Enhanced heat capacity and a new temperature instability in superfluid 4He in the presence of a constant heat flux near t(lambda)

We present the first experimental evidence that the heat capacity of superfluid 4He, at temperatures very close to the lambda point T(lambda), is enhanced by a constant heat flux Q. The heat capacity at constant Q, C(Q), is predicted to diverge at a temperature T(c)(Q)<T(lambda) at which superflow becomes unstable. In agreement with previous measurements, we find that dissipation enters our cell at a temperature, T(DAS)(Q), below the theoretical value, T(c)(Q). We argue that T(DAS)(Q) can be accounted for by a temperature instability at the cell wall, and is therefore distinct from T(c)(Q). The excess heat capacity we measure has the predicted scaling behavior as a function of T and Q, but it is much larger than predicted by current theory.