Second and fourth sound modes for superfluid helium in aerogel

Because of the interest in superfluid onset in porous media (high porosity aerogel in particular) one would like to measure the superfluid fraction as well as the heat capacity near Tc. However, standard techniques such as torsional oscillations and fourth sound have encountered difficulties because the compliant aerogel allows the viscous normal fluid to move. Using data we obtained for fourth sound propagation below 1.8 K, we develop a theory which fits the data with no adjustable parameters, and show that the theory predicts another second-sound-like mode which may not be damped near Tc.