How Fast Would an Unheated Ocean Freeze? Conductive Freezing Timescales for Europa, Enceladus and Titan

If tidal and radiogenic heating were switched off, how long would each ocean survive against its own ice shell? A Stefan-type freezing calculation gives 0.08093 billion years for a 100-kilometre Europan ocean, 0.00566 billion years for a 30-kilometre Enceladus ocean and 0.6861 billion years for a 300-kilometre Titan ocean, with initial freezing rates through a 20-kilometre shell of 3.089, 3.974 and 3.279 millimetres per year respectively. Every timescale is far shorter than the age of the solar system: no ocean in this set is a passive fossil, and each present-day ocean certifies sustained heating over geological time. Enceladus is the extreme case, its ocean freezing in a few million years unheated. Computed from stated assumptions, not measured.