Probabilistic Forecasting of the Masses and Radii of Other Worlds (1603.08614v2)

Abstract: Mass and radius are two of the most fundamental properties of an astronomical object. Increasingly, new planet discoveries are being announced with a measurement of one of these terms, but not both. This has led to a growing need to forecast the missing quantity using the other, especially when predicting the detectability of certain follow-up observations. We present am unbiased forecasting model built upon a probabilistic mass-radius relation conditioned on a sample of 316 well-constrained objects. Our publicly available code, Forecaster, accounts for observational errors, hyper-parameter uncertainties and the intrinsic dispersions observed in the calibration sample. By conditioning our model upon a sample spanning dwarf planets to late-type stars, Forecaster can predict the mass (or radius) from the radius (or mass) for objects covering nine orders-of-magnitude in mass. Classification is naturally performed by our model, which uses four classes we label as Terran worlds, Neptunian worlds, Jovian worlds and stars. Our classification identifies dwarf planets as merely low-mass Terrans (like the Earth), and brown dwarfs as merely high-mass Jovians (like Jupiter). We detect a transition in the mass-radius relation at $2.0_{-0.6}^{+0.7} M_\oplus$, which we associate with the divide between solid, Terran worlds and Neptunian worlds. This independent analysis adds further weight to the emerging consensus that rocky Super-Earths represent a narrower region of parameter space than originally thought. Effectively, then, the Earth is the Super-Earth we have been looking for.

• The paper presents a robust probabilistic model for forecasting the mass or radius of exoplanets when one parameter is known, using a mass-radius relation derived from 316 bodies.
• A key finding is the identification of a transition at ~2.0 Earth masses in the mass-radius relation, suggesting a narrower parameter space for rocky Super-Earths.
• The research provides a publicly available software package for predicting missing planetary parameters, which can aid in prioritizing targets for follow-up observations and mission design.

Probabilistic Forecasting of the Masses and Radii of Other Worlds

In the paper titled "Probabilistic Forecasting of the Masses and Radii of Other Worlds," Chen and Kipping address the crucial task of forecasting the mass or radius of astronomical bodies when one of these is known. This capability is particularly pertinent in the context of thousands of exoplanets being discovered with either mass or radius measured, but often not both. The research presents a robust probabilistic model that exploits a mass-radius (MR) relation supported by a dataset of 316 bodies, encompassing objects from dwarf planets to late-type stars.

The key innovation in this paper is the application of a probabilistic framework that acknowledges and incorporates observational uncertainties, hyper-parameter uncertainties, and natural dispersions in the data. The model classifies objects into four distinct categories: Terran, Neptunian, Jovian, and Stellar worlds. This classification is not merely nominal but is intrinsic to the model, which assigns transition points between these categories based on the MR relation.

One of the significant findings of the paper is the identification of a transition in the MR relation at approximately $2.0_{-0.6}^{+0.7}$ Earth masses, suggesting the boundary between terrestrial (rocky) and Neptunian (gaseous envelope) worlds. This result implies that the parameter space for rocky Super-Earths is narrower than previously supposed, a notion that challenges the prevailing understanding of such planets.

The team's approach to model selection involved a rigorous comparison between three-segment and four-segment broken power-law models of the MR relation, with statistical analyses significantly favoring the four-segment model. Each segment, corresponding to a different class of astronomical objects, is characterized by its own power-law index and intrinsic dispersion, leading to a fluid but structured classification scheme.

The implications of this research are manifold. Theoretically, it provides a statistical backbone to the narrative of planetary classification by MR relations, facilitating distinctions between different classes of celestial bodies. Practically, the resulting model holds the potential to significantly impact observational strategies and mission designs, such as those for the TESS and JWST missions. This forecasting model aids in the prioritization of targets for follow-up observations and enhances the understanding of the feasibility of measuring missing planetary parameters.

This work provides a publicly available package, which can be utilized by the research community to predict missing masses or radii with a confidence that factors in both the observational errors and the intrinsic model uncertainties. This tool, accessible on GitHub, can be instrumental for astronomers aiming to efficiently allocate observational resources and refine the scope of future exoplanetary missions.

In essence, the paper by Chen and Kipping emphasizes a robust, probabilistic approach to predicting planetary characteristics and highlights important transitions in planetary formation theories. These insights open avenues for refining the search for Earth-like exoplanets, fundamentally influencing both the statistical assessment of planetary populations and the empirical strategies adopted in planetary science.