Growth model interpretation of planet size distribution

Abstract

The radii and orbital periods of 4000+ confirmed/candidate exoplanets have been precisely measured by the Kepler mission. The radii show a bimodal distribution, with two peaks corresponding to smaller planets (likely rocky) and larger intermediate-size planets, respectively. While only the masses of the planets orbiting the brightest stars can be determined by ground-based spectroscopic observations, these observations allow calculation of their average densities placing constraints on the bulk compositions and internal structures. Yet an important question about the composition of planets ranging from 2 to 4 Earth radii (RÅ) still remains. They may either have a rocky core enveloped in a H2-He gaseous envelope (gas dwarfs) or contain a significant amount of multi-component, H2O-dominated ices/fluids (water worlds). Planets in the mass range of 10-15 MÅ, if half-ice and half-rock by mass, have radii of 2.5 RÅ, which exactly match the second peak of the exoplanet radius bimodal distribution. Any planet in the 2-4 RÅ range requires a gas envelope of at most a few mass%, regardless of the core composition. To resolve the ambiguity of internal compositions, we use a growth model and conduct Monte Carlo simulations to demonstrate that many intermediate-size planets are "water worlds". Keywords: exoplanets / bimodal distribution / ices / water worlds / planet formation Significance Statement: The discovery of numerous exoplanet systems containing diverse populations of planets orbiting very close to their host stars challenges the planet formation theories based on the Solar system. Here we focus on the planets with radii of 2-4 RÅ, whose compositions are debated. They are thought to be either gas dwarfs consisting of rocky cores embedded in H2-rich gas envelopes or water worlds containing significant amounts of H2Odominated fluid/ice in addition to rock and gas. We argue that these planets are water worlds.

Deflating Super-puffs: Impact of Photochemical Hazes on the Observed Mass–Radius Relationship of Low-mass Planets

“…Our clear atmosphere results are similar to those of previous works that considered the impact of adding a H 2 /He atmosphere to a rocky core. For example, we are able to reproduce the rapid increase in planet radius with the addition of only small abundances of gas, the increase in planet radius with temperature for a fixed gas mass fraction, and the increase in planet radius along fixed gas mass fraction contours towards both small and large core masses (Seager et al 2007;Mordasini et al 2012;Zeng et al 2019). Rogers et al (2011) evaluated the impact of atmospheric loss via energy limited escape on the gas mass fraction of planets with a given radius, but did not map the atmospheric lifetimes directly onto their mass-radius diagram.…”

“…Our efforts allow us to produce "hazy" mass-radius diagrams of low-mass planets that take into account atmospheric lifetimes. Mass-radius diagrams have long been used to estimate the composition of planets (Stevenson 1982), with renewed interest in the era of exoplanets (Seager et al 2007;Fortney et al 2007;Rogers et al 2011;Mordasini et al 2012;Zeng et al 2016Zeng et al , 2019. Comparisons of the observed masses and radii of the growing population of worlds beyond our Solar System with standard mass-radius diagrams have shown possible transitions in composition with increasing mass from pure rocks to rocky planets with gas envelopes (or water worlds) to Neptune-like worlds to gas giants (Rogers 2015;Chen & Kipping 2017).…”

“…Given the evolutionary curves of Lopez & Fortney (2014), we use T int = 75 K to represent ∼0.1-3 Gyr old planets, and T int = 30 K to represent >3 Gyr old planets, though we note that T int is higher for higher mass planets than lower mass planets of the same age. The core mass is varied from 1.5M ⊕ to 7.5M ⊕ , and the core radius r c is computed assuming an Earth-like (32.5% Fe+67.5% MgSiO 3 ) mass-radius relationship taken from Zeng et al (2019). The atmospheric mass is varied from 0.1% to 30% of the core mass, capturing the inferred atmospheric mass fractions of sub-Neptunes and superpuffs (Lopez & Fortney 2014).…”

“…Of the remaining super-puffs, Kepler-51d and Kepler-87c cannot be explained by atmospheric masses <0.3M c assuming T int = 75 K. Smaller atmospheric mass fractions are possible if their cores contain more ices, such that they are more like water-worlds (Zeng et al 2019). Alternatively, they could possess higher T int due to a combination of tides and high masses.…”

“…An alternate hypothesis states that at least some of the larger radii population are water worlds (e.g. Zeng et al 2019), where a core of rock and ice underlies a thin gas layer.…”