Effect of Helium Elasticity on Torsional Oscillator Measurements

In 2004 Kim and Chan performed a torsional oscillator measurement of the rotational inertia of solid helium-4. They found frequency changes which were interpreted in terms of a non-classical rotational inertia, that is a partial superfluidity or “supersolidity” of solid helium-4. Since then there have been many further studies using various versions of this technique. One important question that arises in these experiments is the possible effect on the oscillator frequency of changes in the elasticity of the solid helium; this can produce a change in frequency that adds to any effect due to superfluidity. In this paper we give a general discussion of the effect of changes in elasticity on the oscillator frequency and consider how the magnitude of the effect is influenced by the oscillator design. Our results should help make it possible to discriminate between frequency changes due to changes in elasticity and changes due to supersolidity.