Revisiting mass–radius relationships for exoplanet populations: a machine learning insight

Abstract

The growing number of exoplanet discoveries and advances in machine learning techniques have opened new avenues for exploring and understanding the characteristics of worlds beyond our Solar system. In this study, we employ efficient machine learning approaches to analyse a data set comprising 762 confirmed exoplanets and eight Solar system planets, aiming to characterize their fundamental quantities. By applying different unsupervised clustering algorithms, we classify the data into two main classes: ‘small’ and ‘giant’ planets, with cut-off values at Rp = 8.13R⊕ and Mp = 52.48M⊕. This classification reveals an intriguing distinction: giant planets have lower densities, suggesting higher H–He mass fractions, while small planets are denser, composed mainly of heavier elements. We apply various regression models to uncover correlations between physical parameters and their predictive power for exoplanet radius. Our analysis highlights that planetary mass, orbital period, and stellar mass play crucial roles in predicting exoplanet radius. Among the models evaluated, the Support Vector Regression consistently outperforms others, demonstrating its promise for obtaining accurate planetary radius estimates. Furthermore, we derive parametric equations using the M5P and Markov Chain Monte Carlo methods. Notably, our study reveals a noteworthy result: small planets exhibit a positive linear mass–radius relation, aligning with previous findings. Conversely, for giant planets, we observe a strong correlation between planetary radius and the mass of their host stars, which might provide intriguing insights into the relationship between giant planet formation and stellar characteristics.

The Statistical Analysis of Exoplanet and Host Stars Based on Multi-Satellite Data Observations

“…In the study of small planet data, we have also made an interesting discovery [34], namely, that the mass of a minor planet is roughly proportional to the planet's radius (as shown in Figure 10). If the minor planet is treated as a spheroid and fits the density formula, this finding indicates that the density of the minor planet tends to a certain value, it also means that the planet is proportional to the radius squared.…”