  Titan's moment of inertia, calculated assuming hydrostatic equilibrium from
gravity field data obtained during the Cassini-Huygens mission, implies an
internal mass distribution that may be incompatible with complete
differentiation. This suggests that Titan may have a mixed ice/rock core,
possibly consistent with slow accretion in a gas-starved disk, which may
initially spare Titan from widespread ice melting and subsequent
differentiation. A partially differentiated Titan, however, must still
efficiently remove radiogenic heat over geologic time. We argue that
compositional heterogeneity in the major Saturnian satellites indicates that
Titan formed from planetesimals with disparate densities. The resulting
compositional anomalies would quickly redistribute to form a vertical density
gradient that would oppose thermal convection. We use elements of the theory of
double-diffusive convection to create a parameterized model for the thermal
evolution of ice/rock mixtures with a stabilizing compositional gradient.
Simulations are performed for a wide range of initial conditions to account for
large uncertainties in material properties and accretionary processes.
Ultimately, for realistic density gradients, double-diffusive convection in the
ice/rock interior can delay, but not prevent, ice melting and differentiation,
even if a substantial fraction of potassium is leached from the rock component.
Consequently, Titan is not partially differentiated.
