Values of (a) ice-ocean heat flux and (b) thickness under which a conductive steady state is expected at particular basal viscosities in an ice shell with no internal heat source. The Rayleigh number is shown in color; here the critical Rayleigh number is taken to be 106 . The white section of the color plot in (b) as well as in (c) corresponds to the region for which steady-state conductive thicknesses would exceed the critical Rayleigh number. (c) Values of ice-ocean heat flux and thickness (inset) under which a conductive steady state is expected at particular basal viscosities in an internally-heating ice shell (I = 10−6 Wm−3 ). Rayleigh number is in color. Related steady-state conductive thicknesses are shown in the inset.(d) Relationship between ice shell thickness and ice-ocean heat flux for different values of internal heating (color) in steady-state. Depth-dependent internal heating following the prescription in Equation 7 for particular reference viscosities are shown by the black dots (ηb = 1013 Pa s), plus signs (ηb = 1015 Pa s), and stars (ηb = 1017 Pa s). The black dots with the gray outline indicate ice thicknesses which would be unstable to convection for the given reference viscosity and a critical Rayleigh number of O(106 ). — astro-ph.EP
Europa’s icy surface likely overlies an ocean, but the ice thickness is not known.
Here we model the temporal growth of a Europan shell of pure ice subject to varying ice-ocean heat fluxes, ice rheologies, and internal heating rates. Both constant and viscosity-dependent internal heating rates are included, yielding similar results for particular viscosities.
A growing shell starting from an ice-free initial state transitions from conduction to convection at O(105) to O(107) years, with thicknesses O(1-10) km.
For low ice-ocean heat fluxes and larger viscosities, the time to reach a steady-state thickness exceeds the estimated age of Europa’s surface, whence the shell may still be growing.
We conclude by presenting a method for inferring ice-ocean heat fluxes and vertical ocean velocities from the ice-thickness measurements expected from the upcoming Clipper mission, assuming the shell is in a conductive steady state.
Nicole C. Shibley, Jeremy Goodman
Comments: 16 pages, 4 figures, submitted to Icarus Subjects: Earth and Planetary Astrophysics (astro-ph.EP) Cite as: arXiv:2309.16821 [astro-ph.EP] (or arXiv:2309.16821v1 [astro-ph.EP] for this version) Submission history From: Nicole Shibley [v1] Thu, 28 Sep 2023 20:00:59 UTC (3,947 KB) https://arxiv.org/abs/2309.16821 Astrobiology
Explorers Club Fellow, ex-NASA Space Station Payload manager/space biologist, Away Teams, Journalist, Lapsed climber, Synaesthete, Na’Vi-Jedi-Freman-Buddhist-mix, ASL, Devon Island and Everest Base Camp veteran, (he/him) 🖖🏻
