Planetary evolution with atmospheric photoevaporation I. Analytical derivation and numerical study of the evaporation valley and transition from super-Earths to sub-Neptunes

Abstract

Observations have revealed in the Kepler data a depleted region separating smaller super-Earths from larger sub-Neptunes. This can be explained as an evaporation valley between planets with and without H/He that is caused by atmospheric escape. First, we conduct numerical simulations of the evolution of close-in low-mass planets with H/He undergoing escape. Second, we develop an analytical model for the valley locus. We find that the bottom of the valley quantified by the radius of the largest stripped core $R_{\mathrm{b}}$ at a given orbital distance depends only weakly on post-formation H/He mass. The reason is that a high initial H/He mass means that there is more gas to evaporate, but also that the planet density is lower, increasing loss. Regarding stellar $L_{\mathrm{XUV}}$, $R_{\mathrm{b}}$ scales as $L_{\mathrm{XUV}}^{0.135}$. The same weak dependency applies to the efficiency factor $\epsilon$ of energy-limited evaporation. As found numerically and analytically, $R_{\mathrm{b}}$ varies as function of orbital period $P$ for a constant $\epsilon$ as $P^{-2p_{\mathrm{c}}/3}\approx P^{-0.18}$ where $M\propto R^{p_{\mathrm{c}}}$ is the mass-radius relation of solid cores. $R_{\mathrm{b}}$ is about 1.7 $R_{\oplus }$ at a 10-day orbit for an Earth-like composition, increasing linearly with ice mass fraction. The numerical results are explained very well with the analytical model where complete evaporation occurs if the temporal integral over the stellar XUV irradiation absorbed by the planet is larger than binding energy of the envelope in the gravitational potential of the core. The weak dependency on primordial H/He mass, $L_{\mathrm{XUV}}$ and $\epsilon$ explains why observationally the valley is visible, and why theoretically models find similar results. At the same time, given the large observed spread of $L_{\mathrm{XUV}}$, the dependency on it is still strong enough to explain why the valley is not completely empty.

arXiv comment32 pages, 16 figures. Accepted to A&A

References in corpus (73)

• Disk Frequencies and Lifetimes in Young Clusters
• The California-Kepler Survey. III. A Gap in the Radius Distribution of Small Planets
• The PLATO 2.0 Mission
• Planetary Radii across Five Orders of Magnitude in Mass and Stellar Insolation: Application to Transits
• Using FU Orionis Outbursts to Constrain Self-Regulated Protostellar Disk Models
• Evolution of the Solar Activity over Time and Effects on Planetary Atmospheres: I. High-energy Irradiances (1-1700 A)
• Mass-Radius Relationships for Solid Exoplanets
• Most 1.6 Earth-Radius Planets are not Rocky
• Atmospheric Escape from Hot Jupiters
• Models of Giant Planet formation with migration and disc evolution
• Transiting exoplanets from the CoRoT space mission VIII. CoRoT-7b: the first Super-Earth with measured radius
• Growth Model Interpretation of Planet Size Distribution
• The formation and retention of gas giant planets around stars with a range of metallicities
• Internal Structure of Massive Terrestrial Planets
• Extrasolar planet population synthesis I: Method, formation tracks and mass-distance distribution
• A giant comet-like cloud of hydrogen escaping the warm Neptune-mass exoplanet GJ 436b
• An asteroseismic view of the radius valley: stripped cores, not born rocky
• Core-powered mass loss and the radius distribution of small exoplanets
• Planetary evaporation by UV & X-ray radiation: basic hydrodynamics
• Sculpting the Valley in the Radius Distribution of Small Exoplanets as a by-product of Planet Formation: The Core-Powered Mass-Loss Mechanism
• The imprint of exoplanet formation history on observable present-day spectra of hot Jupiters
• Kepler-36: A Pair of Planets with Neighboring Orbits and Dissimilar Densities
• Possible Solutions to the Radius Anomalies of Transiting Giant Planets
• Planetary population synthesis coupled with atmospheric escape: a statistical view of evaporation
• A Framework for Quantifying the Degeneracies of Exoplanet Interior Compositions
• Structure and evolution of super-Earth to super-Jupiter exoplanets: I. heavy element enrichment in the interior
• Characterization of exoplanets from their formation I: Models of combined planet formation and evolution
• The California-Kepler Survey. I. High Resolution Spectroscopy of 1305 Stars Hosting Kepler Transiting Planets
• Revised Radii of Kepler Stars and Planets Using Gaia Data Release 2
• A Framework for Characterizing the Atmospheres of Low-Mass Low-Density Transiting Planets
• Formation and Structure of Low Density Exo-Neptunes
• Characterization of exoplanets from their formation II: The planetary mass-radius relationship
• Atmospheric Escape from Hot Jupiters
• Hot super-Earths stripped by their host stars
• Ab initio Equation of State data for hydrogen, helium, and water and the internal structure of Jupiter
• Highly Siderophile Elements in the Earth's Mantle as a Clock for the Moon-forming Impact
• The coronal X-ray - age relation and its implications for the evaporation of exoplanets
• Atmospheres of low-mass planets: the "boil-off"
• The Mass of Kepler-93b and The Composition of Terrestrial Planets
• Stellar Winds on the Main-Sequence II: the Evolution of Rotation and Winds
• A generalized bayesian inference method for constraining the interiors of super Earths and sub-Neptunes
• In-situ Accretion of Hydrogen-Rich Atmospheres on Short-Period Super-Earths: Implications for the Kepler-11 Planets
• Bulk Composition of GJ 1214b and other sub-Neptune exoplanets
• Formation of Jupiter using opacities based on detailed grain physics
• Atmospheric Mass Loss During Planet Formation: The Importance of Planetesimal Impacts
• Signatures of the Core-Powered Mass-Loss Mechanism in the Exoplanet Population: Dependence on Stellar Properties and Observational Predictions
• Hubble PanCET: An extended upper atmosphere of neutral hydrogen around the warm Neptune GJ 3470 b
• All Six Planets Known to Orbit Kepler-11 Have Low Densities
• A Study of the Accuracy of Mass-Radius Relationships for Silicate-Rich and Ice-Rich Planets up to 100 Earth Masses
• The Formation of Super-Earths and Mini-Neptunes with Giant Impacts
• Born Dry in the Photo-Evaporation Desert: Kepler's Ultra-Short-Period Planets Formed Water-Poor
• Retrieval analysis of 38 WFC3 transmission spectra and resolution of the normalisation degeneracy
• Jupiter's composition: sign of a (relatively) late formation in a chemically evolved protosolar disk
• How formation time-scales affect the period dependence of the transition between rocky super-Earths and gaseous sub-Neptunes and implications for ${\eta }_{\oplus }$
• Metallicity, planet formation, and disc lifetimes
• Hydrodynamics of embedded planets' first atmospheres - III. The role of radiation transport for super-Earth planets
• Impacts of planet migration models on planetary populations. Effects of saturation, cooling and stellar irradiation
• Grain opacity and the bulk composition of extrasolar planets. II. An analytical model for the grain opacity in protoplanetary atmospheres
• Grain opacity and the bulk composition of extrasolar planets. I. Results from scaling the ISM opacity
• Formation, Orbital and Internal Evolutions of Young Planetary Systems
• Testing exoplanet evaporation with multi-transiting systems
• Atmospheric mass loss due to giant impacts: the importance of the thermal component for hydrogen-helium envelopes
• The transiting multi-planet system HD3167: a 5.7 MEarth Super-Earth and a 8.3 MEarth mini-Neptune
• Metallicity-Dependent Signatures in the Kepler Planets
• The sub-Neptune desert and its dependence on stellar type: Controlled by lifetime X-ray irradiation
• K2-106, a system containing a metal-rich planet and a planet of lower density
• Threshold radii of volatile-rich planets
• Hot, rocky and warm, puffy super-Earths orbiting TOI-402 (HD 15337)
• Origin Scenarios for the Kepler 36 Planetary System
• Efficiency of Planetesimal Ablation in Giant Planetary Envelopes
• Formation of compact systems of super-Earths via dynamical instabilities and giant impacts
• Effects of Magnetic Fields on the Location of the Evaporation Valley for Low-Mass Exoplanets
• Examining the Radius Valley: a Machine Learning Approach

Cited by in corpus (83)

• The Nature of the Radius Valley: Hints from Formation and Evolution Models
• AQUA: A Collection of H${}_2$O Equations of State for Planetary Models
• The New Generation Planetary Population Synthesis (NGPPS). II. Planetary population of solar-like stars and overview of statistical results
• Persistence of Flare-Driven Atmospheric Chemistry on Rocky Habitable Zone Worlds
• Conclusive evidence for a population of water-worlds around M-dwarfs remains elusive
• A super-Earth and a sub-Neptune orbiting the bright, quiet M3 dwarf TOI-1266
• Investigating the young AU~Mic system with SPIRou: large-scale stellar magnetic field and close-in planet mass
• Masses and compositions of three small planets orbiting the nearby M dwarf L231-32 (TOI-270) and the M dwarf radius valley
• The Upper Edge of the Neptune Desert Is Stable Against Photoevaporation
• The Exoplanet Radius Valley from Gas-driven Planet Migration and Breaking of Resonant Chains
• Evidence of Three Mechanisms Explaining the Radius Anomaly of Hot Jupiters
• A new perspective on interiors of ice-rich planets: Ice-rock mixture instead of ice on top of rock
• A deep radius valley revealed by Kepler short cadence observations
• How to identify exoplanet surfaces using atmospheric trace species in hydrogen-dominated atmospheres
• Creating the Radius Gap without Mass Loss
• A fading radius valley towards M-dwarfs, a persistent density valley across stellar types
• The New Generation Planetary Population Synthesis (NGPPS). V. Predetermination of planet types in global core accretion models
• TOI-1452 b: SPIRou and TESS reveal a super-Earth in a temperate orbit transiting an M4 dwarf
• Most super-Earths formed by dry pebble accretion are less massive than 5 Earth masses
• A planetary system with two transiting mini-Neptunes near the radius valley transition around the bright M dwarf TOI-776
• The young HD 73583 (TOI-560) planetary system: Two 10-M${}_{\oplus }$ mini-Neptunes transiting a 500-Myr-old, bright, and active K dwarf
• Chemical variation with altitude and longitude on exo-Neptunes: Predictions for Ariel phase-curve observations
• The JADE code: Coupling secular exoplanetary dynamics and photo-evaporation
• New Perspectives on the Exoplanet Radius Gap from a Mathematica Tool and Visualized Water Equation of State
• Shallower radius valley around low-mass hosts: Evidence for icy planets, collisions or high-energy radiation scatter
• Characterisation of the upper atmospheres of HAT-P-32 b, WASP-69 b, GJ 1214 b, and WASP-76 b through their He I triplet absorption
• Cleaning our Hazy Lens: Exploring Trends in Transmission Spectra of Warm Exoplanets
• The mass-radius relation of intermediate-mass planets outlined by hydrodynamic escape and thermal evolution
• Possibilities for an Aerial Biosphere in Temperate Sub Neptune-Sized Exoplanet Atmospheres
• Possible Atmospheric Diversity of Low Mass Exoplanets, some Central Aspects
• Unveiling the internal structure and formation history of the three planets transiting HIP 29442 (TOI-469) with CHEOPS
• Bioverse: The Habitable Zone Inner Edge Discontinuity as an Imprint of Runaway Greenhouse Climates on Exoplanet Demographics
• Bridging the Planet Radius Valley: Stellar Clustering as a Key Driver for Turning Sub-Neptunes into Super-Earths
• Two super-Earths at the edge of the habitable zone of the nearby M dwarf TOI-2095
• Potential long-term habitable conditions on planets with primordial H-He atmospheres
• The influence of host star activity evolution on the population of super-Earths and mini-Neptunes
• Planetary evolution with atmospheric photoevaporation II: Fitting the slope of the radius valley by combining boil-off and XUV-driven escape
• A Spectroscopic Analysis of the California-Kepler Survey Sample: II. Correlations of Stellar Metallicities with Planetary Architectures
• Dynamical Evolution of Closely Packed Multiple Planetary Systems Subject to Atmospheric Mass-Loss
• Revisiting Kepler-444. II. Rotational, orbital and high-energy fluxes evolution of the system
• The HARPS search for southern extra-solar planets. XLVI: 12 super-Earths around the solar type stars HD39194, HD93385, HD96700, HD154088, and HD189567
• Exoplanet atmosphere evolution: emulation with neural networks
• A CHEOPS-enhanced view of the HD3167 system
• Evolution of steam worlds: energetic aspects
• How planets form by pebble accretion V. Silicate rainout delays contraction of sub-Neptunes
• Giant Outer Transiting Exoplanet Mass (GOT 'EM) Survey: III. Recovery and Confirmation of a Temperate, Mildly Eccentric, Single-Transit Jupiter Orbiting TOI-2010
• Observing atmospheric escape in sub-Jovian worlds with JWST
• Validation and atmospheric exploration of the sub-Neptune TOI-2136b around a nearby M3 dwarf
• Rocky sub-Neptunes formed by pebble accretion: Rain of rocks from polluted envelopes
• Role of Planetary Radius on Atmospheric Escape of Rocky Exoplanets
• Discovery of a massive giant planet with extreme density around a sub-giant star TOI-4603
• Formation of Planetary Populations III: Core Composition & Atmospheric Evaporation
• Three Saturn-mass planets transiting F-type stars revealed with TESS and HARPS
• Unveiling the Planet Population at Birth
• NIGHT: a compact, near-infrared, high-resolution spectrograph to survey helium in exoplanet systems
• On the origin of Jupiter's fuzzy core: constraints from N-body, impact and evolution simulations
• A primordial radius valley as a consequence of planet formation
• The high-energy environment of the heavy sub-Earth GJ 367 b indicates likely complete evaporation of its atmosphere
• 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
• Coupled Thermal-Chemical Evolution Models of Sub-Neptunes Reveal Atmospheric Signatures of Their Formation Location
• The Diffusion Limit of Photoevaporation in Primordial Planetary Atmospheres
• Relative occurrence rates of terrestrial planets orbiting FGK stars
• An upper limit for the growth of inner planets?
• The New Generation Planetary Population Synthesis (NGPPS) VIII. Impact of host star metallicity on planet occurrence rates, orbital periods, eccentricities, and radius valley morphology
• Stellar rotation and its connection to the evolution of hydrogen-dominated atmospheres of exoplanets
• TOI-3568 b: a super-Neptune in the sub-Jovian desert
• Formation of organic hazes in CO${}_2$-rich sub-Neptune atmospheres within the graphite-stability regime
• Three young planets around the K-dwarf K2-198: High-energy environment, evaporation history and expected future
• Takeout and Delivery: Erasing the Dusty Signature of Late-stage Terrestrial Planet Formation
• Exploring the habitability and interior composition of exoplanets lying within the extended habitable zone
• Evolution of gas envelopes and outgassed atmospheres of rocky planets formed via pebble accretion
• Confirmation of the hot super-Neptune TOI-672 b with NIRPS and HARPS and Insights into the Neptunian desert around M dwarfs
• Oxygen left behind: Atmospheric Enrichment due to Fractionation in Sub-Neptunes using BOREAS
• On the Ordering of Exoplanet Systems
• Evolution and Observable Properties of Rocky Planet Atmospheres
• A Validated Low-to-Intermediate Mass Planetary Interior Structure Model and New Mass-Radius Relations
• Bioverse: Potentially Observable Exoplanet Biosignature Patterns Under the UV Threshold Hypothesis for the Origin of Life
• Retention of primordial atmospheres through giant impacts
• Atmospheric mass loss and stellar wind effects in young and old systems II: Is TOI-942 the past of TOI-421 system?
• Did Uranus' regular moons form via a rocky giant impactor?
• Evolution of Mercury's Earliest Atmosphere
• TOI-1201 b: A mini-Neptune transiting a bright and moderately young M dwarf
• A Search for helium in the atmospheres of three sub-Neptunes and a super-Earth around M-dwarfs