Lichtenberg, T. & Miguel, Y. in Treatise on Geochemistry 3rd edn., Vol. 7 (eds Anbar, A. & Weis, D.) Ch. 3 (Elsevier, 2025).

Fulton, B. J. & Petigura, E. A. The California-Kepler Survey. VII. Precise planet radii leveraging Gaia DR2 reveal the stellar mass dependence of the planet radius gap. Astron. J. 156, 264 (2018).

Article 
ADS 

Google Scholar
 

David, T. J. et al. Evolution of the exoplanet size distribution: forming large super-earths over billions of years. Astron. J. 161, 265 (2021).

Article 
ADS 

Google Scholar
 

Valencia, D., Moro-Martin, A. & Teske, J. in Treatise on Geochemistry 3rd edn., Vol. 7 (eds Anbar, A. & Weis, D.) Ch. 2 (Elsevier, 2025).

Zeng, L. et al. Growth model interpretation of planet size distribution. Proc. Natl Acad. Sci. USA 116, 9723–9728 (2019).

Article 
ADS 

Google Scholar
 

Owen, J. E. Atmospheric escape and the evolution of close-in exoplanets. Annu. Rev. Earth Planet. Sci. 47, 67–90 (2019).

Article 
ADS 

Google Scholar
 

Lopez, E. D. Born dry in the photoevaporation desert: Kepler’s ultra-short-period planets formed water-poor. Mon. Not. R. Astron. Soc. 472, 245–253 (2017).

Article 
ADS 

Google Scholar
 

Mousis, O. et al. Irradiated ocean planets bridge super-earth and sub-neptune populations. Astrophys. J. Lett. 896, 22 (2020).

Article 
ADS 

Google Scholar
 

Luque, R. & Palle, E. Density, not radius, separates rocky and water-rich small planets orbiting M dwarf stars. Science 377, 1211–1214 (2022).

Article 
ADS 

Google Scholar
 

Lacedelli, G. et al. Investigating the architecture and internal structure of the Toi-561 system planets with Cheops, Harps-n, and Tess. Mon. Not. R. Astron. Soc. 511, 4551–4571 (2022).

Article 
ADS 

Google Scholar
 

Burn, R. et al. A radius valley between migrated steam worlds and evaporated rocky cores. Nat. Astron. 8, 463–471 (2024).

Article 
ADS 

Google Scholar
 

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).

Article 
ADS 

Google Scholar
 

Rogers, J. G. On the road to the radius valley: distinguishing between gas dwarfs and water worlds with young transiting exoplanets. Mon. Not. R. Astron. Soc. 539, 2230–2241 (2025).

Article 
ADS 

Google Scholar
 

Fernandes, R. B. et al. Signatures of atmospheric mass loss and planet migration in the time evolution of short-period transiting exoplanets. Astron. J. 169, 208 (2025).

Article 
ADS 

Google Scholar
 

Demangeon, O. D. S. et al. Warm terrestrial planet with half the mass of Venus transiting a nearby star. Astron. Astrophys. 653, 41 (2021).

Article 

Google Scholar
 

Kostov, V. B. et al. The L 98-59 system: three transiting, terrestrial-size planets orbiting a nearby M dwarf. Astron. J. 158, 32 (2019).

Article 
ADS 

Google Scholar
 

Zhou, L., Ma, B., Wang, Y. & Zhu, Y. Hubble WFC3 spectroscopy of the rocky planet L 98-59 b: no evidence for a cloud-free primordial atmosphere. Astron. J. 164, 203 (2022).

Article 
ADS 

Google Scholar
 

Bello-Arufe, A. et al. Evidence for a volcanic atmosphere on the sub-Earth L 98-59 b. Astrophys. J. Lett. 980, L26 (2025).

Article 
ADS 

Google Scholar
 

Zhou, L., Ma, B., Wang, Y.-H. & Zhu, Y.-N. Hubble WFC3 spectroscopy of the terrestrial planets L 98-59 c and d: no evidence for a clear hydrogen dominated primary atmosphere. Res. Astron. Astrophys. 23, 025011 (2023).

Article 
ADS 

Google Scholar
 

Cadieux, C. et al. Detailed architecture of the L 98-59 system and confirmation of a fifth planet in the habitable zone. Astron. J. 170, 154 (2025).

Article 
ADS 

Google Scholar
 

Gressier, A. et al. Hints of a sulfur-rich atmosphere around the 1.6 R ⊕ super-Earth L98-59 d from JWST NIRspec G395H transmission spectroscopy. Astrophys. J. Lett. 975, 10 (2024).

Article 
ADS 

Google Scholar
 

Banerjee, A. et al. Atmospheric retrievals suggest the presence of a secondary atmosphere and possible sulfur species on l98-59 d from JWST nirspec g395h transmission spectroscopy. Astrophys. J. Lett. 975, 11 (2024).

Article 
ADS 

Google Scholar
 

Parc, L., Bouchy, F., Venturini, J., Dorn, C. & Helled, R. From super-Earths to sub-Neptunes: observational constraints and connections to theoretical models. Astron. Astrophys. 688, 59 (2024).

Article 
ADS 

Google Scholar
 

Rajpaul, V. M., Barragán, O. & Zicher, N. A non-zero Doppler amplitude is not enough: revisiting the putative radial velocity detection of sub-Venus exoplanet L 98-59b. Mon. Not. R. Astron. Soc. 530, 4665–4675 (2024).

Article 
ADS 

Google Scholar
 

Lichtenberg, T. et al. Vertically resolved magma ocean-protoatmosphere evolution: H2, H2 O, CO2, CH4, CO, O2, and N2 as PRIMARY ABSORBERS. J. Geophys. Res.: Planets 126, e2020JE006711 (2021).

Article 
ADS 

Google Scholar
 

Nicholls, H., Lichtenberg, T., Bower, D. J. & Pierrehumbert, R. Magma ocean evolution at arbitrary redox state. J. Geophys. Res.: Planets 129, e2024JE008576 (2024).

Article 
ADS 

Google Scholar
 

Nicholls, H., Pierrehumbert, R. T., Lichtenberg, T., Soucasse, L. & Smeets, S. Convective shutdown in the atmospheres of lava worlds. Mon. Not. R. Astron. Soc. 536, 2957–2971 (2024).

Article 
ADS 

Google Scholar
 

Nicholls, H. et al. Self-limited tidal heating and prolonged magma oceans in the L 98-59 system. Mon. Not. R. Astron. Soc. 541, 2566–2584 (2025).

Article 
ADS 

Google Scholar
 

Innes, H., Tsai, S.-M. & Pierrehumbert, R. T. The runaway greenhouse effect on hycean worlds. Astrophys. J. 953, 168 (2023).

Article 
ADS 

Google Scholar
 

Lehmer, O. R. & Catling, D. C. Rocky worlds limited to 1.8 earth radii by atmospheric escape during a star’s extreme UV saturation. Astrophys. J. 845, 130 (2017).

Article 
ADS 

Google Scholar
 

Venturini, J. et al. The nature of the radius valley. Hints from formation and evolution models. Astron. Astrophys. 643, 1 (2020).

Article 

Google Scholar
 

Righter, K., Sutton, S. R., Danielson, L., Pando, K. & Newville, M. Redox variations in the inner solar system with new constraints from vanadium XANES in spinels. Am. Mineral. 101, 1928–1942 (2016).

Article 
ADS 

Google Scholar
 

Gaillard, F. et al. Redox controls during magma ocean degassing. Earth Planet. Sci. Lett. 577, 117255 (2022).

Article 

Google Scholar
 

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).

Article 
ADS 

Google Scholar
 

Krijt, S. et al. in Protostars and Planets VII (eds Inutsuka, S. et al.) Ch. 28 (Astronomical Society of the Pacific, 2023).

Owen, J. E. & Wu, Y. The evaporation valley in the Kepler planets. Astrophys. J. 847, 29 (2017).

Article 
ADS 

Google Scholar
 

Costa, A., Caricchi, L. & Bagdassarov, N. A model for the rheology of particle-bearing suspensions and partially molten rocks. Geochem. Geophys. Geosys. 10, Q03010 (2009).

Article 
ADS 

Google Scholar
 

Namur, O., Charlier, B., Holtz, F., Cartier, C. & McCammon, C. Sulfur solubility in reduced mafic silicate melts: implications for the speciation and distribution of sulfur on mercury. Earth Planet. Sci. Lett. 448, 102–114 (2016).

Article 
ADS 

Google Scholar
 

Kubyshkina, D., Vidotto, A. A., Fossati, L. & Farrell, E. Coupling thermal evolution of planets and hydrodynamic atmospheric escape in mesa. Mon. Not. R. Astron. Soc. 499, 77–88 (2020).

Article 
ADS 

Google Scholar
 

Lopez, E. D. & Fortney, J. J. Understanding the mass-radius relation for sub-neptunes: radius as a proxy for composition. Astrophys. J. 792, 1 (2014).

Article 
ADS 

Google Scholar
 

Pierrehumbert, R. Principles of Planetary Climate (Cambridge Univ. Press, 2010).

Dorn, C. & Lichtenberg, T. Hidden water in magma ocean exoplanets. Astrophys. J. Lett. 922, 4 (2021).

Article 
ADS 

Google Scholar
 

Shorttle, O., Jordan, S., Nicholls, H., Lichtenberg, T. & Bower, D. J. Distinguishing oceans of water from magma on mini-Neptune k2-18b. Astrophys. J. Lett. 962, 8 (2024).

Article 
ADS 

Google Scholar
 

Elkins-Tanton, L. T. Magma oceans in the inner solar system. Annu. Rev. Earth Planet. Sci. 40, 113–139 (2012).

Hirschmann, M. M. Magma ocean influence on early atmosphere mass and composition. Earth Planet. Sci. Lett. 341-344, 48–57 (2012).

Article 
ADS 

Google Scholar
 

Marty, B., Zimmermann, L., Pujol, M., Burgess, R. & Philippot, P. Nitrogen isotopic composition and density of the Archean atmosphere. Science 342, 101–104 (2013).

Article 
ADS 

Google Scholar
 

Halliday, A. N. & Canup, R. M. The accretion of planet earth. Nat. Rev. Earth Environ. 4, 19–35 (2023).

Article 
ADS 

Google Scholar
 

Tsai, S.-M. et al. Photochemically produced SO2 in the atmosphere of WASP-39b. Nature 617, 483–487 (2023).

Article 
ADS 

Google Scholar
 

Powell, D. et al. Sulfur dioxide in the mid-infrared transmission spectrum of wasp-39b. Nature 626, 979–983 (2024).

Article 
ADS 

Google Scholar
 

Gressier, A. et al. JWST-TST DREAMS: sulfur dioxide in the atmosphere of the Neptune-mass planet hat-p-26 b from nirspec g395h transmission spectroscopy. Astron. J. 170, 292 (2025).

Article 
ADS 

Google Scholar
 

Wang, H. S., Lineweaver, C. H. & Ireland, T. R. The elemental abundances (with uncertainties) of the most earth-like planet. Icarus 299, 460–474 (2018).

Article 
ADS 

Google Scholar
 

Wade, J. & Wood, B. J. Core formation and the oxidation state of the Earth. Earth Planet. Sci. Lett. 236, 78–95 (2005).

Article 
ADS 

Google Scholar
 

Peslier, A. H., Schonbachler, M., Busemann, H. & Karato, S.-I. Water in the earth’s interior: distribution and origin. Space Sci. Rev. 212, 743–810 (2017).

Article 
ADS 

Google Scholar
 

Kite, E. S., Fegley Jr, B. F., Schaefer, L. & Gaidos, E. Atmosphere-interior exchange on hot, rocky exoplanets. Astrophys. J. 828, 80 (2016).

Article 
ADS 

Google Scholar
 

Kite, E. S. & Barnett, M. N. Exoplanet secondary atmosphere loss and revival. Proc. Natl Acad. Sci. USA 117, 18264–18271 (2020).

Article 
ADS 

Google Scholar
 

Bower, D. J., Sanan, P. & Wolf, A. S. Numerical solution of a non-linear conservation law applicable to the interior dynamics of partially molten planets. Phys. Earth Planet. Inter. 274, 49–62 (2018).

Article 
ADS 

Google Scholar
 

Bower, D. J., Hakim, K., Sossi, P. A. & Sanan, P. Retention of water in terrestrial magma oceans and carbon-rich early atmospheres. Planet. Sci. J. 3, 93 (2022).

Article 

Google Scholar
 

Nicholls, H., Pierrehumbert, R. & Lichtenberg, T. Agni: a radiative-convective model for lava planet atmospheres. J. Open Source Softw. 10, 7726 (2025).

Article 
ADS 

Google Scholar
 

Sossi, P. A., Tollan, P. M. E., Badro, J. & Bower, D. J. Solubility of water in peridotite liquids and the prevalence of steam atmospheres on rocky planets. Earth Planet. Sci. Lett. 601, 117894 (2023).

Article 

Google Scholar
 

Hier-Majumder, S. & Hirschmann, M. M. The origin of volatiles in the earth’s mantle. Geochem. Geophys. Geosys. 18, 3078–3092 (2017).

Article 
ADS 

Google Scholar
 

Sim, S. J., Hirschmann, M. M. & Hier-Majumder, S. Volatile and trace element storage in a crystallizing martian magma ocean. J. Geophys. Res.: Planets 129, e2024JE008346 (2024).

Article 
ADS 

Google Scholar
 

Guimond, C. M., Shorttle, O. & Rudge, J. F. Mantle mineralogy limits to rocky planet water inventories. Mon. Not. R. Astron. Soc. 521, 2535–2552 (2023).

Article 
ADS 

Google Scholar
 

Liggins, P., Jordan, S., Rimmer, P. B. & Shorttle, O. Growth and evolution of secondary volcanic atmospheres: I. Identifying the geological character of hot rocky planets. J. Geophys. Res. Planets 127, e2021JE007123 (2022).

Article 
ADS 

Google Scholar
 

Gaillard, F. et al. The diverse planetary ingassing/outgassing paths produced over billions of years of magmatic activity. Space Sci. Rev. 217, 22 (2021).

Article 
ADS 

Google Scholar
 

Guimond, C. M., Noack, L., Ortenzi, G. & Sohl, F. Low volcanic outgassing rates for a stagnant lid Archean earth with graphite-saturated magmas. Phys. Earth Planet. Inter. 320, 106788 (2021).

Article 

Google Scholar
 

Hay, H. C. F. C., Trinh, A. & Matsuyama, I. Powering the Galilean satellites with moon-moon tides. Geophys. Res. Lett. 47, 88317 (2020).

Article 
ADS 

Google Scholar
 

Kervazo, M. et al. Solid tides in Io’s partially molten interior – contribution of bulk dissipation. Astron. Astrophys. 650, 72 (2021).

Article 

Google Scholar
 

Renaud, J. P. & Henning, W. G. Increased tidal dissipation using advanced rheological models implications for Io and tidally active exoplanets. Astrophys. J. 857, 98 (2017).

Article 
ADS 

Google Scholar
 

Farhat, M., Auclair-Desrotour, P., Boué, G., Lichtenberg, T. & Laskar, J. Tides on lava worlds: application to close-in exoplanets and the early earth–moon system. Astrophys. J. 979, 133 (2025).

Article 
ADS 

Google Scholar
 

Hamano, K., Kawahara, H., Abe, Y., Onishi, M. & Hashimoto, G. L. Lifetime and spectral evolution of a magma ocean with a steam atmosphere: its detectability by future direct imaging. Astrophys. J. 806, 216 (2015).

Article 
ADS 

Google Scholar
 

Schaefer, L., Wordsworth, R. D., Berta-Thompson, Z. & Sasselov, D. Predictions of the atmospheric composition of gj 1132b. Astrophys. J. 829, 63 (2016).

Article 
ADS 

Google Scholar
 

Dziewonski, A. M. & Anderson, D. L. Preliminary reference earth model. Phys. Earth Planet. Inter. 25, 297–356 (1981).

Article 
ADS 

Google Scholar
 

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).

Article 
ADS 

Google Scholar
 

Hirose, K., Wood, B. & Vocadlo, L. Light elements in the earth’s core. Nat. Rev. Earth Environ. 2, 645–658 (2021).

Article 
ADS 

Google Scholar
 

Bower, D. J. et al. Linking the evolution of terrestrial interiors and an early outgassed atmosphere to astrophysical observations. Astron. Astrophys. 631, 103 (2019).

Article 

Google Scholar
 

Wolf, A. S. & Bower, D. J. An equation of state for high pressure-temperature liquids (rtpress) with application to mgsio3 melt. Phys. Earth Planet. Inter. 278, 59–74 (2018).

Article 
ADS 

Google Scholar
 

Lodders, K. & Fegley, B. The Planetary Scientist’s Companion (Oxford Univ. Press, 1998).

Boley, K. M. et al. Fizzy super-earths: impacts of magma composition on the bulk density and structure of lava worlds. Astrophys. J. 954, 202 (2023).

Article 
ADS 

Google Scholar
 

Unterborn, C. T. & Panero, W. R. The pressure and temperature limits of likely rocky exoplanets. J. Geophys. Res. Planets 124, 1704–1716 (2019).

Article 
ADS 

Google Scholar
 

Edwards, J. M. & Slingo, A. Studies with a flexible new radiation code. I: Choosing a configuration for a large-scale model. Q. J. R. Meteorol. Soc. 122, 689–719 (1996).

ADS 

Google Scholar
 

Amundsen, D. et al. Accuracy tests of radiation schemes used in hot Jupiter global circulation models. Astron. Astrophys. 564, 59 (2014).

Article 

Google Scholar
 

Joyce, M. & Tayar, J. A review of the mixing length theory of convection in 1D stellar modeling. Galaxies 11, 75 (2023).

Article 
ADS 

Google Scholar
 

Johnstone, C. P., Bartel, M. & Gudel, M. The active lives of stars: a complete description of the rotation and XUV evolution of F, G, K, and M dwarfs. Astron. Astrophys. 649, 96 (2021).

Article 
ADS 

Google Scholar
 

Engle, S. G. & Guinan, E. F. Living with a red dwarf: the rotation-age relationships of m dwarfs. Astrophys. J. Lett. 954, 50 (2023).

Article 
ADS 

Google Scholar
 

Behr, P. R. et al. The MUSCLES extension for atmospheric transmission spectroscopy: UV and X-ray host-star observations for JWST ERS & GTO targets. Astron. J. 166, 35 (2023).

Article 
ADS 

Google Scholar
 

Tang, Y., Fortney, J. J. & Murray-Clay, R. Assessing core-powered mass loss in the context of early boil-off: minimal long-lived mass loss for the sub-neptune population. Astrophys. J. 976, 221 (2024).

Article 
ADS 

Google Scholar
 

Lichtenberg, T. et al. in Protostars and Planets VII (eds Inutsuka, S. et al.) Ch. 25 (Astronomical Society of the Pacific, 2023).

Johnstone, C. P. Hydrodynamic escape of water vapor atmospheres near very active stars. Astrophys. J. 890, 79 (2020).

Article 
ADS 

Google Scholar
 

Yoshida, T., Terada, N. & Kuramoto, K. Suppression of hydrodynamic escape of an H2-rich early earth atmosphere by radiative cooling of carbon oxides. Prog. Earth Planet. Sci. 11, 59 (2024).

Article 
ADS 

Google Scholar
 

Nicholls, H. Volatile-rich evolution of molten super-Earth L 98-59 d (simulations and code). Zenodo https://doi.org/10.5281/zenodo.17368256 (2025)