Energy Deposition into the Ionosphere during a Solar Flare with Extreme-ultraviolet Late Phase

Solar extreme-ultraviolet (EUV) irradiance is the dominant energy source for ionizing and heating the Earth’s upper atmosphere. It is common to assume that the spectra of different EUV lines have the same trend to fill the solar EUV irradiance gap for modeling purposes due to inadequate EUV irradiance measurements. However, the spectra across the EUV bands may not vary in the same trend. The flare radiation energy release in the EUV (10–120 nm) is about twice as much as X-rays (0.1–10 nm) during flare interval ∼03–06 UT on 2012 October 23. By assimilating the observed nonuniform varying, time-dependent, and high-resolution solar spectrum from the Solar Dynamics Observatory mission into the modeling framework, we provide the first direct evidence of nonuniform varying solar EUV fluxes during the solar flare EUV late phase (ELP) having appreciable effects on the dayside ionosphere. The total EUV radiation energy release (5.838 × 1028 erg) during the flare ELP is larger than that (5.698 × 1028 erg) during the flare main phase. The ELP of an X1.8-class solar flare on 2012 October 23 can increase the dayside ionospheric density at the subsolar point by ∼5 TECU and the ionospheric density enhancements extend from the bottom to the peak of the F2 region at low latitudes with relative changes ranging from ∼20% to ∼100%. Our results highlight the importance of incorporating a realistic, high spectral and temporal resolution solar irradiance spectrum into numerical models to capture the observed time-varying ionospheric response to solar flares.


Introduction
A typical solar flare, which is an intense localized eruption of solar electromagnetic radiation, has an impulsive phase with significant nonthermal signatures lasting from seconds to minutes and a slow gradual (decay) phase with a timescale ranging from minutes to hours (Hudson 2011;Woods 2014).Woods et al. (2011) discovered a new flare phase-EUV late phase (ELP)-using the EUV irradiance observations from the EUV Variability Experiment (EVE) on board the Solar Dynamics Observatory (SDO).They showed that some flares have two different flux peaks in the EVE warm line 33.5 nm irradiance with the first one peaking at nearly the same time as the X-ray peak in the flare impulsive phase and the second one lagging the first X-ray peak by about tens of minutes to a few hours.The ELP has the following characteristics: (1) a second EUV irradiance peak in the warm emissions (e.g., Fe XV and Fe XVI) after the first X-ray peak; (2) no significant enhancements of X-ray and hot emissions (e.g., Fe XX/Fe XXIII 13.3 nm) during the second peak; (3) an eruptive event seen in imaging observations; and (4) originating from a second set of higher and longer loops relative to the main flaring loops (Liu et al. 2013;Zhou et al. 2019).Such an ELP has been found in about 39% of X-class flares.
Solar irradiance can be increased by 3-4 orders of magnitude in the X-ray (0.1-10 nm), by up to more than a factor of 2 in the EUV (10-120 nm) and the far-ultraviolet (FUV; 120-200 nm) during large X-class solar flares (Tsurutani et al. 2005;Woods et al. 2005;Scherliess 2016).The Earth's upper atmosphere responds to the changes in solar radiation through photoionization and associated heating.The enhanced solar irradiance in the X-ray and EUV bands during solar flares cause extra ionization to the neutral species on the dayside and increases ionospheric plasma density within minutes (Tsurutani et al. 2005;Sojka et al. 2013).X-ray can penetrate deep into the atmosphere and increase the electron density in the D region by 1 order of magnitude or more, while EUV flux enhances the electron density in the E region by 50%-200% and in the F region by 10%-100%.The flare-enhanced photoionization at various altitudes in the ionosphere increases the total electron content (TEC) suddenly, causes short radio wave fadeout and sudden frequency deviation, changes the field-aligned plasma motion (Mendillo et al. 2018;Liu et al. 2022), and alters global ionospheric electrodynamics and currents (Liu et al. 2021a;Chen et al. 2021).These effects can even propagate into the magnetosphere because flares enhance dayside ionospheric conductance, change day-to-night conductance gradients, and thereby affect the magnetosphere and ionosphere coupling (Liu et al. 2021a(Liu et al. , 2021b(Liu et al. , 2023)).
The total solar energy input to the upper atmosphere during this type of solar flares including the ELP can be increased by 40% as compared to the flares without a late phase (Woods et al. 2011, Qian et al. 2011).The flare ELP is important to understand solar flare effects on the Earth's upper atmosphere since it provides additional EUV energy for several hours as compared to the flares without an ELP and thus provide extra ionization of the neutral constituents in the Earth's upper atmosphere.It is still unknown how geoeffective the previously unrecognized extra energy source during solar ELP is and how sensitive the ionosphere reacts to it.Keeping track of the EUV energy absorption in the Earth's upper atmosphere is an important topic of space weather and will advance space weather operations into more reliable forecasts.

Solar Dynamics Observatory
The SDO satellite was launched into geosynchronous orbit in 2010 February.There are three instruments on board the SDO satellite including the EUV Variability Experiment (EVE; Woods et al. 2012), Atmospheric Imaging Assembly (AIA; Lemen et al. 2011), and Helioseismic and Magnetic Imager (HMI;Scherrer et al. 2012).EVE measures the solar EUV and soft X-ray in the wavelength range of 0.1-105 nm, which is the primary energy source for the Earth's upper atmosphere.The solar EUV irradiance spectrum from EVE has unprecedented spectral resolution (0.1 nm) and temporal resolution (10 s).The detailed evolution of a flare is observed using EUV/UV images taken by the AIA.AIA provides full disk images with a pixel scale of 0 6 pixels and a cadence of 12 s for seven EUV channels and 24 s for UV passbands.

Ionosonde and Global Navigation Satellite System TEC Observations
Data from an ionosonde chain in the 88°-130°E longitudinal sector spanning from geomagnetic latitudes 51°.3N to 8°. 1N are used for current analysis as shown in Table 1 in the Appendix.The vertical electron density profile is calculated from the O (red) and X (green) polarization echo traces (Reinisch et al. 2009).The electron density above the peak height is extended by assuming an α-Chapman electron density distribution and is not considered in this study.All the ionograms during this event were manually scaled using the SAO Explorer software to ensure data accuracy.
The standard ground-based Global Navigation Satellite System (GNSS) network-observed TEC product with a 5 minute resolution and 1°spatial resolution provided by the Massachusetts Institute of Technology Haystack Observatory Madrigal database is used to monitor solar flare effects on the ionosphere (Coster & Komjathy 2008).

Thermosphere Ionosphere Electrodynamics General
Circulation Model (TIEGCM) The thermosphere ionosphere electrodynamics general circulation model (TIEGCM) is a first-principles, threedimensional, nonlinear representation of the coupled ionosphere-thermosphere system, which solves momentum, energy, and continuity equations for neutral and ion species (Qian et al. 2014).This model has a spatial resolution of 2°.5 × 2°.5 in both latitude and longitude, and 1/4 scale height in the vertical direction.The main external drivers of the TIEGCM include high-latitude potential (Weimer 2005) and auroral precipitation, and lower boundary from the global-scale wave model (GSWM; Hagan et al. 1997).The output cadences of these simulations are 1 minute.
The way of incorporating SDO/EVE line data into the empirical flare irradiance spectral model (FISM) is specified in the Appendix.To separate different solar flare phases effects on the Earth's upper atmosphere, we performed three TIEGCM runs including the no flare run (Run 0), flare run with only the impulsive phase (Run 1), and flare run with impulsive phase and the ELP (Run 2).Thus, the differences between Run 1 and Run 0 stand for the solar flare impulsive phase effects, and the differences between Run 2 and Run 1 give the solar flare ELP effects.

Results
The impulsive phase of the X1.8-class solar flare on 2012 October 23 started at ∼03:13 UT, peaked at 03:15 UT, and was followed by the gradual phase lasting for about 3 hr according to the GOES soft X-ray flux (Figure 1(a)).The irradiance variabilities (normalized) of four emission lines from the EVE with wavelength centered at 9.3 nm (green line), 13.1 nm (yellow line), 17.1 nm (purple line), and 33.5 nm (blue line) are shown in Figure 1(a).Two of these EVE lines such as 13.1 and 33.5 nm have complementary images from AIA measurements as illustrated in Figures 1(b)-(i).The temporal variations of four EVE lines show similar patterns to the soft X-ray curve during the flare rising and early decay phases.These four EVE lines attained their maxima almost simultaneously with the GOES X-ray flux at ∼03:17 UT with a small time offset.However, the 33.5 nm EVE line had two peaks: one peak near the X-ray flare peak and a second stronger and broader peak occurring 1.5 hr later.This second period occurred without obvious enhancements in the X-ray, which is the identification of ELP.The 17.1 nm EVE line also had a second intensity peak at ∼04:51 UT.Integrating over the wavelength range of 6-37 nm, the radiative energy-loss rate is displayed by the shaded area in Figure 1(a) (Liu et al. 2015;Zhou et al. 2019).The profile of the EUV radiative energy-loss rate exhibits two peaks with the first peaking around the impulsive phase peak and the second peak lagging behind the 33.5 nm EVE line second peak by ∼6 minutes.Given the higher and stronger latephase peak as compared to that during the main phase in the 33.5 nm EVE line, the total EUV radiation energy release (5.838 × 10 28 erg) during the flare ELP (04:00-05:30 UT) is larger than that (5.698 × 10 28 erg) during the flare main phase (03:10-04:00 UT).
To determine the source region responsible for the late-phase emission, Figures 1(b)-(f) show the snapshots of AIA images during the flare evolution: preflare, main phase flare peak, pre-ELP, and ELP peak.AIA 13.1 nm emission peaked around the flare main phase peak and did not have a second peak.However, AIA 33.5 nm emission was quite weak in the main phase peak and had a very strong second peak at 04:42 UT.These AIA images are quite consistent with the EVE lines in capturing the variability of different EUV bands.
To provide a global perspective of the ELP effects on the ionosphere TEC, Figure 2 shows global GNSS TEC distributions at 03:10 UT (preflare) and 04:45 UT (ELP peak) and their differences (ELP peak-preflare) for the nonflare reference (left column) on October 22 and a flare event (right column) on 2012 October 23.Because of solar illumination effects on the ionosphere, the dayside TEC generally follows the cosine function of the solar zenith angle with larger values at lower latitudes.At low-and equatorial-ionosphere, a well-defined equatorial ionization anomaly structure with a TEC trough over the dip equator and two peaks around ∼±15°magnetic latitudes can be seen over the American sector at these four snapshots.On 2012 October 22, the differential TEC in Figure 2(c) was enhanced in the longitudinal sector from 10°-120°and these enhancements also tend to be stronger at lower latitudes.The obvious change is due to a local time offset at these two UTs (1 hr and 35 minutes difference).On 2012 October 23, the differential TEC in Figure 2(f) shows a similar pattern as that in Figure 2(c) but with larger differences at low latitudes.For example, the differential TEC at the subsolar point near the Sanya ionosonde station is ∼20 TECU (Figure 2(c)) on October 22 and ∼25 TECU (Figure 2(e)) on October 23, respectively.The relatively larger TEC enhancements observed near the subsolar point on October 23 mostly arise from solar flare ELP effects.These TEC enhancements were less obvious with increasing distance from the subsolar point.
To have a deep insight into how the ionosphere varies at different altitudes during ELP, from the top to the bottom in Figure 3 are the percentage changes of electron density profiles from the 1 hr (02:10-03:10 UT) preflare mean values at Yakutsk (YA), Beijing (BJ), Wuhan (WH), and Sanya (SY) on 2012 October 22 (no flare reference) and 2012 October 23 (flare condition), respectively.A similar approach was also used by Handzo et al. (2014) to obtain solar flare-induced ionosphere electron density changes from ionosonde data.In the impulsive phase, the electron densities below F 2 layer peak (hmF 2 ) for all stations have obvious enhancements due to flare photoionization.These enhancements have latitudinal dependencies and are stronger at lower latitudes.
At SY, a dropout in the ionosonde data took place during the flare impulsive phase from 03:00 to 03:15 UT.This arose from the fact that D region electron density was greatly elevated due to the dramatically enhanced X-ray, leading to radio wave absorption below the detectability limit of the ionosonde.About 5 minutes after the flare peak, peak ionospheric electron density enhancement was as much as 55% between 130 and 300 km as compared with the day before, which is then gradually decaying until 04:18 UT.Electron densities at the altitude of 130-300 km underwent another evident enhancement with a magnitude of ∼40% between 04:18 UT and 05:15 UT.This coincided with the ELP peak and was indicative of the ELP effects on the ionosphere.
At WH, like SY, a dropout was also seen in the ionosonde data around the flare peak (Figure 3(g)).The electron density had a gradual decreasing trend during 3-7 UT nonflare reference day on 2012 October 22 (Figure 3(c)).In the impulsive phase, flare-induced maximum electron density enhancements attained ∼50% at 150-220 km and lasted until around ∼04:20 UT (Figure 3(g)).The electron density increased again afterward and peaked around ∼05:00 UT, consistent with the ELP effects.At midlatitude latitudes, such as in YA and BJ, similar enhancements took place as in WH with the first enhancement in the initial phase and the second brief enhancement around ∼05:00 UT (Figures 3(f) and (h)).Only partial blackouts were seen in the two middle-latitude stations (YA and BJ).This could be related to that larger solar zenith angle and thus the absolute density increase in the D region is not as large as that at lower latitudes so cannot affect radio wave absorption that much.
To further separate the effects of the impulsive phase and ELP on the ionosphere, Figure 4   300-400 km and lasted for several hours.As a response to the solar flare impulsive phase, Pedersen conductivity was increased in the altitude range of 100-200 km and these increments persisted for about 40 minutes.
As a response to the ELP, the electron density enhancements started around 05 UT, mainly took place above 200 km, and lasted for about 6 hr as indicated in Figure 4(c).A progressive delayed ionosphere response to the ELP is seen at higher altitudes above 200 km.The ionospheric electron density enhancements are stronger during ELP than during the flare main phase.Apart from the electron density enhancement, decrease in electron density was also obvious for ∼300 km for both the flare main phase and ELP.Smithtro et al. (2006) showed that the E and F1 region ionosphere were intensified but peak electron density unexpectedly decreased as revealed by an ionosonde at Bear Lake Observatory, Utah, and the timedependent ionospheric model during an X1-class solar flare.They proposed that decreased NmF2 mostly arose from the upward diffusion of plasmas to higher altitudes due to flareinduced rapid electron density and temperature increases (e.g., Mendillo et al. 2018;Liu et al. 2022).The conductivity is mainly determined by plasma density and plasma-neutral collision frequencies and thus peaks at a relatively lower altitude near the E region.The Pedersen conductivity enhancements around 120 km started at ∼03:50 UT and ended at ∼05:00 UT for both cases (Run 1 and 2; Figures 3(e) and (f)).These enhancements are mostly because of the solar spectrum shorter than 10 nm as indicated by EVE line 9.3 nm (Figure 1(a)) causing a high ion production rate plus higher plasma-neutral collision frequencies at ∼120 km than at higher altitudes.As shown by Qian et al. (2010), X-ray and ultraviolet (0.05-23 nm) ionization peaks in the E region in the 100-150 altitude range, while EUV (23-105 nm) ionization peaks above 200 km.

Discussion and Summary
The solar irradiance spectrum was reconstructed for the first time by using the output from FISM and SDO/EVE observations and was incorporated into a physical-based ionospherethermosphere coupled model to calculate ionization and heating of Earth's upper atmosphere by a flare on 2012 October 23 that has both the flare main phase and ELP.The ionosonde observations and numerical simulations show that electron densities were enhanced almost simultaneously from high to low latitudes and these enhancements tend to be weaker at higher latitudes right after the solar flare X-ray peak.Another density enhancement took place at mid-and low latitudes around the second EUV peak and lasted for about 2 hr, which is indicative of ELP effects.
Not only the intensity of solar flares but also the details of the solar spectrum are important in determining the ionospheric response to the solar flares.Tsurutani et al. (2005) compared the global dayside TEC variations during four strong flares on October 28 and 29 and 2003 November 4 (the "Halloween" events) and the 2000 July 14 (the "Bastille day") event.The Oct 28 flare (X28 disk flare) induced ionospheric TEC peak enhancement at the subsolar point is ∼25 TECU (30% above background), while the November 4 (∼X45 limb flare; Thomson et al. 2004;Tsurutani et al. 2009), October 29 (X10 disk flare) and the Bastille Day (X10 disk flare) events have ∼5-7 TECU peak enhancements above background (less than ∼10%).The peculiarity of the October 28 flare is the largest event in EUV among these four flares.In the 26.0-34.0nm wavelength range, the October 28 flare is found to have a peak intensity greater than twice that of the November 4 flare, leading to a ∼3 to 4 times difference in ionospheric TECU.A rough estimation of the total flare energy for the X-ray (0.1-10 nm) and EUV (10-120 nm) during this flare period (03-06 UT) on 2012 October 23 was performed based on the adjusted FISM solar spectrum.The total radiation energy release is larger in the EUV flux (∼2.0 × 10 30 erg) as compared to X-rays (∼1.1 × 10 30 erg) during this flare interval since the wavelength band for EUV is much wider than for X-rays.Another factor in determining the ionosphere and thermosphere response to solar flares is flare location on the solar disk.By analyzing the correlation between TEC enhancement, soft X-ray peak flux in the 0.1-0.8nm and EUV increase in the 0.1-50 and 26-34 nm regions observed by the Solar and Heliospheric Observatory Solar EUV Monitor EUV detector, Zhang et al. (2011) showed that the flares near the solar disk center are more effective in increasing TEC than the flares near the solar limb.Emissions in the X-ray band are optically thin and thus weakly rely on the locations of the flare, but emissions in the EUV band originating from the lower solar atmosphere are mostly optically thick and are relatively weaker for the flares in the limb than those in the center of the solar disk because of absorption by the solar atmosphere.During the ELP, the EUV emissions originate from a second set of higher and longer loops relative to the first main flaring loops.It would be expected that the effects of center-to-limb variations of solar flares on the ionosphere and thermosphere system during ELP should be weaker than those during the impulsive phase because of less absorption by the solar atmosphere.
It is a common practice to use X-ray in the 0.1-0.8nm as measured by GOES spacecraft to study the solar flare impacts on the terrestrial upper atmosphere before (e.g., Mendillo et al. 2006).However, the flare emission increases across the entire electromagnetic spectrum but not with a uniform magnitude.The discovery of a strong effect of solar flare ELP on the ionosphere has an important implication for the magnetosphere-ionosphere-thermosphere coupling.It is shown that there were double peaks in the EVE line 9.3 nm, which have a significant effect on the ionosphere conductance.Our results indicated that low-latitude ionospheric electron density and thus ionospheric conductances were enhanced evidently at the altitudes of ∼100-250 km due to flare photoionization during ELP.Ionospheric conductance is a key parameter in the magnetosphere-ionosphere-thermosphere coupling processes by regulating solar wind-magnetosphere coupling, convection, magnetic-field-aligned currents, and Joule heating dissipation into the upper atmosphere (Liu et al. 2021b(Liu et al. , 2023)).
In summary, there was an extreme ELP event that took place during the 2012 October 23 X1.8 solar flare in which the X-ray had a single peak around the main phase peak, but EVE lines 33.5 and 17.1 nm had two peaks with the first occurring around the main phase peak and second broad peak lagging ∼1.5 hr.The total EUV energy input during the ELP was larger than that during the flare main phase.To address the solar flare ELP effects on the Earth's upper atmosphere, high-resolution solar spectral data from SDO/EVE were assimilated into the FISM model, and these near-realistic solar spectral products are used to drive the TIEGCM and compare with ionospheric GNSS/ TEC and ionosonde observations.The simulation and observational results showed that because of the enhanced solar EUV radiation in the ELP, the ionosphere TEC near the subsolar point was increased by several total electron content units, and electron density within ∼200-300 km was also enhanced by 20%-60% at mid-and low latitudes near local noon.Our results also showed that the 9.3 nm EVE line exhibited another weaker and ∼1 hr later peak with respect to the first main phase peak, producing noticeable changes in the ionospheric Pedersen conductivity in the E region.The radio wave was strongly absorbed in the impulsive phase because of the enhanced X-ray ionization.This resulted in a total blackout in the low-latitude ionosondes (SY and WH) and a partial blackout in the middle-latitude ionosondes (YA and BJ) in the impulsive phase for this event.However, no obvious radio wave blackout took place at these four ionosonde stations during the ELP on 2012 October 23.

Figure 1 .
Figure 1.Time evolution of each spectral channel for the 2012 October 23 X1.8 solar flare.Panel (a) shows the normalized solar irradiance in four EVE lines including 9.3, 13.1, 17.1, and 33.5 nm and GOES 0.1-0.8nm flux, with the total EUV radiative energy-loss rate overplotted (shaded area) as indicated in the right Yaxis.Panels (b)-(i) show snapshots of AIA images illustrating the evolution of solar flare at the preeruption, main phase peak, pre-ELP peak, and ELP peak as indicated by the four vertical dashed lines in Figure 1(a).
shows the simulated electron density (left column) and Pedersen conductivity (right column) at the geographic equator and local noon in the coordinate of altitude and universal time.Figures 4(b), (e), (c), and (f) show the changes in electron density ((a)-(c)) and Pedersen conductivity ((d)-(f)) due to impulsive phase ((b) and (e)) and ELP effects ((c) and (f)).In Figure 4(b) for TIEGCM run with just the solar flare impulsive phase, the ionosphere E region varies in concert with the solar flare X-ray.The ionospheric electron density was intensified immediately as a response to the onset of the solar flare impulsive phase and recovered as the flare decayed as shown in Figure 4(b).The F region ionosphere also had a quick response to the solar flare's impulsive phase and took 2-3 hr to recover.After about 2 hr, negative perturbation in electron density took place around

Figure 2 .
Figure 2. Snapshots of global GNSS TEC distributions at 03:10 UT (top row) and 04:45 UT (middle row) and their differences (bottom row).The left and right columns are for no flare references on October 22 and flare day on 2012 October 23, respectively.The magenta crosses denote the locations of the four ionosonde stations.

Figure 3 .
Figure 3. Percentage changes of electron density profiles at Yakutsk, Beijing, Wuhan, and Sanya on 2012 October 22 (left column; no flare) and 2012 October 23 (right column; flare).The percentage changes of electron density were calculated with respect to a 1 hr (02:10-03:10 UT) preflare mean values.The black lines indicate the height of the F 2 layer peak.

Figure 4 .
Figure 4.The simulated temporal variations of electron density (left column) and Pedersen conductivity profiles (right column) at the geographic equator and local noon without solar flare effects ((a) and (d), Run 0).Figures (b), (c), (e), and (f) show the changes in electron density and Pedersen conductivity due to solar flare impulsive phase ((b) and (e), Run 1-Run 0) and ELP effects ((c) and (f), Run 2-Run 1).