difficulty: Very hardComparing and Contrasting Models

The solar system's current architecture of giant planets (Jupiter, Saturn, Uranus, and Neptune) is thought to have evolved from a different initial configuration. Scientists have proposed three competing models to explain the early migration of these planets.

Model 1 (Disk-Driven Migration)
During the first few million years of the solar system, a thick protoplanetary disk of gas and dust was present. Jupiter, forming first, experienced Type II migration, where viscous torques from the surrounding gas disk drove it rapidly inward from its birth site at 3.5 AU3.5\text{ AU} to 1.5 AU1.5\text{ AU}. As Saturn formed and also migrated inward, it was captured into a 3:23:2 mean-motion resonance with Jupiter. In this configuration, the combined gravitational torques of the two planets cleared a gap in the gas disk, reversing their migration direction and forcing both planets to migrate outward until the gas disk dispersed.

Model 2 (Planet-Planet Scattering)
Giant planets formed in a very compact, unstable configuration immediately after the gas disk dissipated (around 10 million years10\text{ million years} after solar system formation). The system remained dynamically stable for a short period until the gravitational influence of the planets on one another triggered a chaotic phase of direct planet-planet scattering. During this phase, close encounters between the planets rapidly modified their orbits. One ice giant was completely ejected from the solar system, while Jupiter was scattered slightly inward and Saturn, Uranus, and Neptune were scattered outward to their current, stable orbits.

Model 3 (Planetesimal-Driven Migration)
Following gas disk dispersal, the giant planets occupied a stable, compact, circular configuration surrounded by a massive outer disk of solid planetesimals. Over approximately 500 million years500\text{ million years}, slow gravitational interactions between the outer planets and the planetesimal disk caused planetesimals to be scattered inward. In reaction to ejecting these planetesimals, Saturn, Uranus, and Neptune slowly migrated outward, while Jupiter migrated slightly inward. This slow migration eventually drove Jupiter and Saturn to cross a 1:21:2 mean-motion resonance. The resonance crossing abruptly increased the eccentricities of Jupiter and Saturn, destabilizing the orbits of Uranus and Neptune and rapidly scattering them into the outer planetesimal disk.

According to the descriptions of the models, both Model 1 and Model 3 rely on a mean-motion resonance between Jupiter and Saturn to explain changes in planetary orbits. Which of the following statements best describes how the two models differ regarding the environment in which this resonance occurs and its primary effect on Jupiter's migration?

  1. In Model 1, the resonance occurs in a gas-rich protoplanetary disk and reverses Jupiter's migration from inward to outward, whereas in Model 3, the resonance occurs in a gas-free planetesimal disk and triggers an orbital instability that leads to Jupiter migrating slightly inward.Answer
  2. B
    In Model 1, the resonance occurs in a gas-free planetesimal disk and reverses Jupiter's migration from inward to outward, whereas in Model 3, the resonance occurs in a gas-rich protoplanetary disk and triggers an orbital instability that leads to Jupiter migrating slightly inward.
  3. C
    In Model 1, the resonance occurs in a gas-rich protoplanetary disk and triggers an orbital instability that leads to Jupiter migrating slightly inward, whereas in Model 3, the resonance occurs in a gas-free planetesimal disk and reverses Jupiter's migration from inward to outward.
  4. D
    In Model 1, the resonance occurs in a gas-free planetesimal disk and triggers an orbital instability that leads to Jupiter migrating slightly inward, whereas in Model 3, the resonance occurs in a gas-rich protoplanetary disk and reverses Jupiter's migration from inward to outward.

Answer

In Model 1, the resonance occurs in a gas-rich protoplanetary disk and reverses Jupiter's migration from inward to outward, whereas in Model 3, the resonance occurs in a gas-free planetesimal disk and triggers an orbital instability that leads to Jupiter migrating slightly inward.
The correct answer accurately states that in Model 1, the resonance occurs during the early gas-rich phase and drives the planets outward, whereas in Model 3, the resonance occurs after the gas disk has dispersed (gas-free) inside a solid planetesimal disk and results in orbital instability with Jupiter migrating slightly inward.

Step-by-Step Solution

1
Analyze the environment and resonance details for Model 1.
Model 1 takes place 'during the first few million years' when a 'thick protoplanetary disk of gas' was present. The 3:23:2 resonance occurs in this gas-rich environment and causes the planets to clear a gap, 'reversing their migration direction' to migrate outward.
Understanding the physical setting and dynamics of Model 1 is necessary to perform a comparison.
2
Analyze the environment and resonance details for Model 3.
Model 3 takes place 'following gas disk dispersal' in an environment surrounded by a 'disk of solid planetesimals'. The 1:21:2 resonance crossing occurs after slow migration (where Jupiter has migrated slightly inward) and triggers orbital instability.
Understanding the physical setting and dynamics of Model 3 completes the profile needed for comparison.
3
Compare the environment and migration outcomes of both models to identify the correct description.
Comparing the two profiles shows that Model 1 features a gas-rich disk with an outward-reversing migration effect, whereas Model 3 features a gas-free planetesimal disk with a migration effect that includes Jupiter moving inward.
Selecting the option that correctly represents these paired differences matches the correct answer.

Key Concept

Comparing the physical environments (gas-rich vs. gas-free planetesimal disks) and dynamic consequences of resonances across different scientific models.
Estimated Time:2m 30s
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