Understanding the Mass-Radius Relation for Sub-Neptunes: Radius as a Proxy for Composition

Abstract

Transiting planet surveys like Kepler have provided a wealth of information on the distribution of planetary radii, particularly for the new populations of super-Earth and sub-Neptune sized planets. In order to aid in the physical interpretation of these radii, we compute model radii for low-mass rocky planets with hydrogen-helium envelopes. We provide model radii for planets 1-20 Earth masses, with envelope fractions from 0.01-20%, levels of irradiation 0.1-1000x Earth's, and ages from 100 Myr to 10 Gyr. In addition we provide simple analytic fits that summarize how radius depends on each of these parameters. Most importantly, we show that at fixed composition, radii show little dependence on mass for planets with more than ~1% of their mass in their envelope. Consequently, planetary radius is to first order a proxy for planetary composition for Neptune and sub-Neptune sized planets. We recast the observed mass-radius relationship as a mass-composition relationship and discuss it in light of traditional core accretion theory. We discuss the transition from rocky super-Earths to sub-Neptune planets with large volatile envelopes. We suggest 1.75 Earth radii as a physically motivated dividing line between these two populations of planets. Finally, we discuss these results in light of the observed radius occurrence distribution found by Kepler.

17 pages, 9 figures, 7 tables, submitted to ApJ

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• Detection and characterization of an ultra-dense sub-Neptune planet orbiting the Sun-like star HD 119130
• Examining the Radius Valley: a Machine Learning Approach
• Potential long-term habitable conditions on planets with primordial H-He atmospheres
• Atmospheric C/O Ratios of Sub-Neptunes with Magma Oceans: Homemade rather than Inherited
• TESS discovery of a sub-Neptune orbiting a mid-M dwarf TOI-2136
• TOI-969: a late-K dwarf with a hot mini-Neptune in the desert and an eccentric cold Jupiter
• Near Mean-motion Resonances in the Systems Observed by Kepler: Affected by Mass Accretion and Type I Migration
• Quantitative estimates of the surface habitability of Kepler-452b
• The influence of host star activity evolution on the population of super-Earths and mini-Neptunes
• Close-in Super-Earths: The first and the last stages of planet formation in an MRI-accreting disc
• Migration and Growth of Protoplanetary Embryos III: Mass and Metallicity Dependence for FGKM main-sequence stars
• A Framework for Characterizing Transmission Spectra of Exoplanets with Circumplanetary Rings
• Kepler's Dark Worlds: a Low Albedo for an Ensemble of Neptunian and Terran Exoplanets
• Physical Parameters of the Multi-Planet Systems HD 106315 and GJ 9827
• Unified simulations of planetary formation and atmospheric evolution II: Rapid disk clearing by photoevaporation yields low-mass super-Earth atmospheres
• Challenges in the detection of gases in exoplanet atmospheres
• Characterisation of 92 Southern TESS Candidate Planet Hosts and a New Photometric [Fe/H] Relation for Cool Dwarfs
• Detection of Exoplanet as a Binary Source of Microlensing Events in WFIRST Survey
• Longevity is the key factor in the search for technosignatures
• Thermal Evolution and magnetic history of rocky planets
• Tidal Heating of Young Super-Earth Atmospheres
• Planetary parameters, XUV environments and mass-loss rates for nearby gaseous planets with X-ray detected host-stars
• The three regimes of atmospheric evaporation for super-Earths and sub-Neptunes
• Planetary evolution with atmospheric photoevaporation II: Fitting the slope of the radius valley by combining boil-off and XUV-driven escape
• The HD 93963 A transiting system: A 1.04d super-Earth and a 3.65 d sub-Neptune discovered by TESS and CHEOPS
• Water content trends in K2-138 and other low-mass multiplanetary systems
• Effect of Core Cooling on the Radius of Sub-Neptune Planets
• K2-291 b: A rocky super-Earth in a 2.2 day orbit
• GJ 3090 b: one of the most favourable mini-Neptune for atmospheric characterisation
• HD207897 b: A dense sub-Neptune transiting a nearby and bright K-type star
• A HARDCORE model for constraining an exoplanet's core size
• TOI-179: a young system with a transiting compact Neptune-mass planet and a low-mass companion in outer orbit
• Atmosphere Loss in Oblique Super-Earth Impacts
• Two Terrestrial Planet Families With Different Origins
• A Mini-Neptune Orbiting the Metal-poor K Dwarf BD+29 2654
• The shared evaporation history of three sub-Neptunes spanning the radius-period valley of a Hyades star
• TKS V. Twin sub-Neptunes Transiting the Nearby G Star HD 63935
• Characterisation of the Warm-Jupiter TOI-1130 system with CHEOPS and photo-dynamical approach
• The TESS-Keck Survey. VI. Two Eccentric sub-Neptunes Orbiting HIP-97166
• Revisiting Kepler-444. II. Rotational, orbital and high-energy fluxes evolution of the system
• Evaluating the Evidence for Water World Populations using Mixture Models
• On the radial velocity detection of additional planets in transiting, slowly rotating M-dwarf systems: the case of GJ 1132
• WASP-169, WASP-171, WASP-175 and WASP-182: three hot Jupiters and one bloated sub-Saturn mass planet discovered by WASP-south
• Sub-Neptunes Are Drier Than They Seem: Rethinking the Origins of Water-Rich Worlds
• Envelopes of embedded super-Earths I. Two-dimensional simulations
• Effects of Dynamical Evolution of Giant Planets on the Delivery of Atmophile Elements During Terrestrial Planet Formation
• Hot-Jupiter Core Mass from Roche-lobe Overflow
• No Metallicity Correlation Associated with the Kepler Dichotomy
• Dynamics and Collisional Evolution of Closely Packed Planetary Systems
• Using HARPS-N to characterise the long-period planets in the PH-2 and Kepler-103 systems
• Predictions of planet detections with near infrared radial velocities in the up-coming SPIRou Legacy Survey-Planet Search
• High resolution near-infrared spectroscopy of a flare around the ultracool dwarf vB 10
• The TEMPO Survey I: Predicting Yields of the Transiting Exosatellites, Moons, and Planets from a 30-day Survey of Orion with the Nancy Grace Roman Space Telescope
• Modification of the radioactive heat budget of Earth-like exoplanets by the loss of primordial atmospheres
• Hot planets around cool stars -- two short-period mini-Neptunes transiting the late K-dwarf TOI-1260
• The Cosmic Shoreline Revisited: A Metric for Atmospheric Retention Informed by Hydrodynamic Escape
• Sub-Jovian desert of exoplanets at its boundaries. Parameter dependence along the main sequence
• Constraining the Densities of the Three Kepler-289 Planets with Transit Timing Variations
• Size evolution of close-in super-Earths through giant impacts and photoevaporation
• Cold Jupiters and small planets: Friends, foes, or indifferent? A search for correlations with the largest exoplanet samples
• Biases in retrieving planetary signals in the presence of quasi-periodic stellar activity
• Survival Function Analysis of Planet Size Distribution with GAIA Data Release 2 Updates
• Atmospheric mass loss of extrasolar planets orbiting magnetically active host stars
• Why do more massive stars host larger planets?
• Interior-atmosphere modelling to assess the observability of rocky planets with JWST
• Hyades Member K2-136c: The Smallest Planet in an Open Cluster with a Precisely Measured Mass
• Hazy with a chance of star spots: constraining the atmosphere of the young planet, K2-33b
• The bulk metallicity of giant planets around M stars
• On the Formation of Super-Earths with Implications for the Solar System
• How planets form by pebble accretion V. Silicate rainout delays contraction of sub-Neptunes
• Another super-dense sub-Neptune in K2-182 b and refined mass measurements for K2-199 b and c
• Evolution of steam worlds: energetic aspects
• Absence of extended atmospheres in low-mass star radius-gap planets GJ 9827 b, GJ 9827 d and TOI-1235 b
• A systematic validation of hot Neptunes in TESS data
• A dense mini-Neptune orbiting the bright young star HD 18599
• Updated Planetary Mass Constraints of the Young V1298 Tau System Using MAROON-X
• TOI-3785 b: A Low-Density Neptune Orbiting an M2-Dwarf Star
• Magnetic Field Evolution of Hot Exoplanets
• A young progenitor for the most common planetary systems in the Galaxy
• Formation of Super-Earths by Tidally-Forced Turbulence
• Rocky sub-Neptunes formed by pebble accretion: Rain of rocks from polluted envelopes
• CHEOPS and TESS view of the ultra-short period super-Earth TOI-561 b
• The Dynamic Proto-atmospheres around Low-Mass Planets with Eccentric Orbits
• From Super-Earths to Mini-Neptunes: Implications of a Surface on Atmospheric Circulation
• Role of Planetary Radius on Atmospheric Escape of Rocky Exoplanets
• Atmospheric Characterization via Broadband Color Filters on the PLAnetary Transits and Oscillations of stars (PLATO) Mission
• Impact of M-dwarf Stellar Wind and Photoevaporation on the Atmospheric Evolution of Small Planets
• Methane Planets and their Mass-Radius Relation
• VaTEST I: Validation of Sub-Saturn Exoplanet TOI-181b in Narrow Orbit from its Host Star
• Dynamical rearrangement of super-Earths during disk dispersal II. Assessment of the magnetospheric rebound model for planet formation scenarios
• A sub-Neptune planet around TOI-1695 discovered and characterized with SPIRou and TESS
• A limit on gas accretion onto close-in super-Earth cores from disk accretion
• The evolutionary track of H/He envelope in the observed population of sub-Neptunes and Super-Earths planets
• TOI-1055 b: Neptunian planet characterised with HARPS, TESS, and CHEOPS
• A Multi-Year Search For Transits Of Proxima Centauri. I: Light Curves Corresponding To Published Ephemerides
• A Holistic and Probabilistic Approach to the Ground-based Data of HAT-P-19 System
• GJ 357 b: A Super-Earth Orbiting an Extremely Inactive Host Star
• Revisiting the HD 21749 Planetary System with Stellar Activity Modeling
• XUV irradiation of young planetary atmospheres. Results from a joint XMM-Newton and HST observation of HIP67522
• An Earth-sized Planet around an M5 Dwarf Star at 22 pc
• Three Warm Jupiters orbiting TOI-6628, TOI-3837, TOI-5027 and one sub-Saturn orbiting TOI-2328
• Assessing the Interior Structure of Terrestrial Exoplanets with Implications for Habitability
• TOI-837 b: characterisation, formation and evolutionary history of an infant warm Saturn-mass planet
• Chemistry During the Gas-rich Stage of Planet Formation
• Prospects for detecting the Rossiter-McLaughlin effect of Earth-like planets: the test case of TRAPPIST-1b and c
• Characterizing K2 Candidate Planetary Systems Orbiting Low-Mass Stars III: A High Mass & Low Envelope Fraction for the Warm Neptune K2-55b
• The GAPS programme at TNG LXIV: An inner eccentric sub-Neptune and an outer sub-Neptune-mass candidate around BD+00 444 (TOI-2443)
• A Homogeneous Catalog of Oscillating Solar-Type Stars Observed by the Kepler Mission and a New Amplitude Scaling Relation Including Chromospheric Activity
• Transit least-squares survey -- III. A $1.9R_{\oplus }$ transit candidate in the habitable zone of Kepler-160 and a nontransiting planet characterized by transit-timing variations
• TOI-908: a planet at the edge of the Neptune desert transiting a G-type star
• Discovery of TOI-1260d and the characterisation of the multi-planet system
• TOI-5108 b and TOI 5786 b: Two transiting sub-Saturns detected and characterized with TESS, MaHPS and SOPHIE
• Tidal Heating of Exomoons in Resonance and Implications for Detection
• The TESS-Keck Survey. XIII. An Eccentric Hot Neptune with a Similar-Mass Outer Companion around TOI-1272
• Possible Evidence for the Presence of Volatiles on the Warm Super-Earth TOI-270 b
• Water-Cooled (sub)-Neptunes Get Better Gas Mileage
• A primordial radius valley as a consequence of planet formation
• Constraining the volatile fraction of planets from transit observations
• Orbital Evolution of Close-in Super-Earths Driven by Atmospheric Escape
• Blowin' in the non-isothermal wind: core-powered mass loss with hydrodynamic radiative transfer
• Identifying Exo-Earth Candidates in Direct Imaging Data through Bayesian Classification
• Transit Depth Variations Reveal TOI-216 b to be a Super-Puff
• Can Rocky Exoplanets with Rings Pose as Sub-Neptunes?
• Not All Sub-Neptune Exoplanets Have Magma Oceans
• In-depth characterization of the Kepler-10 three-planet system with HARPS-N radial velocities and Kepler transit timing variations
• Is planetary inward migration responsible for GJ 504's fast rotation and bright X-ray luminosity? New constraints from eROSITA
• Precise characterisation of HD 15337 with CHEOPS: a laboratory for planet formation and evolution
• Carbon-rich Sub-Neptune Interiors Are Compatible with JWST Observations
• Volatile-rich evolution of molten super-Earth L 98-59 d
• Searching for Hot Water World Candidates with CHEOPS: Refining the radii and analysing the internal structures and atmospheric lifetimes of TOI-238 b and TOI-1685 b
• TOI-733 b: a planet in the small-planet radius valley orbiting a Sun-like star
• Kepler-102: Masses and Compositions for a Super-Earth and Sub-Neptune Orbiting an Active Star
• The Diffusion Limit of Photoevaporation in Primordial Planetary Atmospheres
• The SPACE Program. I. The featureless spectrum of HD 86226 c challenges sub-Neptune atmosphere trends
• The stellar activity-rotation-age relationship under the lens of asteroseismology
• The Impact of Irradiation on the Radius and Thermal Evolution of Transiting Brown Dwarfs
• The GAPS Programme at TNG. LXV. Precise density measurement of TOI-1430 b, a young planet with an evaporating atmosphere
• Diversity of disc viscosities can explain the period ratios of resonant and non-resonant systems of hot super-Earths and mini-Neptunes
• Estimating photoevaporative mass loss of exoplanets with PLATYPOS
• A low-mass sub-Neptune planet transiting the bright active star HD 73344
• Tidal Distortions as a Bottleneck on Constraining Exoplanet Compositions
• Formation of Super-Earths
• The Flare-Activity of 2MASSJ16111534-1757214 in the Upper Scorpius association
• Hydrodynamical simulations of proton ingestion flashes in Type I X-ray Bursts
• Using Kepler Candidates to Examine the Properties of Habitable Zone Exoplanets
• A high stellar multiplicity rate amongst TESS planet candidates in the Neptunian desert using Gaia DR3 astrometry
• A joint effort to discover and characterize two resonant mini Neptunes around TOI-1803 with TESS, HARPS-N and CHEOPS
• Takeout and Delivery: Erasing the Dusty Signature of Late-stage Terrestrial Planet Formation
• Transit Timing Variations in HIP 41378: CHEOPS and TESS confirm a non-transiting sixth planet in the system
• The GAPS Programme at TNG. LIX. A characterisation study of the $\sim$300 Myr old multi-planetary system orbiting the star BD+40 2790 (TOI-2076)
• TESS and HARPS-N unveil two planets transiting TOI-1453. A super-Earth and one of the lowest mass sub-Neptunes
• Three young planets around the K-dwarf K2-198: High-energy environment, evaporation history and expected future
• Mass Derivation of planets K2-21b and K2-21c from Transit Timing Variations
• Exploring the habitability and interior composition of exoplanets lying within the extended habitable zone
• The Dynamical Viability of an Extended Jupiter Ring System
• A Pair of Dynamically Interacting Sub-Neptunes Around TOI-6054
• A tidally detached super Neptune on a strongly misaligned retrograde orbit
• On the Utility of Transmission Color Analysis I: Differentiating Super-Earths and Sub-Neptunes
• X-ray irradiation of three planets around Hyades star K2-136
• Effects of Self-gravity on Mass-loss of the Post-impact Super-Earths
• ASTEP confirmation of a pair of long-period Jupiter-sized planets with extremely low densities transiting TOI-791
• A distant brown dwarf coplanar to a warm Jupiter and a hot super-Earth
• Evidence of a gap in the envelope mass fraction of sub-Saturns
• Characterizing the bolometric-photoevaporative transition in young sub-Neptunes with radiation-hydrodynamic simulations
• The Occurrence-weighted Median Planets Discovered by Transit Surveys Orbiting Solar-type Stars and Their Implications for Planet Formation and Evolution
• Disentangling Atmospheric Compositions of K2-18 b with Next Generation Facilities
• Gas-depleted planet formation occurred in the four-planet system around the red dwarf LHS 1903
• Ohmic dissipation during the formation of super-Earth
• TOI-1634 b: an Ultra-Short Period Keystone Planet Sitting Inside the M Dwarf Radius Valley
• Radio prospects of extrasolar aurorae polaris as a probe of planetary magnetism
• Quantitative Nonequilibrium Pathway from Fundamental Physics to the Emergence and Persistence of Exoplanetary Biospheres
• A Validated Low-to-Intermediate Mass Planetary Interior Structure Model and New Mass-Radius Relations
• Sub-Neptunes Show a Stronger Correlation with Cold Jupiters than Super-Earths Especially in Metal-rich Systems
• NIRPS tightens the mass estimate of GJ 3090 b and detects a planet near the stellar rotation period
• A sub-Saturn Mass-Radius Desert for Planets with Equilibrium Temperature Less than 600 K
• Grain Growth in Escaping Atmospheres: Implications for the Radius Inflation of Super-Puffs
• Refining the Masses and Radii of the Star Kepler-33 and its Five Transiting Planets
• Constraining stellar rotation and planetary atmospheric evolution of a dozen systems hosting sub-Neptunes and super-Earths
• Rapid and Predictive Planet Population Synthesis Model (RAPPS) I. Upgraded model and resulting synthetic populations
• The orbit of Planet Nine
• Impact of Clouds on the Atmosphere-Mantle Interface of Sub-Neptunes
• Sibling Sub-Neptunes Around Sibling M Dwarfs: TOI-521 and TOI-912
• TOI-1201 b: A mini-Neptune transiting a bright and moderately young M dwarf
• TOI-333b: A Neptune Desert planet around a F7V star
• Split Peas in a Pod: Intra-System Uniformity of Super-Earths and Sub-Neptunes
• Atmospheric mass loss and stellar wind effects in young and old systems I: comparative 3D study of TOI-942 and TOI-421 systems
• The TESS-Keck Survey. XI. Mass Measurements for Four Transiting sub-Neptunes orbiting K dwarf TOI-1246
• L 98-59: a Benchmark System of Small Planets for Future Atmospheric Characterization
• The GAPS Programme at the TNG: LXX. TOI-5734b: A hot sub-Neptune orbiting a relatively young K dwarf with an Earth-like density
• TOI-3757 b: A low density gas giant orbiting a solar-metallicity M dwarf
• Improved characterization of the TOI-2141 system: a dense sub-Neptune with non-transiting inner and outer companions
• Thermoelastic Contraction as a Suppressor of Atmospheric Escape in Close-in Exoplanets
• Probing habitable regions with SRG/eROSITA