Factors Affecting the Radii of Close-in Transiting Exoplanets

TL;DR

This study uses multivariate regression to analyze how factors like irradiation, mass, metallicity, and tidal heating influence the radii of close-in transiting exoplanets, providing equations that accurately predict observed radii.

Contribution

It introduces specific empirical models linking planetary radius to multiple factors, highlighting the distinct influences on different mass regimes of exoplanets.

Findings

Heating increases planetary radii.

Metallicity correlates with smaller radii.

Different models fit Saturn, Jupiter, and high-mass planets.

Abstract

The radius of an exoplanet may be affected by various factors, including irradiation, planet mass and heavy element content. A significant number of transiting exoplanets have now been discovered for which the mass, radius, semi-major axis, host star metallicity and stellar effective temperature are known. We use multivariate regression models to determine the dependence of planetary radius on planetary equilibrium temperature T_eq, planetary mass M_p, stellar metallicity [Fe/H], orbital semi-major axis a, and tidal heating rate H_tidal, for 119 transiting planets in three distinct mass regimes. We determine that heating leads to larger planet radii, as expected, increasing mass leads to increased or decreased radii of low-mass (<0.5R_J) and high-mass (>2.0R_J) planets, respectively (with no mass effect on Jupiter-mass planets), and increased host-star metallicity leads to smaller planetary radii, indicating a relationship between host-star metallicity and planet heavy element content. For Saturn-mass planets, a good fit to the radii may be obtained from log(R_p/R_J)=-0.077+0.450 log(M_p/M_J)-0.314[Fe/H]+0.671 log(a/AU)+0.398 log(T_eq/K). The radii of Jupiter-mass planets may be fit by log(R_p/R_J)=-2.217+0.856 log(T_eq/K)+0.291 log(a/AU). High-mass planets' radii are best fit by log(R_p/R_J)=-1.067+0.380 log(T_eq/K)-0.093 log(M_p/M_J)-0.057[Fe/H]+0.019 log(H_tidal/1x10^{20}). These equations produce a very good fit to the observed radii, with a mean absolute difference between fitted and observed radius of 0.11R_J. A clear distinction is seen between the core-dominated Saturn-mass (0.1-0.5M_J) planets, whose radii are determined almost exclusively by their mass and heavy element content, and the gaseous envelope-dominated Jupiter-mass (0.5-2.0M_J) planets, whose radii increase strongly with irradiating flux, partially offset by a power-law dependence on orbital separation.