  The ice shell on Enceladus, an icy moon of Saturn, exhibits strong asymmetry
between the northern and southern hemispheres, with all known geysers
concentrated over the south pole, even though the expected pattern of
tidal-rotational deformation should be symmetric between the north and south
poles. Using an idealized ice evolution model, we demonstrate that this
asymmetry may form spontaneously, without any noticeable a priori asymmetry
(such as a giant impact or a monopole structure of geological activity), in
contrast to previous studies. Infinitesimal asymmetry in the ice shell
thickness due to random perturbations are found to be able to grow
indefinitely, ending up significantly thinning the ice shell at one of the
poles, thereby allowing fracture formation there. Necessary conditions to
trigger this hemispheric symmetry breaking mechanism are found analytically. A
rule of thumb we find is that, for Galilean and Saturnian icy moons, the ice
shell can undergo hemispheric symmetry breaking only if the mean shell
thickness is around 10-30~km.
