Elevated Eccentricities in the Radius Valley Hint at Water-Rich Mini-Neptunes

Abstract

While recent planet-formation models broadly reproduce the observed population of super-Earths and mini-Neptunes, as well as the bimodal radius distribution (the ``radius valley''), it remains unclear whether all these planets share a common rocky composition (a single popoulation of planets) or instead comprise two distinct populations -- rocky planets and icy planets (two populations of planets). The inferred eccentricity-radius relation, which shows a modest peak near the radius valley, provides a useful diagnostic for distinguishing between these scenarios. Here we use N-body simulations to examine how the radii and eccentricities of close-in planets depend on the masses and orbital configurations of their progenitor protoplanets. We find that final planetary eccentricities scale with the system initial Safronov number. In two-population systems, energy equipartition between rocky and relatively more massive icy protoplanets creates a strong eccentricity contrast between the two groups, which appears as a peak near the radius valley. This signature does not appear if planetary systems are composed exclusively of rocky planets (with or without H-rich atmospheres), as assumed in photoevaporation and core-powered mass loss models. Because the eccentricity-radius relation traces a dichotomy in the underlying protoplanet mass distribution -- most plausibly arising from formation at different disk locations -- our results suggest that a significant fraction of mini-Neptunes are water-worlds. The observed radius and eccentricity distributions may reflect a mixture of systems that host exclusively rocky planets, systems dominated by icy planets, and systems with both rocky and icy planets.

Figures (18)

• Figure 1: Time evolution of the protoplanet's semi-major axis in one representative simulation with $N_{0}=10$, $M_{0}=1 M_\oplus$, and $a_{0,0}=0.05,\mathrm{au}$. The color-coding shows the planetary mass. Gray lines show the pericenter and apocenter of protoplanets' orbits. The IDs of each protoplanet are shown on the right side of the panel.
• Figure 2: Panel-(a): mean eccentricity of planets as a function of their physical radius. Filled circles connected with solid lines show the mean eccentricity of planets in each bin. Different colors correspond to scenarios with different initial masses of protoplanets $M_\mathrm{0}$, as shown in the legend box. The black dashed line combines all simulations. Panel-(b): histogram showing the distribution of planetary radius. The bin size is the same as that in panel (a). Scenarios corresponds to cases where $N_\mathrm{0}=10$ and $a_\mathrm{in,0}=0.05$ au.
• Figure 3: Panel-(a): mean eccentricity of planets as a function of their orbital period. Filled circles connected with solid lines show the mean eccentricity of planets in each bin. We use 11 logarithm bins between 3--100 days. Different colors correspond to cases with different initial masses of protoplanets $M_\mathrm{0}$, as shown in the legend box. Vertical dashed lines show the semi-major axis of the outermost protoplanet at the beggining of the simulations. Scenarios corresponds to cases where $N_\mathrm{0}=10$ and $a_\mathrm{in,0}=0.05$ au. Panel-(b): distribution of the final averaged atmosperic mass fraction $f_\mathrm{atm}$. The bin size is the same as in panel (a).
• Figure 4: Same as Fig. \ref{['fig: Rp_Ecc_single_psMp']}, but for scenarios considering a different initial number of protoplanets. It corresponds to scenarios cases where $M_\mathrm{0}=1M_\oplus$ and $a_\mathrm{in,0}=0.05 \mathrm{au}$. The vertical dotted line shows the core radius at the beginning of the simulations.
• Figure 5: Same as Fig. \ref{['fig: Per_Ecc_single_psMp']}, but for a set of scenarios considering different initial protoplanet number $N_0$. The bin size is same as Fig. \ref{['fig: Per_Ecc_single_psMp']}, but extended to $P=1000$ days.