Hill model of transpolar potential saturation: Comparisons with MHD simulations

Abstract

[1] We present a comparison between a simple but general model of solar windmagnetosphere-ionosphere coupling (the Hill model) and the output of a global magnetospheric MHD code, the Integrated Space Weather Prediction Model (ISM). The Hill model predicts transpolar potential and region 1 currents from environmental conditions specified at both boundaries of the magnetosphere: at the solar wind boundary, electric field strength, ram pressure, and interplanetary magnetic field direction; at the ionospheric boundary, conductance and dipole strength. As its defining feature, the Hill model predicts saturation of the transpolar potential for high electric field intensities in the solar wind, which accords with observations. The model predicts how saturation depends on boundary conditions. We compare the output from ISM runs against these predictions. The agreement is quite good for non-storm conditions (differences less than 10%) and still good for storm conditions (differences up to 20%). The comparison demonstrates that global MHD codes (like ISM) can also exhibit saturation of transpolar potential for high electric field intensities in the solar wind. We use both models to explore how the strength of solar wind-magnetosphere-ionosphere coupling depends on the strength of Earth's magnetic dipole, which varies on short geological timescales. As measured by power into the ionosphere, these models suggest that magnetic storms might be considerably more active for high dipole strengths. [2] Total region 1 current, I 1 , and transpolar potential, È pc , epitomize solar wind-magnetosphere-ionosphere (SW-M-I) coupling. Progress in understanding this subject can almost be measured by how well the field predicts these quantities. (Region 2 currents, which this paper does not treat, are also an important aspect of the story. In section 7 we discuss how they might affect results presented here.) First models of SW-M-I coupling, reviewed by Reiff and Luhmann [1986], assumed one-way coupling from the solar wind to the ionosphere in which magnetic reconnection at the magnetopause taps a fraction of the solar wind potential across the magnetosphere, È sw , to yield an available magnetospheric convection potential È m . È m is then impressed via equipotential magnetic field lines onto the ionosphere, where it becomes the È pc that generates region 1 currents. The envisioned process was therefore linear. Empirical formulas based on this linear assumption work fairly well, except they tend to overpredict È pc for big values of È sw . This tendency has been called saturation of the transpolar potential at high values [Reiff and Luhmann, 1986;Russell et al., 2000].[3] Hill et al. [1976] presented a model of SW-M-I coupling that manifests saturation intrinsically and at about the observed value. (Hill [1984] developed the implications of the model further. We therefore refer to it as the Hill model.) Saturation is a nonlinear process that, in the Hill model, results from a feedback in which the magnetic field generated by region 1 cu...

Concerning long-term geomagnetic variations and space climatology

“…This scaling is mainly influenced by a saturation of the transpolar potential (e.g. Siscoe et al, 2002) governing the ionospheric electric field. Though the ionospheric conductances increase with decreasing dipole moment this saturation effect leads to the weak, positive dependence of the PEJ on M.…”

“…To first order the region 1 current system can be described as a figure-8 meridional current system (Siscoe et al, 2002), whose magnetic field exhibits a southward field component at the magnetopause in the equatorial plane. Dayside reconnection is thus diminished due to these currents and saturation of the transpolar electric potential results.…”

Predicting global average thermospheric temperature changes resulting from auroral heating

“…[43] It is known that the electric potentials in the polar cap exhibit a saturation effect when the z-component of the IMF becomes increasingly negative [Hill et al, 1976;Siscoe et al, 2002]. This saturation curve has been investigated extensively through observations and theory, as reviewed by Shepherd [2007], and it may explain why the nonlinear correction is required.…”

The response of the magnetosphere-ionosphere system to a sudden dynamic pressure enhancement under southward IMF conditions

“…Yu (yiqunyu@umich.edu) studies have shown that the solar wind density has little to no effect on the electric potential in the ionosphere, while the velocity can help to control the electric potential (e.g., Gonzalez, 1990;Weimer, 1995;Boyle et al, 1997). Recently, it has been suggested that the solar wind pressure helps to control the energy transfer from the solar wind to the ionosphere (Lopez et al, 2004;Boudouridis et al, 2003) and whether the ionospheric potential will be saturated (Siscoe et al, 2002). While the role of the relatively calm solar wind pressure/density is questionable in driving the magnetosphere, transient or step changes in the pressure or density appear to have a strong influence on the magnetosphere for a short period of time.…”