Long-term stability of Enceladus’ uneven ice shell

•Ice shell thickness on Enceladus ranges from 5 km to more than 30 km.•Ice thickness variations are maintained by phase changes at ice/water interface.•Gravity and shape data suggest that the shell is close to dynamic equilibrium.•Steady state is obtained only if basal viscosity is larger than 3.1014Pa s.•Amplitudes of ocean heat flux exceed 60 mW/m2 in polar regions.