  It has been long puzzling whether the ice thickness variations observed on
Enceladus can be sustained sorely by a polar-amplified bottom heating. The key
to this question is to understand how the upward heat transport by convective
plumes would be interfered by the temperature and salinity variations beneath
the ice due to the ice thickness variations, which however, has yet to be
explored. Here, we find that the horizontal temperature variation induced by
the ice topography can easily be orders of magnitude greater than the vertical
temperature variation induced by bottom heating using scaling analysis. Due to
the dominance of horizontal temperature gradient, convective plumes are
completely shut off by a stratified layer under the thin ice formed out of
baroclinic adjustment, largely slowing down the vertical tracer transport. The
stratified layer will also deflect almost all of the core-generated heating
toward the regions with thicker ice shell, destroying the ice thickness
gradient. These results allow us to put an upper bound on the core-generated
heating on Enceladus, which is crucial for the estimate of habitability.
Scaling laws for the bottom heat flux to penetrate the stratification is
derived and examined. This scaling can be used to constrain the maximum ice
thickness variations induced by heterogeneous bottom heating on icy satellites
in general, which can be used to differentiate icy satellites that generate the
majority of heat in the ice shell from those that generate the majority of heat
in the silicate core.
