Probabilistic Mass-Radius Relationship for Sub-Neptune-Sized Planets (1504.07557v2)

Abstract: The Kepler Mission has discovered thousands of planets with radii $<4\ R_\oplus$, paving the way for the first statistical studies of the dynamics, formation, and evolution of these sub-Neptunes and super-Earths. Planetary masses are an important physical property for these studies, and yet the vast majority of Kepler planet candidates do not have theirs measured. A key concern is therefore how to map the measured radii to mass estimates in this Earth-to-Neptune size range where there are no Solar System analogs. Previous works have derived deterministic, one-to-one relationships between radius and mass. However, if these planets span a range of compositions as expected, then an intrinsic scatter about this relationship must exist in the population. Here we present the first probabilistic mass-radius relationship (M-R relation) evaluated within a Bayesian framework, which both quantifies this intrinsic dispersion and the uncertainties on the M-R relation parameters. We analyze how the results depend on the radius range of the sample, and on how the masses were measured. Assuming that the M-R relation can be described as a power law with a dispersion that is constant and normally distributed, we find that $M/M_\oplus=2.7(R/R_\oplus)^{1.3}$, a scatter in mass of $1.9\ M_\oplus$, and a mass constraint to physically plausible densities, is the "best-fit" probabilistic M-R relation for the sample of RV-measured transiting sub-Neptunes ($R_{pl}<4\ R_\oplus$). More broadly, this work provides a framework for further analyses of the M-R relation and its probable dependencies on period and stellar properties.

Probabilistic Mass-Radius Relationship for Sub-Neptune-Sized Planets

This paper advances our understanding of the mass-radius (M-R) relationship for small exoplanets, specifically those falling between Earth and Neptune in size. The researchers introduce a probabilistic M-R relationship, contrasting with the traditionally deterministic models used to estimate planetary masses from known radii. Utilizing a Bayesian framework, they highlight the inherent variability in composition that necessitates a probabilistic relationship, providing parameters capturing the uncertainties of this model.

Key Findings

• Probabilistic Framework: The authors propose a probabilistic M-R relationship using Bayesian statistics, a novel approach that accounts for intrinsic scatter within the planetary population and uncertainties in mass-radius parameters. Their relationship suggests that small exoplanets cannot be accurately described using one-to-one deterministic models due to compositional diversity.
• Model Parameters: The fitted power law suggests the best-fit M-R relation as $M/M_\oplus=2.7(R/R_\oplus)^{1.3}$ with an intrinsic scatter in mass of $1.9M_\oplus$. This scatter is critical for understanding the diversity in sub-Neptune compositions.
• Sample Variability: The paper employs radial velocity (RV) and transit timing variation (TTV) measurements to delineate sample-dependent biases. RV measurements tend to indicate denser planets relative to TTV measurements, highlighting methodological biases or potentially distinct compositional populations.

Implications

• Exoplanet Studies: The introduction of a probabilistic model provides a framework for analyzing mass distributions more accurately, accounting for compositional diversity and measurement uncertainties. This is crucial for refining exoplanet formation and evolutionary theories.
• Data Integration: Future models should consider incorporating additional physical parameters, such as orbital period dependencies, which might further explain variations in the planet’s density and composition. Integrating wider datasets from missions like TESS will enrich the statistical validity.
• Methodology Advancement: The use of hierarchical Bayesian modeling offers pathways to improve data interpretation across astronomy, especially when dealing with heterogeneous datasets and measurement uncertainties.

Speculations on Future Developments

With the anticipated influx of new data from upcoming missions, the probabilistic M-R relationship could evolve to incorporate multi-dimensional dependencies beyond radius alone. This enhancement will arguably provide insights into compositional evolution influenced by proximity to the host star or stellar properties themselves, shaping the landscape for planetology research.

The paper reflects a critical step towards understanding sub-Neptune-sized planets, paving the way for improved models that capture the diversity and complexity inherent in exoplanetary science. Through rigorous probabilistic methodologies, researchers can now glean more accurate insights into these distant worlds.