Response of Global Ionospheric Currents to Solar Flares with Extreme Ultraviolet Late Phases

It is known that solar flares can affect the current system of the middle- and low-latitude ionosphere. Most earlier studies have focused on such effects during their impulsive phases. Recent studies have reported flares with a significant extreme ultraviolet (EUV) late phase, the effects of which on ionospheric currents have not yet been investigated. Here, we examine the solar quiet (Sq) currents and equatorial electrojets during two X-class flares with EUV late phases using data from more than 200 ground magnetometers. Our results indicate that the ionospheric currents could be significantly enhanced during the impulsive phase, while the effects of the EUV late phase may increase the global ionospheric currents, but are often weak and thus could be obscured by a change in solar wind conditions. In the X1.8 flare event on 2012 October 23, besides the solar flare effects, the currents were modulated by solar wind pressure. In the X1.3 flare event on 2014 April 25, the solar wind pressure was weak and stable, and the Sq currents were enhanced compared to nonflare conditions. We also found that even weak changes in the solar wind dynamic pressure, with magnitudes as low as ∼2 nPa, which are often ignored, may have an appreciable impact on the global ionospheric current system.


Introduction
Plasmas in the E region of the ionosphere (∼90 to ∼150 km altitude) are ionized by solar radiation.Their motion and the embedded electric fields and current system are driven by the direct heating from the radiation emitted by the solar atmosphere (e.g., Campbell & Schiffmacher 1985;Yamazaki et al. 2011).The terrestrial solar quiet (Sq) geomagnetic field variations accountable for Sq ionospheric currents are fundamental for the understanding of ionospheric electrodynamics (Richmond 1995).The Sq ionospheric currents exhibit two global horizontal current vortices on the sunlit side of Earth, one flowing clockwise in the Southern Hemisphere and the other counterclockwise in the Northern Hemisphere (e.g., Yamazaki & Maute 2017;Owolabi et al. 2022).In addition, these ionospheric Sq currents create secondary currents in the conductive Earth (internal source current), which account for about one-third of the horizontal component daily changes observed on Earth (e.g., Price 1967).There is a strong eastward current flowing along the dayside magnetic equator, named the equatorial electrojet (EEJ), which is defined as the superposition of the equatorial portion of the global Sq current system and concentrated eastward electric currents separated from Sq currents (Chapman 1951;Yamazaki & Maute 2017).
Solar flares come with increased electromagnetic emissions in almost all electromagnetic wavelengths.The classification of a solar flare is based on the peak soft X-ray flux intensity as measured by the Geostationary Operational Environmental Satellites 15 (GOES-15) mission (e.g., Bai & Sturrock 1989;Oloketuyi et al. 2019).Typical flares have three phases, including the rising phase, the impulsive phase, and the decay phase.Recent studies have reported the existence of an additional phase, called the extreme ultraviolet (EUV) late phase, during which the flares exhibit a second large peak, mainly in the warm EUV emission, according to the data recorded by the EUV Variability Experiment (EVE; Woods et al. 2012) and the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory (SDO) mission (e.g., Pesnell et al. 2012).Such an EUV late phase has been found in about 8% of all solar flares and about 39% of X-class flares (Woods et al. 2011;Woods 2014;Qian & Woods 2021).
The sudden enhancement of X-ray and EUV irradiance from solar flares can cause sudden ionospheric disturbances due to the rapid increase of the photoionization rate and the corresponding short-term change.The ionospheric current response to solar flares is interpreted as a consequence of the enhancement in conductivity induced by photoionization (Rastogi et al. 1999).As a result, the ionospheric current is enhanced and the geomagnetic fields are affected, known as solar flare effects (SFEs) or geomagnetic crochets (Rastogi et al. 1999;Yamazaki & Maute 2017).The shorter the wavelength, the deeper it can reach.The X-ray irradiance often impacts the D region, while the EUV usually reaches the E and F regions, forming a nonuniform distribution of conductivity (Van Sabben 1961;Thome & Wagner 1971;Scherliess 2016).
Generally, the SFE and Sq currents are similar in morphology, with a displaced focus position, also called the concentration region (Volland & Taubenheim 1958;Veldkamp & van Sabben 1960;Roy 1977;Annadurai et al. 2018;Owolabi et al. 2020).The SFE currents for some events even show distinct patterns (Annadurai et al. 2018).These discrepancies might be a consequence of the enhancement of Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
the conductivity in the D region caused by photoionization in response to the enhancement of X-rays, which extends the currents from the E region down to the D region.Besides, the enhanced electron density and temperature induced by EUV irradiance at the ionospheric F region can push the plasma upward (Liu et al. 2021b(Liu et al. , 2022)).Earlier studies of the SFE on the ionospheric current system showed that the ionospheric currents during impulsive phases of solar flares are higher than those during quiet times on the dayside and nightside, especially the EEJ (Rishbeth 1997;Abdu et al. 2017).The EEJ could be augmented in response to a solar flare during normal or counter-electrojet periods (Rishbeth 1997;Sripathi et al. 2013;Zhang et al. 2017).
Due to the enhanced conductivity in middle and low latitudes in response to solar flare radiation, the high-latitude electric potential reduces, and the high-latitude convection electric field promptly penetrates the equatorial and low latitudes, which results in the so-called prompt penetration electric field (PPEF; Liu et al. 2021a).In addition, the PPEF can also be generated by changes in magnetosphereionosphere electrodynamic coupling driven by rapid changes in the solar wind (Nishida 1968;Senior & Blanc 1984;Kikuchi et al. 1996Kikuchi et al. , 2000)).The supersonic solar wind plasmas carry the magnetic field from the Sun, known as the interplanetary magnetic field (IMF).According to Faradayʼs law of electromagnetic induction, as the plasma cuts the IMF line, an electric field called the interplanetary electric field (IEF) is produced.
Solar wind pressure can modulate the middle-and lowlatitude ionosphere indirectly, by changing the size of the magnetosphere, during which electric fields are generated and penetrate the midlatitude ionosphere (Huang et al. 2001(Huang et al. , 2002)).The geomagnetic field perturbations at high and low latitudes in response to the IMF could be a consequence of the IEF penetrating the equatorial ionosphere during IMF reorientations (Nishida 1968;Huang 2019).However, the enhanced conductivity induced by solar flares would make it harder for the solar wind to penetrate the ionosphere (Liu et al. 2021b(Liu et al. , 2023)).Therefore, besides the SFE, it is essential to take the solar wind effect into consideration.
There have been many prior studies aiming at the SFE on ionospheric currents.About 39% of X-class flares have EUV late phases (Qian & Woods 2021).Most prior studies have focused on the ionospheric current variabilities during impulsive phases (Volland & Taubenheim 1958;Veldkamp & van Sabben 1960;Van Sabben 1961;Richmond & Venkateswaran 1971;Annadurai et al. 2018;Owolabi et al. 2020).There have not been quantitative studies on whether there are observable variations in ionosphere currents due to the EUVʼs late phases and weak but rapid solar wind changes.It is necessary to examine their SFEs on ionospheric currents in the presence of varying solar winds, even under geomagnetically "quiet" conditions.For this purpose, we chose two X-class solar flares with EUV late phases: the X1.8 flare of 2012 October 23 and the X1.3 flare of 2014 April 25.Both flares show expanding behavior and have large EUV flux intensities during the EUV late phase.We aim to examine the ionospheric current variabilities during impulsive phases and EUV late phases under different interplanetary solar wind conditions.
2. Data Sources and Method of Analysis

Geomagnetic Observatories
The ionospheric currents discussed in this study are measured by ground magnetometers.The locations of the ground magnetometers utilized in this study are shown in Figure 1.
The technique to calculate the Sq currents is known as spherical harmonic analysis (Yamazaki & Maute 2017;Owolabi et al. 2020).This method fits the magnetic potential, which is given by a spherical harmonic function expanded to some order, with the magnetic field perturbation vectors measured by ground magnetometers located at latitudes between 3°and 60°.During the X1.8 and X1.3 solar flares, observations were gathered from 291 and 273 stations, respectively, each distributing data on horizontal (H), decl.(D), and vertical (Z) components of the geomagnetic field.To avoid overfitting, we expanded the spherical harmonic function to the fourth order.The first step is to subtract the baseline from each component and station to obtain the perturbation.The baseline is defined as the mean value at local times less than 02:00 or greater than 23:00.It is noteworthy that this methodology has been applied in previous studies, such as Owolabi et al. (2020).The overdetermined equations are shown in Equations (1)-( 3): q , is derived from the function of Schmidt, where θ denotes the geomagnetic colatitude of the observational stations (Chapman & Bartels 1940).ΔH and ΔD components are employed to acquire the harmonic terms a n m and b n m .Subsequently, the spherical harmonic coefficients, derived from a least-squares approach, as depicted in Equations (1)-( 3), are used to compute the Gaussian coefficients relevant to the external field contribution, as illustrated in Equations (4)-( 5): It is crucial to delineate the terms E n m and e n m , which serve as empirical constants within this context and are denominated as the external Gaussian coefficients (Yamazaki & Maute 2017).The external magnetic potential function U e can subsequently be expressed in the following manner: where R is represented as 6371 km, defining the radius of the Earth.The variable r represents the radius vector originating from the Earthʼs center, whereas λ denotes the longitude.
Given the substantial difference in magnitude between the height of the ionosphere and the Earth's radius, it is hypothesized that the currents are confined to flow within a shell characterized by the radius.The hypothesis r = R, when in contrast to the situation of r = R + 120 km, and the consequent underestimation of the external current intensity is very weak, with a difference of only a few percent (∼3%; Yamazaki et al. 2011).And the current intensity is given by Equation (7): The unit of the magnetic field is nT and the unit of the current intensity is kA.
Two pairs of magnetometers are used to estimate the daytime EEJs.These pairs include the equatorial stations Tirunelveli (76.95°E, 8.48°N, 0.57°N geomagnetic) and Bac_Lieu (105.71°E , 9.3°N, 1.41°N geomagnetic), as well as the off-equatorial stations Hyderabad (78.6°E,17.4°N,10.36°N geomagnetic) and Dalat (108.48°E,11.94°N,2.12°N geomagnetic).To estimate the EEJ, the horizontal magnetic field perturbation at a dipequatorial station is subtracted from that at an off-equatorial station.The pairs of magnetometers used to calculate the EEJs are connected by the dashed lines in Figure 1.

SDO/EVE Data
SDO/EVE measures the spectral irradiance in both the soft X-ray and EUV bands, with a wavelength range from 0.1 to 105 nm and 0.1 nm spectral resolution (Woods et al. 2012).Woods et al. (2011) identified that certain flares exhibit two distinguishable peaks in the EVE warm line at 33.5 nm.The primary peak is identified during the flare's impulsive or main phase, while the subsequent peak has been identified as the EUV late phase.
The X1.8 flare on 2012 October 23 has been chosen for our simulation analysis, specifically addressing the ionospheric current densities in response to the EUV late phase.Observations from the 33.5 nm profile, denoted by the purple line in Figure 2(a), indicate that the flare initiated at 3:13 UT and attained its maximum at 3:17 UT (the first peak).The peak of the EUV late phase was around 4:45 UT (the second peak).

Thermosphere-Ionosphere-Electrodynamics General Circulation Model
The Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIEGCM) is a fully coupled theoretical model for studying the interrelated phenomena within the ionosphere and thermosphere.This model solves the nonlinear, hydrodynamic, and continuity equations governing neutral gas.Additionally, it solves the energy and momentum equations for ions and electrons, the ion continuity equation, and the neutral wind dynamo (Roble et al. 1988;Richmond et al. 1992; Qian

FISM
FISM is an empirical solar irradiance model that encompasses wavelengths spanning the range from 0.1 to 190 nm with a spectral resolution of 0.1 nm (Chamberlin et al. 2007(Chamberlin et al. , 2008)).The solar spectrum is discreated into 37 channels and used in TIEGCM to calculate the rates of photoionization and photodissociation (Solomon & Qian 2005).The FISM flare spectrum includes both the impulsive and gradual phase, but does not include the EUV late phase.To incorporate the EUV late phase, we used the SDO/EVE data spanning from 3 UT (preflare) to 23 UT.Because the EVE line data are not from a continuous wave band, we select spectral lines of high quality to replace the corresponding FISM spectral channels.In the process of replacement, the trend of the SDO data serves as a scaling factor for the FISM spectrum, to eliminate the offset between the data sets from FISM and the EVE line data.The scaling factor is the ratio of the FISM data to the EVE data at 3 UT.After multiplying the EVE data from 3 UT to 23 UT by this scaling factor, the FISM data are replaced, resulting in a modified spectrum that includes both the impulsive and EUV late phase of the flare.
To obtain a spectrum with only the impulsive phase, we removed the EUV radiation values between the minimum EUV value after the impulsive phase and 7 UT from the modified spectrum.The original values are then replaced by using interpolation with the piecewise cubic Hermite interpolating polynomial.To obtain a spectrum with only the EUV late phase, we removed the EUV radiation values between 3 UT and the minimum EUV value after the impulsive phase from the modified spectrum, and then interpolated the original values using the piecewise cubic Hermite interpolating polynomial.
Figure 2(a) depicts the solar flux of the EVE warm line at 33.5 nm with the purple line, with the scale on the right Y-axis.The solar flux of the 28th channel of the FISM flare spectrum is represented by the black line, signifying a wavelength range extending from 32 to 54 nm, and is scaled on the left Y-axis.The blue line, also displayed on the left Y-axis, represents the solar flux of the FISM flare spectrum after adding the EVE line data.This methodology is correspondingly used for the remaining channels, as depicted in Figures 2(b)-(e).Table 1 lists selected EVE line data, along with the adjusted FISM channels.The variations of the ionospheric height-integrated current densities during the EUV late phase of the X1.8 flare on 2012 October 23 are examined using TIEGCM.We performed two runs, including X1.8 flare with both the impulsive and EUV late phases (Case 1) and only the impulsive phase effect (Case 2).Consequently, the difference between the Case 1 and Case 2 simulations denotes the SFE in the EUV late phase.

Observations
The dynamic variations of the ionospheric currents during solar flare events discussed in this study are presented below.Figures 3(a)-(d) represent the solar irradiation and interplanetary solar wind conditions, and Figures 3(e)-(f) represent the currents derived from the magnetic fields measured by ground magnetometers.The X-ray and EUV passbands discussed here correspond to the wavelengths of 0.1-0.8nm measured by the GOES-15 satellite and the 33.5 nm band measured by SDO.
During the X1.8 flare event on 2012 October 23, the X-ray irradiance began to increase at 03:13 UT and reached its peak at 03:17 UT, with a magnitude of approximately 1.85 × 10 −4 W m −2 .The EUV irradiance showed a similar pattern, increasing from a magnitude of about 5.40 × 10 −5 to 6.26 × 10 −5 W m −2 , until it reached its first valley at 03:45 UT, with a magnitude of about 5.75 × 10 −5 W m −2 .After that, the EUV irradiance began to increase again and reached its second peak at 04:43 UT, with a magnitude of about 6.75 × 10 −5 W m −2 .
During the X1.3 flare event, the X-ray irradiance began to increase at 00:17 UT and reached its maximum at 00:27 UT, with a magnitude of about 1.39 × 10 −4 W m −2 .The EUV irradiance showed a similar pattern, increasing from a magnitude of approximately 4.25 × 10 −5 to 4.50 × 10 −5 W m −2 , before returning to its preflare level.After that, the EUV irradiance began to increase again and reached its second peak, which is broad and high, at 04:43 UT, with a  magnitude of about 5.18 × 10 −5 W m −2 .In both flare events, the EUV fluxes during their late phases were much higher than those in the impulsive phases.
To understand the ionospheric electrodynamics influenced by the solar flare and the solar wind plasma, Figures 3(d)-(f) present derived parameters from geomagnetic field data recorded by ground magnetometers.These figures show the variations in ionospheric currents during the events.The intensity of the Sq currents is obtained by differentiating the maximum current intensity value in the Northern Hemisphere from the minimum current intensity value in the Southern Hemisphere.This intensity represents variations on the dayside.Note that the EEJs plotted are in the early morning sector at the beginning of the events.
The Sq currents and dayside EEJs responded to the solar flare.When comparing flare days with reference days, the trends were similar.During the X1.8 event, the Sq currents followed the solar wind pressure closely.A sharp decrease and increase were observed before the onset of the solar flare.Both the Sq and EEJ currents ceased increasing before the X-ray flux increased.When the flare erupted, the Sq and EEJ currents increased again.The Sq current and EEJ promptly reacted to the enhanced solar irradiance.The effects of the EUV late phases were not as remarkable as the effects of impulsive phase or solar wind.From the ground magnetometer pair of Bac_Lieu and Dalat, the EEJ increased from 44 to 70 nT.Comparing flare days with reference days showed that the currents were modulated by solar flares and solar wind plasma conditions.For the X1.3 flare event, the ionospheric current responded to X-ray significantly.During the impulsive phase, the Sq current increased by ∼30%.The EUV flux did not increase sharply, as the X-ray did; there were several minutes of delays for the currents to respond.During the EUV late phase, the ionospheric current showed an increasing pattern.Compared with the reference day, the Sq current was enhanced by about onefourth.
Figure 4 presents some noteworthy moments of the Sq current intensity during the X1.8 flare event.The directions of the red arrows signify the directions of the ionospheric currents at various stations, denoting the vector of ΔH and ΔD.The lengths of these arrows correspond to the magnitudes of the ionospheric currents at each station.Figures 4(b) and (c) show the impulsive phase effects on the ionospheric currents.At 03:00 UT, before the solar flare erupted, the Sq current intensity was small and covered only the dayside region, specifically the Asian-Australian sector, recording current intensities of 206 and −196 kA in the Northern and Southern Hemispheres, respectively.The focus position in the Northern Hemisphere was around (∼41°N, ∼11 LT).At 03:18 UT, when the X-ray flux reached its peak, the Sq currents were enhanced, and the Sq current loops expanded to the nightside ionosphere, recording current intensities of 323 and −368 kA in the Northern and Southern Hemispheres, respectively.The focus position in the Northern Hemisphere was around (∼44°N , ∼11 LT), which was 3°higher in latitude.
Figures 4(d  first valley, but the solar wind pressure was at its peak, the Sq currents decreased slightly, with current intensities of 293 and −286 kA in the Northern and Southern Hemispheres, respectively.The focus position in the Northern Hemisphere was around (∼60°N, ∼12 LT).At 04:43 UT, when the EUV flux peaked again, and the solar wind pressure had dropped to about 1 nPa, nearly half of its earlier value, the intensity of the Sq currents was low.The currents mainly flowed within the sunspot region, with intensities of 209 and −177 kA in the Northern and Southern Hemispheres being recorded, respectively.The focus position in the Northern Hemisphere was around (∼38°N, ∼12 LT).The current intensity in the northern ionosphere was lower than that in the southern during the impulsive phase and higher in the EUV late phase.
Figure 5 presents some noteworthy moments of the Sq current intensity during the X1.3 flare event.Figures 5(b) and 4(c) present the impulsive phase effects on the ionospheric currents.At 00:00 UT, the intensity of the Sq currents was low and only covered the dayside region in the Asian-Australian sector.Current intensities of 148 and −171 kA were recorded in the Northern and Southern Hemispheres, respectively.The focus position in the Northern Hemisphere was around (∼32°N , ∼12 LT).At 00:27 UT, approximately 10 minutes after the X-ray flux peak, the Sq currents were weakly enhanced, and current intensities of 153 and −195 kA in the Northern and Southern Hemispheres were recorded, respectively.The ionospheric current did not respond to the X1.3 flare as quickly as it did to the X1.8 flare.The key difference in the solar irradiance of these two events is that during the X1.8 flare event, both the X-ray and EUV flux increased sharply at the same time.In contrast, during the X1.3 flare event, the EUV flux intensity begun to increase a few minutes later than that of the X-ray flux.In Figure 5(c), the focus position in the Northern Hemisphere was around (∼33°N, ∼12 LT), which was 1°h igher in latitude.At 02:00 UT, when the X-ray flux was low, and the EUV flux reached its first valley, the Sq current intensities decreased to 151 and −167 kA in the Northern and Southern Hemispheres, respectively.The focus position in the Northern Hemisphere was around (∼34°N, ∼11 LT).At 03:34 UT, when the EUV flux reached its peak again, the intensity of the Sq currents was larger, recording current intensities of 204 and −182 kA in the Northern and Southern Hemispheres, respectively.The focus position in the Northern Hemisphere was around (∼37°N, ∼11 LT), which was 3°higher in latitude.
To show the perturbations along the longitudinal magnetometer chain in Figure 6, a moving window of 3 hr is used to remove the potential gradual variation in the magnetic field.Near the magnetic equator, the geomagnetic fields increased in a manner similar to the amplitude of the Sq current, which further proved the close relationship between the geomagnetic fields and the Sq current system for both events.The left panel shows that during the X1.8 flare event, the perturbations caused by X-ray and solar wind pressure can be seen across the latitude.The right panel shows that during the X1.3 flare event, the perturbations caused by X-ray can be seen across the latitude.

Discussion
In this study, we have conducted a detailed analysis of the Sq currents and EEJ in response to two significant X-class solar flares with accompanying EUV late phases.The first flare is an X1.8 limb flare that appeared at the solar active region (AR) 11598 on 2012 October 23.The other is an X1.3 flare that occurred in AR 12035 on 2014 April 25, located just behind the solar limb.The ionospheric currents respond significantly to enhanced levels of X-ray and EUV flux during the impulsive phase of solar flares, and these enhancements exhibit hemispheric asymmetry (Volland & Taubenheim 1958;Van Sabben 1961;Raja Rao & Panduranga Rao 1963;Nagata 1966;Richmond & Venkateswaran 1971;Gaya-Piqué et al. 2008;Annadurai et al. 2018;Curto et al. 2018;Owolabi et al. 2020).At the peak of the X1.8 flare, the current in the Southern Hemisphere was much more intense than the one in the Northern Hemisphere.And in the X1.8 flare event, the solar flare had a stronger impact on EEJ than the Sq currents during the impulsive phase.
The EUV late phase of a solar flare can modulate the focus positions.In the X1.8 flare events, the focus position of the SFE currents in the Northern Hemisphere moved about 3°h igher than that of the Sq currents.These discrepancies were the result of photoionization caused by the EUV radiation, which made the currents flow at different altitudes, further proving that the EUV late phase of the solar flare could modulate the focus positions by enhancing the ionospheric currents (Gaya-Piqué et al. 2008;Annadurai et al. 2018;Curto et al. 2018).
On 2012 October 23, the variation of the EEJ and Sq currents and geomagnetic disturbance closely and promptly followed the variation of the solar wind pressure, indicating that sudden changes in solar wind pressure might result in ionospheric perturbations at the middle and low latitudes of the ionosphere.A PPEF was generated when the solar wind compressed or decompressed the magnetosphere, which can penetrate the ionosphere and change the currents.The influence of the PPEF can extend across latitudes and reach the equator almost immediately (Huang et al. 2007;Kikuchi et al. 2008;Manoj et al. 2008;Guo et al. 2011;Bhaskar & Vichare 2013;Kikuchi & Hashimoto 2016;Vineeth et al. 2019).In addition to the variations in current intensity, the two large-scale current vortices in the Sq current system become more observable when the solar wind pressure is relatively low and stable.
During the X1.3 flare event on 2014 April 25, the variation in solar wind pressure was weaker and more stable than during the X1.8 flare event.During the impulsive phase, the Sq current increased by ∼30%.Note that the EUV flux peak was several minutes later than that of the X-ray flux, and the currents did not respond as promptly as they did in the X1.8 flare event, suggesting that the EUV plays a more important role in ionospheric currents.During the EUV late phase, the currents showed an increasing trend and increased by about 25%.However, there was a northward turning of the IMF Bz around the peak of the EUV late phase, which might reduce the currents and obscure the analysis.
In these two cases, the Sq currents and the EEJ showed similar patterns, suggesting that even though the origins may be different, the underlying disturbing mechanism caused by the effects of either the solar flare or the solar wind plasma could be the same for these two current systems.As shown in this work, the ionospheric currents present very complex spatial and temporal variations, which can be influenced by multiple factors, including changes in solar irradiation, solar wind, and lower-atmosphere forcing.Given that we have limited observational resources available, further numerical simulations are needed to distinguish these external forces from the effects of the EUV late phase on the global ionospheric currents.
In Figure 7, a comparative analysis of the height-integrated zonal current densities (Jx, positive eastward) and meridional current densities (Jy, positive northward) between Case 1 and Case 2 is presented.The simulation results represent only the EUV late-phase effects during the X1.8 flare event on 2017 October 23.It was noted that the height-integrated current density differences (ΔJx and ΔJy) with and without the EUV late phase prior to the X1.8 flare event at 03:00 UT Notably, during the EUV late phase of the X1.8 flare, ΔJx exhibited an eastward component at low latitudes (<30°m agnetic latitude or MLAT) and a westward component at midlatitudes (>30°MLAT).Furthermore, ΔJx predominantly aligned with the background current direction, implying that Jx was increased by the influence of the EUV late phase.Specifically, at 3:45 UT, the eastward component of ΔJx reached its maximum value of 1.2 mA m −1 around the magnetic equator.Subsequently, at the peak of the EUV late phase, occurring at 4:43 UT, the eastward component of ΔJx reached its maximum at 1.5 mA m −1 , representing an increase relative to the initial stages of the EUV late phase.
In the Northern Hemisphere, ΔJy exhibited a southward (negative) component in the morning and a northward (positive) component in the afternoon, due to the EUV latephase effects.Conversely, in the Southern Hemisphere, ΔJy displayed a reverse trend, changing from a northward (southward) component before (after) noon.Notably, ΔJy exhibited a predominant alignment with the background current, thereby signifying that the ΔJy were significantly intensified because of the EUV late phase.During the peak of the EUV late phase, the northward component of ΔJy attained its maximum value, reaching 0.52 mA m −1 .

Conclusions
In this study, observations of mid-and low-latitude ionospheric currents derived from the global magnetic field have been presented.The association between these currents and two distinct solar flare events with EUV late phases and solar wind variations has been examined.The major findings are summarized as follows:  conditions.This observation suggests that even weak and sudden changes in solar wind pressure may lead to detectable ionospheric perturbations at mid-and low latitudes.4. To separate the effects of interplanetary solar wind effects on the ionospheric currents from solar irradiation during the X1.8 flare event, we performed simulations with and without solar flare EUV late-phase effects under the same solar wind conditions.These simulations revealed an increase in the height-integrated current densities at low and midlatitudes with EUV late-phase effects during the X1.8 solar flare.
d n m of the spherical harmonics are of order m and degree n.And the t denotes the longitude.The normalized associated Legendre function,

Figure 1 .
Figure1.Locations of the geomagnetic observatories utilized in the spherical harmonic analysis.The full red, blue, green, and brown circles depict the selected magnetometers, which are from SuperMAG, INTERMAGNET, the Chinese Meridian Project, and LISN, respectively.The dashed curve on the map indicates the geographic equator.One latitudinal magnetometer chain is denoted by squares.One longitudinal magnetometer chain is connected by the black dashed line.

Figure 2 .
Figure 2. Solar irradiance of FISM (black line), modified FISM (blue line), and SDO (purple line; the scale is given on the right Y-axes) spectra on 2012 October 23.
) and (e) show the EUV late-phase effects on the global ionospheric currents on 2012 October 23.At 03:45 UT, when X-ray flux was low, and the EUV flux had reached its

Figure 3 .
Figure 3. Temporal variations of the solar irradiation, solar wind, geomagnetic conditions, and ionospheric currents during the X1.8 and X1.3 flares.(a) Solar X-ray flux in the 0.1-0.8nm band as measured by the GOES-15 satellite and EUV flux in the 33.5 nm band as measured by EVE on board the SDO satellite.(b) The meridional IMF (B z ).(c) The solar wind dynamic pressure.(d) The Sq current intensity during flares.(e) and (f) EEJs, from the equatorial stations Tirunelveli (76.95°E , 8.48°N, 0.57°N geomagnetic) / Bac_Lieu (105.71°E,9.3°N, 1.41°N geomagnetic) and the off-equatorial stations Hyderabad (78.6°E, 17.4°N, 10.36°N geomagnetic) / Dalat (108.48°E,11.94°N, 2.12°N geomagnetic), during flares.The two vertical dashed lines in red mark the two EUV peaks.The black dashed line represents a nonflare reference in the left panel on 2012 October 20, and in the right panel, it represents a nonflare reference on 2014 April 26.

Figure 4 .
Figure 4.The magnetic perturbations during the event are superimposed on the contour plots as red arrows with the vector scale of 50 nT.The vertical dashed lines in the top panels indicate the X-ray and EUV fluxes at the onset and peak of the solar flare, as well as the valley and second peak of the EUV flux.Currents of 50 kA flow within the streamlines.The gray dashed curves on the contours indicate the geomagnetic equators.The black stars denote the locations of the maximum and minimum current intensity.The red dashed vertical lines denote the peaks and valleys of the EUV flux.

Figure 5 .
Figure 5.The magnetic perturbations during the event are superimposed on the contour plots as red arrows with the vector scale of 50 nT.The vertical dashed lines in the top panels show the X-ray and EUV fluxes at the onset and peak of the solar flare, the valley of EUV flux, and the second peak of EUV flux.50 kA currents flow within the streamlines.The gray dashed curves on the contours indicate the geomagnetic equators.The black stars denote the locations of the maximum and minimum current intensity.The red dashed vertical lines denote the peaks and valleys of the EUV flux.

Figure 6 .
Figure 6.Comparison between solar flare pulsations and solar wind effects on EEJ measured by a longitudinal magnetometer chain.The dashed vertical lines denote the peaks (red lines) and valleys (black lines) of the EUV flux.
1.During the X1.3 flare on 2014 April 26, both the impulsive and EUV late phases of the flare exhibited a noticeable influence on the Sq current.During the impulsive phase, the Sq current increased by approximately 30%, and during the EUV late phase, it increased by ∼25%.2. At the peak of the impulsive phase of the X1.3 flare, the focus position of the Sq current in the Northern Hemisphere moved poleward by 1°compared to the preflare state.However, during the peak of the EUV late phase, this focus position in the Northern Hemisphere moved poleward by ∼3°with respect to the onset of the EUV late phase.3.In comparison to the impulsive phase of the X1.8 flare on 2012 October 23, the effects of the EUV late phase were overshadowed by the impact of interplanetary solar wind

Figure 7 .
Figure 7. Differences of the height-integrated zonal current densities (ΔJx, positive eastward) and the height-integrated meridional current densities (ΔJy, positive northward) between the simulations with and without the flare's EUV late-phase effects in the coordinates of magnetic local time (MLT) and MLAT during the X1.8 flare on 2017 October 23.The vertical dashed lines in the top panels show the X-ray and EUV fluxes at the onset and peak of the solar flare, the valley of the EUV flux, and the second peak of the EUV flux.

Table 1
The Wavelength Range for Modifying the FISM Spectrum Using SDO Data