Elastic effects in torsional oscillators containing solid helium

A number of recent experiments have used torsional oscillators to study the behavior of solid helium. The oscillator frequencies increased at temperatures below 200 mK, an effect attributed to decoupling of a fraction of the helium mass-the signature of a supersolid phase. However, helium's shear modulus also increases below 200 mK and the frequency of a torsional oscillator depends on its elastic properties, as well as on its inertia. In many experiments helium is introduced via a hole in the torsion rod, where its shear modulus contributes to the stiffness of the rod. In oscillators with relatively large torsion rod holes, changes in the helium's shear modulus could produce the entire low temperature frequency shifts that have been interpreted as mass decoupling. For these oscillators we also find that the known elastic properties of helium in the torsion rod can explain the observed TO amplitude dependence (which has been interpreted as a critical velocity) and the TO dissipation peak. However, in other oscillators these elastic effects are small and the observed frequency changes must have a different origin.