Effects of a series of large flares from a sunspot group eruption on VLF propagation

Sunspot groups are constantly evolving, causing flare eruption under the action of the solar atmospheric magnetic field. After the flare, the ejected X-rays cause the electron concentration of the Earth’s ionosphere to increase and the equivalent reflection height of the ionosphere to decrease. We studied the correlation between a series of flares erupted by sunspot groups and VLF signal propagation. Using NOAA sunspot activity area data and solar flare data released by the GOES satellite, we counted a series of flares erupted by sunspot groups in 2000. It is found that the AR9077 sunspot group continuously erupted 15 M-class and above flares and 3 X-class flares. Alpha VLF navigation station data were received in Haikou, and the phase anomalies of the VLF signal caused by a series of large flares erupted by AR9077 were observed. According to the phase anomaly, the flare is analyzed, and the relationship between X-ray flux density and ionospheric equivalent reflection height is fitted. We incorporated the change of solar zenith angle at the observation point in our calculation to correct the equivalent reflection height of the ionosphere and thus improve the accuracy of flare prediction. The calculated results are consistent with the data released by the GOES satellite. The observation results show that VLF phase anomaly correlates well with solar flares and sunspots. VLF signal can be used as a reliable scheme to predict the space environment, avoiding the impact of sunspot flares.


Introduction
Solar activity is the source that affects the space weather. The burst of solar activity causes sudden and short-term changes in the space environment of the Earth's magnetosphere, ionosphere, and thermosphere in solar-terrestrial space, which is harmful to space weather (Cander 2008). Solar activity affects the whole solar atmosphere, and flares are usually accompanied by sudden and drastic changes in brightness. The prediction of the space environment is to predict the outbreak of solar activity in time and effectively. The parameters of the active area composed of sunspot groups are important indicators of solar activity, and the characteristics of sunspot groups are important factors in predicting solar flares (Fang et al. 2019). The evolution of sunspot groups is closely related to the outbreak of solar flares, and the movement of sunspot groups can help the solar atmosphere accumulate the energy needed for flare outbreaks (Nagovitsyn and Kuleshova 2013). Jiang et al. (2012) studied the sunspot activity region AR11158 in 2012, and it was found that the rapid shearing and rotational motion of sunspots caused the outbreak of X2.2 class solar flares. Ruan et al. (2014) found that the rapid rotation of sunspots in the sunspot active area AR11283 led to the eruption of X2.1 solar flare. Yan et al. (2015) found that in the dark streak formation event of AR11884 in the sunspot active area, the dark streak was more twisted due to the long rotation of sunspots, which led to the dark streak explosion and the eruption of Mclass solar flare. Wheatland (2001) studied the flares in the solar active areas from 1981 to 1999 and found that 61.5% Y. Niu x15836098319@126.com 1 of the flares above grade C can correspond to the independently numbered sunspot group active areas, while the flares of grade X and M are 94% and 82%, respectively. Bornmann and Shaw (1994) used multiple linear regression to analyze the relationship between McIntosh classification of sunspot group active area and the yield of M and X flares observed by GOES satellite. The power of sunspot group evolution comes from the inside of the Sun, and solar flare will break out due to the action of the solar atmospheric magnetic field. From the analysis of the causality of solar activity, the evolution of the sunspot group is the cause, while the outbreak of solar flare is the result. If the sunspot group gets enough power, it will keep moving, causing a series of flares (Grimes et al. 2020). A solar flare is the most intense solar activity. After the solar flare erupts, many X-rays, charged particles, and ultraviolet rays are emitted. After all kinds of electromagnetic radiation reach near-earth space, they will affect the ionosphere and disturb the relatively calm environment of near-earth space. They have a great impact on the satellites in space, threatening the life safety of astronauts who are engaged in space activities. Electromagnetic radiation impacts our life, such as power system damage, communication quality degradation, navigation, positioning failure, etc. Many scientists have made great efforts to predict the space weather and made some progress. Many scientists have studied the prediction methods of space weather, but it is very difficult to directly measure the magnetic field in the upper atmosphere of the Sun. Many flare prediction methods are based on the photosphere observation in the active area (Barnes et al. 2016;Florios et al. 2018;Kontogiannis et al. 2018;Kim et al. 2019;Korsós et al. 2019).
Very Low Frequency (VLF) signals have small attenuation, long distance, stable amplitude and phase propagation, and good predictability. VLF signals propagate in the earthionosphere waveguide and are influenced by the Earth's surface and ionosphere when propagating in the waveguide (Šulić et al. 2016). Sudden ionospheric disturbance (SID) causes abnormal propagation of VLF signal. X-rays emitted from solar flares reach near-earth space first, which increases ionospheric electron concentration and the SID phenomenon (Thomson and Clilverd 2001). Kolarski and Grubor (2014) used VLF signals to detect the Earth's lower ionosphere during solar flares. Hayes et al. (2021) used VLF and GOES X-ray sensors to observe solar flare events and studied their influence on the ionospheric D area. Kumar and Kumar (2018) used VLF to observe the effect of a solar flare on ionospheric D-depletion in the 24th solar cycle. Therefore, we can monitor the solar flare by observing the abnormal phenomena of VLF signal propagation and then forecast the space weather. This method is economical and convenient.
Many scholars have studied the identification and classification of sunspot groups, the yield of sunspot groups and flares, the relationship between solar flares and the area of sunspot groups, and the prediction of solar flares by using the morphological characteristics of sunspots. Wu et al. (2000) counted the data of sunspot groups during the peak year of Solar Cycle 22. They found that the larger the area of sunspot groups, the higher the flare rate and the share of sunspot activity areas. Zhao et al. (2014) selected the data of the 24th solar peak year and the 23rd solar valley year to confirm the good correlation between flare burst and sunspot group activity. Lee et al. (2012) collected the NOAA active region data and GOES solar flare data for 15 years (from January 1996 to December 2010). They studied the types of sunspot groups that produce the most flares and the relationship between flare incidence and sunspot group area. Romano, combining the morphological parameters of sunspot groups and statistical techniques, observes the morphological characteristics of sunspot groups daily to analyze the flare probability in a specific energy range. However, there is little research on the influence of sunspot group eruption series flares on VLF signal in the active area. In this paper, the influence of a series of large solar flares erupted by sunspot group AR9077 on VLF signal propagation was observed at Haikou Station, and the VLF signal data with abnormal phase was analyzed and processed. According to the change of solar zenith angle, the grade of the sunspot group's continuous solar flare is predicted, and then the energy change of the sunspot group is monitored according to the flare size, which provides a basis for monitoring the space environment to avoid causing great losses. Figure 1 is the block diagram of the VLF signal observation system. The design idea of this system is based on software radio technology, and the hardware functions are realized by software. The observation system consists of a single whip antenna, digital VLF signal software radio receiver, rubidium atomic frequency standard, and computer. The single whip antenna is connected to a digital VLF software radio receiver and receives the amplitude, phase, signal-to-noise ratio, and other data of VLF signals from three stations of the Alpha VLF navigation system. Rubidium atomic frequency standard has high stability, which provides the observation system with a 5 MHz sine wave with an accuracy higher than 1 × 10 −11 and serves as the local frequency standard of the observation system (Niu et al. 2009;Niu et al. 2014c;Niu and Bi 2016). The computer processes and displays the amplitude, phase, and signal-to-noise ratio curves of VLF signals and records and stores VLF data in real-time. Figure 2 shows the propagation path of the Alpha VLF navigation system to Haikou, in which the main station is   (Němec et al. 2021). Each station has three working frequencies of 11.904 kHz, 12.649 kHz, and 14.881 kHz. Haikou Station is located in the north of Hainan Island, and its geographical coordinates are (22 • 02 45.97 N, 110 • 11 38.39 E). In Haikou, Hainan province, the observation system receives VLF signals of 11.904 kHz, 12.649 kHz, and 14.881 kHz from Alpha VLF navigation stations. The digital VLF software radio receiver designed 3 min Fig. 1 records and monitors data every 3 minutes and receives VLF signals all day.

Observation principles
The working frequency of the VLF signal is between 3-30 kHz, its wavelength is long, its attenuation is low, and its phase stability is good. VLF is widely used in many fields, such as long-distance radio communication, earthquake prediction, submarine communication, ground penetrating engineering, and astronomical prediction. In recent years, a large number of data has shown that VLF phase variation is very sensitive to SID caused by X-rays (Selvakumaran et al. 2015) and high-energy particles (Peter et al. 2006) erupting from solar activities.
The wavelength of the VLF signal emitted by the VLF antenna is comparable to the distance between the ground and the ionosphere. The VLF signal propagates in the earthionosphere waveguide composed of the Earth and the ionosphere, which is usually analyzed by the concept of "waveguide mode". The propagation mode is shown in Fig. 3. The ionosphere is usually divided into three regions, from top to bottom, F layer, E layer, and D layer. The D layer is 70 km away from the Earth's surface, and the electron concentration is low during the day and basically disappears at night. After the flare burst, the equivalent reflection height of the D layer ionosphere is reduced, and the short wave of the radio wave is greatly absorbed. The E layer is about 90 km from the Earth's surface, and its electron density has diurnal and seasonal changes. The electron density can increase during the day, and the electron density decreases by an order of magnitude at night compared with that during the day, and the height of the E layer will rise at night. The F layer is about 130 km away from the Earth's surface. There are irregular and abnormal changes in the F layer, which exists day and night. It is divided into the F1 layer and F2 layer during the day and is combined into one layer at night. The upper wall of the earth-ionospheric waveguide is the ionospheric D layer during the day, the D layer disappears at night, and the reflective upper wall is the E layer (Devi et al. 2008). The geomagnetic field causes the ionosphere to become an anisotropic medium, which changes periodically with the latitude and longitude of sunspots, seasons, and 11 years. When the VLF signal propagates in the waveguide space between the transmitting station and the receiving station, it is refracted many times in the ground-ionosphere waveguide and propagates forward in the waveguide cavity.
Ionosphere D is mainly formed by Lyman-α rays of solar radiation, and the atmosphere is ionized by X-rays. When a solar flare erupts, the change of Lyman-α ray flux is small, while the X-ray flux tends to increase by 2-3 orders of magnitude in a short time. The X-ray travels at the speed of light and reaches near-earth space in about 8.3 min. As the electron concentration in the ionosphere increases, the equivalent reflection height will decrease, resulting in the phase anomaly of the VLF signal. The offset ϕ of VLF signal phase anomaly is related to the propagation direction, great circle distance of path, working frequency, ground conductivity, equivalent reflection height of solar zenith angle and low ionosphere, etc. The distance between the transmitting and receiving stations of the VLF signal is far. As long as part of the propagation path is on the sunshine surface, the outbreak of solar flare can be observed. Solar activity can be observed all day if more than two propagation paths exist.
In the process of VLF signal propagating in the groundionosphere waveguide, the transmitting antenna will excite multi-order modes when it is relatively close to the transmitting station, and the phenomenon of multi-order mode propagation will occur in the waveguide, and the attenuation of high-order modes will increase with the propagation distance. In this paper, the VLF signal-receiving antenna is located in Haikou, far away from the transmitting antenna, and it mainly propagates in the first-order mode. For the first-order mode, the phase velocity v p of the VLF signal propagating in the waveguide is (Zhao and Wang 1990): Where: v c is the propagation speed of light in space, which is about 3 × 10 8 m/s; h 0 is the equivalent reflection height of the ionosphere, about 72 km in summer and autumn, 70 km in winter and spring, and 90 km at night; f is the frequency of VLF signal. Each transmitting station of the Alpha VLF navigation system has three frequencies of 11.904 kHz, 12.649 kHz, and 14.881 kHz, and the corresponding value f is selected according to different transmitting stations; a is the average radius of the Earth, about 6371 km. When the VLF signal is abnormal, the phase change ϕ is (Niu et al. 2009): From formula (2), according to the phase change ϕ, the phase velocity v p of VLF when the sunspot group erupts solar flare can be obtained: Where: D is the great circle path distance; through programming calculation, the great circle distance from Russian Alpha navigation station KRA to Haikou receiving station in Hainan province is 7060.98 km; the distance from NOV to Haikou receiving station in Hainan Province is 4508.875 km; the distance from HAB to Haikou receiving station in Hainan Province is 4066.35 km.
After a sunspot group erupts solar flare, the decrease of ionospheric equivalent height h 0 is (Liu 1987): Where: ϕ is the arc system, ϕ = 2πf · ϕ, the phase change is expressed in radians; the wavelength of VLF signal λ = v c /f ; the relationship between h 0 and phase ϕ (Unit S) can be obtained by introducing the above formula: Therefore, through the phase change ϕ of VLF when the solar flare breaks out, the phase velocity v p when the solar flare breaks out and the equivalent height drop h 0 of the low ionosphere are calculated.

Observations and analysis discussion
Solar activity will reach a peak every 11 years. The peak year of solar activity in the 23rd solar cycle (1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008) was in 2000-2001(Xiong et al. 2021, when the Sun would throw out many materials, and solar flare was the most intense solar activity. Flares with small grades (A, B, C) have relatively little impact on the space environment. The statistical analysis in this paper does not include flare events with small grades, but only counts flare events with an M grade and above. In this paper, a total of 223 flares with M-level and above in 2000, the peak year of solar activity, were counted, among which 180 flares corresponding to sunspot groups accounted for 80.7% of the total number of flares, and 43 flares without corresponding sunspot groups accounted for 19.3% of the total number of flares.
In 2000, a total of 62 sunspot groups erupted large flares with magnitude M or above, as shown in Fig. 4. The number of flares corresponding to each sunspot group can be observed in the figure. The number of flares erupted by sunspot groups with more than 5 flares is represented by a red histogram. There were as many as 15 large flares in the sunspot group numbered AR9077. Figure 5 shows the corresponding relationship between sunspot groups and flare grades. The blue circle indicates the grade of flare M series, and the red circle indicates the size of the flare X series. Among them, the M-class flares account for the vast majority. Compared with other sunspot groups, the number of flares emitted by the sunspot group AR9077 is more, and the level is higher, which is beneficial to analyze the influence on VLF propagation.    Table 1 counts the solar flares erupted by the sunspot group numbered AR9077. There are 15 solar flares above the M level. There are 3 X-class flares and 12 M-class flares. The largest flare was X5.7, and the eruption time was 10: 03 am (UT) on 14 July 2000. Three representative flares were selected from the series of flares erupted by the sunspot group of AR9077, and the influence of flare on VLF propagation was analyzed.
The diurnal variation of the VLF signal when the space environment is relatively calm is helpful in understanding the influence of flare on VLF signal propagation. Figure 6 shows the VLF data of three frequencies from the west and middle sub-stations of the Alpha VLF navigation system re- Compared with the data released by the GOES satellite on the same day, it is found that there is no big flare above the C level. When the space is relatively calm, the propagation of the VLF signal will not fluctuate greatly. Figure 7 shows the VLF curve from the west Sub-station to Haikou observed on 9 July 2000. In the figure, the black curve is 11.904 kHz, the blue curve is 12.649 kHz, the red curve is 14.884 kHz, and the green ellipse is the area with abnormal phase change. The phase change of the VLF signal can be seen from the green ellipse box in the figure. Because the observation system is located in the local area, in order to calculate the flare time more accurately, it is necessary to convert the local time into uni-versal time and the relationship between local time (LT) and universal time (UT) LT = UT + 8. According to the leading time of the VLF phase in Fig. 7, it can be estimated that the time of flare burst is from 07:15 to 08:02 UT on 9 July 2000. Figure 8 shows the VLF curve from the west Sub-station to Haikou observed on 12 July 2000. It is found that at 12:55 to 13:30 LT and 18:18 to 20:00 LT on the same day, the phase of VLF signal is abnormally advanced, and the change range is large. According to the changing relationship between LT and UT, it is speculated that the phase anomaly of a large flare occurred at 04:55 to 5:30 UT and 10:18 to 12:00 UT.  Figure 9 shows the VLF amplitude and phase curves of three frequencies in the Alpha VLF navigation system KRA received in Haikou on 14 July 2000. We observed that the abnormal phase advance of VLF signal propagation occurred at 18:03-18:48 LT, that is, the green ellipse in Fig. 9. According to the conversion relationship between local time and universal time, it is predicted that there will be a big flare at 10:03-10:48 UT, which will cause the phase propagation anomaly.
By observing the diurnal variation curves of VLF phase from Alpha VLF navigation system west sub-station to Haikou station on 4, 9, 12, and 14 July 2000, we found that the series of large flares emitted by the sunspot group AR9077 had a large influence on VLF, making the VLF phase appear to be anomalously ahead. According to the phase change, the time of flare in universal time is calculated and compared with the X-ray flow chart released by the GOES satellite in the United States. The duration of flare observed by the VLF method is based on the time from when the phase of flare starts to suddenly change to when the phase returns to normal. At the same time, the duration of flare released by the GOES satellite is calculated according to the X-ray streamline, so the duration of flare observed by the VLF method is longer than that in the X-ray flow chart released by the GOES satellite. Although the two methods calculate flare time differently, they do not affect the accuracy of VLF observation. Figure 10 shows the X-ray flux on 9, 12, and 14 July 2000, respectively. In the figure, the curve of the big flare caused by the sunspot group AR9077 in three days is marked with a green circle. The observed flare outbreak time is consistent with the release time of the GOES satellite.
According to the X-ray flux, flare grades can be divided into five grades (Niu et al. 2014a), as shown in Table 2. Among them, each grade in A, B, C, and M is divided into 1 to 9 grades according to intensity, while grade X has no upper limit.
In Fig. 10, according to the X-ray flux released by the GOES satellite, the levels of X-rays are M5.7, M1.2, X1.9, and X5.7 on the day of the outbreak. From the observed VLF phase change curves, as shown in Fig. 6, Fig. 7, and Fig. 8, the abrupt phase change ϕ is calculated as 25 cec, 21 cec, 57 cec, and 68 cec, according to the abnormal phase change of the black curve. Based on the theoretical analysis above, the equivalent reflection height h 0 of the ionosphere is calculated as 8.996 km, 4.342 km, 11.812 km, and 14.092 km.
The observation site selected in this paper is different from the previous observation sites, and the propagation path is also different (Niu et al. 2014b). It is necessary to re-fit the relationship between the solar X-ray flux density and the equivalent descent height of the ionosphere. The fitting solution of the West Sub-station is carried out by a large amount of observation data and the least square method. From the variation of the VLF phase and the variation of equivalent reflection height of the ionosphere, a new fitting West substation fitting formula: Where: F is the solar X-ray flux density, the unit is erg/cm 2 · s. The zenith angle is the angle between the incident direction of the Sun's rays and the vertical direction of the zenith (Cronin 2014). The change of the Sun's zenith angle will affect the equivalent reflection height of the ionosphere. From sunrise to noon to sunset, the Sun's zenith angle first decreases to a minimum and then gradually increases, and the equivalent reflection height of the ionosphere will change to some extent (Han and Cummer 2010). The series of flares erupted by AR9077 were observed in summer, and the time of sunrise and sunset was almost the same as the change of zenith angle. The daily change was regarded as consistency, and the middle day of observation was selected as the reference value. Divide the zenith angle of the Sun at each moment at the receiving station. As shown in Fig. 11, the zenith angle of the sunrise and sunset changes with time, and calculate the zenith angle of the Sun at the whole point. The zenith angle is the smallest when the sunlight is vertically incident between 12:00-13:00 LT. Because of the influence of the solar zenith angle on the ionosphere, the prediction accuracy of flare in this paper will be wrong, so the prediction system needs to be further revised. In this paper, the effect of the solar zenith angle is reduced by correcting the equivalent height of the ionosphere. According to the change of solar zenith angle, the ionospheric equivalent height is corrected, and the correction coefficient is co. The corresponding values of the change of the zenith angle and the correction coefficient co are shown in Table 3. From 11:00 to 14:00 LT, the small change of the solar zenith angle has little impact on the ionosphere and the correction coefficient co = 1. When calculating, the corresponding coefficient can be selected according to the zenith angle corresponding to the time change to reduce the error. The X-ray flux density F calculated by formula (6) is compared with the flare grade classification in Table 2, and the flare grade can be predicted. In this paper, after observing the series of flares erupted by the sunspot group AR9077, the flare level is predicted by calculation to obtain the observed flare data in Table 4. The VLF data of 11.904 kHz from Alpha West Sub-station to Haikou are monitored in Table 4. In the table, when the flares of M1.4 and M5.7 on the 10th, M1.2 on the 13th, M3.7 on the 14th, M1.4 on the 16th, and M3.3 on the 18th occur, the propagation paths are all in the dark, so VLF data cannot observe the big flares completely at night, so there is a data gap. The prediction of flare level in daytime or part of daytime in the propagation path is consistent with the flare level released by the GOES satellite, which confirms the correctness of the observed data. At the same time, we should pay attention to the errors in the calculation results caused by various factors when VLF signals propagate in the earthionosphere waveguide and further correct them.

Conclusion
Based on the statistical analysis of a series of flares erupted by sunspot groups in 2000, the following conclusions are obtained: 1. In 2000, there were 233 flares above M, 80.7% of which were related to sunspot groups, and M flares accounted for most of the total flares.

2.
A series of large flares erupted by the sunspot group of AR9077 were observed in Haikou, and it was found that the VLF signal exhibited an abnormal phase in the propagation path after the flare burst. In the same propagation path, the variation of phase anomaly is proportional to the flare level. 3. According to the phase change and the change of the zenith angle of the receiving station, the ionospheric equivalent height is corrected to obtain the change of the accurate ionospheric equivalent height, which is substituted into the fitting equation of the X-ray flux and the change of the ionospheric equivalent height to calculate the flare size. According to the data released by the GOES satellite, we can know the validity of our observed data.
After the flare, a large number of X-rays reach the nearearth space, causing the electron concentration in the ionosphere to increase and the equivalent reflection height of the ionosphere to decrease, resulting in the phase advance of the VLF signal in the propagation process. In this paper, there are some errors between the time of the VLF signal phase anomaly and the time of the flare burst released by the GOES satellite. The parameters, such as the observation system and propagation path, must be corrected. According to the obtained energy, the sunspot group erupts at different flares. The sunspot group with higher energy can erupt a series of large flares continuously, thus causing a great impact on the space environment, navigation system, shortwave communication, and power system. Therefore, solar flares should be monitored to predict the energy of sunspots to avoid property losses.