The rudiments of a theory of solar wind/magnetosphere coupling derived from first principles

Abstract

A formula that expresses the dayside reconnection rate in terms of upstream solar wind parameters is derived and tested. The derivation is based on the hypothesis that dayside reconnection is governed by local plasma parameters and that whatever controls those parameters controls the reconnection rate. The starting point of the derivation is the Cassak‐Shay formula (from energy conservation principles), which expresses the dayside reconnection rate in terms of four parameters: the magnetic field strengths Bm and Bs in the magnetosphere and magnetosheath and the plasma mass densities ρm and ρs in the magnetosphere and magnetosheath. Using the Rankine‐Hugoniot relations at the bow shock and an analysis of the magnetosheath flow, three of these parameters are expressed in terms of upstream solar wind parameters. These three expressions are then used in the Cassak‐Shay formula to obtain the “solar wind control function.” The interpretation of the control function is that solar wind pressure largely sets the reconnection rate. The solar wind magnetic field enters into the control function because of a bow shock Mach number dependence. The onset of a “plasmasphere effect” occurs when ρm > MA0.87ρsolarwind, wherein the magnetosphere begins to exert control over solar wind/magnetosphere coupling. Using the OMNI2 data set and seven geomagnetic indices, the solar wind control function is tested on its ability to describe the variance in the geomagnetic indices. The control function is found to be successful, statistically as good as the best “solar wind driver function” in the literature. This picture opens a new pathway to understanding and calculating solar wind/magnetosphere coupling.