Specific heat of liquid helium in zero gravity very near the lambda point

We report the details and revised analysis of an experiment to measure the specific heat of helium with subnanokelvin temperature resolution near the lambda point. The measurements were made at the vapor pressure spanning the region from 22 mK below the superfluid transition to $4\mu \mathrm{K}$ above. The experiment was performed in Earth orbit to reduce the rounding of the transition caused by gravitationally induced pressure gradients on Earth. Specific-heat measurements were made deep in the asymptotic region to within 2 nK of the transition. No evidence of rounding was found to this resolution. The optimum value of the critical exponent describing the specific-heat singularity was found to be $\alpha =-0.0127\pm \mathrm{0.0003.}$ This is bracketed by two recent estimates based on renormalization-group techniques, but is slightly outside the range of the error of the most recent result. The ratio of the coefficients of the leading-order singularity on the two sides of the transition is $A^{+}{/A}^{-}=1.053\mathrm{}\pm 0.002,$ which agrees well with a recent estimate. By combining the specific-heat and superfluid density exponents a test of the Josephson scaling relation can be made. Excellent agreement is found based on high-precision measurements of the superfluid density made elsewhere. These results represent the most precise tests of theoretical predictions for critical phenomena to date.