The semiannual variation of transpolar arc incidence and its relationship to the Russell–McPherron effect

Earth's aurora is a luminescent phenomenon generated by the interaction between magnetospheric precipitating particles and the upper atmosphere; it plays an important role in magnetosphere–ionosphere (M‐I) coupling. The transpolar arc (TPA) is a discrete auroral arc distributed in the noon‐midnight direction poleward of the auroral oval and connects the dayside to the nightside sectors of the auroral oval. Studying the seasonal variation of TPA events can help us better understand the long‐term variation of the interaction between the solar wind, the magnetosphere, and M‐I coupling. However, a statistical study of the seasonal variation of TPA incidence has not previously been carried out. In this paper, we have identified 532 TPA events from the IMAGE database (2000–2005) and the Polar database (1996–2002), and calculated the incidence of TPA events for different months. We find a semiannual variation in TPA incidence. Clear peaks in the incidence of TPAs occur in March and September; a less pronounced peak appears in November. We also examine seasonal variation in the northward interplanetary magnetic field (IMF) over the same time period. The intensity and occurrence rate of the northward IMF exhibit patterns similar to that of the TPA incidence. Having studied IMFB z before TPA onset, we find that strong and steady northward IMF conditions are favorable for TPA formation. We suggest that the semiannual variation observed in TPA incidence may be related to the Russell–McPherron (R‐M) effect due to the projection effect of the IMFB y under northward IMF conditions.


Introduction
Earth's aurora occurs when magnetospheric particles (electrons and protons) precipitate along magnetic field lines into the ionosphere and collide with neutral atomic or molecular species, causing spectral line emission (and ionization) (Rees, 1963;Shi QQ et al., 2009, 2013. The brightness of the aurora is not constant and may fluctuate momentarily (Zhou XZ et al., 2012). Previous studies have recorded the geographical positions of the aurora observed at night and have found that the center of the oval structure is roughly at the geomagnetic pole (Feldstein and Starkov, 1967;Frank et al., 1982;Yokoyama et al., 1998).
The transpolar arc (TPA), also known as "Sun-aligned auroral arc" and "theta aurora", is a discrete auroral arc distributed in the noon-midnight direction poleward of the auroral oval; it usually connects the dayside and nightside sectors of the auroral oval (Frank et al., 1986). TPAs, first reported by Frank et al. (1982), appear under northward interplanetary magnetic field (IMF) conditions. They are more likely to be observed in the dayside of the polar cap region (Lassen and Danielsen, 1989); however, in the northern and southern hemispheres, branches of a TPA originating from the dayside and nightside can be observed simultaneously (Craven et al., 1991;Eriksson et al., 2005;Mailyan et al., 2015;Carter et al., 2017).
Previous studies suggest that TPAs may form on closed magnetic field lines (Peterson and Shelley, 1984;Frank et al., 1986;Tanaka et al., 2004), while other suggest that TPAs occur on open magnetic field lines (Gussenhoven and Mullen, 1989). The generation and evolution of TPAs are related to the polarity and strength of the IMF. Therefore, the incidence of TPAs should also be related. Sev-eral models have been proposed to explain the generation of TPAs under different IMF conditions (Kullen, 2000;Milan et al., 2005). Previous statistical studies have shown that TPAs are more likely to occur under northward IMF conditions with strong northward B z components (Berkey et al., 1976;Gussenhoven, 1982;Kullen et al., 2002); that TPAs generally occur during quiet times under northward IMF conditions, and disappear after substorm onset (Hultqvist, 1974); that shapes and positions of TPAs may change or remain constant over time (Kullen, 2012); and that the strength and variation of the IMF B y directly affects the position and motion of the TPA (Frank et al., 1985;Kullen et al., 2002;Fear and Milan, 2012).
It is known that both solar wind disturbance and IMF conditions have important influence on geomagnetic activities Zhang XY et al., 2010;Yue C et al., 2010Yue C and Zong QG, 2011). The IMF conditions relative to Earth's dipole tilt significantly affect geomagnetic activity, which exhibits semiannual variation, peaks in March and September, and reaches minima in June and December (Russell and McPherron, 1973;Cliver et al., 2000Cliver et al., , 2002. The Russell-McPherron (R-M) effect (Russell and McPherron, 1973) is the prevailing hypothesis to explain this variation. The R-M effect considers that the seasonal variation of the intensity of the negative IMF B z in GSM coordinates is the key parameter that explains the semiannual variation of the geomagnetic activity. According to the R-M effect, the amplitude of the IMF B z component has semiannual variation which reaches its maximum near the Spring and Autumn Equinoxes and reaches its minimum near the summer and the winter solstices. Given that the generation of the TPA is affected by IMF strength, while IMF strength is modulated by the Russell and McPherron (R-M) effect, it is logical to expect that the TPA incidence might also have a semi-annual variation due to the R-M effect (Russell and McPherron, 1973).
TPAs are the energy release process of the magnetosphere under northward IMF conditions; as such, they can be considered as counterparts of the substorm under southward IMF conditions (Crooker, 1992). The long-term variation of mass transport and energy dissipation under southward IMF conditions have been discussed extensively (Liou et al., 2001). However, no statistical study of the seasonal variation of TPA incidence, which reflects the longterm variation of mass transport and energy dissipation under northward IMF conditions, has yet been carried out. In this paper, we investigate the seasonal variation of the incidence of TPAs and correlate these events to the IMF conditions at the time of each. In addition, we discuss the mechanisms proposed to have causal relationship to the seasonal variation in the incidence of TPAs.

Data
The Imager for Magnetopause-to-Aurora Global Exploration (IMAGE) spacecraft was launched in March 2000 and operated until December 2005. The spacecraft was able to capture images of the entire auroral oval. The Wideband Imaging Camera (WIC) onboard the IMAGE spacecraft captured auroral images with a size of 256 × 256 pixels and a spatial resolution of about 100 km at apogee (Mende et al., 2000a, b). The camera was sensitive to the spectral wavelength band from 140 to 190 nm (Lyman−Birge−Hop-field) and captured images every 2 minutes (Mende et al., 2000c). In this paper, we use IMAGE satellite data from 2000−2003 (imaging in the northern hemisphere) and 2003−2005 (imaging in the southern hemisphere), with a small amount of imaging data in both hemispheres in 2003.
The Polar spacecraft was launched in 1996 and operated until 2008. The satellite was placed in an elliptical orbit with an inclination of about 86° and an orbital period of 17 hours. The Polar UVI (Ultraviolet Imager) had an 8° field of view, capturing images approximately every half minute (Torr et al., 1995). In this paper, we use data from 1996−2002 (in Northern Hemisphere Imaging).
To study the seasonal variation of the northward IMF (B z > 0), we use IMF data from the OMNI database with 1 hour resolution (in order to calculate monthly ensemble averages of IMF B z for the years of the aurora data that we use, 1996 to 2005) and 1 minute resolution (in order to calculate the characteristics of IMF values prior to each TPA event).

TPA Incidence
This study calculates the incidence of TPAs in every month by two different methods, duration of events and number of events: (1) The ratio between the total occurrence time of TPAs T TPA and the total occurrence time of aurora T A in a given month is defined as the occurrence rate P of TPAs for that month: (1) (2) The ratio between the number of TPA events N TPA (instead of total TPA occurrence time) to total aurora time T A in a given month is defined to be occurrence rate R for that month: (2) X To calculate the uncertainty in TPA incidence, the statistical uncertainties from multiple observations of T TPA and T A are calculated using the definition of sample standard deviation given in Equation (3), where X i , is a set of N observations with mean : The uncertainty in N TPA is given by the value of its square root, based on counting statistics. Then the uncertainty in TPA incidence is obtained by using the law of error propagation.
We record the time periods during which a clear portion of the auroral oval is observed, and aggregate these times to find the total time of the aurora per month. Similarly, we choose the intervals during which a TPA occurs and aggregate these times to calculate the total time of TPA presence per month. The start/end time of each period is determined by the time when the auroral oval or TPA appears/disappears in the satellite images.
We define the start/end times of the auroral oval when a portion of the auroral oval starts to be visible/invisible in the satellite image that spans a range in magnetic local time (MLT) of greater than 12 hours (i.e. greater than 50% of the entire oval). To rule out effects caused by the duration of TPAs, we record only the number of the TPA events that last longer than half an hour, and we treat two consecutive TPA events as one event if the two events appear at the same location and the time interval between them is less than half an hour. We exclude the time periods from statistics whenever the aurora image is incomplete, missing, or fuzzy, and we cannot thus be certain that a TPA has occurred. Dayglow strongly affects the polar imaging in both hemispheres, so during these times we use the auroral images in which the contamination caused by dayglow has been reduced using an image processing technique (Li X et al., 2004). Figure 1 shows typical examples of auroral ovals and TPA events. The color indicates the intensity of the aurora. The extreme brightness of the images on the dayside is caused by dayglow. From Figure 1(a−c), we can clearly see the evolution of the "glowing circle" between magnetic latitudes of 60° and 80°; this is the auroral oval. Using the criteria given above, the start time of the auroral oval can be determined as 11:02:17 in Figure 1a. A TPA case starting at 12:24:01 UT and ending at 16:00:47 UT is shown in Figure 1(d−i). It reaches its peak intensity at 15:17:50 UT in Figure 1g, when the TPA is shown to be crossing the entire auroral oval in the dusk side.
Based on the statistical criteria listed above, we identified 532 TPA events in total. Among these events, 437 occured in the northern hemisphere and 95 events in the southern hemisphere. A total of 278 events come from the IMAGE satellite database and 254 events from the Polar satellite database. The TPA events in the Southern Hemisphere were all observed by IMAGE. Since the IMAGE and Polar satellites were imaging in the southern hemisphere only during the final working period, the data volume in the southern hemisphere is relatively small. Therefore, the segregation of TPA incidence to the northern and southern hemispheres is not considered in this study. The number and total time of the TPA events and the total time of the auroral oval in the different  Table 1. Figure 2 shows the monthly occurrence rate of observed TPAs in both hemispheres, calculated according to Equations (1) and (2). The error bar is added on the histogram. Both of these results show similar trends. Clearly significant peaks in the incidence of TPAs occur in March and September. A somewhat less prominent peak appears to occur in November. Significant troughs appear in December/January, and May/June. The data also show a weak local trough in October (separating the peaks in September and November). These results clearly show that the incidence of TPAs has a significant semiannual variation.  Figure 3a and Figure 3b. The horizontal axis represents the seasonal variation and the vertical axis represents the diurnal variation. The B z mean ( Figure 3a) and the probability of B z > 2 nT (Figure 3b) are calculated in a 24 × 24 grid, smoothed by means of 3 × 3 averaging. As can be seen from Figure 3a and Figure 3b, the observation of B z is in good agreement with the predicted result of the R-M effect (Russell and McPherron, 1973;Zhao H and Zong QG, 2012;Bai et al., 2018), which suggests that the R-M effect can also predict the semiannual variation of the northward IMF. Figure 3c presents a histogram of the average value of the northward IMF B z data for each month. Figure 3d is a histogram of the probability of greater than 2 nT in the northward IMF B z data for each month. The reason for using the 2 nT threshold in Figure 3b   Figure 4a, which will be discussed later. Figure 3d shows a clear semiannual variation trend, with peaks in March and September and valleys in December/January and June. From Figure 3c, we can see a vague semiannual variation trend, while there seems to be another peak in November, consistent with the apparent November peak in TPA incidence seen in Figure 2.

IMF B z Observation
Previous studies considering the time delay between TPA observations and corresponding IMF observations have shown that the production of TPAs is related to the IMF 1−2 hours (Kullen et al., 2002) or 3−4 hours (Fear and Milan, 2012) before the occurrence of a TPA. Here we use OMNI 1-minute-resolution solar wind data to study IMF B z before TPA onset. Figure 4 shows the characteristics of IMF B z before the occurrence of TPAs in each month. The four colored lines in the figure represent the characteristics of IMF B z in this month 1, 2, 3, 4 hours before the appearance of each TPA (the start time and the end time of a TPA event are moved forward simultaneously, so that the time used to calculate IMF B z is equal to the duration of TPA). They are calculated from the OMNI 1-minute-resolution solar wind data; the northward and southward IMF are calculated separately. The dotted black line (present-ing background values) is calculated based on all the OMNI 1hour-resolution solar wind data from 1996 to 2005 (corresponding to the times of the IMAGE and Polar satellite data), reflecting the long-term characteristics of IMF B z . Figure 4a shows the monthly binned average of IMF B z prior to each TPA; Figure 4b shows the probabilities of IMF B z > 2 nT and B z < −2 nT before the occurrence of each TPA. These two figures show similar characteristics; that is, for southward IMF, the IMF B z before each TPA is almost the same as the background value (dotted black line), but for the northward IMF, the IMF B z before TPA is about twice the background value, which is consistent with previous research results. In other words, TPAs are more likely to occur when conditions are dominated by northward IMF with strong northward B z components (Berkey et al., 1976;Gussenhoven, 1982;Kullen et al., 2002). Figure 4c shows the percentage of time allocated between the north and south directions of the IMF B z before the TPA occurs. The upper part of the figure presents northward IMF (B z > 0 nT); the lower part shows the southward IMF (B z < 0 nT). It is clear from the figure that the northward IMF is more likely to be observed before the occurrence of a TPA, confirming again that the preferred condition for occurrence of TPAs  As can be seen from Figure 4a, the northward component of IMF before a TPA is generally larger than 2 nT, while the average value of the southward component is basically around 2 nT. This indicates that a TPA is more likely to occur when the northward component exceeds 2 nT. It is for this reason that we chose the value of 2 nT as a threshold to produce Figures 3b and 3d.

Summary and Discussion
In this study, we have used aurora data from appropriate auroral imaging satellites (IMAGE and Polar) and solar wind data from OMNI satellites for a statistical analysis of semi-annual variation in occurrence of transpolar arcs. We identify 532 TPA events, of which 437 occurred in the northern hemisphere and 95 in the southern hemisphere, and find that the incidence of TPAs is subject to a clear, systematic semiannual variation. A statistical analysis of the B z component reveals that the ensemble average value of IMF B z per month also exhibits a semiannual variation. The in-cidence of TPAs appears to have two peaks in the second half of the year, that is, September and November, but on the whole, TPA incidence shows a semiannual variation. From 1996 to 2005, the value of B z exhibited a second, November, peak in the second half of the year. As we can see from Figure 4 the northward component of IMF B z is dominant, and the amplitude is on average larger than that of the background before the occurrence of each TPA. Comparing the long term variation of TPA incidence and IMF, we find that the incidence of TPAs is related to the polarity and amplitude of the B z component, which is consistent with the previous research results (Berkey et al., 1976;Gussenhoven, 1982;Kullen et al., 2002).
Although the R-M effect is a hypothesis to explain the semiannual variation of geomagnetic activity under southward IMF conditions, our analysis shows that it can also predict the semiannual variation of the northward IMF. Since the occurrence of TPAs is related to the amplitude of the northward B z , it follows logically that the semiannual variation in the incidence of TPAs may be related Here we use OMNI 1 minute resolution solar wind data to study IMF B z before TPA onset. The time used to calculate IMF B z is equal to the duration of TPA. (a) The average value of the IMF B z for 1, 2, 3, 4 hours before the occurrence of TPA using 1min resolution IMNI data; the dotted black line indicates the background value (long-term average value of B z ). (b) Probability of IMF B z > 2 nT and B z < −2 nT for 1, 2, 3, 4 hours before TPA occurs; the dotted black line indicates the background value of probability of IMF B z > 2 nT and B z < −2 nT. The curves in the upper and the lower parts of both (a) and (b) correspond to the northward and southward IMF circumstances, respectively. (c) The percentage of time allocated between the north (upper) and south (lower) sides of the IMF B z for 1, 2, 3, 4 hours before the TPA occurred. The dotted red line reflects the proportion of southward or northward IMF that is 50 percent.
to the R-M effect.
In summary, we suggest that the semiannual variation of the TPA incidence may be related to the R-M effect. Consistent with the R-M effect, both the northward IMF B z component and the incidence of TPAs appear follow a similar 6-month cycle; however, disagreement appears in November between the incidence of TPAs/IMF B z and the prediction of the R-M effect. This anomaly will be further investigated in the future.