A study of the viscous interaction between the solar wind and earth's magnetosphere using an MHD simulation.

摘要

The solar wind interacts with Earth's magnetosphere largely through magnetic reconnection and a "viscous-like" interaction that is not fully understood. The ionospheric cross-polar cap potential (phi PC) component due to reconnection (phiR) is typically much larger than the viscous component (phiV) and very dynamic, making detailed studies of the viscous potential difficult. We used the Lyon-Fedder-Mobarry (LFM) magnetohydrodynamic (MHD) simulation to study the viscous potential by running LFM for a variety of solar wind density and velocity values and ionospheric Pedersen conductance (SigmaP) values, but no solar wind magnetic field, so that phiPC was entirely due to the viscous interaction. We found that phiV increased with solar wind density, scaling as n0.439 (n in cm -3), and phiV increased with solar wind velocity, scaling as V1.33 (V in km s -1); these results were combined to create a formula for phi V in LFM, using a SigmaP value that produces realistic potentials: phiV = (0.00431)n0.439 V1.33 (in kV), which matches simulation results very well. phiV also varied inversely with SigmaP, as predicted by previous theory. The form of this formula is similar to results from the Newell et al. [2008] empirical study, which tested a list of viscous coupling functions and found that n 1/2V2 worked best (but did not create a formula to predict potentials, so actual viscous potential values could not be compared).;The Bruntz et al. formula was also compared to LFM results from a run with real solar wind input, from the Whole Heliosphere Interval (WHI), which lasted from 20 March to 16 April 2008. LFM was first run with the full solar wind from the WHI, then with the same solar wind but zero interplanetary magnetic field (IMF), which meant that phiPC = phiV for that run. These runs were performed with the empirical ionospheric solver, using the average F10.7 flux value from the WHI as input. This empirical ionosphere is known to produce potentials that are higher than observations, so the output was scaled down to match the range of the Bruntz et al. formula with a scaling factor gamma = 1.542, which was found from 11 steady periods in the WHI. Those same periods were also used to calibrate the Newell et al. viscous scaling factor, turning it into a predictive formula: phiV = (6.39x10 -5)n1/2V2 (in kV). Both viscous potential formulas were compared to phiPC from the zero-IMF run, producing phiV values that were very close to the LFM phiPC values, differing in opposite ways in some places, but with essentially identical correlation coefficients.;We also used the gamma factor to scale phiPC from the full-IMF LFM run down, then compared it to phiPC from the Weimer05 empirical model. The two matched well in the higher phiPC values, but the Weimer05 phiPC values reached a minimum "floor" value, while the LFM phiPC has no such floor, and so dropped much lower in some places. The fact that gamma scaled the full-IMF LFM down to match the Weimer05 values, even though gamma was derived from very different runs and conditions, is interpreted to support the idea that the cause of high LFM potentials is in the ionospheric conductivity, since gamma is derived from the higher-conductivity-based Bruntz et al. formula.