Solar Wind Speed-Temperature-Acceleration Relation

It has been suggested that the well known correlation between solar wind speed and temperature arises naturally from symmetries in the solar wind energy equation. In the presence of turbulent heating this explanation is only valid for high Alfven Mach number wind undergoing uniform expansion. We provide supporting evidence for this theory by studying the temperature of solar wind protons at 1 AU as a function of proton speed, Alfven Mach number, and the acceleration of the wind defined as the rate of change of speed over a range of time-scales. We confirm earlier evidence of the sensitivity of temperature to acceleration in addition to velocity. We show that the proton temperature for all solar wind with mach number greater than eight and proton speed between 300 and 800 km/s is reproduced by a three-parameter model that depends only on velocity and acceleration. The continuity of the model across this range in speeds is surprising, given the different coronal conditions and acceleration mechanisms generally attributed to slow and fast solar wind. We investigate the accuracy of the model as a function of the averaging time-scale used to calculate the acceleration and discuss the implications of those time-scales on future measurements by Solar Probe Plus and Solar Orbiter.