Anomaly distribution of ionospheric total electron content responses to some solar flares

Previous studies have shown that the ionospheric responses to a solar flare are significantly dependent on the solar zenith angle (SZA): the ionospheric responses are negatively related to the SZAs. The largest enhancement in electron density always occurs around the subsolar point. However, from 2001 to 2014, the global distribution of total electron content (TEC) responses showed no obvious relationship between the increases in TEC and the SZA during some solar flares. During these solar flares, the greatest enhancements in TEC did not appear around the subsolar point, but rather far away from the subsolar point. The distribution of TEC enhancements showed larger TEC enhancements along the same latitude. The distribution of anomalous ionospheric responses to the solar flares was not structured the same as traveling ionospheric disturbances. This anomaly distribution was also unrelated to the distribution of background neutral density. It could not be explained by changes in the photochemical process induced by the solar flares. Thus, the transport process could be one of the main reasons for the anomaly distribution of ionospheric responses to the solar flares. This anomaly distribution also suggests that not only the photochemical process but also the transport process could significantly affect the variation in ionospheric electron density during some solar flares.


Introduction
Solar flares can cause a sudden enhancement in solar irradiation ranging from X-rays to extreme ultraviolet (EUV) rays. During flares, the sudden enhanced solar irradiation produces extra ionization in the ionosphere. These extra ionizations cause electron density enhancements from low to high heights. Thus, the total electron content (TEC) also shows significant enhancements, which manifest as sudden increases in TEC (SITEC). The rapid development of global positioning systems (GPSs) and the corresponding GPS receiving stations have opened a new era in which ionospheric TEC can be measured. Using GPS TEC data, scientists have carried out many studies on the ionospheric responses to solar flares (e.g., Afraimovich, 2000; Le HJ et al., 2007Leonovich et al., 2002Leonovich et al., , 2010Liu JY et al., 2004, 2006Mendillo and Evans, 1974;Tsurutani et al., 2005;Wan WX et al., 2005;Xiong B et al., 2011Xiong B et al., , 2014Xiong B et al., , 2016Xiong B et al., , 2019Zhang DH and Xiao Z, 2005;Zhang DH et al., 2002. Wan WX et al. (2005) analyzed GPS data during the July 14, 2000, flare and studied the SITEC. They found that both the rate of variation and the enhancement in TEC were pro-portional to the flare radiation and inversely proportional to the Chapman function. Tsurutani et al. (2005) reported a significant enhancement of more than 15 TEC units (TECU, 10 16 electron/m 2 ) for several hours during the X17.2 solar flare on October 28, 2003.
The solar zenith angle (SZA) is an important factor in the ion production rate. A smaller SZA results in a larger ionization rate. In general, the photochemical process is considered the most important factor in the short time change of solar EUV rays. Thus, the global distribution of ionospheric responses to a solar flare is significantly dependent on the SZA. The largest enhancement in electron density is around the subsolar region and the smallest is around the sunset region. Zhang DH et al. (2002) reported that, as a whole, the sudden enhancement in TEC caused by the solar flare on July 14, 2000, increased as the SZA decreased. Le HJ et al. (2013) further investigated the dependence of the SZA on the SITEC by analyzing global TEC enhancements for more than 100 solar flare events. Some modeling studies have also shown that the SZA has an important effect on the ionospheric responses to solar flares Ridley, 2008, 2011;Qian LY et al., 2010;Le HJ et al., 2007. In this study, we found that TEC enhancements were not significantly dependent on the SZA for some solar flare events, including the X1.

Data Sources
Global positioning system-derived TEC data were used to study the global distribution of ionospheric responses to solar flares. Solar radiation for the nightside ionosphere does not change; thus, we calculated the variation in the TEC derived from the sunlit-side GPS receivers to monitor the ionospheric TEC variations during the solar flares. The raw TEC values were integrated TEC values from a certain GPS satellite to a receiver station on the ground, which usually was a slant TEC. The slant TEC was converted to a vertical TEC by assuming an ionospheric spherical shell at an altitude of 350 km. To reduce the error of the transformation from the slant TEC to the vertical TEC, we used only the TEC data derived from the satellite with a median elevation angle during solar flares greater than 40°. To obtain the variation in the TEC induced by a solar flare for each observed TEC series, we calculated the background TEC values by fitting the curve of the TEC before and after a solar flare. We then calculated the enhancement of the TEC by subtracting this background value from the TEC series. The peak enhancement (ΔTEC) was used to describe the TEC responses to the solar flare.

Results and Discussion
As previous studies have pointed out (Afraimovich, 2000;Wan WX et al., 2005;Le HJ et al., 2007Manju et al., 2012), the SZA is an important factor in the ionospheric responses to solar flares. Thus, one can expect to find the greatest enhancement in electron density around the subsolar point during a solar flare. We analyzed the global distribution of SITEC for more than 100 X-class solar flares in [2001][2002][2003][2004][2005][2006]   One can observe that during the six solar flares, the greatest enhancements in TEC did not occur at a subsolar point, but rather far away from the subsolar point. The region of large ΔTEC seemed to be a zonal belt located in the same latitude. Furthermore, during the solar flares on October 19, 2003, and September 9, 2005, the spatial distribution of the ΔTEC showed a wave-like structure. Figure 2 illustrates plots of the ΔTEC versus the cosine of the SZA (cos(χ)) for the six solar flares. As reported by Le HJ et al. (2013), a high linear correlation exists between the ΔTEC and cos(χ) for most solar flares. However, Figure 2 shows that the correlation coefficients between them for the six solar flares were very low, which means the SZA was not the main controlling factor in the distribution of ΔTEC values during the six solar flares. Other factors significantly affected the ionospheric responses to the solar flares, although the linear fitting lines still showed that, on the whole, the larger SZAs caused smaller ionospheric responses.
To further check the anomaly distribution of ionospheric responses to the solar flares, we calculated the temporal variations in ΔTEC in the different regions. For example, Figure 3 illustrates the temporal variations in ΔTEC in the four regions with different SZA during the solar flare on September 9, 2009. In the region of longitudes 250°-270° and latitudes 15°-20°, the mean SZA was 24.25°. We could not find an apparent TEC enhancement in this region, nor could we find a remarkable ΔTEC. In the region of longitudes 250°-270° and latitudes 25°-30°, the mean SZA was 33.68°. In this region, we did find a significant TEC enhancement as well as a remarkable ΔTEC. The mean ΔTEC value for all the observations in this region was approximately 3 TECU. In the region farther from the subsolar point (longitudes 240°-250° and latitudes 36°-42°, with a mean SZA of 40.06°), the TEC enhancement again became smaller, with a mean ΔTEC value of approximately 1 TECU. Finally, in the region of longitudes 230°-240° and latitudes 45°-50°, the mean SZA was 45.48°. We found that the TEC enhancement again became larger when the mean ΔTEC value was approximately 1.8 TECU.
The results illustrated in Figure 3 show  smaller SZA would result in a greater production of electrons. The duration of a sudden increase in solar EUV rays during a solar flare is in the range of several minutes to several tens of minutes. Because the photochemical process is much faster than the transport process during a solar flare, the effect of the transport process is usually neglected. Thus, we can find a significant dependence of the ΔTEC on the SZA during most solar flares. However, we found no apparent relationship between the ΔTEC values and the SZA during the six solar flares, as illustrated in Figure 2. In addition, according to the balance of the photochemical process, the electron density is positively related to the ratio O/N 2 . Figure  that of the ΔTEC. But during the solar flare, the SZA in North America was much larger than that in South America. The mean SZA in the region of North America with high ΔTEC values reached about 70°. As shown in Figure 5, the greater value of O/N 2 in North America was not enough to cause the much larger ΔTEC in the region than at the subsolar point. Figure 5 also shows that no significant anomaly distributions in O/N 2 occurred during the other three solar flares. Thus, the anomaly distribution of ionospheric responses to the solar flares was unrelated to the distribution of the background neutral density.
As mentioned, the photochemical process could not have produced the anomaly distribution of ionospheric responses during the six solar flares. In addition, some studies have suggested that the electrodynamic process at low latitudes could have been influenced by the sudden enhancements in solar irradiances (e.g., Qian LY et al., 2012;Nogueira et al., 2015;Zhang RL et al., 2017), which could have caused a weaker eastward electric field and a weakened equatorial ionization anomaly (EIA) crest structure. The two EIA crests would be located at the lower latitudes. Such a weakened EIA would cause a change in the latitudinal structure in the middle-and low-latitude regions. The region equatorward of the EIA crest would have fewer enhancements in the TEC and the region poleward of the EIA crest would have more enhancements in the TEC. In addition, some studies (Le HJ et al., 2015;Pawlowski and Ridley, 2011) have shown that solar flares would result in changes in the horizontal neutral wind. The strength of a neutral wind would be different and the effects of a neutral wind on the vertical drift of plasma would also be different at different latitudes because of the differences in geomagnetic inclination. Thus, a change in the neutral wind would also cause different electron density variations along the different latitudes. Additionally, the plasma transport process resulting from a change in the eastward electric field and the horizontal neutral wind might play an important role in the anomaly distribution. However, we lacked the observations of plasma transport process like the ion drift velocity in the F 2 region during these solar flares to support the explanation for the anomaly distribution. Thus, the main process in the anomaly distribution is still unclear. In addition, it is interesting to note that all the anomaly distributions in the ΔTEC during the six solar flares occurred mainly in the region of North America and that these solar flares occurred in the three months of September, October, and November.
It should be noted that significant geomagnetic disturbances occurred during the six solar flares. Figure 6 shows the variations in the Kp index and the Dst index on the days of the six solar flares. Many studies (e.g., Foster, 1993;Maruyama, 2006;Yizengaw et al., 2006;Coster and Skone, 2009;Zou SS et al., 2013Cherniak et al., 2015) have reported that the storm-time enhanced density (SED) occurs at middle and high latitudes during medium-and large-sized magnetic storms. The SED is characterized by a plume of enhanced ionospheric electron density. However, the TEC enhancement patterns during the six solar flares took the form of narrow zonal belts along the same latitudes. Furthermore, we found no SED events during these solar flares. Thus, as discussed, the TEC enhancements during the solar flares ( Figure 1) were not affected by SED events. However, as shown in Figure 6, significant geomagnetic disturbances during the six solar flares could possibly have affected the plasma transport process because of electrical field and neutral wind changes. During geomagnetic storms, the ionosphere, especially in the North American sector, tends to be affected because this region is closer to the north magnetic pole than are other longitudinal sectors. Thus, the anomaly distribution in ΔTEC values may be due to the combined effect of EUV enhancements and a disturbed transport process.

Summary
In this study, the global distribution of solar flare effects on the ionosphere were investigated by using GPS TEC data.  September 10, 2005, and the X3.1 flare on October 24, 2014. The enhancements in TEC were not significantly dependent on the SZA during these solar flares. The largest was not around the subsolar point, but rather far away from the subsolar point. The region with the largest TEC enhancements seemed to be a zonal belt along the same latitude. Spatial analysis of the TEC enhancements showed that such an anomaly distribution was not due to traveling ionospheric disturbances, and the anomaly distribution was not related to the background neutral density. The transport process may be the cause of the anomaly distribution, but no observed data could be used to explain this phenomenon. In addition, it should be noted that the anomaly distributions of TEC enhancements during the six solar flares occurred mainly in the region of North America and that the flares appeared in September, October, and November. Significant geomagnetic disturbances during the six solar flares possibly affected the plasma transport process. The anomaly distribution of TEC enhancements may therefore be due to the combined effect of an enhancement in EUV rays and a disturbed transport process.