Magnetosheath Control of the Cross Polar Cap Potential: Correcting for Measurement Uncertainty in Space Weather

Abstract

This study quantifies the variation and apparent saturation of the cross polar cap potential $\left({\varphi }_{PC}\right)$ with respect to the motional electric field $\left(E_M\right)$ in the solar wind and magnetosheath. The electric potential across the polar cap $\left({\varphi }_{PC}\right)$ is often observed to respond linearly to solar wind driving during weak driving and nonlinearly during strong driving, with ${\varphi }_{PC}$ eventually responding less and less to increased driving. This effect is called “polar cap potential saturation” and has been observed in many studies that correlate some measure of solar wind driving (typically the motional electric field $E_M$) with ${\varphi }_{PC}$. In this study, it is shown that measurement error in the solar wind driver creates a nonlinear bias in its variation relative to ${\varphi }_{PC}$. This is accomplished by associating a decade of radar measurements of ${\varphi }_{PC}$ with simultaneous probabilistic predictions of $E_M$ in the solar wind just upstream of the bow shock and in the magnetosheath. After correcting for the bias in the solar wind and magnetosheath $E_M$ caused by measurement uncertainty, the extent of saturation between ${\varphi }_{PC}$ and the corrected solar wind $E_M$ is reduced. More importantly, ${\varphi }_{PC}$ saturates with respect to the solar wind $E_M$ but not the magnetosheath $E_M$. This effect is caused by the magnetosheath $E_M$ being reduced relative to the solar wind $E_M$ when the solar wind Alfvén Mach number is low. Both of these findings support the theory that the ${\varphi }_{PC}$ saturation is due to the magnetosheath flow being magnetically dominated for large solar wind magnetic field magnitudes.