Tidal Inflation Reconciles Low-Density Sub-Saturns with Core Accretion

TL;DR

This paper introduces a model incorporating tidal heating effects to explain the inflated radii of sub-Saturn exoplanets, revealing that many have lower envelope fractions than previously estimated, aligning them more closely with sub-Neptunes.

Contribution

The study presents a new framework for modeling sub-Saturn interiors that accounts for tidal inflation, resolving discrepancies in envelope mass estimates caused by neglecting tidal effects.

Findings

Tidal heating significantly inflates planetary radii, affecting envelope fraction estimates.

Most sub-Saturns have envelope fractions of 10-20%, not 50%.

Tidal inflation explains the low-density nature of some ultra-low-density planets.

Abstract

While the Solar System contains no planets between the sizes of Uranus and Saturn, our current exoplanet census includes several dozen such planets with well-measured masses and radii. These sub-Saturns exhibit a diversity of bulk densities, ranging from ~$0.1-3\ \rm{g\ cm}^{-3}$. When modeled simply as hydrogen/helium envelopes atop rocky cores, this diversity in densities translates to a diversity in planetary envelope fractions, $f_\rm{env}=M_\rm{env}/M_p$ ranging from ~$10\%$ to ~$50\%$. Planets with $f_\rm{env}\sim50\%$ pose a challenge to traditional models of giant planet formation by core-nucleated accretion, which predict the onset of runaway gas accretion when $M_\rm{env}\sim M_\rm{core}$. Here we show that many of these apparent $f_\rm{env}\sim50\%$ planets are less envelope rich than they seem, after accounting for tidal heating. We present a new framework for modeling sub-Saturn interiors that incorporates envelope inflation due to tides, which are driven by the observed non-zero eccentricities, as well as potential obliquities. Consequently, when we apply our models to known sub-Saturns, we infer lower $f_\rm{env}$ than tides-free estimates. We present a case study of K2-19 b, a moderately eccentric sub-Saturn. Neglecting tides, K2-19 b appears to have $f_\rm{env}\sim50\%$, poised precariously near the runaway threshold; by including tides, we find $f_\rm{env}\sim10\%$, resolving the tension. Through a systematic analysis of $4-8\ R_{\oplus}$ planets, we find that most (but not all) of the similarly envelope-rich planets have more modest envelopes of $f_\rm{env}\sim10\%-20\%$. Thus, many sub-Saturns may be understood as sub-Neptunes that have undergone significant radius inflation, rather than a separate class of objects. Tidal radius inflation likely plays an important role in other size classes of planets including ultra-low-density Jupiter-size planets like WASP-107 b.