Fulton, B. J. et al. The California-Kepler survey. III. A gap in the radius distribution of small planets. Astron. J. 154, 109 (2017).
Bean, J. L., Raymond, S. N. & Owen, J. E. The nature and origins of sub-Neptune size planets. J. Geophys. Res. Planets 126, e2020JE006639 (2021).
Bitsch, B. et al. Dry or water world? How the water contents of inner sub-Neptunes constrain giant planet formation and the location of the water ice line. Astron. Astrophys. 649, L5 (2021).
Misener, W., Schlichting, H. E. & Young, E. D. Atmospheres as windows into sub-Neptune interiors: coupled chemistry and structure of hydrogen–silane–water envelopes. Mon. Not. R. Astron. Soc. 524, 981–992 (2023).
Schlichting, H. E. & Young, E. D. Chemical equilibrium between cores, mantles, and atmospheres of super-Earths and sub-Neptunes and implications for their compositions, interiors, and evolution. Planet. Sci. J. 3, 127 (2022).
Morbidelli, A. et al. Source regions and timescales for the delivery of water to the Earth. Meteorit. Planet. Sci. 35, 1309–1320 (2000).
Ikoma, M. & Genda, H. Constraints on the mass of a habitable planet with water of nebular origin. Astrophys. J. 648, 696 (2006).
Hallis, L. J. et al. Evidence for primordial water in Earth’s deep mantle. Science 350, 795–797 (2015).
Young, E. D., Shahar, A. & Schlichting, H. E. Earth shaped by primordial H2 atmospheres. Nature 616, 306–311 (2023).
Howard, A. W. et al. Planet occurrence within 0.25 AU of solar-type stars from Kepler. Astrophys. J. Suppl. Ser. 201, 15 (2012).
Owen, J. E. & Wu, Y. Kepler planets: a tale of evaporation. Astrophys. J. 775, 105 (2013).
Ginzburg, S., Schlichting, H. E. & Sari, R. Core-powered mass-loss and the radius distribution of small exoplanets. Mon. Not. R. Astron. Soc. 476, 759–765 (2018).
Zeng, L. et al. Growth model interpretation of planet size distribution. Proc. Natl Acad. Sci. USA 116, 9723–9728 (2019).
Venturini, J. & Helled, R. Jupiter’s heavy-element enrichment expected from formation models. Astron. Astrophys. 634, A31 (2020).
Luque, R. & Pallé, E. Density, not radius, separates rocky and water-rich small planets orbiting M dwarf stars. Science 377, 1211–1214 (2022).
Piaulet, C. et al. Evidence for the volatile-rich composition of a 1.5-Earth-radius planet. Nat. Astron. 7, 206–222 (2022).
Piaulet-Ghorayeb, C. et al. JWST/NIRISS reveals the water-rich “Steam World” atmosphere of GJ 9827 d. Astrophys. J. Lett. 974, L10 (2024).
Hirschmann, M. M., Withers, A. C., Ardia, P. & Foley, N. T. Solubility of molecular hydrogen in silicate melts and consequences for volatile evolution of terrestrial planets. Earth Planet. Sci. Lett. 345, 38–48 (2012).
Kite, E. S., Fegley, B. Jr, Schaefer, L. & Ford, E. B. Superabundance of exoplanet sub-neptunes explained by fugacity crisis. Astrophys. J. Lett. 887, L33 (2019).
Sabat, K. C., Rajput, P., Paramguru, R. K., Bhoi, B. & Mishra, B. K. Reduction of oxide minerals by hydrogen plasma: an overview. Plasma Chem. Plasma Process. 34, 1–23 (2014).
Kimura, T. & Ikoma, M. Predicted diversity in water content of terrestrial exoplanets orbiting M dwarfs. Nat. Astron. 6, 1296–1307 (2022).
Krissansen-Totton, J., Wogan, N., Thompson, M. & Fortney, J. J. The erosion of large primary atmospheres typically leaves behind substantial secondary atmospheres on temperate rocky planets. Nat. Commun. 15, 8374 (2024).
Horn, H. W., Prakapenka, V., Chariton, S., Speziale, S. & Shim, S.-H. Reaction between hydrogen and ferrous/ferric oxides at high pressures and high temperatures—implications for sub-neptunes and super-earths. Planet. Sci. J. 4, 30 (2023).
Kim, T. et al. Stability of hydrides in sub-Neptune exoplanets with thick hydrogen-rich atmospheres. Proc. Natl Acad. Sci. USA 120, e2309786120 (2023).
Shinozaki, A. et al. Influence of H2 fluid on the stability and dissolution of Mg2SiO4 forsterite under high pressure and high temperature. Am. Mineral. 98, 1604–1609 (2013).
Shinozaki, A. et al. Formation of SiH4 and H2O by the dissolution of quartz in H2 fluid under high pressure and temperature. Am. Mineral. 99, 1265–1269 (2014).
Stökl, A., Dorfi, E. A., Johnstone, C. P. & Lammer, H. Dynamical accretion of primordial atmospheres around planets with masses between 0.1 and 5 M⊕ in the habitable zone. Astrophys. J. 825, 86 (2016).
Vazan, A., Ormel, C. W., Noack, L. & Dominik, C. Contribution of the core to the thermal evolution of sub-Neptunes. Astrophys. J. 869, 163 (2018).
Goncharov, A. F. et al. X-ray diffraction in the pulsed laser heated diamond anvil cell. Rev. Sci. Instrum. 81, 113902 (2010).
Shen, G. & Lazor, P. Measurement of melting temperatures of some minerals under lower mantle pressures. J. Geophys. Res. Solid Earth 100, 17699–17713 (1995).
Gupta, A., Stixrude, L. & Schlichting, H. E. The miscibility of hydrogen and water in planetary atmospheres and interiors. Astrophys. J. Lett. 982, L35 (2025).
Kim, T. et al. Atomic-scale mixing between MgO and H2O in the deep interiors of water-rich planets. Nat. Astron. 5, 815–821 (2021).
Hirschmann, M. M., Aubaud, C. & Withers, A. C. Storage capacity of H2O in nominally anhydrous minerals in the upper mantle. Earth Planet. Sci. Lett. 236, 167–181 (2005).
Karki, B. B., Ghosh, D. B. & Bajgain, S. K. in Magmas Under Pressure 419–453 (Elsevier, 2018).
Putirka, K. D. & Xu, S. Polluted white dwarfs reveal exotic mantle rock types on exoplanets in our solar neighborhood. Nat. Commun. 12, 6168 (2021).
Aguichine, A., Mousis, O., Deleuil, M. & Marcq, E. Mass–radius relationships for irradiated ocean planets. Astrophys. J. 914, 84 (2021).
Vazan, A., Sari, R. & Kessel, R. A new perspective on the interiors of ice-rich planets: ice-rock mixture instead of ice on top of rock. Astrophys. J. 926, 150 (2022).
Luo, H., Dorn, C. & Deng, J. The interior as the dominant water reservoir in super-Earths and sub-Neptunes. Nat. Astron. 8, 1399–1407 (2024).
Venturini, J., Guilera, O. M., Haldemann, J., Ronco, M. P. & Mordasini, C. The nature of the radius valley: hints from formation and evolution models. Astron. Astrophys. 643, L1 (2020).
Burn, R. et al. A radius valley between migrated steam worlds and evaporated rocky cores. Nat. Astron. 8, 463–471 (2024).
Madhusudhan, N., Piette, A. A. A. & Constantinou, S. Habitability and biosignatures of hycean worlds. Astrophys. J. 918, 1 (2021).
Cherubim, C. et al. TOI-1695 b: a water world orbiting an early-M dwarf in the planet radius valley. Astron. J. 165, 167 (2023).
Osborne, H. L. M. et al. TOI-544 b: a potential water-world inside the radius valley in a two-planet system. Mon. Not. R. Astron. Soc. 527, 11138–11157 (2023).
Izidoro, A. et al. The exoplanet radius valley from gas-driven planet migration and breaking of resonant chains. Astrophys. J. Lett. 939, L19 (2022).
Piermarini, G. J., Block, S., Barnett, J. D. & Forman, R. A. Calibration of the pressure dependence of the R1 ruby fluorescence line to 195 kbar. J. Appl. Phys. 46, 2774–2780 (1975).
Prakapenka, V. et al. Advanced flat top laser heating system for high pressure research at GSECARS: application to the melting behavior of germanium. High Press. Res. 28, 225–235 (2008).
Deemyad, S. et al. Pulsed laser heating and temperature determination in a diamond anvil cell. Rev. Sci. Instrum. 76, 125104 (2005).
Fu, S., Chariton, S., Prakapenka, V. B., Chizmeshya, A. & Shim, S.-H. Stable hexagonal ternary alloy phase in Fe-Si-H at 28.6–42.2 GPa and 3000 K. Phys. Rev. B 105, 104111 (2022).
Fu, S., Chariton, S., Prakapenka, V. B. & Shim, S.-H. Core origin of seismic velocity anomalies at Earth’s core–mantle boundary. Nature 615, 646–651 (2023).
Kulka, B. L., Dolinschi, J. D., Leinenweber, K. D., Prakapenka, V. B. & Shim, S.-H. The bridgmanite–akimotoite–majorite triple point determined in large volume press and laser-heated diamond anvil cell. Minerals 10, 67 (2020).
Prescher, C. & Prakapenka, V. B. DIOPTAS: a program for reduction of two-dimensional X-ray diffraction data and data exploration. High Press. Res. 35, 223–230 (2015).
Shim, S.-H. PeakPo: a python software for x-ray diffraction analysis at high pressure and high temperature. Zenodo https://doi.org/10.5281/zenodo.3376238 (2019).
Ye, Y., Prakapenka, V., Meng, Y. & Shim, S.-H. Intercomparison of the gold, platinum, and MgO pressure scales up to 140 GPa and 2500 K. J. Geophys. Res. Solid Earth 122, 3450–3464 (2017).
Dewaele, A., Fiquet, G. & Gillet, P. Temperature and pressure distribution in the laser-heated diamond–anvil cell. Rev. Sci. Instrum. 69, 2421–2426 (1998).
Holtgrewe, N., Greenberg, E., Prescher, C., Prakapenka, V. B. & Goncharov, A. F. Advanced integrated optical spectroscopy system for diamond anvil cell studies at GSECARS. High Press. Res. 39, 457–470 (2019).
Vazan, A., Helled, R., Kovetz, A. & Podolak, M. Convection and mixing in giant planet evolution. Astrophys. J. 803, 32 (2015).
Saumon, D., Chabrier, G. & van Horn, H. M. An equation of state for low-mass stars and giant planets. Astrophys. J. Suppl. Ser. 99, 713 (1995).
Vazan, A., Kovetz, A., Podolak, M. & Helled, R. The effect of composition on the evolution of giant and intermediate-mass planets. Mon. Not. R. Astron. Soc. 434, 3283–3292 (2013).
Freedman, R. S. et al. Gaseous mean opacities for giant planet and ultracool dwarf atmospheres over a range of metallicities and temperatures. Astrophys. J. Suppl. Ser. 214, 25 (2014).
Shim, S.-H. Experimental data for hydrogen-silicate reaction [Data set]. Zenodo https://doi.org/10.5281/zenodo.15586691 (2025).
Shim, S.-H. Jupyter notebooks for Supplementary Codes (0.0.1). Zenodo https://doi.org/10.5281/zenodo.15678598 (2025).
Sakamaki, K. et al. Melting phase relation of FeHx up to 20 GPa: implication for the temperature of the Earth’s core. Phys. Earth Planet. Interiors 174, 192–201 (2009).
Mosenfelder, J. L., Asimow, P. D. & Ahrens, T. J. Thermodynamic properties of Mg2SiO4 liquid at ultra-high pressures from shock measurements to 200 GPa on forsterite and wadsleyite. J. Geophys. Res. Solid Earth 112, B06208 (2007).
Ohtani, E. Melting relation of Fe2SiO4 up to about 200 kbar. J. Phys. Earth 27, 189–208 (1979).
Andrault, D. et al. Melting behavior of SiO2 up to 120 GPa. Phys. Chem. Miner. 47, 10 (2020).
Zha, C., Liu, H., Tse, J. S. & Hemley, R. J. Melting and high P–T transitions of hydrogen up to 300 GPa. Phys. Rev. Lett. 119, 075302 (2017).
Narygina, O. et al. X-ray diffraction and Mössbauer spectroscopy study of fcc iron hydride FeH at high pressures and implications for the composition of the Earth’s core. Earth Planet. Sci. Lett. 307, 409–414 (2011).
Thompson, E. et al. High-pressure geophysical properties of fcc phase FeHX. Geochem. Geophys. Geosyst. 19, 305–314 (2018).
Kato, C. et al. Stability of fcc phase FeH to 137 GPa. Am. Mineral. 105, 917–921 (2020).
Tagawa, S., Gomi, H., Hirose, K. & Ohishi, Y. High-temperature equation of state of FeH: implications for hydrogen in Earth’s inner core. Geophys. Res. Lett. 49, e2021GL096260 (2022).
Ikuta, D. et al. Interstitial hydrogen atoms in face-centered cubic iron in the Earth’s core. Sci. Rep. 9, 7108 (2019).
Shibazaki, Y. et al. High-pressure and high-temperature phase diagram for Fe0.9Ni0.1–H alloy. Phys. Earth Planet. Inter. 228, 192–201 (2014).
Ohta, K., Suehiro, S., Hirose, K. & Ohishi, Y. Electrical resistivity of fcc phase iron hydrides at high pressures and temperatures. Comptes Rendus Geosci. 351, 147–153 (2019).
Dorogokupets, P. I., Dymshits, A. M., Litasov, K. D. & Sokolova, T. S. Thermodynamics and equations of state of iron to 350 GPa and 6000 K. Sci. Rep. 7, 41863 (2017).
Piet, H. et al. Superstoichiometric alloying of H and close-packed Fe-Ni metal under high pressures: implications for hydrogen storage in planetary core. Geophys. Res. Lett. 50, e2022GL101155 (2023).
