To consider outer space as a place for deploying advanced space activities, a common fundamental system, called space infrastructure, is required. To build and use a space infrastructure safely, it is important to accurately understand the current state of the solar-terrestrial environment, which is strongly influenced by solar activity. Among the solar activity, solar flares have one of the greatest influences on the solar-terrestrial environment. When solar flares occur, powerful electromagnetic radiation and large amounts of high-energy particles are released. Among these, it is well known that X-ray and extreme ultraviolet (EUV) emissions of solar flares, in particular, influence the Earth’s communication network. When X-ray and EUV emissions from solar flares reach the Earth’s upper atmosphere, especially the D layer of the ionosphere, oxygen and nitrogen in the D layer are ionized. Consequently, the electron density in the D layer increases rapidly, and radio waves (especially at high-frequency ranges) propagating through the D layer are absorbed. This phenomenon is called the Dellinger phenomenon (Dellinger 1937), which is widely known as a sudden ionospheric disturbances (SIDs). Solar flare emissions reach the Earth in ~ 8 min, and the lead time from solar flares to SIDs is extremely short. Therefore, it is important for the solar irradiance, especially X-ray and EUV emissions, to be constantly monitored.
In general, SIDs are considered to be caused by the occurrence of solar flares of the M-class or higher and can be predicted using the flare class. However, it has been reported that SIDs have occurred due to C-class flares but not due to X-class flares. These observational results suggest that flare emissions contributing to the occurrence of SIDs is not necessarily proportional to the X-ray intensity. Observational data of the full solar flare emission spectrum are required to verify the influence of solar flare emission wavelengths on the occurrence of SIDs. However, spectral observations of EUV and X-ray emissions, which are considered to contribute significantly to SIDs, are limited.
X-ray emissions have been continuously observed since 1974 using X-ray Sensors (XRS) on board the Geostationary Operational Environmental Satellite (GOES). GOES/XRS observes two wavelength bands, 0.5–4 Å (GOES/XRS-A) and 1–8 Å (GOES/XRS-B) (Bornmann et al. 1996).
EUV emissions have been observed using various instruments because of their importance in space weather forecasting. The Solar and Heliospheric Observatory (SOHO) satellite, which was launched in December 1995, has a Solar EUV Monitor (SEM) (Judge et al. 1998). This instrument has been observing EUV emissions with a 15-s time resolution since January 1996. However, SOHO/SEM only has two wavelength bands, 260–340 Å and 1–500 Å, without a wavelength resolution. Hence, only the temporal variation in these EUV emissions can be determined from the SOHO/SEM data. The Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) satellite, which was launched in December 2001, has an EUV observation instrument called the Solar EUV Experiment (SEE) (Woods et al. 2005). TIMED/SEE has been observing the wavelength range of 1–1940 Å with a 4 Å resolution since January 2002 and has superior spectral resolution compared to SOHO/SEM. However, its time resolution is ~ 1 day, and as hence, short-term fluctuations such as solar flares cannot be measured. The Extreme Ultraviolet Sensors (EUVS) onboard the GOES-R observes the eight EUV lines or bands in the wavelength range of 250–2850 Å with a 10.24 s cadence since 2016 (Eparvier et al. 2009; Thiemann et al. 2019). The Solar Dynamics Observatory (SDO) satellite launched in February 2010 includes the Extreme Ultraviolet Variability Experiment (EVE) (Woods et al. 2012). The Multiple EUV Grating Spectrograph (MEGS), a subsystem of the SDO/EVE, has measured full disk solar irradiance in the 1–1060 Å range with 1 Å spectral resolution and a 10 s time cadence since May 2010. MEGS-A observes a wavelength range of 50–370 Å, while MEGS-B observes a wavelength range of 350–1050 Å. MEGS-A was the only instrument that could make observations throughout the day with sufficient spectral and temporal resolution to study the EUV flare emission spectra; however, this device was terminated in May 2014 due to a charge-coupled device (CCD) power anomaly. Although MEGS-B remains in operation today, it is possible that some flares may not be observed because MEGS-B can only operate for ~ 3 h a day. Therefore, the observation of high-resolution EUV emission spectra during the occurrence of a solar flare occur is not guaranteed.
To model the emission spectra, it is necessary to understand the emission mechanism in solar flares. The basic conceptual model for solar flares is the CSHKP model (Carmichael 1964; Sturrock 1966; Hirayama 1974; Kopp and Pneuman 1976; Yokoyama and Shibata 1998; Shiota et al. 2005). According to this model, solar flares are caused by “magnetic reconnection” generated in the solar corona (Innes et al. 2003; Imada et al. 2013; Warren et al. 2018). The strong magnetic tension generated by the magnetic reconnection accelerates the electrons or protons in the solar corona. The accelerated particles travel downward along the magnetic field lines, fall into the chromosphere, and rapidly heat the high-density plasma. High-temperature and high-density plasma rise from the chromosphere along the magnetic field lines and form a loop-shaped structure; this phenomenon is called “chromospheric evaporation” (Milligan and Dennis 2009; Imada et al. 2015; Lee et al. 2017). The loop structure observed by soft X-ray and EUV formed from chromospheric evaporation is called the “flare ribbon”. Soft X-ray and EUV emissions are emitted from the flare loop. The time evaporation of the EUV emissions is characterized by the temperature of the emitting plasmas. A typical flare light curve of an EUV emission has an impulsive peak initially, followed by a gradual peak, called the impulsive and gradual phases, respectively. In general, relatively cooler EUV line emissions from the plasma below the transition region are observed in the impulsive phase corresponding to the rapid heating in the early stages of chromospheric evaporation. Hotter EUV line emissions are observed in the gradual phase corresponding to the radiative cooling of the flare loop. Therefore, there are differences between the emission spectra of the impulsive and gradual phases because their origins are different.
Different flare EUV emission prediction models were constructed based on the above flare emission mechanism. The most widely used model is the Flare Emission Spectral Model (FISM) (Chamberlin et al. 2006, 2007, 2008). The FISM is an empirical model that derives EUV emission spectra using GOES soft X-ray flux observations. The FISM estimates the wavelength range of 1–1900 Å with a 10 Å spectral resolution and 60 s cadence. It has been reported that the FISM can accurately estimate the solar flare emission spectra within 40% for wavelengths in the range of 140–1900 Å. However, FISM has a low accuracy for wavelengths shorter than 140 Å; this is the wavelength range containing the EUV emission lines that are primarily enhanced during the gradual phase of a flare. This is because the FISM considers the time evolution of all EUV line emissions to be the same as the time evolution of the soft X-ray during the flare, and the cooling of the flare loop (time difference of EUV line emissions) is not well represented. Consequently, the FISM underpredicts the flare duration and deposited energy (Thiemann et al. 2017).
The QEUV, for which the 0–450 Å EUV band is an important indicator of the EUV irradiance input to the Earth’s upper atmosphere (Strickland et al. 1995). The EUV irradiance in the 0–70 Å and 70–170 Å bands has the greatest contribution to the QEUV (Woods et al. 2011). Therefore, the EUV irradiance at wavelengths shorter than 140 Å is important but cannot be accurately estimated by the FISM. To solve this discrepancy, it is necessary to accurately estimate the time evolution of the EUV emissions.
Other physics-based models have been constructed for this purpose; however, the EUV emission was only partially reproduced (Li et al. 2014; Zeng et al. 2014). Thiemann et al. (2017) partially succeeded in modeling the timing of coronal loop cooling using an empirical rule. These studies used a zero-dimensional hydrodynamic model to simulate the thermal evolution of the coronal loops, called the Enthalpy-based Thermal Evolution of Loops (EBTEL) model, which can calculate the temperature and density in the flare loop without calculating the spatial loop evolution (Klimchuk et al. 2008; Cargill et al. 2012). However, the EBTEL model did not calculate the spatial distribution of the emitting plasma in the flare loop; hence, it is possible that the emission from the transition region plasma would not be reproduced accurately (Kawai et al. 2020). Kawai et al. (2020) introduced a new method for reproducing EUV flare emission spectra by considering the time evolution of the plasma distribution in the flare loop. This method was constructed using a one-dimensional hydrodynamic calculation and an atomic database. The details of this method are described in Sects. 3 and 4.
In this paper, we present the statistical results of the EUV emission spectra observed by SDO/EVE for 21 flare events and compare these with the spectra reproduced by Kawai et al. (2020). The purpose of this study is to investigate the accuracy of reproducing solar flare emission spectra using a simple method based on the physics of flare loops and to examine the important parameters for reproducing solar flare emissions.
The remainder of this paper is organized as follows: Sect. 2 presents the extraction of the comparative parameters using GOES/XRS and SDO/EVE. Section 3 introduces the models used in this study. Section 4 describes an example of the derivation of the solar flare emission spectra using the proposed model. Section 5 presents the statistical results of the comparison between the proposed model simulations and observations and verifies the solar flare emission spectra. Section 6 discusses and summarizes the results of the comparison.