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

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.