Radial Variation of the Solar Wind Proton Temperature: Heat Flow or Addition?

The proton temperature profile of the asymptotic solar wind plasma can be modified by four different physical effects: PdV work, external heat deposition, Q D , divergence of heat, q ·  , and collisional energy exchange with other species in the plasma. Suggestions in the literature that Q D heating is “required” to explain the proton profile have often been deduced while neglecting qp and energy exchange. Despite the adiabatic approximation q 0 p = having no rigorous justification in low-density plasmas, the simultaneous neglect of energy exchange unnaturally forces the “need” for Q D to balance adiabatic cooling caused by the wind’s expansion. In this paper, the asymptotic wind proton heat flux is determined which balances the inner Heliosphere’s steady state entropy equation for the protons, ignoring heat addition and energy exchange. The solutions of the energy equation recover both the power-law trend and amplitude of the 5 year averaged Helios temperature profiles that were segregated by speed. The dimensionless skewness  of the heat flow is empirically shown to scale for all wind states below 600 km s as if it were equal to the Knudsen number determined by Coulomb collisions, a relation that is rigorously demonstrated for an infinitesimal Knudsen number, bridging the unusual adiabatic protons forU 250  km s and the higher speed states of the winds that remain hotter over a wider radial domain. Higher speed states (U 650 > km s) may require additional scattering beyond what Coulomb effects can provide, although the averaged profiles for these speeds are not as accurate as those below 600 km s.