Subsurface ocean salinity and dissipation rate inferred from Enceladus ice shell morphology

Abstract

The habitability of Enceladus' subsurface ocean and the detectability of potential biosignatures depend on efficient ocean circulation and suitable ocean conditions. Directly probing the ocean is challenging because it lies beneath a thick ice shell; however, the ice thickness distribution is relatively well constrained and provides indirect insight into the underlying ocean dynamics. This study investigates how ocean circulation and the associated heat transport depend on ocean salinity and tide-induced vertical mixing using scaling analysis, supported by numerical simulations. We find that ocean circulation and equatorward heat convergence are stronger under extremely high or low salinity conditions than under intermediate salinity, and both increase with tidal mixing rates. Because the poleward thinning of Enceladus' ice shell cannot be maintained in the presence of strong equatorward ocean heat transport, these results place constraints on the ocean salinity, diffusivity, circulation timescale, and ocean dissipation rate. Energetic analysis further shows that Enceladus' ocean behaves like an extremely efficient heat pump (inefficient heat engine), potentially transporting up to 1000 times more heat across latitudes than the energy dissipated within the ocean itself, thereby placing strong constraints on the ocean's energy dissipation rate.

Figures (6)

• Figure 1: Temperature and salinity forcings exerted on Enceladus ocean. Panel (a) presents the domain geometry and boundary condition at the water-ice interface. Panel (b) presents profiles of Enceladus ice thickness profile $H_i$ (solid) and the imposed freezing rate $q$. $q$ is set such that it balances out the ice flow (SI Text S2). Since water's freezing point $T_f$ depends almost linearly with $H_i$, a second y-axis is added to show the freezing point at water-ice interface. This study aims to estimate the ocean heat transport, $\mathcal{F}$, across a range of mean salinities ($S_0$) and vertical diffusivities ($\kappa_v$) to determine which combinations enable equatorial ice to freeze so that the ice thickness variations can be sustained against ice flow.
• Figure 2: Scaling laws for ocean heat transport tested using Oceananigans simulations. Panels (A) and (B) examine Eq. \ref{['eq:Psi']} in the regimes of $\Delta b>0$ and $\Delta b<0$, respectively. Panel (C) tests the balance of vertical tracer transport (Eq. \ref{['eq:vertical-transport-balance']}), and Panel (D) tests the balance of horizontal salinity transport (Eq. \ref{['eq:salinity-flux-balance']}). Colored symbols represent the experiments conducted in this work: different colors correspond to different ocean salinities, while different shapes denote different ocean diffusivities. Black squares indicate experiments presented in Zhang-Kang-Marshall-2025:how.
• Figure 3: Panels (A-C) present analytical predictions for the equator-to-pole salinity contrast $\Delta S$, the circulation strength $|\Psi^\dagger|$ and the equatorward heat transport $\mathcal{F}$. Separated by the grey curves, the upper part of the parameter space follows the D-limit scaling and the lower part follows the $\kappa_v$-limit scaling. Circulation reversal is denoted by the zero contour in the $\Psi^\dagger$ figure (panel B). The $\mathcal{F}=1,~2,~4$ GW (corresponding to 2,4,8 GW equatorward heat convergence) contours in panel (C) for reference. Besides the solution presented in panel (A-C), for the parameter regime with $\Psi^\dagger<0$, there is a set of different solution as presented in Panels (D-F). Shaded regions in panels (D-F) are identical to those in panel (A-C). The characteristics of ocean circulation (arrows) and isopycnals (contours) are sketched in panel (G) for the 4 scenarios with increasing ocean salinity from left to right. Their regimes are also marked on panel (B,E). Also denoted are the definitions of isopycnal slope $s$, the buoyancy contrast between equatorial and polar regions $\Delta b$.
• Figure 4: Numerical solutions for the three high-diffusivity ($\kappa_v=10^{-2}$ m$^2$/s) simulations with different salinities. Shadings in panels (A-C) show the zonal-mean time-mean temperature $T$, salinity $S$ and zonal flow $U$ respectively. Thin gray contours in each panel present density. The spacing between two adjacent contours is set to $2\times 10^{-3}$ kg/m$^3$, and density increases with depth in all cases. Thick black contours with arrows in panels (A,B) show the diagnosed residual circulation streamfunction $\Psi^\dagger$, and solid/dashed $\Psi^\dagger$ contours denote clockwise/counter-clockwise circulation, respectively. The contour levels are $\pm 1.2\times 10^7,\ \pm 5\times 10^7,\ \pm 2\times 10^8$ kg/s. The arrows in panel (A) present the diagnosed eddy heat transport. Panels (D) show the time-mean meridional heat transport with positive values denote northward heat transport.
• Figure 5: Same as Fig. \ref{['fig:3D-solution']}A-D, except for the lower-diffusivity ($\kappa_v=10^{-3}$ m$^2$/s) simulations.