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The test devised by Vasyliunas et al. (1982) of proposed IMF orientation factors, Aθ(θ), where θ is the IMF clock angle in the GSM frame: (orange line) sin2(θ/2); (cyan line) sin3(θ/2); (blue line) sin4(θ/2); (mauve line) sin5(θ/2); and (black line) U(θ)cos(θ), where U(θ) = 0 for [BZ]GSM > 0 and U(θ) = 1 for [BZ]GSM ≤ 0. The black dots are s(SML/G) + c where s and c are the best-fit linear regression coefficients, SML is the SuperMAG westward electrojet index, and G = Pα/Aθ, where Pα is the best fit estimate of the power input into the magnetosphere. The dark pink shaded area is the range over which θ varies due to the R–M effect for [BZ]GSEQ = 0 (i.e., IMF lying in the solar equatorial plane) and the range of variation of the dipole tilt over a full year caused by Earth’s rotational axis tilt. The light pink area is for the full range caused by the annual variation plus the diurnal variation due to the offset of Earth’s rotational and magnetic axes. The light and dark orange regions are the corresponding ranges for [BZ]GSEQ = B (i.e., purely southward field normal to the solar equatorial plane).
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