New Perspectives on the Exoplanet Radius Gap from a Mathematica Tool and Visualized Water Equation of State

Abstract

Recent astronomical observations obtained with the Kepler and TESS missions and their related ground-based follow-ups revealed an abundance of exoplanets with a size intermediate between Earth and Neptune. A low occurrence rate of planets has been identified at around twice the size of Earth, known as the exoplanet radius gap or radius valley. We explore the geometry of this gap in the mass-radius diagram, with the help of a Mathematica plotting tool developed with the capability of manipulating exoplanet data in multidimensional parameter space, and with the help of visualized water equations of state in the temperature-density graph and the entropy-pressure graph. We show that the radius valley can be explained by a compositional difference between smaller, predominantly rocky planets and larger planets that exhibit greater compositional diversity including cosmic ices (water, ammonia, methane) and gaseous envelopes. In particular, among the larger planets, when viewed from the perspective of planet equilibrium temperature, the hot ones are consistent with ice-dominated composition without significant gaseous envelopes, while the cold ones have more diverse compositions, including various amounts of gaseous envelopes.

arXiv comment30 pages, 15 figures

References in corpus (72)

• The chemical composition of the Sun
• The Transiting Exoplanet Survey Satellite
• The K2 Mission: Characterization and Early results
• The California-Kepler Survey. III. A Gap in the Radius Distribution of Small Planets
• The NASA Exoplanet Archive: Data and Tools for Exoplanet Research
• Growth Model Interpretation of Planet Size Distribution
• Homogeneous studies of transiting extrasolar planets. IV. Thirty systems with space-based light curves
• The California Kepler Survey VII. Precise Planet Radii Leveraging Gaia DR2 Reveal the Stellar Mass Dependence of the Planet Radius Gap
• An asteroseismic view of the radius valley: stripped cores, not born rocky
• Core-powered mass loss and the radius distribution of small exoplanets
• Mass-Radius Relation for Rocky Planets based on PREM
• Planetary Candidates Observed by Kepler. VIII. A Fully Automated Catalog With Measured Completeness and Reliability Based on Data Release 25
• Sculpting the Valley in the Radius Distribution of Small Exoplanets as a by-product of Planet Formation: The Core-Powered Mass-Loss Mechanism
• The California-Kepler Survey. IV. Metal-rich Stars Host a Greater Diversity of Planets
• Revised Radii of Kepler Stars and Planets Using Gaia Data Release 2
• Detailed Models of super-Earths: How well can we infer bulk properties?
• A Detailed Model Grid for Solid Planets from 0.1 through 100 Earth Masses
• How to Characterize Habitable Worlds and Signs of Life
• Revisited Mass-Radius relations for exoplanets below 120 Earth masses
• Radius and Structure models for the First Super-Earth Planet
• Signatures of the Core-Powered Mass-Loss Mechanism in the Exoplanet Population: Dependence on Stellar Properties and Observational Predictions
• Six transiting planets and a chain of Laplace resonances in TOI-178
• The Gaia-Kepler Stellar Properties Catalog. II. Planet Radius Demographics as a Function of Stellar Mass and Age
• A new equation of state for dense hydrogen-helium mixtures
• Ab Initio Equation of State for Hydrogen-Helium Mixtures with Recalibration of the Giant-Planet Mass-Radius Relation
• Evolution of the radius valley around low mass stars from $Kepler$ and $K2$
• Ab initio equations of state for hydrogen (H-REOS.3) and helium (He-REOS.3) and their implications for the interior of Brown Dwarfs
• AQUA: A Collection of H${}_2$O Equations of State for Planetary Models
• Irradiated ocean planets bridge super-Earth and sub-Neptune populations
• Planetary evolution with atmospheric photoevaporation I. Analytical derivation and numerical study of the evaporation valley and transition from super-Earths to sub-Neptunes
• Atmosphere Origins for Exoplanet Sub-Neptunes
• Mass and Mass Scalings of Super-Earths
• A Spectroscopic Analysis of the California-Kepler Survey Sample: I. Stellar Parameters, Planetary Radii and a Slope in the Radius Gap
• Scaling K2. I. Revised Parameters for 222,088 K2 Stars and a K2 Planet Radius Valley at 1.9 $R_{\oplus }$
• A pair of TESS planets spanning the radius valley around the nearby mid-M dwarf LTT 3780
• Water on Hot Rocky Exoplanets
• Superabundance of Exoplanet Sub-Neptunes Explained by Fugacity Crisis
• Masses and compositions of three small planets orbiting the nearby M dwarf L231-32 (TOI-270) and the M dwarf radius valley
• Primordial Radius Gap and Potentially Broad Core Mass Distributions of Super-Earths and Sub-Neptunes
• Ab initio based equation of state of dense water for planetary and exoplanetary modeling
• Planetary Ices and the Linear Mixing Approximation
• Testing exoplanet evaporation with multi-transiting systems
• EUV irradiation of exoplanet atmospheres occurs on Gyr timescales
• The sub-Neptune desert and its dependence on stellar type: Controlled by lifetime X-ray irradiation
• An unusually low density ultra-short period super-Earth and three mini-Neptunes around the old star TOI-561
• Evolution of the Exoplanet Size Distribution: Forming Large Super-Earths Over Billions of Years
• A planetary system with two transiting mini-Neptunes near the radius valley transition around the bright M dwarf TOI-776
• The TESS-Keck Survey II: An Ultra-Short Period Rocky Planet and its Siblings Transiting the Galactic Thick-Disk Star TOI-561
• Silicate Melting and Vaporization during Rocky Planet Formation
• TOI-1235 b: a keystone super-Earth for testing radius valley emergence models around early M dwarfs
• Caught in the Act: Core-powered Mass-loss Predictions for Observing Atmospheric Escape
• The Ice Cap Zone: A Unique Habitable Zone for Ocean Worlds
• A sub-Neptune and a non-transiting Neptune-mass companion unveiled by ESPRESSO around the bright late-F dwarf HD 5278 (TOI-130)
• Metallization of Shock-Compressed Liquid Ammonia
• Transits of Known Planets Orbiting a Naked-Eye Star
• Material Properties for the Interiors of Massive Giant Planets and Brown Dwarfs
• Effects of Magnetic Fields on the Location of the Evaporation Valley for Low-Mass Exoplanets
• The Abundance of Atmospheric CO2 in Ocean Exoplanets: A Novel CO2 Deposition Mechanism
• Structure and Dynamics of Cold Water Super-Earths: The Case of Occluded CH4 and its Outgassing
• Abrupt climate transition of icy worlds from snowball to moist or runaway greenhouse
• Bridging the Planet Radius Valley: Stellar Clustering as a Key Driver for Turning Sub-Neptunes into Super-Earths
• Exoplanet Radius Gap Dependence on Host Star Type
• Examining the Radius Valley: a Machine Learning Approach
• A Variable Polytrope Index Applied to Planet and Material Models
• TOI 122b and TOI 237b, two small warm planets orbiting inactive M dwarfs, found by \textit{TESS}
• Survival Function Analysis of Planet Size Distribution with GAIA Data Release 2 Updates
• Star-planet interactions VI. Tides, stellar activity and planet evaporation
• Formation of Planetary Populations III: Core Composition & Atmospheric Evaporation
• The Equation of State of MH-III: a possible deep CH${}_4$ reservoir in Titan, Super-Titan exoplanets and moons
• H-Atmospheres of Icy Super-Earths Formed in situ in the Outer Solar System: An Application to a Possible Planet Nine
• K2-79b and K2-222b: Mass measurements of two small exoplanets with periods beyond 10 days that overlap with periodic magnetic activity signals
• A New Desalination Pump Help Define the pH of Ocean Worlds

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• Cold Jupiters and improved masses in 38 Kepler and K2 small planet systems from 3661 HARPS-N radial velocities. No excess of cold Jupiters in small planet systems
• The Exoplanet Radius Valley from Gas-driven Planet Migration and Breaking of Resonant Chains
• Solubility of water in peridotite liquids and the prevalence of steam atmospheres on rocky planets
• A super-massive Neptune-sized planet
• The mass-radius relation of intermediate-mass planets outlined by hydrodynamic escape and thermal evolution
• MAGRATHEA: an open-source spherical symmetric planet interior structure code
• Role of magma oceans in controlling carbon and oxygen of sub-Neptune atmospheres
• The influence of host star activity evolution on the population of super-Earths and mini-Neptunes
• TOI-1075 b: A Dense, Massive, Ultra-Short Period Hot Super-Earth Straddling the Radius Gap
• A warm super-Neptune around the G-dwarf star TOI-1710 revealed with TESS, SOPHIE and HARPS-N
• A Bayesian Analysis of Technological Intelligence in Land and Oceans
• A sub-Neptune planet around TOI-1695 discovered and characterized with SPIRou and TESS
• Stability of Hydrides in Sub-Neptune Exoplanets with Thick Hydrogen-Rich Atmospheres
• DMPP-4: Candidate sub-Neptune mass planets orbiting a naked-eye star
• Can metal-rich worlds form by giant impacts?
• TOI-733 b: a planet in the small-planet radius valley orbiting a Sun-like star
• Discovery and characterization of a dense sub-Saturn TOI-6651b
• Confronting compositional confusion through the characterisation of the sub-Neptune orbiting HD 77946
• Cosmic Hydrogen and Ice Loss Lines
• JWST unveils a high mean molecular weight atmosphere for mini-Neptune TOI-1130b: Evidence for formation beyond the water ice line
• The impact of two non-transiting planets and stellar activity on mass determinations for the super-Earth CoRoT-7b