In the subsections below, we exhibit the results of statistical examinations for the FS3 anomalies in association with different global space parameters. These results lead out our discussion that derives new understandings and relative importance of the relationships between the FS3 anomalies and these space weather parameters in the section “Discussion”.
Solar wind conditions
We examined the dependences of the FS3 anomalies on solar wind conditions. To derive the relationship between the FS3 anomalies and each of the solar wind speed, dynamic pressure, and the z component of the IMF, superposed epoch analysis was applied to these three solar wind parameters, as shown in Fig. 2. However, no significant variations in these three parameters are found before, after, or at the times of the anomalies. This indicates that high solar wind driving is not a primary cause or prerequisite of the space weather condition inducing the FS3 anomalies.
Relationship to geomagnetic activity
Many previous studies suggested that satellite anomalies are typically associated with high geomagnetic activity. To verify whether the FS3 anomalies are consistent with this finding, the Kp index (https://www.gfz-potsdam.de/en/kp-index/) was used to evaluate the state of geomagnetic activity (Allen 1982; Mayaud 1980). Since the flux of charged particles can accumulate during periods of high Kp values and persists in space environment even after the Kp value decreases, the possible influence of high geomagnetic activity by delay time was considered in this study. The daily maximum Kp value was chosen to indicate geomagnetic state, and the number of the FS3 anomalies that occurred under the condition of each Kp value was counted, as displayed in Fig. 3a. It is found that most anomalies occurred with Kp less than 4, which is generally considered as low geomagnetic activity. This result demonstrates that most of the FS3 anomalies occurred under low geomagnetic activity, but does not in itself indicate that FS3 was more likely to experience an anomaly when geomagnetic activity was low.
It is possible that the days during the mission period have more counts under low geomagnetic activity than under high geomagnetic activity. For this reason, the number of the anomalies needs to be normalized by the relative amount of time for each Kp value to determine the occurrence rate of the FS3 anomalies. Since our method used the maximum daily Kp value, this was also used for the normalization. Figure 3b shows that the occurrence rate decreases with increasing Kp value for low Kp values and then increases at a turning point near Kp = 6. The occurrence rate and the Kp value were therefore fitted after splitting into two intervals of Kp ≥ 6 and Kp ≤ 6. A linear fitting by the least-squares method for these two intervals was performed. The relationship illustrates a positive correlation for Kp ≥ 6 and a negative correlation for Kp ≤ 6. However, in the case that an anomaly occurred at the beginning of a particular day, the Kp value for this case was probably chosen from a 3-h interval after the anomaly. The chosen value could be highly variable, so the accuracy of the statistics will be affected. To improve the accuracy, we used a 2-day window to recalculate the anomaly occurrence rates. The representative Kp value for a day is the maximum Kp value in the 2 days that includes the day and the previous day. Figure 3c shows the occurrence rate of the anomalies in terms of Kp for the 2-day window. Its trend is similar to that for the 1-day window (Fig. 3b). It should be noted that the amounts of mission days with Kp ≥ 7 are only 0.6% and 1.1% for the 1-day and 2-day windows, respectively. Therefore, if we only consider most cases of the FS3 anomalies and geomagnetic conditions (Kp ≤ 6), the occurrence rate of the FS3 anomalies is anti-correlated with the level of geomagnetic activity.
Relationship to solar activity
As described in the section “Introduction”, under high solar activity, CMEs and other special solar wind structures can frequently occur and produce more high energetic particles via shock acceleration, leading to high-speed solar wind, strong southward IMFs, and high geomagnetic activity. Most previous studies inferred these space weather conditions are more likely to spark off satellite anomalies. The number of satellite anomalies then would be expected to be higher during solar maximum than during solar minimum. However, our initial analysis did not obtain such results, in some cases obtaining the opposite results. To resolve this discrepancy, the relationship between the solar cycle and the FS3 anomalies was reexamined. The daily sunspot numbers (SSN) were averaged for individual years to determine solar cycle variations, and then compared to the annual numbers of the FS3 anomalies. As illustrated in Fig. 4a, the number of the FS3 anomalies is the highest during solar minimum and the lowest during solar maximum. The number increases in the trailing edge of the solar cycle and decreases in the leading edge of the solar cycle. This feature illustrates an anti-correlation between the number of the FS3 anomalies and SSN.
To further investigate the relationship between the FS3 anomalies and solar activity in a shorter time scale, the occurrence rates of the FS3 anomalies in terms of SSN were calculated using the same time resolution (1 day) as the analysis of “Relationship to geomagnetic activity”. The result is displayed in Fig. 4b. Considering a time delay for the influences of solar activity on Earth, here, SSN of each day is represented by the maximum value of the day and the previous day. It is found that the relationship between the occurrence rate and SSN shows a negative correlation for SSN < 120 and a positive correlation for SSN > 120. However, note that counts of SSN greater than 120 only account for a small percentage during the mission period of FS3, and most of the FS3 anomalies were accompanied with SSN lower than 120. For most cases, the occurrence rate of the FS3 anomalies is anti-correlated with the level of solar activity.
Relationship to galactic cosmic rays
The results presented in the previous section indicate that an FS3 anomaly did not favorably occur under high solar or geomagnetic activity, except for a small number of extreme conditions. When solar activity is high, the Sun releases more magnetic clouds into the interplanetary space. These magnetic clouds would accumulate at the heliopause and the termination shock of the solar wind, effectively blocking interstellar matter and Galactic Cosmic Rays (GCR) from entering the solar system. Therefore, the intensity of GCR observed is opposite to the level of solar activity (Zhang 2003; Schwadron et al. 2014). Moreover, Likar et al. (2012) reported that GCR can also create an anomaly on a satellite. According to the relationship between the solar cycle and the FS3 anomalies derived from the present study, it may be speculated that the GCR intensity was relatively high near the times when the FS3 anomalies occurred.
To examine the intensity of GCR at the times of the FS3 anomalies, the data of eight neutron monitors were used to conduct a superposed epoch analysis. Although the magnitudes of GCR measured at different latitudes have a larger difference during high Kp than during low Kp (Okpala 2015), they show a similar trend over time. As shown in Fig. 5a, the neutron counts detected by different monitors are in different scale ranges, and thus, we adopted their relative variations instead of their actual values for subsequent analysis. The relative variations of neutron count for each monitor can be calculated by (C − < C >)/ < C > , where C represents neutron count and < > means the average for whole interval. However, some of these monitors have data gaps at different times, and these gaps needed to be filled before we calculate relative variations of neutron count.
Figure 5b exhibits a schematic diagram for explaining how data gaps were filled. In this diagram, there are four neutron monitors for the demonstration, i.e., monitors 1–4. A data gap of monitor 1 is centered at TA. To fill this gap, four parameters are used: TB, A, B, and C. TB represents the times that all monitors have values. A is the average of the values detected at TB by monitor 1; and B (C) is the average of the values detected at TB (TA) by the monitors (i.e., monitors 2–4) that have values at TA. The missing value at TA for monitor 1 is then calculated by C × A/B. This approach was applied to the data of eight monitors used in this study. After data gaps of a monitor were filled, the relative variations of neutron count detected by this monitor can then be calculated. We averaged the relative variations of all the eight monitors at each time to produce an average curve, which was used as the relative variations of the GCR intensity.
A superposed epoch analysis on the relative variations of the GCR intensity in reference to the times of the FS3 anomalies is displayed in Fig. 5c. A peak is found during the period between 3 h before and 1 h after zero epoch time, indicating that the GCR intensity was relatively high at the times of the FS3 anomalies. This result demonstrates that one of the main causes for these anomalies was likely due to GCR.