The effect of phase transformations at the inner core boundary on the Slichter modes

We analyze the effect of phase transformations at the inner core boundary on the period of Slichter modes. We show that the presence of phase transformations can lead to qualitatively new phenomena. In particular, the frequency is inversely proportional to the density contrast at the inner core boundary. We offer a thought experiment that demonstrates this effect. The complete analysis combines an instantaneous kinetics model for phase transformations with a simple planetary model: a rigid inner core, an inviscid, incompressible, constant density outer core, a stationary mantle. The reciprocal dependence on the density contrast leads to periods that are an order of magnitude shorter than those predicted by models that disallow phase transformations.