Evidence of a gap in the envelope mass fraction of sub-Saturns

TL;DR

This work investigates whether core-accretion leaves observable imprints in the envelope mass fractions of warm sub-Saturns by deriving $f_{env}$ for 26–28 planets using the GASTLI interior-structure model coupled to atmospheric grids. By testing three atmospheric metallicity regimes, the authors reveal a metallicity-dependent bimodality in $f_{env}$ and a consistent gap near $f_{env}\approx0.5$ that could reflect the onset of runaway accretion, in line with theoretical expectations. The results suggest better agreement with planet-formation models at medium-to-high atmospheric metallicities and indicate that direct measurements of atmospheric metallicity are critical to breaking degeneracies and pinning down formation pathways. They also find no significant difference between sub-Saturns in the Neptunian savanna and ridge when comparing envelope fractions, though larger samples are needed to draw firm conclusions. Overall, the study links interior structure inversions to planet-formation physics and underscores the role of envelope enrichment in shaping gas-giant assembly.

Abstract

Under the core-accretion model, gas giants form via runaway accretion. This process starts when the mass of the accreted envelope becomes equal to the mass of the core. Here, we model a population of warm sub-Saturns to search for imprints of their formation history in their internal structure. Using the GAS gianT modeL for Interiors (GASTLI), we calculate a grid of interior structure models on which we perform retrievals for our sample of 28 sub-Saturns to derive their envelope mass fractions ($f_{env}$). For each planet, we run three different retrievals assuming low (-2.0 < log(Fe/H) < 0.5), medium ( 0.5 < log(Fe/H) < 1.4), and high (1.4 < log(Fe/H) < 1.7) atmospheric metallicity. The distribution of $f_{env}$ in our sample is then compared to predictions of planet formation models. When compared to the outcomes of a planetesimal accretion model, we find that we require medium to high atmospheric metallicities to reproduce the simulated planet population. Additionally, we find a bimodal distribution of $f_{env}$ in our sample with a gap that is located at different values of $f_{env}$ for different atmospheric metallicities. For the high atmospheric metallicity case, the gap in the $f_{env}$ distribution is located between 0.5 and 0.7, which is consistent with assumptions by the core-accretion model where runaway accretion starts when $M_{env} \approx M_{core}$ ($f_{env} \sim 0.5$). We also find a bimodal distribution of the hydrogen and helium mass fraction ($f_{H/He}$) with a gap at $f_{H/He} = 0.3$. The location of this gap is independent of the assumed atmospheric metallicity. Lastly, we compare the distributions of our sub-Saturns in the Neptunian savanna to a population of sub-Saturns in the Neptune desert and ridge. We find that the observed $f_{env}$ distribution of savanna and ridge sub-Saturns is consistent with the planets coming from the same underlying population.

Figures (10)

• Figure 1: Mass-radius diagram of the sub-Saturns in our sample. The colored points show the exoplanet population with radii and masses measured to the precision of our selection criteria. Their colors indicate the orbital periods of the planets. The sub-Saturns that were analyzed in this work are overplotted in black.
• Figure 2: Thermal evolution curves for a planet with a CMF of 0.35 and a mass of $0.2\, \mathrm{M}_{\mathrm{J}}$ with varying atmospheric metallicities. The input internal temperatures are converted to ages, and the planet radius at each step is calculated by GASTLI. A higher assumed atmospheric metallicity leads to a lower total radius. After $\sim 1$ Gyr, the change in radius due to the contraction of the planetary envelope is small even for low-metallicity atmospheres.
• Figure 3: Corner plots of the interior structure retrieval for Kepler-280 b. Shown in black is the retrieval without any constraint on $\log(\mathrm{Fe}/\mathrm{H})$. While the CMF is uncorrelated for the majority of $\log(\mathrm{Fe}/\mathrm{H})$ values, for high atmospheric metallicities the inferred CMF decreases significantly. To illustrate this, the contours for low ($-2.0 < \log(\mathrm{Fe}/\mathrm{H}) < 0.5$), medium ($0.5 < \log(\mathrm{Fe}/\mathrm{H}) < 1.4$), and high ($1.4 < \log(\mathrm{Fe}/\mathrm{H}) < 1.7$) atmospheric metallicity retrievals are overplotted in red, blue, and green, respectively.
• Figure 4: Histograms showing the distribution of core masses for the planets in our sample. For low and medium atmospheric metallicities, the inferred core masses are mostly between $10$ and $30~\text{M}_\oplus$. The high $\log(\mathrm{Fe}/\mathrm{H})$ retrievals produce lower core masses. Three large outliers can be seen with core masses $>50~\text{M}_\oplus$.
• Figure 5: Distribution of $f_{env}$ as a function of planet mass for the sub-Saturns in our sample. We derived three different $f_{env}$ for a low (left panel), medium (middle panel), and high (right panel) atmospheric metallicity case. The two planets with unreliable mass or radius measurements are indicated by the diamond markers. Black points are synthetic planets from the planetesimal accretion formation model of APC2020. The gray shaded area indicates planets with masses below the mass limit of our sample. The synthetic planets represent young planets at a time just after their natal disk has photo-evaporated. While they will contract their envelope over time, this does not affect the total mass and envelope mass fraction.