On the scaling of the subsolar magnetopause parallel electric field: Resistive MHD theory

Recently, Cassak and Shay [Phys. Plasmas, 14, 2007] applied two-dimensional MHD conservation laws to derive an analytic expression for the reconnection rate at Earth's dayside magnetopause. Borovsky [JGR, in press, 2008] used the Cassak-Shay formula as a starting point to derive a first principles solar wind-magnetosphere coupling function. Based on 3D MHD numerical experiments (using the BATSRUS global MHD code), Borovsky argued that dayside reconnection is not driven by the solar wind. Rather, the reconnection rate is determined by the local plasma densities and magnetic field magnitudes on the two sides of the magnetopause current sheet, consistent with the Cassak-Shay formula. However, due to the three-dimensional nature of the subsolar magnetopause flow, the relevance of the Cassak-Shay formula to dayside magnetopause reconnection is questionable. In this talk, we revisit the problem of determining the subsolar magnetopause reconnection electric field in the context of the resistive MHD equations. We derive an analytic expression for the parallel electric field at Earth's subsolar magnetopause, demonstrating that neither the popular Sonnerup-Gonzalez expression [Sonnerup, B. U. O., JGR, 79, 1974; Gonzalez, W. D. and F. S. Mozer, JGR, 79, 1974] nor the Cassak-Shay formula is relevant in 3D resistive MHD. In particular, our expression predicts that if the plasma resistivity is constant, the subsolar parallel electric field should scale like the fourth root of the resistivity. In contrast, the Cassak-Shay formula predicts a square root scaling when the resistivity is constant. In principle, THEMIS could be used to address this question by determining the amount of magnetic flux pileup upstream of the magnetopause current sheet under various conditions.