Exoplanets Prediction in Multi-Planetary Systems and Determining the Correlation Between the Parameters of Planets and Host Stars Using Artificial Intelligence

TL;DR

The paper investigates the predictive power of the Titius–Bode (TB) relation for undetected planets in 229 multi-planet systems and complements this with AI-driven analysis of exoplanet–host parameter correlations. It uses TB in log space with Markov chain Monte Carlo (MCMC) to interpolate or extrapolate planetary periods, evaluating dynamical stability and transit probability to predict 426 additional planets, of which 47 lie in habitable zones. Separately, it analyzes 762 confirmed exoplanets (plus Solar System planets) with machine-learning regression and clustering to derive a robust radius predictor—most strongly tied to planetary mass, orbital period, and host-star mass—with the support vector regression (SVR) achieving RMSE ≈ 0.093 across the full dataset. The study uncovers a distinct two-regime structure in the exoplanet population (small vs giant) and a strong radius–host-star mass relation for giants, contributing to our understanding of planet formation and guiding future observations with upcoming facilities.

Abstract

The number of extrasolar planets discovered is increasing, so that more than five thousand exoplanets have been confirmed to date. Now we have an opportunity to test the validity of the laws governing planetary systems and take steps to discover the relationships between the physical parameters of planets and stars. Firstly, we present the results of a search for additional exoplanets in 229 multi-planetary systems that house at least three or more confirmed planets, employing a logarithmic spacing between planets in our Solar System known as the Titius-Bode (TB) relation. We find that the planets in $\sim53\%$ of these systems adhere to a logarithmic spacing relation remarkably better than the Solar System planets. We predict the presence of 426 additional exoplanets, 47 of which are located within the habitable zone (HZ), and five of the 47 planets have a maximum mass limit of 0.1-2$M_{\oplus}$ and a maximum radius lower than 1.25$R_{\oplus}$. Secondly, we employ efficient machine learning approaches to analyze a dataset comprising 762 confirmed exoplanets and eight Solar System planets, aiming to characterize their fundamental quantities. We classify the data into two main classes: 'small' and 'giant' planets, with cut-off values at $R_{p}=8.13R_{\oplus}$ and $M_{p}=52.48M_{\oplus}$. Giant planets have lower densities, suggesting higher H-He mass fractions, while small planets are denser, composed mainly of heavier elements. We highlight that planetary mass, orbital period, and stellar mass play crucial roles in predicting exoplanet radius. Notably, our study reveals a noteworthy result: 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.

Figures (52)

• Figure 1: Classification of young stellar objects (YSOs) based on the slope of their spectral energy distribution (SED). [The image has been reproduced from 2021PhDT........30S.]
• Figure 2: A small element is located in the disk at a distance $a$ from the star. The distance of the element along the disk is $r$, and its distance from the mid-plane of the disk is represented by $z$. [The image has been reproduced from 2009pps..book.....E.]
• Figure 3: The condensation sequence is the order in which chemical compounds go from gas to solid in a protoplanetary disk based on the condensation temperature of each compound. It explains why the solar system has two groups of planets: large, low-density Jovian planets in the outer parts and small, high-density terrestrial planets in the inner parts.
• Figure 4: Overview of the planet formation process. The bottom axis shows the size of objects involved in the process. [Image source: 2021PhDT........30S.]
• Figure 5: Three types of collisions between planetesimals. The two planetesimals can bounce off each other, break into pieces, or stick together.