Seasonal and diurnal variation of geomagnetic activity: Russell-McPherron effect during different IMF polarity and/or extreme solar wind conditions

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117,, doi:10.1029/2012ja017845, 2012 Seasonal and diurnal variation of geomagnetic activity: Russell-McPherron effect during different IMF polarity and/or extreme solar wind conditions H. Zhao 1,2 and Q.-G. Zong 1,3 Received 23 April 2012; revised 1 October 2012; accepted 2 October 2012; published 29 November 2012. [1] The Russell-McPherron (R-M) effect is one of the most prevailing hypotheses accounting for semiannual variation of geomagnetic activity. To validate the R-M effect and investigate the difference of geomagnetic activity variation under different interplanetary magnetic field (IMF) polarity and during extreme solar wind conditions (interplanetary shock), we have analyzed 42 years interplanetary magnetic field and geomagnetic indices data and 1270 SSC (storm sudden commencement) events from the year 1968 to 2010 by defining the R-M effect with positive/negative IMF polarity (IMF away/toward the Sun). The results obtained in this study have shown that the response of geomagnetic activity to the R-M effect with positive/negative IMF polarity are rather profound: the geomagnetic activity is much more intense around fall equinox when the direction of IMF is away the Sun, while much more intense around spring equinox when the direction of IMF is toward the Sun. The seasonal and diurnal variation of geomagnetic activity after SSCs can be attributed to both R-M effect and the equinoctial hypothesis; the R-M effect explains most part of variance of southward IMF, while the equinoctial hypothesis explains similar variance of ring current injection and geomagnetic indices as the R-M effect. However, the R-M effect with positive/negative IMF polarity explains the difference between SSCs with positive/negative IMF B y accurately, while the equinoctial hypothesis cannot explain such difference at the spring and fall equinoxes. Thus, the R-M effect with positive/negative IMF polarity is more reasonable to explain seasonal and diurnal variation of geomagnetic activity under extreme solar wind conditions. Citation: Zhao, H., and Q.-G. Zong (2012), Seasonal and diurnal variation of geomagnetic activity: Russell-McPherron effect during different IMF polarity and/or extreme solar wind conditions, J. Geophys. Res., 117,, doi:10.1029/2012ja017845. 1. Introduction [2] The semiannual variation in geomagnetic activity has been recognized for a long period of time [Cortie, 1912], which shows the maximum appears around equinoxes while the minimum appears around solstices, e.g., geomagnetic storm annual distribution [Echer et al., 2011]. Over the decades, several explanations for this variation have been 1 Institute of Space Physics and Applied Technology, Peking University, Beijing, China. 2 Laboratory for Atmospheric and Space Physics, Department of Aerospace Engineering Sciences, University of Colorado Boulder, Boulder, Colorado, USA. 3 Center for Atmospheric Research, University of Massachusetts Lowell, Lowell, Massachusetts, USA. Corresponding author: Q.-G. Zong, Institute of Space Physics and Applied Technology, Peking University, Beijing 100871, China. (qgzong@gmail.com) 2012. American Geophysical Union. All Rights Reserved. 0148-0227/12/2012JA017845 put forward, such as the axial hypothesis, the equinoctial hypothesis and the Russell-McPherron effect [Cortie, 1912; Bartels, 1932; McIntosh, 1959; Svalgaard, 1977; Russell and McPherron, 1973]. [3] The axial hypothesis takes the varying heliographic latitude of the earth into consideration; the equinoctial hypothesis is based on the angle between Earth-Sun line and the dipole axis of the Earth; the R-M effect holds that the angle between Z axis in geocentric solar magnetospheric (GSM) coordinate system and Y axis in geocentric solar equatorial (GSEQ) coordinate system plays an important role. Figure 1a shows the semiannual and diurnal variation of the angle q between the Z axis in GSM coordinate system and the Y axis in GSEQ coordinate system, that is, the controlling parameter of the R-M effect. According to the R-M effect, the probability of southward IMF increases when the angle q, which is smaller than 90 degrees, decreases, so that the dayside reconnection can be more efficient and more energy can be conveyed into the magnetosphere. Figure 1b shows the semiannual and diurnal variation of the angle y between Earth-Sun line and the dipole axis of the Earth, that is, the crucial parameter of the equinoctial hypothesis. 1of15

Figure 1. The Russell-McPherron effect and the equinoctial hypothesis. (a) Seasonal and diurnal variation of q angle between Z axis in GSM coordinate system and Y axis in GSEQ coordinate system. (b) Seasonal and diurnal variation of y angle between Earth-Sun line and the dipole axis of the Earth. Crooker and Siscoe [1986] suggest the field configuration in the Chapman-Ferraro current plane may change and prevent the energy transfer as the y angle changes; whereas Russell et al. [2003] demonstrate that the tilt of dipole axis controls the size of dayside reconnection region and thus the reconnection rate and geomagnetic activity. [4] Nowadays, the R-M effect is one of the most prevailing hypotheses. Orlando et al. [1993] investigated the connection between semiannual variation of the geomagnetic activity and interplanetary magnetic field from 1965 to 1987 and verified the accuracy of R-M effect which suggests the geomagnetic activity is modulated by southward IMF B z. Siscoe and Crooker [1996] analyzed diurnal variation of Dst index for 13 years and found the R-M effect predicts such an diurnal oscillation. Also, O Brien and McPherron [2002] investigated the dynamics of Dst index and demonstrated the R-M effect is indeed valid. [5] However, there are also many studies on the semiannual variation which argued that the R-M effect fails to explain the diurnal variation of the geomagnetic activity and can only explain a small part of seasonal variation of the geomagnetic activity. Cliver et al. [2000] argued that the R-M effect can only predict part of semiannual variation, while the equinoctial hypothesis, which is based on the variation of the angle y between the Earth-Sun line and the dipole axis of the Earth, accounts for a large part of semiannual variation of geomagnetic activity. Cliver et al. [2001] investigated the semiannual variation of Dst index for about 40 years and found the equinoctial hypothesis dominates the storm component of the variation of Dst index and the R-M effect predicts little variance. The similar conclusion has been derived from the analysis of aa index, too [Cliver et al., 2002]. Moreover, Svalgaard et al. [2002] analyzed the largest geomagnetic storms from 1868 to 1998 and indicated the most difference of occurrence frequency between equinoxes and solstices arises from an equinoctial effect. Li et al. [2001] used the models of MeV electron at geostationary orbit and the Dst index to examine the cause of semiannual variation and found the equinoctial hypothesis contributes the largest part to semiannual variation of Dst index and MeV electrons in the inner magnetosphere. Furthermore, Mursula [2011] have studied seasonal variation of substorms and geomagnetic index Ap between 1993 and 2008 and showed that semiannual variation is mainly due to the artifact of annual maximum alternating from spring to fall; however, Svalgaard [2011] disprove this conclusion by showing the well-established UT variation of geomagnetic activity and lack of organized annual variations of the solar driver, and confirm that the semiannual variation is not overestimated nor an artifact. [6] On the other hand, the contribution of solar wind, especially during extreme solar wind conditions, like interplanetary shocks, to seasonal and diurnal variation of geomagnetic activity has been rare studied although it may play significant role. [7] SSCs indicate the arrival of the interplanetary discontinuities/shocks [Gonzalez et al., 1994]. A SSC is a sudden increase in the H component of geomagnetic field preceding a geomagnetic storm. It differs from a sudden impulse (SI), which is physically the same phenomenon but without following a geomagnetic storm [Siscoe et al., 1968; Joselyn and Tsurutani, 1990; Araki, 1994; Echer et al., 2005]. MHD discontinuities have four types: rotational discontinuities, tangential discontinuities, contact discontinuities, and shocks. Shocks also have three different types, that is, fast, intermediate and slow. Either shocks or tangential discontinuities which have different densities across them can cause SIs or SSCs. Interplanetary shocks have a great impact on the Earth s magnetosphere. Fast shocks, which are most likely to cause a SSC or SI, can also lead to particle energization [Zong et al., 2009], dayside aurora, creation of new radiation belts, and substorms [Colburn and Sonett, 1966; Tsurutani et al., 2011]. Through the study of SSCs and shocks between 1978 and 1980, Smith et al. [1986] found that 80 90% of SSCs were associated with interplanetary shocks. Wang et al. [2006] observed 278 SSCs from January 1995 to December 2004 and found 225 of them were associated with interplanetary shocks, that is, the 2of15

probability that a SSC is associated with a interplanetary shock is 0.75. [8] Interplanetary shocks can cause intense geomagnetic storms. Jurac et al. [2002] found, 40% of forward shocks with shock normals perpendicular to the IMF cause intense storms(dst < 100 nt), while 10 15% of shocks without normals perpendicular to the IMF lead to intense storms. Also, Echer and Gonzalez [2004] reported 57% of interplanetary shocks are followed by moderate and intense geomagnetic storms(dst 50 nt). Interplanetary shocks can also trigger substorms [Zhou and Tsurutani, 2001; Tsurutani and Zhou, 2003]. The upstream IMF of shocks strongly affect auroral responses: southward IMF can lead to substorm expansion phase triggerings, nearly zero IMF leads to pseudobreakup events, and northward IMF for quiescent events. Yue et al. [2010] investigated 106 interplanetary shocks during 1997 2007 and found that IMF B z keep southward or northward before the shock arrival and turns out to be more negative or positive after the arrival of the shock. [9] In this study, we have examined the validity and precision of the R-M effect and interplanetary shock related R-M effect by analyzing a large amount of the data of magnetic field and geomagnetic indices from 1968 to 2010 and 1270 SSC (storm sudden commencement) events under different IMF polarity. We showed that the IMF polarity is one of the most important parameters when investigating seasonal and diurnal variation of geomagnetic activity. Geomagnetic activity are rather strong at spring and fall equinoxes with different IMF orientations: the geomagnetic activity is much more intense around fall equinox when the direction of IMF is away the Sun, while much more intense around spring equinox when the direction of IMF is toward the Sun, which is identical with the R-M effect under different IMF polarity. This feature also exists before and after SSCs. 2. Seasonal and Diurnal Variation of Geomagnetic Activity: The R-M Effect With Positive/Negative IMF Polarity [10] Since the R-M effect was first put forward in 1973, it becomes the most prevailing hypothesis accounting for the semiannual variation of geomagnetic activity. The R-M effect explains the semiannual variation of geomagnetic activity by the varying probability of IMF southward component in GSM coordinate system, which is caused by the varying orientation of the GSM coordinate system relative to GSEQ coordinate system. The IMF southward component is widely believed to be the controlling factor of geomagnetic activity. The Earth rotation axis tilts 23.5 from Z axis in geocentric solar ecliptic (GSE) coordinate system, causes the seasonal variation of the projection of IMF onto Z axis in GSM, and thus causes the seasonal variation of the probability of southward IMF in GSM. The dipole axis inclines 11.5 from the rotation axis and leads to the diurnal variation of the southward IMF projection. [11] There are three main assumptions in the R-M effect: the IMF is always along the Parker spiral direction and its magnitude is constant; the IMF is either away or toward the Sun with equal possibility; and the northward IMF has no effect on the geomagnetic activity. Since different directions of IMF can have different effects on the magnetosphere, we study the R-M effect under different IMF polarity, that is, away the Sun (positive polarity, IMF B y > 0 in GSE coordinate system), we define it as the R-M effect with positive IMF polarity, and toward the Sun (negative polarity, IMF B y < 0), defined as the R-M effect with negative IMF polarity. [12] Figure 2 shows the R-M effect with positive/negative IMF polarity, namely, the contour plot of IMF B z southward component in GSM coordinate system under the situation that IMF is away/toward the Sun, assuming IMF B y of 1 g in GSEQ coordinate system, and the schematic diagram of the R-M effect under different IMF polarity. [13] At spring equinox, the Earth rotation axis is pointed 23.5 away from Z axis toward Y axis in GSE coordinate system, so that the IMF toward the Sun makes a negative projection onto the direction of Z axis of GSM coordinate system, which can increase the efficiency of dayside reconnection and enhance the geomagnetic activity, and the IMF away the Sun makes a positive projection onto the direction of Z axis, which has no effect on the geomagnetic activity according to assumptions in the R-M effect. At fall equinox, the angle from the Earth rotation axis to Y axis in GSE coordinate is 113.5, so that the IMF away the Sun projects onto the direction of Z axis in GSM coordinate system with a negative projection, and the IMF toward the Sun projects onto the Z axis with a positive projection. Figure 2 shows that when IMF is away the Sun, corresponding to the R-M effect with positive IMF polarity, the maximum of possibility of southward B z appears around fall equinox, and when IMF is toward the Sun, corresponding to the R-M effect with negative IMF polarity, the maximum appears around spring equinox. [14] To confirm the prospective R-M effect with positive/ negative IMF polarity, we have used the data set with 1 hour resolution from Omniweb (http://omniweb.gsfc.nasa.gov/) from 1968 to 2010 to analyze the contours of vb s, defined as vb z in GSM coordinate system when IMF is southward, and defined to be zero when IMF is northward, in a 24 24 lattice of day of year and UT hour, under different polarity of IMF. Here we divide UT and day of year to 24 bins respectively, with a bin of 1 hour 15.25 days, and calculate the probability of vb s >1mV/m within each bin under different IMF polarity. [15] Figure 3 shows the contour plots of the probability of vb s >1mV/m with IMF B y positive/negative. The patterns of variation showed in Figure 3 are generally identical with the R-M effect with positive/negative IMF polarity, as the maximum appears at about UT 23:00 at spring equinox when IMF B y < 0, as well as the maximum appears around UT 10:00 at fall equinox when IMF B y > 0. The correlation coefficient between the probability of vb s >1mV/m under positive IMF B y and IMF B z southward component in GSM indicated by the R-M effect with positive IMF polarity (as Figure 2 shows) is 0.91, while the coefficient between the probability of vb s >1mV/m under negative IMF B y and IMF B z indicated by the R-M effect with negative IMF polarity is 0.90. The results indicate the R-M effect with positive/ 3of15

Figure 2. The schematic diagram of the R-M effect with positive/negative IMF polarity. At spring equinox, IMF toward the Sun projects onto Z axis of GSM coordinate system and converts into an effective southward component; at fall equinox, IMF away the Sun projects onto Z axis with a southward projection. The R-M effect with positive/negative IMF polarity shows the semiannual variation of IMF B z southward component in GSM coordinate system due to IMF B y in GSEQ coordinate system of 1 g. negative IMF polarity can predict the seasonal and diurnal variation of vb s with positive/negative IMF B y precisely. [16] In order to investigate the seasonal and diurnal variation of variation of ring current injection, we derive the ring current injection function Q from the Burton from the Burton equations [Burton et al., 1975]: ddst* ¼ Qt ðþ Dst* dt t ð1þ p Dst* ¼ Dst b ffiffiffi P þ c ð2þ where Q is assumed as a function of vb s, Dst* is the pressure-corrected Dst index, t is the decay time of ring current, P is the solar wind dynamic pressure, and b is the pressure-correction coefficient. O Brien and McPherron [2000] gave Q(vB s )= 4.4(VB s E c ) when VB s > E c, Q = 0 when VBs < E c. Here E c is the ring current injection cutoff and E c = 0.49 mv/m; t = 2.40e 9.74/(4.69+VBs), and b = 7.26. [17] Then, we divide day of year and UT into a 24 24 lattice and plot contours of the probability of Q < 10 nt/h with positive/negative IMF B y. The contours are shown in Figure 4. It is evident that the pattern of variation of ring current injection with positive/negative IMF B y fits well with R-M effect with positive/negative IMF polarity, with maximum at spring equinox when IMF B y < 0 and at fall equinox when IMF B y > 0. The correlation coefficients of situations during positive and negative B y with the R-M effect with positive/ negative IMF polarity are 0.69 and 0.72 respectively. [18] On the other hand, to examine whether the R-M effect with positive/negative IMF polarity predicts the geomagnetic activity at low as well as high latitudes accurately, we perform the contour plots of variation of Dst index and AE index with different orientations of IMF B y and B z in a 24 24 lattice, too. 4of15

Figure 3. The seasonal and diurnal variation of probability of vb s >1mV/m with positive/negative IMF B y and southward IMF B z, calculated in a 24 24 lattice and smoothed by a 3 3 average. [19] The hourly Dst index, calculated from the magnetic field disturbances measured by midlatitude geomagnetic stations, is a widely accepted indicator of ring current intensity. AE index describes the global auroral electrojet activity so that it can be used as a proxy of geomagnetic activity at high latitude [Rostoker, 1972]. Figures 5 and 6 show the seasonal and diurnal variation of Dst and AE indices under different situations of IMF B y and B z, respectively. [20] From both figures we can find the pattern of semiannual variation with positive IMF B y is consistent with the R-M effect with positive IMF polarity, which shows the maximum at fall equinox, while the pattern with negative IMF B y fits well with the R-M effect with negative IMF polarity, as the maximum appears at spring equinox. The diurnal variation of Dst index, on the other hand, is not as clear as the seasonal variation, but Figures 5a and 5b still reveal some UT variation pattern which is consistent with the R-M effect with positive/negative IMF polarity. [21] Also, compared contours of Dst and AE indices with southward/northward IMF B z, we can find that the average value of geomagnetic indices is much higher when IMF B z is southward than northward, which indicates much more intense geomagnetic activity resulting from more efficient dayside reconnection. [22] Furthermore, by comparing Figures 5a and 5b, we can see that the average value of Dst index is much larger with positive IMF B y, which indicates that the R-M effect with positive IMF polarity can further enhance the geomagnetic activity. On the other hand, Figure 3 doesn t show much difference in IMF B s under positive/negative IMF polarity, which suggests the enhanced geomagnetic activity under positive IMF B y is more likely caused by the enhanced dayside reconnection rate. [23] The correlation coefficients of Figures 5a, 5b, 5c, and 5d with corresponding R-M effect are 0.68, 0.66, 0.67 and 0.72 respectively, and for Figures 6a, 6b, 6c, and 6d, the correlation coefficients are 0.59, 0.58, 0.72 and 0.68 Figure 4. The seasonal and diurnal variation of probability of Q < 10 nt/h with positive/negative IMF B y and southward IMF B z, calculated as Figure 3. 5of15

Figure 5. The seasonal and diurnal variation of Dst index with positive/negative IMF B y and southward/ northward IMF B z, calculated as Figure 3. respectively. The correlation coefficients are summarized in Table 1. 3. Seasonal and Diurnal Variation of Geomagnetic Activity Under Extreme Solar Wind Conditions 3.1. Seasonal and Diurnal Variation of Geomagnetic Activity Before and After SSC Events With Different Orientation of IMF B z [24] To examine seasonal and diurnal variation of geomagnetic activity before and after SSCs, we use vb s from OMNI database to demonstrate the R-M effect is present before and after SSCs. We divide UT and the day of year into 12 bins respectively, with each bin of 2 hours 30.5 days, and calculate the probability of vb s >1mV/m before and after SSCs respectively in each bin. Here we use the SSC list from IAGA Bulletin and analyze 1270 SSCs between 1968 and 2010. [25] According to Zhang et al. [2008], the duration of a CME preceding shock sheath is generally shorter than 24 hours, so we choose a time period of 12 hours before and after each SSC event respectively to perform contour plots before and after SSCs. In order to examine the effect of the orientation of IMF B z on the R-M effect, we perform the contour plots under southward and northward IMF B z. [26] Figure 7 shows the seasonal and diurnal variation of the probability of vb s > 1 mv/m before and after SSCs respectively under southward IMF B z.it s worth mentioning that the scales of two panels color bars are different. From Figure 7, we find that the pattern of vb s variation after SSCs is quite similar with the R-M effect. It shows higher probability of southward IMF B z at the equinoxes and lower at the solstices, as well as higher probability at midnight around spring equinox while at noon around autumn equinox. Before SSCs, the probability of vb s >1mV/m is much smaller than after SSCs, however, the pattern doesn t well fit the R-M effect. The correlation coefficient between the probability of vb s > 1 mv/m before/after SSCs and the angle q, the controlling parameter of the R-M effect, is 0.11/ 0.60. [27] To compare with the R-M effect, we also calculate the correlation coefficient between the probability of vb s > 1 mv/m and the angle y, which is the dominant parameter in the equinoctial hypothesis. The correlation coefficient before/after SSCs is 0.02/0.39 respectively. 6of15

Figure 6. The seasonal and diurnal variation of AE index with positive/negative IMF B y and southward/ northward IMF B z, calculated as Figure 3. It indicates that the R-M effect can explain the probability of southward IMF B z after SSCs more precisely, while the equinoctial hypothesis can hardly explain the semiannual variation of vb s clearly. [28] We also calculate the probability of Q < 10 nt/h in a 12 12 lattice. The results are showed in Figure 8. Figure 8 shows the probability of Q < 10 nt/h before and after SSCs under southward IMF, which reveals prominent semiannual variation as higher at the equinoxes and lower at the solstices. The correlation coefficient of the probability of Q < 10 nt/h before/after SSCs and the angle q is 0.30/ 0.57, while for the angle y the correlation coefficient is 0.15/0.62. The correlation coefficients show that both q and y can explain part of seasonal and diurnal variations of large ring current injection. And also, before SSCs both hypotheses explain less variations of ring current injections than after SSCs. [29] Moreover, in order to show the seasonal and diurnal variation of geomagnetic activity under extreme solar wind conditions, we perform the contour plots of Dst index before and after SSCs in a 12 12 lattice, and compare the contour plots with the R-M effect as well as the equinoctial hypothesis to examine whether these two hypotheses account for variation of Dst index before and after SSCs. Table 1. Summarization of Correlation Coefficients of Contours During Positive/Negative IMF B y and Southward/Northward B z With Corresponding R-M Effect With Positive/Negative IMF Polarity B y >0,B z <0 B y <0,B z <0 B y >0,B z >0 B y <0,B z >0 and R-M Effect (+IMF) and R-M Effect ( IMF) and R-M Effect (+IMF) and R-M Effect ( IMF) vb s 0.91 0.90 Q 0.69 0.72 Dst index 0.68 0.66 0.67 0.72 AE index 0.59 0.58 0.72 0.68 7of15

Figure 7. Seasonal and diurnal variation of the probability of VB s >1mV/m before and after SSCs under southward IMF B z. [30] Figure 9 shows the seasonal and diurnal variation of Dst index before and after SSCs under southward and northward IMF B z conditions, respectively. From Figure 9, we find that the semiannual variation with equinoxes maximum is evident, but the diurnal variation cannot be well explained by both hypotheses. The correlation coefficient of Dst variation before/after SSCs under southward IMF conditions (Figures 9a and 9b) with the q angle is 0.42/0.51; as to the y angle the correlation coefficient is 0.13/ 0.52; under northward IMF conditions (Figures 9c and 9d), the correlation coefficient of Dst variation before/after SSCs with the q is 0.27/0.26, while for y is 0.01/ 0.48. [31] It shows that both hypotheses predict part of the variation of Dst index after SSCs; however, as for the situation before SSCs, both hypotheses, especially the equinoctial hypothesis, cannot predict the variation of Dst index. Compared with different IMF orientations, we find that with southward IMF B z, the absolute value of Dst index is much higher than another two cases, which indicates more energy transfer and larger geomagnetic storms. [32] Moreover, by distinguishing different orientations of IMF B y, we can derive higher correlation coefficients between the R-M effect with positive/negative IMF polarity and variation of geomagnetic activity, which can be seen in the following section. The correlation coefficients of each situation with the angle q and y are summarized in Table 2. 3.2. Seasonal and Diurnal Variation of Geomagnetic Activity Before and After SSCs With Positive/Negative IMF B y [33] The R-M effect explains semiannual variation of geomagnetic activity using the changing IMF southward component, which is caused by the changing of GSM coordinate system relative to GSEQ coordinate system. To confirm the R-M effect is indeed present before and after SSC events and has a great influence on the geomagnetic activity, we perform the contour plots under different IMF B y orientations, that is, positive and negative. The contour plots of semiannual variation of the probability of vb s >1mV/m, the probability of Q < 10 nt/h and the Dst Figure 8. Seasonal and diurnal variation of the probability of Q < 10 nt/h before and after SSCs under southward IMF B z. 8of15

Figure 9. Seasonal and diurnal variation of Dst index before and after SSCs under different IMF B z conditions. index before/after SSCs with different IMF B y are showed in Figures 10, 11, and 12. From these figures, we can find that as to the situation that IMF B y is negative, the geomagnetic activity is more intense at spring equinox and relatively weak at fall equinox; when IMF B y is positive, the geomagnetic activity around fall equinox is much more intense and less intense at the spring equinox, which is consistent with the R-M effect with positive/negative IMF polarity. [34] Meanwhile, we perform contour plots of AE index before/after SSCs under different IMF B y conditions, as shown in Figure 13c, 13d, 13e, and 13f. As a comparison, we also perform contour plots of AE index before/after SSCs under all circumstances (Figures 13a and 13b). The variation of AE index before and after SSCs don t show clear feature of semiannual variation and UT variation as the R-M effect or the equinoctial hypothesis suggested, which is likely caused by the equatorward expansion of the auroral electrojets and the longitudinal station gaps [Ahn et al., 2000]. However, even the seasonal and diurnal variation of AE index is quite distinctive, AE variation with positive/negative IMF B y still shows identical feature as the R-M effect with positive/negative IMF polarity: when IMF B y is negative, AE index is higher around the spring equinox and relatively lower around the fall equinox; when IMF B y is positive, it is Table 2. Summarization of Correlation Coefficients Between Geomagnetic Activity Variation Before and After SSCs With Different IMF B z Conditions and Two Hypotheses Time Period IMF Bz Direction The q Angle The y Angle The probability of vb s >1mV/m before SSCs IMF B z southward 0.11 0.02 after SSCs IMF B z southward 0.60 0.39 The probability of Q < 10 nt/h before SSCs IMF B z southward 0.30 0.15 after SSCs IMF B z southward 0.57 0.62 The Dst index before SSCs IMF B z southward 0.42 0.13 IMF B z northward 0.27 0.01 after SSCs IMF B z southward 0.51 0.52 IMF B z northward 0.26 0.48 9of15

Figure 10. Seasonal and diurnal variation of the probability of VB s >1mV/m before and after SSCs under different IMF B y conditions. higher around the fall equinox and lower around the spring equinox. [35] The correlation coefficients of the variation before/ after SSCs with positive/negative IMF B y and corresponding R-M effect are given in Table 3. For vb s we can find that the R-M effect with positive/negative IMF polarity can explain a large part of seasonal and diurnal variation of vb s, and the correlation coefficients are up to 0.90, which has been improved significantly compared to the R-M effect without distinguishing IMF polarity. For Q and Dst, the correlation coefficients are also improved a lot. AE index, which doesn t show clear semiannual variation and the correlation coefficient of AE variation and the R-M effect before/after SSCs is only 0.0003/0.21, indeed show features identical with the R-M effect with positive/negative IMF polarity when distinguishing the polarity of IMF B y, and the correlation coefficients are increased up to 0.65. [36] The results confirm that the R-M effect is indeed present before and after SSCs and can predict southward IMF accurately as well as a large part of geomagnetic activity. Also, it shows the IMF polarity is an important parameter when investigating semiannual variation as well as the R-M effect. To compare the R-M effect with the equinoctial hypothesis, we also calculate the correlation coefficients of the variation with the y angle, which are also shown in Table 3. [37] We find that the correlation coefficients of the variation and the R-M effect with positive/negative IMF polarity are much higher than that of the equinoctial hypothesis, which can demonstrate the R-M effect can predict the geomagnetic activity more efficiently when we distinguish positive/ negative IMF B y ; although the equinoctial hypothesis also explains part of the variation, it cannot explain the difference between the semiannual variation with positive IMF B y and negative IMF B y. 4. Discussion and Conclusions [38] By defining the R-M effect with positive/negative IMF polarity according to the IMF polarity, that is, away/ toward the Sun, we find that the patterns of semiannual variation predicted by them are totally different. The R-M effect with positive IMF polarity predicts larger IMF B z southward component in GSM coordinate system at fall equinox, which indicates more efficient dayside reconnection and energy input leading to more intense geomagnetic activity, while the R-M effect with negative IMF polarity shows the maximum at spring equinox. [39] To confirm the validity of the R-M effect with positive/ negative IMF polarity, we plot contours of semiannual variation of probability of vb s >1mV/m, probability of large ring current injection Q < 10 nt/h, geomagnetic indices 10 of 15

Figure 11. Seasonal and diurnal variation of the probability of Q < 10 nt/h before and after SSCs under different IMF B y conditions. Dst and AE under different conditions of IMF B y, and find the results are identical with the R-M effect with positive/ negative IMF polarity. It indicates that the R-M effect predicts the semiannual variation of geomagnetic activity more accurately, while other hypotheses cannot explain such difference at equinoxes between different IMF polarity. [40] Also, the contours show the pattern of diurnal variation with positive/negative IMF B y is similar to the R-M effect with positive/negative IMF polarity, which indicates that the R-M effect can also predict part of diurnal variation. Compared to previous studies [O Brien and McPherron, 2002; Cliver et al., 2000], the correlation coefficients between contours of geomagnetic activity and the R-M effect are improved a lot. The correlation coefficient of vb s with the R-M effect with positive/negative IMF polarity in our paper is 0.91/0.90, and the correlation coefficient of Q with the R-M effect with positive/negative IMF polarity is 0.69/ 0.72, while O Brien and McPherron [2002] derived the rank order correlation coefficient of 0.55 0.03 between possibility of vb s > 1 mv/m with angle q, which is the controlling parameter of the R-M effect, and the correlation coefficient of 0.44 0.04 between possibility of Q < 10 nt/h and q. Cliver et al. [2000] calculated the correlation coefficient between Dst index and R-M angle and obtained 0.45, and the seasonal and diurnal variation of AE index in their paper doesn t show a pattern of the R-M effect clearly, while our correlation coefficients with Dst index are much higher and the semiannual variation of AE index with positive/negative IMF polarity also fits the R-M effect with positive/negative IMF polarity well. The results show that the R-M effect with positive/negative IMF polarity explains semiannual variation of geomagnetic activity more precisely. [41] From Figure 5, we find that the average value of Dst index is much larger with positive IMF B y when IMF B z is southward, which indicates that compared to the R-M effect with negative IMF polarity, the R-M effect with positive IMF polarity can further enhance the geomagnetic activity. [42] Also, our results indicate that unlike the R-M effect which assumes the northward IMF has no effect on the geomagnetic activity, the northward IMF can also have effects on the magnetosphere. This is consistent with recent research, although it is much weaker than southward IMF situation. Thus the assumption made by Russell and McPherron [1973] may introduce some errors in the R-M effect. [43] For the seasonal and diurnal variation of geomagnetic activity before and after SSCs, from Figure 7, we find that the R-M effect predicts the seasonal and diurnal variation of southward IMF B z more precisely than the equinoctial hypothesis after SSCs. But when it comes to ring current injections as well as Dst index, the equinoctial hypothesis explains similar amount of variance as the R-M effect, as 11 of 15

Figure 12. conditions. Seasonal and diurnal variation of the Dst index before and after SSCs under different IMF B y shown in Figures 8 and 9. It indicates that the R-M effect predicts southward IMF precisely and explains part of semiannual variation of geomagnetic activity, while the equinoctial hypothesis also explains part of variance of geomagnetic activity after SSCs. Our result is consistent with Cliver et al. [2000], which believes the equinoctial hypothesis contributes to the semiannual variation of geomagnetic activity by reducing the coupling efficiency of dayside reconnection at solstices, as well as O Brien and McPherron [2002]. On the other hand, we also find both the R-M effect and the equinoctial hypothesis can explain seasonal and diurnal variation of geomagnetic activity more accurately after SSCs than before SSCs. This may be because before SSCs IMF B z component is too small to show clear seasonal and diurnal features. [44] However, as shown in Figures 10, 11, 12, and 13, before/after SSCs with positive or negative IMF B y, the semiannual variation of the probability of vb s >1mV/m and Q < 10 nt/h as well as the Dst and AE indices all reveal clear features as much higher at spring equinox when IMF B y < 0, while much higher at fall equinox when IMF B y >0. We find that the R-M effect with positive/negative IMF polarity can explain such difference perfectly, while the equinoctial hypothesis cannot. [45] The results presented in this paper demonstrate before and after SSCs, the R-M effect is actually present and accounts for a large part of semiannual variation of geomagnetic activity. It also shows that the IMF polarity, that is, positive/negative, is a very important parameter when examining semiannual variation of geomagnetic activity or the R-M effect. [46] Crooker et al. [1992] found that differential compression at the shock increases the Parker spiral angle and increases the projected IMF southward component, which results in the enhancement of the R-M effect. Compared our results with O Brien and McPherron [2002], we find that the probability of vb s >1nT as well as Q < 10 nt/h of our study are higher than O Brien and McPherron s, and the correlation coefficients of variation and the angle q as well as the angle y of our study are approximately equal to theirs. It indicates the differential compression at the interplanetary shock can result in the enhancement of the R-M effect, as Crooker et al. [1992] show. And compared the results of the Dst and the AE index with Cliver et al. [2000], we can also derive the same conclusion. [47] However, since we calculate the semiannual and diurnal variation before/after SSCs with positive and negative IMF B y respectively, and derive much higher correlation coefficients with the R-M effect with positive/negative IMF polarity, we can demonstrate the presence of the R-M effect under extreme solar wind conditions more evidently, and show before/after SSCs, the R-M effect with positive/ 12 of 15

Figure 13. Comparison between seasonal and diurnal variation of the AE index before and after SSCs with different IMF B y orientations. negative IMF polarity can explain difference of variance of geomagnetic activity with different IMF B y conditions perfectly while the equinoctial hypothesis cannot. [48] In summary, we have performed contour plots of parameters and calculated the correlation coefficients of each IMF condition with the R-M effect with positive/ negative IMF polarity and interplanetary shock related R-M effect as well as the equinoctial hypothesis by analyzing a large amount of the data of magnetic field and geomagnetic indices from 1968 to 2010 and 1270 SSC (storm sudden commencement) events. The main results in this paper can be summarized as: [49] 1. The polarity of IMF is one of controlling factors for the semiannual and diurnal variation of geomagnetic activity or the R-M effect: the geomagnetic activity is much more intense around fall equinox when the direction of IMF is away the Sun, while much more intense around spring equinox when the direction of IMF is toward the Sun. [50] 2. The average value of Dst index is much higher under the R-M effect with positive IMF polarity when IMF 13 of 15

Table 3. Summarization of Correlation Coefficients Between Geomagnetic Activity Variation Before and After SSCs With Different IMF B y Orientations and Two Hypotheses Time Period +/ IMF B y The R-M Effect With +/ IMF Polarity The Equinoctial Hypothesis The probability of vb s >1mV/m before SSCs B y > 0 0.84 010 B y < 0 087 0.04 after SSCs B y > 0 0.93 0.12 B y < 0 0.92 0.05 The probability of Q < 10 nt/h before SSCs B y > 0 0.67 0.13 B y <0 0.30 0.12 after SSCs B y > 0 0.61 0.59 B y < 0 0.62 0.35 The Dst index before SSCs B y >0 0.58 0.01 B y <0 0.60 0.06 after SSCs B y >0 0.60 0.38 B y <0 0.61 0.45 The AE index before SSCs B y > 0 0.61 0.002 B y < 0 0.61 0.07 after SSCs B y > 0 0.65 0.20 B y < 0 0.64 0.17 B z is southward, which indicates that the R-M effect with positive IMF polarity can indeed enhance the geomagnetic activity. [51] 3. After SSC events, the correlation coefficient between variation of vb s under southward IMF and q angle, the controlling parameter of the R-M effect, is 0.60, while the correlation coefficient between vb s and y angle, the controlling parameter of the equinoctial hypothesis, is only 0.39. It indicates the R-M effect can explain more variation of IMF southward component than the equinoctial hypothesis. However, as for Q and Dst index, the equinoctial hypothesis explains similar amount of variance as the R-M effect. [52] 4. The semiannual and diurnal variations under extreme solar wind conditions with positive and negative IMF B y are quite different: when B y is positive, the maximum of geomagnetic activity appears around the fall equinox; when B y is negative, the maximum appears at the spring equinox. The correlation coefficients between variance of geomagnetic activity before/after SSCs with positive/negative IMF B y and corresponding R-M effect are improved significantly: for vb s, Q, Dst and AE, the correlation coefficients after SSCs with positive/negative IMF B y are 0.93/0.92, 0.61/0.62, 0.60/ 0.61 and 0.65/0.64 respectively. [53] 5. As for the equinoctial hypothesis, the correlation coefficients before/after SSCs with positive/negative IMF B y are much lower than the R-M effect with positive/negative IMF polarity. These results indicate that equinoctial hypothesis cannot explain the difference between geomagnetic activity variation under positive IMF polarity and negative IMF polarity, and its prediction precision is much lower than the R-M effect with positive/negative IMF polarity. 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