Roth, L. et al. Transient water vapor at Europa’s South Pole. Science 343, 171–174 (2014).
Porco, C. C. et al. Cassini observes the active South Pole of Enceladus. Science 311, 1393–1401 (2006).
Fagents, S. A., Lopes, R. M., Quick, L. C. & Gregg, T. K. in Planetary Volcanism across the Solar System (eds Gregg, T. K. P. et al) 161–234 (Elsevier, 2022).
Hussmann, H. & Spohn, T. Thermal-orbital evolution of Io and Europa. Icarus 171, 391–410 (2004).
Showman, A. P., Stevenson, D. J. & Malhotra, R. Coupled orbital and thermal evolution of Ganymede. Icarus 129, 367–383 (1997).
Tobie, G. et al. Tidal deformation and dissipation processes in icy worlds. Space Sci. Rev. 221, 6 (2025).
Moore, W. B. & Schubert, G. The tidal response of Europa. Icarus 147, 317–319 (2000).
Kamata, S., Matsuyama, I. & Nimmo, F. Tidal resonance in icy satellites with subsurface oceans. J. Geophys. Res. E 120, 1528–1542 (2015).
Manga, M. & Wang, C.-Y. Pressurized oceans and the eruption of liquid water on Europa and Enceladus. Geophys. Res. Lett. 34, L07202 (2007).
Beuthe, M. Spatial patterns of tidal heating. Icarus 223, 308–329 (2013).
Běhounková, M., Tobie, G., Choblet, G. & Čadek, O. Tidally-induced melting events as the origin of South-Pole activity on Enceladus. Icarus 219, 655–664 (2012).
Nimmo, F. Stresses generated in cooling viscoelastic ice shells: application to Europa. J. Geophys. Res. E 109, E12001 (2004).
Rudolph, M. L., Manga, M., Walker, M. & Rhoden, A. R. Cooling crusts create concomitant cryovolcanic cracks. Geophys. Res. Lett. 49, e2021GL094421 (2022).
Rhoden, A. R., Walker, M. E., Rudolph, M. L., Bland, M. T. & Manga, M. The evolution of a young ocean within Mimas. Earth Planet. Sci. Lett. 635, 118689 (2024).
Rhoden, A. R., Rudolph, M. L. & Manga, M. The challenges of driving Charon’s cryovolcanism from a freezing ocean. Icarus 392, 115391 (2023).
Tajeddine, R. et al. Constraints on Mimas’ interior from Cassini ISS libration measurements. Science 346, 322–324 (2014).
Lainey, V. et al. A recently formed ocean inside Saturn’s moon Mimas. Nature 626, 280–282 (2024).
Baillié, K., Noyelles, B., Lainey, V., Charnoz, S. & Tobie, G. Formation of the Cassini Division. I. Shaping the rings by Mimas inward migration. Mon. Not. R. Astron. Soc. 486, 2933–2946 (2019).
Noyelles, B., Baillié, K., Charnoz, S., Lainey, V. & Tobie, G. Formation of the Cassini Division. II. Possible histories of Mimas and Enceladus. Mon. Not. R. Astron. Soc. 486, 2947–2963 (2019).
Strom, C., Nordheim, T. A., Patthoff, D. A. & Fieber-Beyer, S. K. Constraining ocean and ice shell thickness on Miranda from surface geological structures and stress modeling. Planet. Sci. J. 5, 226 (2024).
Hemingway, D. J. & Mittal, T. Enceladus’s ice shell structure as a window on internal heat production. Icarus 332, 111–131 (2019).
Fuller, J., Luan, J. & Quataert, E. Resonance locking as the source of rapid tidal migration in the Jupiter and Saturn moon systems. Mon. Not. R. Astron. Soc. 458, 3867–3879 (2016).
Tobie, G., Čadek, O. & Sotin, C. Solid tidal friction above a liquid water reservoir as the origin of the South Pole hotspot on Enceladus. Icarus 196, 642–652 (2008).
Meyer, J. & Wisdom, J. Tidal heating in Enceladus. Icarus 188, 535–539 (2007).
McKinnon, W. B. & Schenk, P. Is Mimas hollow? In Proc. AGU Fall Meeting P32A-05 (American Geophysical Union, 2024); https://agu.confex.com/agu/agu24/meetingapp.cgi/Paper/1707025
McKinnon, W. B. & Schenk, P. Is Mimas a Dyson satellite? The fate of small melting moons. In Proc. 56th Lunar Planetary Science Conference 2897 (USRA, 2025); https://www.hou.usra.edu/meetings/lpsc2025/pdf/2897.pdf
Hemingway, D. J., Rudolph, M. L. & Manga, M. Cascading parallel fractures on Enceladus. Nat. Astron. 4, 234–239 (2020).
Arakawa, M. & Maeno, N. Mechanical strength of polycrystalline ice under uniaxial compression. Cold Reg. Sci. Technol. 26, 215–229 (1997).
Jones, S. J. The confined compressive strength of polycrystalline ice. J. Glaciol. 28, 171–178 (1982).
Schulson, E. M. Brittle failure of ice. Eng. Fract. Mech. 68, 1839–1887 (2001).
Potter, R. S., Cammack, J. M., Braithwaite, C. H., Church, P. D. & Walley, S. M. A study of the compressive mechanical properties of defect-free, porous and sintered water-ice at low and high strain rates. Icarus 351, 113940 (2020).
Schulson, E. M. & Renshaw, C. E. Fracture, friction, and permeability of ice. Annu. Rev. Earth Planet. Sci. 50, 323–343 (2022).
Cochrane, C. J., Vance, S. D., Castillo-Rogez, J. C., Styczinski, M. J. & Liuzzo, L. Stronger evidence of a subsurface ocean within Callisto from a multifrequency investigation of its induced magnetic field. AGU Adv. 6, e2024AV001237 (2025).
Nagel, K., Breuer, D. & Spohn, T. A model for the interior structure, evolution, and differentiation of Callisto. Icarus 169, 402–412 (2004).
Hillier, J. & Squyres, S. W. Thermal stress tectonics on the satellites of Saturn and Uranus. J. Geophys. Res. E 96, 15665–15674 (1991).
Hurford, T. A., Helfenstein, P., Hoppa, G. V., Greenberg, R. & Bills, B. G. Eruptions arising from tidally controlled periodic openings of rifts on Enceladus. Nature 447, 292–294 (2007).
Ingersoll, A. P. & Nakajima, M. Controlled boiling on Enceladus. 2. Model of the liquid-filled cracks. Icarus 272, 319–326 (2016).
Zhu, P., Manucharyan, G. E., Thompson, A. F., Goodman, J. C. & Vance, S. D. The influence of meridional ice transport on Europa’s ocean stratification and heat content. Geophys. Res. Lett. 44, 5969–5977 (2017).
Shibley, N. C. & Laughlin, G. Do oceanic convection and clathrate dissociation drive Europa’s geysers? Planet. Sci. J. 2, 221 (2021).
Mitchell, K. L., Rabinovitch, J., Scamardella, J. C. & Cable, M. L. A proposed model for cryovolcanic activity on Enceladus driven by volatile exsolution. J. Geophys. Res. E 129, e2023JE007977 (2024).
Matson, D. L., Castillo-Rogez, J. C., Davies, A. G. & Johnson, T. V. Enceladus: a hypothesis for bringing both heat and chemicals to the surface. Icarus 221, 53–62 (2012).
Crawford, G. D. & Stevenson, D. J. Gas-driven water volcanism in the resurfacing of Europa. Icarus 73, 66–79 (1988).
Rudolph, M. L. & Manga, M. Fracture penetration in planetary ice shells. Icarus 199, 536–541 (2009).
Buffo, J. J., Meyer, C. R. & Parkinson, J. R. G. Dynamics of a solidifying icy satellite shell. J. Geophys. Res. E 126, e2020JE006741 (2021).
Buffo, J. J., Schmidt, B. E., Huber, C. & Meyer, C. R. Characterizing the ice-ocean interface of icy worlds: a theoretical approach. Icarus 360, 114318 (2021).
Turcotte, D. L. & Schubert, G. Geodynamics 2nd edn (Cambridge Univ. Press, 2002).
Shoji, D., Hussmann, H., Sohl, F. & Kurita, K. Non-steady state tidal heating of Enceladus. Icarus 235, 75–85 (2014).
Goldreich, P., Lithwick, Y. & Luan, J. Enceladus’s limit cycle. Astrophys. J. 992, 28 (2025).
Greenberg, R. et al. in Uranus (eds Bergstralh, J. T. et al.) 693–735 (Univ. Arizona Press, 1991).
Pappalardo, R. T., Reynolds, S. J. & Greeley, R. Extensional tilt blocks on Miranda: evidence for an upwelling origin of Arden Corona. J. Geophys. Res. E 102, 13369–13379 (1997).
Hammond, N. P. & Barr, A. C. Global resurfacing of Uranus’s moon Miranda by convection. Geology 42, 931–934 (2014).
Tittemore, W. C. & Wisdom, J. Tidal evolution of the Uranian satellites. II. An explanation of the anomalously high orbital inclination of Miranda. Icarus 78, 63–89 (1989).
Croft, S. & Soderblom, L. in Uranus (eds Bergstralh, J. T. et al.) 561–628 (Univ. Arizona Press, 1991).
Hussmann, H., Sohl, F. & Spohn, T. Subsurface oceans and deep interiors of medium-sized outer planet satellites and large trans-Neptunian objects. Icarus 185, 258–273 (2006).
Bierson, C. J. & Nimmo, F. A note on the possibility of subsurface oceans on the Uranian satellites. Icarus 373, 114776 (2022).
Beddingfield, C. B., Leonard, E. J., Nordheim, T. A., Cartwright, R. J. & Castillo-Rogez, J. C. Titania’s heat fluxes revealed by Messina Chasmata. Planet. Sci. J. 4, 211 (2023).
Porco, C. C. et al. Cassini imaging science: initial results on Phoebe and Iapetus. Science 307, 1237–1242 (2005).
Giese, B. et al. The topography of Iapetus’ leading side. Icarus 193, 359–371 (2008).
Ip, W.-H. On a ring origin of the equatorial ridge of Iapetus. Geophys. Res. Lett. https://doi.org/10.1029/2005GL025386 (2006).
Levison, H. F., Walsh, K. J., Barr, A. C. & Dones, L. Ridge formation and de-spinning of Iapetus via an impact-generated satellite. Icarus 214, 773–778 (2011).
Dombard, A. J., Cheng, A. F., McKinnon, W. B. & Kay, J. P. Delayed formation of the equatorial ridge on Iapetus from a subsatellite created in a giant impact. J. Geophys. Res. E https://doi.org/10.1029/2011JE004010 (2012).
Detelich, C. E., Byrne, P. K., Dombard, A. J. & Schenk, P. M. The morphology and age of the Iapetus equatorial ridge supports an exogenic origin. Icarus 367, 114559 (2021).
Stickle, A. M. & Roberts, J. H. Modeling an exogenic origin for the equatorial ridge on Iapetus. Icarus 307, 197–206 (2018).
Sandwell, D. & Schubert, G. A contraction model for the flattening and equatorial ridge of Iapetus. Icarus 210, 817–822 (2010).
Ćuk, M. et al. Long-term evolution of the Saturnian system. Space Sci. Rev. 220, 20 (2024).
Castillo-Rogez, J. C. et al. Iapetus’ geophysics: rotation rate, shape, and equatorial ridge. Icarus 190, 179–202 (2007).
National Academies of Sciences, Engineering, and Medicine. Origins, Worlds, and Life: A Decadal Strategy for Planetary Science and Astrobiology 2023-2032 (National Academies Press, 2023).
Jaeger, J. C., Cook, N. G. & Zimmerman, R. Fundamentals of Rock Mechanics (Wiley, 2009).
Petrenko, V. F. & Whitworth, R. W. Physics of Ice (Oxford Univ. Press, 1999).
Rudolph, M. & Rhoden, A. PISTES: planetary ice shell thermal evolution and stress. Zenodo https://doi.org/10.5281/zenodo.17317041 (2025).
Nimmo, F., Bierson, C. & McKinnon, W. B. Pluto and Triton: Interior Structures, Lithospheres and Potential for Oceans (IOP Publishing, 2025).