Question

Difficulty: Very hardAligning Data and Predictions with Viewpoints

Scientist 1
Hot Jupiters—gas giant exoplanets orbiting extremely close to their parent stars (typically <0.1 AU< 0.1 \text{ AU})—form *in situ* (in their current locations). This requires a highly dense protoplanetary disk in the stellar vicinity. Because of the high temperatures near the star (>1,500 K> 1,500 \text{ K}), only refractory materials (like iron and silicates) can condense. Consequently, a hot Jupiter formed *in situ* must possess a massive solid core composed of at least 80%80\% refractory silicates and metals by mass, surrounded by a thin, compressed hydrogen and helium envelope making up no more than 20%20\% of the planet's total mass. Volatile compounds (such as water ice and methane) cannot exist in these cores.

Scientist 2
Hot Jupiters cannot form *in situ* because the stellar wind and high temperatures close to a young star deplete the gas required for envelope accretion. Instead, these planets form beyond the 'ice line' (>3.0 AU> 3.0 \text{ AU}) where temperatures are low enough (<150 K< 150 \text{ K}) for water, ammonia, and methane to freeze into volatile ices. This abundance of solid material allows a core to grow rapidly and accrete a massive gas envelope representing at least 90%90\% of the planet's total mass. Gravitational interactions with the gas disk then cause the planet to migrate inward. Thus, a migrated hot Jupiter must have a core consisting of more than 50%50\% volatile ices, and its gaseous envelope must constitute at least 90%90\% of its total mass.

Consider the following table summarizing data for three newly discovered exoplanets:

PlanetOrbit Distance (AU)Core CompositionEnvelope Mass Fraction
Planet X0.040.0485%85\% refractory silicates15%15\%
Planet Y0.050.0560%60\% volatile ices95%95\%
Planet Z0.080.0855%55\% volatile ices85%85\%

Based on the viewpoints of Scientist 1 and Scientist 2, is the following statement true or false?

'The data for Planet Z is consistent with the predictions of Scientist 2 because its core composition satisfies the requirement of containing more than 50%50\% volatile ices.'

Answer: Answer

Answer

False
The statement is false. Scientist 2's hypothesis has two necessary conditions for a migrated hot Jupiter: a core with more than 50%50\% volatile ices and a gas envelope of at least 90%90\% of the planet's mass. Although Planet Z has a core with 55%55\% volatile ices, its envelope is only 85%85\% of its mass. Since it fails to meet the envelope threshold, Planet Z is not consistent with Scientist 2's predictions, making the statement false.

Step-by-Step Solution

1
Identify Scientist 2's requirements for a migrated hot Jupiter.
Scientist 2 requires both a core composition of >50%> 50\% volatile ices and a gaseous envelope constituting at least 90%90\% of the planet's total mass.
To determine the complete set of criteria that must be satisfied for a planet to be consistent with Scientist 2's viewpoint.
2
Compare Planet Z's properties with Scientist 2's requirements.
Planet Z's core contains 55%55\% volatile ices (which satisfies the core requirement of >50%> 50\%), but its envelope is only 85%85\% of its mass (which fails the envelope requirement of at least 90%90\%).
To evaluate whether all of Scientist 2's predictions are met by Planet Z.
3
Determine the truth value of the statement.
Because Planet Z does not meet the envelope requirement, its data is not consistent with Scientist 2's predictions. Therefore, the statement claiming it is consistent is false.
To conclude the evaluation of the statement.

Key Concept

Aligning experimental data with conflicting scientific hypotheses based on multi-variable quantitative criteria.
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