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

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 to 3 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_(env) = M_(env)/M_p , ranging from ~10% to ~50%. Planets with f_(env) ≈ 50% pose a challenge to traditional models of giant planet formation by core-nucleated accretion, which predict the onset of runaway gas accretion when M_(env) ~ M_(core). Here, we show that many of these apparent f_(env) ≈ 50% 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 nonzero eccentricities, as well as potential obliquities. Consequently, when we apply our models to known sub-Saturns, we infer lower f_(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_(env) ≈ 50%, poised precariously near the runaway threshold; by including tides, however, we find f_(env) ≈ 10%, resolving the tension. Through a systematic analysis of 4–8 R⊕ planets, we find that most (but not all) of the similarly envelope-rich planets have more modest envelopes of f_(env) ≈ 10%–20%. Thus, many sub-Saturns may be understood as sub-Neptunes that have undergone significant radius inflation, rather than a separate class of objects. Tidally induced radius inflation likely plays an important role in other size classes of planets including ultra-low-density Jupiter-size planets like WASP-107 b.