Planetary mass comparison
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Planetary Mass Comparison: Mass-Radius Relations and Population Differences
Mass-Radius Relations for Exoplanets
Research shows that exoplanets can be grouped into two main populations based on their mass and radius: rocky planets and volatile-rich planets. Rocky exoplanets typically have masses up to about 25 Earth masses (M⊕) and show relatively little variation in density, while volatile-rich planets (those with significant atmospheres or water content) overlap in mass and radius but follow a different mass-radius relationship. The transition between these two types occurs in the mass range of 5–25 M⊕ and radius range of 2–3 Earth radii (R⊕) . Empirical formulas describe these relationships: for rocky planets, mass scales with radius to the power of about 3.45, and for volatile-rich planets, mass scales with radius to the power of about 1.58 .
Rocky Planets: Core Mass Fraction and Composition
For rocky planets, the mass-radius relation can be further refined by considering the core mass fraction (CMF). A semi-empirical formula based on Earth's internal structure (PREM) allows for detailed comparison between Earth, Venus, and small exoplanets, showing that rocky planets with masses between 1 and 8 M⊕ and CMF between 0.0 and 0.4 fit well within this model. Earth and Venus, for example, have a CMF of about 0.26 . This approach helps in understanding the internal composition of rocky exoplanets and their similarity to terrestrial planets in our solar system .
Two Regimes in the Mass-Radius Relation
A broader look at planetary populations reveals two regimes in the mass-radius relation: "small" planets (up to about 124 M⊕ and 12.1 R⊕) and "large" planets. For small planets, the radius increases with mass to the power of about 0.55, while for large planets, the radius is almost independent of mass (power of about 0.01). The breakpoint between these regimes is linked to the onset of electron degeneracy in hydrogen, marking the transition to gas giants dominated by hydrogen and helium .
Variations Across Galactic Populations
The mass-radius relationship for solid planets can vary depending on the chemical composition of their host stars, which differs among galactic populations (thin disc, thick disc, halo). For example, planets formed around thick disc stars can have radii 1.5–2% larger than those around thin disc stars for the same mass, due to differences in stellar abundances. These differences become more pronounced for planets with significant water content, especially beyond the ice line .
Planetary Masses in Multi-Planet Systems
Studies of multi-planet systems show that planets within the same system often have similar radii, but their masses can vary significantly. This suggests that while planetary sizes may be uniform, their compositions and densities can differ, especially for planets less massive than about 100 M⊕ and smaller than 10 R⊕ . Additionally, systems with more uniform planetary masses tend to be more dynamically stable, which may explain why many observed multi-planet systems have planets of similar mass .
Differences in Planetary Composition by System Type
Comparisons between single-planet and multi-planet systems, especially around M dwarf stars, reveal that single planets tend to have lower densities than those in multi-planet systems. Rocky planets in multi-planet systems also tend to have lower core mass fractions than single planets. These differences are linked to the metallicity of the host stars, with multi-planet hosts being more metal-poor .
Case Studies: Measured Masses in Multi-Planet Systems
Detailed measurements in systems like K2-32 and K2-233 show a range of planetary masses, from small rocky planets (about 2 M⊕) to Neptune-like planets (up to 15 M⊕). These systems provide important data for understanding the diversity of planetary masses and compositions, especially for planets with short orbital periods and those in the Neptune-mass regime .
Conclusion
Planetary mass comparison reveals clear groupings based on composition, with distinct mass-radius relations for rocky and volatile-rich planets. The transition between these types is well-defined, and variations in mass-radius relations can be linked to both planetary system architecture and the chemical makeup of the host star. Multi-planet systems often show more uniformity in planet size than mass, and systems with similar-mass planets tend to be more stable. These findings are crucial for understanding planet formation, evolution, and the diversity of exoplanetary systems across the galaxy Otegi2019Zeng2015Bashi2017+5 MORE.
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