--- title: Radius valley summary: A shortage of planets between about 1.5 and 2 Earth radii that splits small close-in planets into rocky super-Earths and gas-wrapped sub-Neptunes. science_status: [observed, model] categories: [Planets, Planet formation, Atmospheric science, Exoplanets] aliases: [Fulton gap, Radius gap, Fulton valley, Evaporation valley, Photoevaporation valley, Small planet radius gap] infobox: type: physics_concept name: Radius valley image: File:Radius_valley_histogram.svg definition: "A deficit in the occurrence of close-in planets between about 1.5 and 2.0 Earth radii, separating a population of rocky super-Earths from a population of sub-Neptunes with thin hydrogen-helium envelopes." location_r_earth: {min: 1.5, max: 2.0, note: "around Sun-like stars, orbital periods below about 100 days"} depth: "a factor of 2 or more fewer planets than on either side (Fulton et al. 2017); deeper with the most precise radii (Ho and Van Eylen 2023)" slope_with_period: {value: "R_valley proportional to P^m, m = -0.09 to -0.10", source: "Van Eylen et al. 2018; Petigura et al. 2022"} stellar_mass_dependence: "sub-Neptunes grow from about 2.1 to 2.6 Earth radii over host masses 0.5 to 1.4 M_Sun (R proportional to M_star^0.25)" predicted: "2013 (Owen and Wu; Lopez and Fortney)" discovered: "2017 (California-Kepler Survey, Fulton et al.)" formulae: - "Energy-limited escape: dM/dt = eta pi F_XUV R_p^3 / (G M_p)" - "Valley slope: R_valley proportional to P^m" leading_explanations: [photoevaporation, core-powered mass loss, gas-poor formation, water-rich migrants plus escape] worked_example: "An Earth-like rocky core of 4 to 5 Earth masses is about 1.5 Earth radii across; an envelope of a few per cent of its mass roughly doubles that." sim_use: "Not modelled: the sim assigns super-Earth and mini-Neptune types first and sizes them with type-specific mass-radius laws; envelope loss is not simulated." last_verified: 2026-09-27 refs: - id: fulton2017 type: article-journal author: [{family: "Fulton", given: "Benjamin J."}, {family: "Petigura", given: "Erik A."}, {family: "Howard", given: "Andrew W."}, {family: "Isaacson", given: "Howard"}, {family: "Marcy", given: "Geoffrey W."}, {family: "Cargile", given: "Phillip A."}, {family: "Hebb", given: "Leslie"}, {family: "Weiss", given: "Lauren M."}, {literal: "et al."}] title: "The California-Kepler Survey. III. A gap in the radius distribution of small planets" container-title: "The Astronomical Journal" volume: "154" page: "109" issued: 2017 DOI: 10.3847/1538-3881/aa80eb - id: owen2013 type: article-journal author: [{family: "Owen", given: "James E."}, {family: "Wu", given: "Yanqin"}] title: "Kepler planets: a tale of evaporation" container-title: "The Astrophysical Journal" volume: "775" page: "105" issued: 2013 DOI: 10.1088/0004-637X/775/2/105 - id: lopez2013 type: article-journal author: [{family: "Lopez", given: "Eric D."}, {family: "Fortney", given: "Jonathan J."}] title: "The role of core mass in controlling evaporation: the Kepler radius distribution and the Kepler-36 density dichotomy" container-title: "The Astrophysical Journal" volume: "776" page: "2" issued: 2013 DOI: 10.1088/0004-637X/776/1/2 - id: owen2017 type: article-journal author: [{family: "Owen", given: "James E."}, {family: "Wu", given: "Yanqin"}] title: "The evaporation valley in the Kepler planets" container-title: "The Astrophysical Journal" volume: "847" page: "29" issued: 2017 DOI: 10.3847/1538-4357/aa890a - id: ginzburg2018 type: article-journal author: [{family: "Ginzburg", given: "Sivan"}, {family: "Schlichting", given: "Hilke E."}, {family: "Sari", given: "Re'em"}] title: "Core-powered mass-loss and the radius distribution of small exoplanets" container-title: "Monthly Notices of the Royal Astronomical Society" volume: "476" page: "759-765" issued: 2018 DOI: 10.1093/mnras/sty290 - id: gupta2019 type: article-journal author: [{family: "Gupta", given: "Akash"}, {family: "Schlichting", given: "Hilke E."}] title: "Sculpting the valley in the radius distribution of small exoplanets as a by-product of planet formation: the core-powered mass-loss mechanism" container-title: "Monthly Notices of the Royal Astronomical Society" volume: "487" page: "24-33" issued: 2019 DOI: 10.1093/mnras/stz1230 - id: vaneylen2018 type: article-journal author: [{family: "Van Eylen", given: "V."}, {family: "Agentoft", given: "Camilla"}, {family: "Lundkvist", given: "M. S."}, {family: "Kjeldsen", given: "H."}, {family: "Owen", given: "J. E."}, {family: "Fulton", given: "B. J."}, {family: "Petigura", given: "E."}, {family: "Snellen", given: "I."}] title: "An asteroseismic view of the radius valley: stripped cores, not born rocky" container-title: "Monthly Notices of the Royal Astronomical Society" volume: "479" page: "4786-4795" issued: 2018 DOI: 10.1093/mnras/sty1783 - id: fulton2018 type: article-journal author: [{family: "Fulton", given: "Benjamin J."}, {family: "Petigura", given: "Erik A."}] title: "The California-Kepler Survey. VII. Precise planet radii leveraging Gaia DR2 reveal the stellar mass dependence of the planet radius gap" container-title: "The Astronomical Journal" volume: "156" page: "264" issued: 2018 DOI: 10.3847/1538-3881/aae828 - id: petigura2022 type: article-journal author: [{family: "Petigura", given: "Erik A."}, {family: "Rogers", given: "James G."}, {family: "Isaacson", given: "Howard"}, {family: "Owen", given: "James E."}, {family: "Kraus", given: "Adam L."}, {family: "Winn", given: "Joshua N."}, {family: "MacDougall", given: "Mason G."}, {family: "Howard", given: "Andrew W."}, {literal: "et al."}] title: "The California-Kepler Survey. X. The radius gap as a function of stellar mass, metallicity, and age" container-title: "The Astronomical Journal" volume: "163" page: "179" issued: 2022 DOI: 10.3847/1538-3881/ac51e3 - id: berger2020 type: article-journal author: [{family: "Berger", given: "Travis A."}, {family: "Huber", given: "Daniel"}, {family: "Gaidos", given: "Eric"}, {family: "van Saders", given: "Jennifer L."}, {family: "Weiss", given: "Lauren M."}] title: "The Gaia-Kepler Stellar Properties Catalog. II. Planet radius demographics as a function of stellar mass and age" container-title: "The Astronomical Journal" volume: "160" page: "108" issued: 2020 DOI: 10.3847/1538-3881/aba18a - id: ho2023 type: article-journal author: [{family: "Ho", given: "Cynthia S. K."}, {family: "Van Eylen", given: "Vincent"}] title: "A deep radius valley revealed by Kepler short cadence observations" container-title: "Monthly Notices of the Royal Astronomical Society" volume: "519" page: "4056-4073" issued: 2023 DOI: 10.1093/mnras/stac3802 - id: cloutier2020 type: article-journal author: [{family: "Cloutier", given: "Ryan"}, {family: "Menou", given: "Kristen"}] title: "Evolution of the radius valley around low-mass stars from Kepler and K2" container-title: "The Astronomical Journal" volume: "159" page: "211" issued: 2020 DOI: 10.3847/1538-3881/ab8237 - id: lee2022 type: article-journal author: [{family: "Lee", given: "Eve J."}, {family: "Karalis", given: "Amalia"}, {family: "Thorngren", given: "Daniel P."}] title: "Creating the radius gap without mass loss" container-title: "The Astrophysical Journal" volume: "941" page: "186" issued: 2022 DOI: 10.3847/1538-4357/ac9c66 - id: luque2022 type: article-journal author: [{family: "Luque", given: "R."}, {family: "Pallé", given: "E."}] title: "Density, not radius, separates rocky and water-rich small planets orbiting M dwarf stars" container-title: "Science" volume: "377" page: "1211-1214" issued: 2022 DOI: 10.1126/science.abl7164 - id: rogers2023 type: article-journal author: [{family: "Rogers", given: "James G."}, {family: "Schlichting", given: "Hilke E."}, {family: "Owen", given: "James E."}] title: "Conclusive evidence for a population of water worlds around M dwarfs remains elusive" container-title: "The Astrophysical Journal Letters" volume: "947" page: "L19" issued: 2023 DOI: 10.3847/2041-8213/acc86f - id: venturini2020 type: article-journal author: [{family: "Venturini", given: "Julia"}, {family: "Guilera", given: "Octavio M."}, {family: "Haldemann", given: "Jonas"}, {family: "Ronco", given: "María P."}, {family: "Mordasini", given: "Christoph"}] title: "The nature of the radius valley" container-title: "Astronomy & Astrophysics" volume: "643" page: "L1" issued: 2020 DOI: 10.1051/0004-6361/202039141 - id: burn2024 type: article-journal author: [{family: "Burn", given: "Remo"}, {family: "Mordasini", given: "Christoph"}, {family: "Mishra", given: "Lokesh"}, {family: "Haldemann", given: "Jonas"}, {family: "Venturini", given: "Julia"}, {family: "Emsenhuber", given: "Alexandre"}, {family: "Henning", given: "Thomas"}] title: "A radius valley between migrated steam worlds and evaporated rocky cores" container-title: "Nature Astronomy" volume: "8" page: "463-471" issued: 2024 DOI: 10.1038/s41550-023-02183-7 - id: rogers2015 type: article-journal author: [{family: "Rogers", given: "Leslie A."}] title: "Most 1.6 Earth-radius planets are not rocky" container-title: "The Astrophysical Journal" volume: "801" page: "41" issued: 2015 DOI: 10.1088/0004-637X/801/1/41 - id: ehrenreich2015 type: article-journal author: [{family: "Ehrenreich", given: "David"}, {family: "Bourrier", given: "Vincent"}, {family: "Wheatley", given: "Peter J."}, {family: "Lecavelier des Etangs", given: "Alain"}, {family: "Hébrard", given: "Guillaume"}, {family: "Udry", given: "Stéphane"}, {family: "Bonfils", given: "Xavier"}, {family: "Delfosse", given: "Xavier"}, {literal: "et al."}] title: "A giant comet-like cloud of hydrogen escaping the warm Neptune-mass exoplanet GJ 436b" container-title: "Nature" volume: "522" page: "459-461" issued: 2015 DOI: 10.1038/nature14501 images_wanted: - file: File:Radius_valley_histogram.svg subject: "Diagram: histogram of the radii of small Kepler planets with precise stellar parameters, showing two peaks and the dip between 1.5 and 2.0 Earth radii" source: other note: "Draw our own from the NASA Exoplanet Archive (Kepler planets with Gaia-refined radii, P below 100 days); credit the archive; label 'Diagram'. Do not reproduce the published Fulton et al. figure (AAS copyright)." - file: File:Gliese_436b_hydrogen_tail_ESAHubble.jpg subject: "Artist's impression of the comet-like hydrogen cloud escaping the warm Neptune GJ 436 b" source: esa-hubble page_url: https://esahubble.org/images/heic1515a/ credit: "NASA, ESA, STScI, and G. Bacon" licence: CC BY 4.0 note: "Label 'Artist's concept'." - file: File:Radius_valley_period_radius_sim.svg subject: "Diagram: orbital period against radius for the sim's generated planets between 1 and 4 Earth radii, coloured by type, beside the same plot for real Kepler planets" source: other note: "For a later 'In Pax Abyssi' panel; generate from the committed system sheets and label 'Sim data'." --- The **radius valley**, also called the **Fulton gap**, is a scarcity of planets between about 1.5 and 2 times Earth's radius among worlds that orbit close to their stars. Planets just smaller than the valley are dense and rocky, the [[Super-Earth|super-Earths]]; planets just larger are wrapped in a thin envelope of hydrogen and helium, the [[Mini-Neptune|sub-Neptunes]]. Because the two populations are otherwise so similar, the valley is one of the sharpest clues to how small planets form and how starlight strips their atmospheres. It was predicted in 2013 and found in 2017, and it is still being argued over. ::figure{src="File:Radius_valley_histogram.svg" size=wide alt="A histogram of planet radii from 1 to 4 Earth radii with a tall peak below 1.5, a dip between 1.5 and 2, and a second peak between 2 and 3." caption="Diagram: the number of close-in Kepler planets at each radius. Planets are scarce between about 1.5 and 2 Earth radii."} ## Discovery The Kepler space telescope measured the radii of thousands of planets by the depth of their transits, but a planet's radius is only as good as its star's: a transit gives the ratio of the two sizes. The California-Kepler Survey took spectra of about 1,300 Kepler host stars with the Keck I telescope and cut the uncertainty on their radii to around 11 per cent. With the blur removed, the size distribution of 2,025 planets split in two. There were a factor of two or more fewer planets between 1.5 and 2.0 Earth radii than on either side, with one population below 1.5 Earth radii and another between 2 and 3 :cite[fulton2017]. Later work sharpened the picture. Asteroseismology, which measures stars by their oscillations, gave radii for 117 planets with a median uncertainty of 3.3 per cent and showed the valley to be close to empty :cite[vaneylen2018]. Refitting 431 planets with Kepler's one-minute data found it deeper again :cite[ho2023]. Gaia parallaxes showed that the valley and the planets around it shift with the mass of the host star :cite[fulton2018] :cite[berger2020]. ## Why the valley exists ### The physics of a thin envelope The valley is a consequence of how little gas it takes to make a planet large. An Earth-like mix of rock and iron gets denser as it grows, so its radius rises only slowly with mass: a rocky planet of 4 to 5 Earth masses is only about 1.5 Earth radii across. Hydrogen is so light that an envelope weighing only a few per cent of the planet can double that radius :cite[owen2017]. A planet therefore tends to sit in one of two states: with an envelope it is about twice the size of its core, and without one it is the bare core. Few planets are caught in between, because the in-between state does not last. This also sets a limit on what the valley can tell us from radius alone. A planet above about 1.6 Earth radii is usually too large to be pure rock, which is why most planets of that size have turned out to carry some volatile layer :cite[rogers2015]. ### Photoevaporation The first explanation, and the one that predicted the valley before it was seen, is **photoevaporation**. A young star emits far more X-ray and extreme-ultraviolet (XUV) light than it will later. That radiation heats a planet's upper atmosphere until the gas flows away. In the simplest, "energy-limited" estimate, the rate of mass loss is $$ \dot{M} \approx \frac{\eta\,\pi F_\mathrm{XUV} R_p^3}{G M_p}, $$ where $F_\mathrm{XUV}$ is the XUV flux at the planet, $R_p$ and $M_p$ the planet's radius and mass, $G$ the gravitational constant and $\eta$ an efficiency of order 0.1. The formula shows why the outcome is a split: a puffy planet presents a larger target and holds its gas less tightly, so loss speeds up as a planet swells, and a heavier core resists. Owen and Wu (2013) and Lopez and Fortney (2013) showed that XUV heating over a star's first hundred million years or so should empty a band of radii, leaving stripped cores below it and survivors with envelopes above :cite[owen2013] :cite[lopez2013]. Fitted to the Kepler valley, the model says the stripped cores are rocky and Earth-like in composition, of typically about 3 Earth masses, and formed inside the snow line :cite[owen2017]. Escape of this kind has been seen directly, though on a larger planet. The Hubble Space Telescope found a cloud of hydrogen streaming from the warm Neptune GJ 436 b into a tail far larger than its star :cite[ehrenreich2015]. ::figure{src="File:Gliese_436b_hydrogen_tail_ESAHubble.jpg" size=wide alt="An illustration of a planet in front of a red star, trailing a vast pale cloud of escaping hydrogen." caption="Artist's concept: the hydrogen cloud escaping the warm Neptune GJ 436 b, measured by Hubble. Planets in the radius valley are thought to lose their envelopes in the same way."} ### Core-powered mass loss A second mechanism needs no help from the star's XUV output. A newly formed planet is hot inside, and the heat leaking out of its core and envelope can itself drive the upper atmosphere away, with the star's ordinary light setting how easily the gas escapes. This **core-powered mass loss** works over a billion years rather than a hundred million :cite[ginzburg2018] :cite[gupta2019]. It predicts a valley in almost the same place as photoevaporation, which makes the two hard to tell apart. One test is time. If the valley is carved over billions of years, older stars should host relatively more stripped super-Earths. Using Gaia-refined ages, Berger and colleagues found the ratio of super-Earths to sub-Neptunes rising from 0.61 around stars younger than a billion years to 1.00 around older ones, which favours a slow process :cite[berger2020]. The evidence is not yet decisive, and both processes may act on the same planets. ### Formation without loss, and water worlds Two other ideas put some or all of the valley in place at birth. If some rocky planets assemble late, after the gas disc around the star has mostly dispersed, they never gather an envelope in the first place and can create a gap without any later loss :cite[lee2022]. And if some sub-Neptunes formed beyond the snow line and migrated inward, their bulk could be rich in water rather than being rock with a little hydrogen. Formation models of this kind can reproduce the valley's position, with water-rich migrants above it and stripped rocky cores below; one widely cited model finds that the match to observations needs photoevaporation as well :cite[venturini2020] :cite[burn2024]. ## How the valley moves The valley's shape carries the fingerprints of whatever made it. **With orbital period.** Measured across periods of a few days to about 100 days, the centre of the valley falls slowly toward smaller radii as the orbit widens, as $R_\mathrm{valley} \propto P^{m}$ with $m$ between $-0.09$ and $-0.10$ :cite[vaneylen2018] :cite[petigura2022]. Planets farther out receive less energy, so only smaller, lighter cores are stripped there. Both mass-loss models predict a slope of this sign; gas-poor formation on its own predicts the opposite sign, which is one reason the mass-loss explanations are favoured for Sun-like stars :cite[vaneylen2018]. **With stellar mass.** Around heavier stars both the valley and the sub-Neptunes above it shift to larger radii. Across host masses from 0.5 to 1.4 solar masses, the typical sub-Neptune grows from about 2.1 to 2.6 Earth radii :cite[fulton2018] :cite[petigura2022]. **Around red dwarfs.** For the smallest stars the pattern changes. Around M dwarfs the valley's dependence on the flux a planet receives appears to reverse, and rocky planets outnumber non-rocky ones by a growing margin as the star gets smaller :cite[cloutier2020]. Luque and Pallé (2022) argued that for M-dwarf planets a gap in **density** separates two groups better than radius does, one consistent with pure rock and one with roughly half rock and half water by mass :cite[luque2022]. Others have shown that the same data can be fitted by rocky cores with thin hydrogen envelopes, so the case for a population of water worlds is not yet settled :cite[rogers2023]. See [[Ocean world]] for what a true water world would be like. ## Why it matters The valley ties the sizes of planets to the history of their stars. It says that most close-in super-Earths are probably the stripped cores of planets that were born with hydrogen, and that sub-Neptunes are, for the most part, rocky or water-rich cores carrying a small fraction of their mass as gas. It also marks the practical boundary for anyone looking for rocky worlds with a transit survey: below about 1.5 Earth radii a close-in planet is probably rock, and above 2 it probably is not. :::callout{type=sim title="In Pax Abyssi"} The sim does not simulate the loss of planetary envelopes, so it does not grow a radius valley from physics. It assigns a planet's type first, from its orbital zone and the chemistry of its star's disc, and then sizes it with a mass-radius law chosen for that type: rocky super-Earths, icy super-Earths and mini-Neptunes each have their own. The valley appears on the wiki as observed science, and the [[Super-Earth]] and [[Mini-Neptune]] pages describe how the sim's classes line up against it. ::: ## See also - [[Super-Earth]] - [[Mini-Neptune]] - [[Ocean world]] - [[Hot Neptune desert]] - [[Atmospheric escape]] - [[Planet classification]] - [[Red dwarf]]