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Figure 2

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Schematic of the Russell-McPherron (R-M) effect. Part (a) illustrates Earth in its orbit at the June and December solstices and the March and September equinoxes, showing the orientation of Earth’s rotational axis in red and defining the ecliptic plane (shaded yellow) and the GSE reference frame. Also shown is the GSEQ reference frame (defined in Fig. 4); (b), (c) and (d) are views looking toward Earth from the Sun (i.e., in the −XGSEQ direction) and show the ZGSEQ and YGSEQ axes and the projections of and Earth’s magnetic axis (in blue): precesses around the ZGSEQ axis once per year and precesses around every 24 h. The cone angles of these annual and daily precessions are δa = 23.5° and δa ≈ 9.6°, respectively. (Note that δa of 9.6° is an approximate figure because Earth’s field in not a geocentric dipole; for example, in 2007 the geomagnetic pole was 6.05° from the rotation pole in the Northern hemisphere but 25.55° from it in the Southern hemisphere; (b) is the view for the March equinox, (c) for the June and December solstices and (d) is for the September equinox. The GSM (Geocentric Solar Magnetospheric) reference frame is, like GSE and GSEQ, a right handed set and GSEQ, GSE and GSM share the same X axis, but the ZGSM and YGSM axes are rotated through an angle βGSEQ (that varies with Universal Time, UT, and time-of-year, F) such that ZGSM is aligned with the projection of onto the Z-Y plane. The idea of the R-M effect is that geomagnetic activity is driven by a coupling function that depends of the southward interplanetary magnetic field (IMF) in the GSM fame, for example, the “half-wave rectified” southward component BS in the GSM frame (where BS = −[BZ]GSM for [BZ]GSM < 0 and BS = 0 for [BZ]GSM ≥ 0) but the dominant IMF reaching Earth lies in the GSEQ X-Y plane (so [Bz]GSEQ = 0). The resulting F-UT pattern of BS for |[BY]GSEQ| = 1 nT is set by sin(βGSEQ) and is shown in the upper panel of part (e) and daily means as a function of F are given in the lower panel. The F variation (currently, 2019) due to R-M peaks around 4 April (F = 0.257) and October 7 (F = 0.769) whereas the equinoxes are March 20 (F = 0.216) and September 22 (F = 0.726).

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