'Heat from above' heat capacity measurements in liquid ⁴He

We have made heat capacity measurements of superfluid ⁴He at temperatures very close to the lambda point, Tλ, in a constant heat flux, Q, when the helium sample is heated from above. In this configuration the helium enters a self-organized (SOC) heat transport state at a temperature T_SOC(Q), which for Q ≥ 100 n W/cm² lies below Tλ. At low Q we observe little or no deviation from the Q = 0 heat capacity up to T_SOC(Q); beyond this temperature the heat capacity appears to be sharply depressed, deviating dramatically from its bulk behaviour. This marks the formation and propagation of a SOC/superfluid two phase state, which we confirm with a simple model. The excellent agreement between data and model serves as an independent confirmation of the existence of the SOC state. As Q is increased (up to 6 μ W/cm²) we observe a Q dependent depression in the heat capacity that occurs just below T_SOC(Q), when the entire sample is still superfluid. This is due to the emergence of a large thermal resistance in the sample, which we have measured and used to model the observed heat capacity depression. Our measurements of the superfluid thermal resistivity are a factor of ten larger than previous measurements by Baddar et al.