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

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.