  Of profound astrobiological interest, Enceladus appears to have a global
subsurface ocean that is salty, indicating water-rock reaction at present or in
the past, important for its habitability. Here, we investigate how salinity and
the partition of heat production between the silicate core and the ice shell
affect ocean dynamics and the associated heat transport -- a key factor that
determines the equilibrium ice shell geometry. Assuming steady state
conditions, we show that the meridional overturning circulation of the ocean,
driven by heat and salt exchange with the ice, has opposing signs at very low
and very high salinities. Regardless of these differing circulations, heat and
freshwater converge towards the equator, where the ice is thick, acting to
homogenize thickness variations. In order to maintain the observed ice
thickness variation, the polar-amplified ice dissipation needs to be strong
enough and ocean heat convergence cannot overwhelm well-constrained heat loss
rates through the thick equatorial ice sheet. This requirement is found
violated if the main heat source is in the core rather than the ice shell, or
if the ocean is very fresh or very salty. Instead, with a salinity of
intermediate range, the temperature- and salinity-induced density gradient
largely cancel one another, leading to much reduced overturning and equatorial
heat convergence rates and consistent budgets in appearance of a significant
ice dissipation.
