An empirical determination of the polytropic index for the free-streaming solar wind using Helios 1 data

Observations of solar wind proton temperatures indicate that the solar wind is heated as it moves outward toward the orbit of Earth. This heating, which may be the results of electron heat conduction and perhaps MHD waves, has proven difficult to quantify and hence is often neglected in MHD models of the solar wind. An alternate approach to finding explicit heating terms for the MHD energy equation is to use a polytropic approximation. This paper discusses the properties of the polytropic approximation and its application to the solar wind plasma. By using data from the Helios 1 spacecraft, an empirical value for the polytropic index of the free-streaming solar wind is determined. Various corrections to the data are made to account for velocity, nonuniformity in radial sampling, and stream interaction regions. The polytropic index, as derived from proton data, is found to indepedent of speed state, within statistical error, and has an average value of 1.46. If magnetic pressure is included, the polytropic index has an average value of 1.58.