Correlation of speed and temperature in the solar wind

We show that the well-known correlation between solar wind speed and temperature can be understood as a consequence of an elementary symmetry of the solar wind transport equations. Under a reasonably wide range of circumstances, even when including nonadiabatic turbulence effects, the solutions of the transport equations may depend only upon the ratio r/U of distance to solar wind speed. Applied to the temperature equation, the familiar correlation emerges immediately. For a turbulence model of heating, this property is obtained in regions where the Alfvén speed is much smaller than the flow speed, where pickup ions are negligible, and where the flow is locally a spherical, constant-speed expansion. These fundamental properties, illustrated here using analysis of ACE data, clarify why the correlation is reduced in ensembles that include highly nonspherical effects such as CMEs.