Can Tides Keep Europa's Ocean Liquid? A Heating-Versus-Loss Balance Across Shell Thickness

Europa's ocean persists because tidal heating replaces the heat the ice shell conducts away, and this study checks that balance explicitly. Tidal dissipation at fixed dissipation factors of 0.005 to 0.02 spans 2.12 to 8.478 terawatts, while conductive loss through shells of 15 to 40 kilometres spans only 1.333 down to 0.4999 terawatts. At a fixed dissipation factor the income exceeds the loss at every thickness computed, so a fixed-factor shell cannot sit in balance: it would thin until the dissipation factor itself fell. Balance therefore requires the self-regulation that coupled models describe, in which a thinner, warmer shell dissipates less per unit forcing. The ocean is maintainable by tides with a wide margin; the shell thickness is set by the regulation, not by a simple crossing of the two curves. Computed from stated assumptions, not measured.