arXiv:1909.10715v2 [astro-ph.SR] 16 Sep 2020 · 2020. 9. 17. · pion decays (π0 → 2γ) observed by the Fermi-LAT satellite Ackermann et al. (2017). The appearance of neutral pions

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Solar PhysicsDOI: 10.1007/•••••-•••-•••-••••-•

Development of a Method for Determining the

Search Window for Solar Flare Neutrinos

K. Okamoto1 · Y. Nakano2 ·S. Masuda3 · Y. Itow3,4 · M. Miyake5 ·T. Terasawa6 · S. Ito7 · M. Nakahata1,8

c© Springer ••••

AbstractNeutrinos generated during solar flares remain elusive. However, after 50 years ofdiscussion and search, the potential knowledge unleashed by their discovery keepsthe search crucial. Neutrinos associated with solar flares provide informationon otherwise poorly known particle acceleration mechanisms during solar flare.For neutrino detectors, the separation between atmospheric neutrinos and solarflare neutrinos is technically encumbered by an energy band overlap. To improvedifferentiation from background neutrinos, we developed a method to determinethe temporal search window for neutrino production during solar flares. Our

B K. [email protected]

B Y. [email protected]

1 Kamioka Observatory, Institute for Cosmic Ray Research, The University of Tokyo,Kamioka, Gifu 506-1205, Japan

2 Department of Physics, Kobe University, Kobe, Hyogo 657-8501, Japan

3 Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Aichi464-8601, Japan

4 Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, NagoyaUniversity, Nagoya, Aichi 464-8602, Japan

5 Department of Physics, Nagoya University, Nagoya, Aichi 464-8602, Japan

6 Institute for Cosmic Ray Research, The University of Tokyo, Kashiwa, Chiba277-8582, Japan

7 Faculty of Science, Okayama University, Okayama, Okayama 700-8530, Japan

8 Kavli Institute for the Physics and Mathematics of the Universe (WPI), TheUniversity of Tokyo Institutes for Advanced Study, The University of Tokyo,Kashiwa, Chiba 277-8583, Japan

SOLA: flare_draft_revise.tex; 17 September 2020; 0:31; p. 1

http://arxiv.org/abs/1909.10715v2http://orcid.org/0000-0002-4280-6593http://orcid.org/0000-0003-1572-3888http://orcid.org/0000-0002-8198-1968mailto:[email protected]:[email protected]

K. Okamoto et al.

method is based on data recorded by solar satellites, such as GeostationaryOperational Environmental Satellite (GOES), Reuven Ramaty High Energy So-lar Spectroscopic Imager (RHESSI), and GEOTAIL. In this study, we selected23 solar flares above the X5.0 class that occurred between 1996 and 2018. Weanalyzed the light curves of soft X-rays, hard X-rays, γ-rays, line γ-rays fromneutron capture as well as the derivative of soft X-rays. The average searchwindows are determined as follows: 4, 178 s for soft X-ray, 700 s for derivativeof soft X-ray, 944 s for hard X-ray (100–800 keV), 1, 586 s for line γ-ray fromneutron captures, and 776 s for hard X-ray (above 50 keV). This method allowsneutrino detectors to improve their sensitivity to solar flare neutrinos.

Keywords: Solar flare, Neutrino, γ-ray, X-ray, Neutron, Particle acceleration

1. Introduction

1.1. Neutrino Production in Solar Flare

A solar flare is an explosive event at the surface of the Sun and is character-ized by a rapid increase in the radiative flux. Through a process of magneticreconnection, a solar flare converts its magnetic energy into thermal and kineticenergies of charged particles (Parker, 1957). A typical solar flare is estimatedto release 1026–1032 erg (Ellison, 1963). On the basis of optical observations, atypical energy release time scale is 100–1, 000 s depending on the wavelengthrange (Kane, 1974). The occurrence rate of flares is also well studied, as it is thefrequency distribution as a function of energy released. This distribution can bedescribed by an inverse power-law in the energy range above 1027 erg (Shimizu,1995; Feldman et al., 1996).

Solar flares accelerate charged particles, such as electrons and protons, andcarry non-thermal energy from the acceleration site to the energy loss site inthe chromosphere. These accelerated particles reach relativistic velocities ina short time, becoming so-called energetic particles. Additional counterparts,such as high energy particles (Drake, Gibson, and van Allan, 1969; Datlowe,Hudson, and Peterson, 1974b; Masuda et al., 1994) and electromagnetic waves,have been observed and recorded in several satellites, for example, the OrbitingSolar Observatory series (Datlowe, Elcan, and Hudson, 1974a), theGeostationaryOperational Environmental Satellite (GOES) series (Hanser and Sellers, 1996),the International Sun-Earth Explorer 3 (ISEE 3) (Kane et al., 1983), the SolarMaximum Mission (SMM) (Bohlin et al., 1980), the Reuven Ramaty High EnergySolar Spectroscopic Imager (RHESSI) (Lin et al., 2002; Hurford et al., 2002), theCompton Gamma Ray Observatory (Trottet et al., 2003), HINOTORI (Enome,1982), Yohkoh (Kosugi et al., 1991), Konus-Wind (Aptekar et al., 1995), and theFermi-LAT (Large Area Telescope) satellite (Atwood et al., 2009).

Although several models have been proposed to explain the particle accelera-tion associated with solar flares (Tsuneta and Naito, 1998; Karlický and Kosugi,2004; Liu et al., 2008), the acceleration mechanism remains unknown. As neutralparticles, such as neutrons, neutrinos, X-ray photons, and γ-ray photons, are not


Determining the Search Window for Solar Flare Neutrinos

affected by magnetic field between the Sun and the Earth, these particles havean important role to play in our understanding of both the location and the timeprofile of particle acceleration during solar flares.

In particular, neutrinos associated with solar flares (hereafter solar flare neu-trinos) attract significant attention in the field of astrophysics. If protons areaccelerated during solar flares to sufficiently high energies (more than 300 MeV),pions are produced by collisions with other nuclei in the solar atmosphere (Hud-son and Ryan, 1995; Ramaty, Kozlovsky, and Lingenfelter, 1975). Finally, neu-trinos are generated via the decay of those charged pions such as atmosphericneutrinos. Because of this hadronic origin, solar flare neutrinos give informationabout the acceleration of protons as well as subsequent interactions in the solarchromosphere.

1.2. Brief History of Neutrinos Associated with Solar Flare

Because the process of neutrino production is the same as that of atmosphericneutrinos, the energy range of solar flare neutrinos overlaps with that of atmo-spheric neutrinos. Hence, a technical difficulty arises in separating atmosphericneutrinos from solar flare neutrinos in neutrino experiments such as Super-Kamiokande (Super-K) (Fukuda et al., 2003), IceCube (Aartsen et al., 2017),and so on. For the last 60 years, neutrinos from solar flares have been experi-mentally sought by Homestake (Davis, 1994), Kamiokande (Hirata et al., 1988),SNO (Aharmim et al., 2014) and Borexino experiments (Agostini et al., 2019)but remain unidentified.

In 1988, the Homestake experiment reported an excess of neutrino eventswhen energetic solar flares occurred. This observation suggested a relation be-tween solar flares and the neutrino capture rate on 37Cl (Bahcall, Field, andPress, 1987; Bahcall, 1988) and proposed neutrino magnetic moment spin pre-cession to explain the time variation of the capture rate (Cisneros, 1971; Okun,Voloshin, and Vysotsky, 1986). However, the Kamiokande, SNO and Borexinoexperiments searched for neutrino signals using different solar flare samples andfound no candidate signal related to solar flares.

Last several decades, some emission models of solar flare neutrinos have beentheoretically discussed (Wilson, 2000; Boyarkin, 1996; Boyarkin and Boyark-ina, 2016; Fargion and Moscato, 2003; Fargion, 2004; Kocharov, Kovaltsov, andUsoskin, 1991; Takeishi, Toshio, and Kotoku, 2013). For example, Fargion andMoscato, 2003 and Fargion, 2004 predicted a possibility of observing neutrinosfrom a large solar flare of energy greater than 1032 erg using Super-K andIceCube. On the other hand, Takeishi, Toshio, and Kotoku, 2013 predicted nopossibility of observing neutrinos in Hyper-Kamiokande (Abe et al., 2018) bynumerical simulations.

1.3. Time Window for Neutrino Search

As explained above, the separation of atmospheric neutrinos from solar flareneutrinos is technically difficult. Although atmospheric neutrinos are constantlygenerated, solar flare neutrinos are expected to be released only during the time


K. Okamoto et al.

scale of particle acceleration. Therefore, the signal-to-noise ratio for observingsolar flare neutrinos can be improved by setting an appropriate search window.

The National Oceanic and Atmospheric Administration (NOAA) maintains alist of solar flares observed by the GOES satellite. This list summarizes the dateof each solar flare, its location, its class, its start and end times, and so on. Thisinformation can be used to estimate the time scale of solar flares. However itis questionable whether this time window is appropriate for solar flare neutrinosearches, because the GOES satellite provides data relating only to the intensityof soft X-rays produced by thermal electrons. For this reason, the GOES dataare not particularly useful in identifying the production time scale of solar flareneutrinos.

In the previous study, de Wasseige, 2016 proposed a method for determiningthe search window for solar flare neutrinos using γ-rays above 70 MeV for neutralpion decays (π0 → 2γ) observed by the Fermi-LAT satellite Ackermann et al.(2017). The appearance of neutral pions implies the generation of neutrinos insolar flares, because neutral pions in solar flares are produced simultaneouslywith the charged pions. Therefore, it is natural to set the search window forsolar flare neutrinos based on occurrence time frame of γ-ray emission causedby neutral pions. However, as the Fermi-LAT satellite was launched only in2008, the earlier period is not covered and the observation of such γ-ray emis-sion is rare (Kuznetsov et al., 2011). Notably, this restriction prevents the useof this method for the largest solar flare on record November 04, 2003, classX28.0 (Kane, McTiernan, and Hurley, 2005).

For the above reasons, the appropriate time window for searching for solarflare neutrinos must be set using an alternative method. In this study, we ana-lyzed not only soft X-rays but also γ-rays and hard X-rays because an acceleratedproton during a solar flare also has a chance of generating γ-rays and neutrons.As mentioned above, γ-rays indicate the timing of proton interactions in the solaratmosphere, with neutrinos expected to be produced simultaneously. Therefore,timing information recorded by either γ-ray or X-ray instruments allows neutrinodetectors to set the appropriate time window for solar flare neutrino searches.

This paper is organized as follows. In Section 2, we provide a brief overview ofX-rays and γ-rays for solar flares. In Section 3, we describe a method for deter-mining the time window to search for neutrinos from solar flares. In Section 4,we present the analysis result. In the final section, we discuss the conclusionsand future prospects.

2. Overview of Electromagnetic Observations Related toAccelerated Particles

The measurement of electromagnetic wave energy allows the identification ofits production and origin. The different mechanisms generate different kinds ofbrightening or dimming in the energy flux (Kane, 1974). Several observations ofneutrons and electromagnetic waves associated with solar flares have been per-formed by space satellites since the 1960s. Alothough there are electromagnegicobservations in Extreme Ultraviolet, radio and visible light range, we focus onX-ray and γ-ray observations to discuss neutrino emission in solar flares.



2.1. Soft X-rays

Soft X-rays are originally produced by bremsstrahlung from electrons in thermalmotion. Because the energy of a particle accelerated by a solar flare is ultimatelyconverted into thermal energy, the total intensity of the soft X-ray is used torepresent the total energy released by the solar flare. A peak value for the softX-ray flux in the range of 1–8 Å (1.5–12 keV) observed by GOES is widelyused as an indicator in the classification of solar flares. On the Basis of thisclassification, a solar flare whose peak value exceeds 1.0 × 10−4 W/m2 (X1.0class) is considered to be the largest order (Heckman et al., 1996).

2.2. Hard X-rays

Hard X-rays are produced by bremsstrahlung from non-thermal electrons andthe energy ranges from a few keV to MeV. Such non-thermal electrons areaccelerated by the solar flare; hence they provide information about the en-ergy distribution of the non-thermal electrons. Non-thermal electrons lose theirenergy by scattering in the solar atmosphere and eventually generate thermalbremsstrahlung. In contrast with soft X-rays, hard X-rays provide informationabout the electron acceleration site and its time frame (Fletcher et al., 2011;Holman, G. D. et al., 2011; Kontar et al., 2011).

Neupert (1968) found that the timing of the soft X-ray derivative maximumis almost the same as the peak time of the non-thermal microwave emissionsin the impulsive phase of solar flares and interpreted that the heating may bethe result of collisional losses by energetic accelerated electrons. This is calledthe Neupert effect and can be applied in the case of non-thermal hard X-raysemissions instead of microwave emission (Veronig, A. et al., 2002; Veronig et al.,2005).

Using this effect, we can extract information about electron acceleration fromsoft X-ray data because a light curve of soft X-rays differentiated by time isexpected to be similar to a light curve of hard X-rays. This method is useful toestimate a time profile of electron acceleration even when hard X-ray data arenot available during a solar flare.

2.3. γ-rays

Because neutrinos are produced via hadronic decay, the timing of these inter-actions should be identified in order to determine the search window. The timeprofile of γ-rays is the most important in this study because an observation ofγ-rays implies the acceleration and nuclear reactions of protons. In a solar flare,there are several different reactions produce γ-rays; γ-rays due to bremsstrahlungfrom high energy electrons, γ-rays due to electron-positron annihilation, line γ-rays due to neutron capture on hydrogen nuclei, and γ-rays due to de-excitationfrom nuclei, such as carbon (12C) and oxygen (16O) (Chupp et al., 1973; Smithet al., 2003). Among these, line γ-rays due to neutron capture on hydrogennuclei are the most important channel and are discussed below, along with γ-rayemission due to neutral pions.


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2.3.1. Line γ-ray from Neutron

High energy protons accelerated by a solar flare collide with helium in the solarchromosphere and finally produce neutrons. Such neutrons undergo thermaliza-tion and ultimately produce 2.223 MeV of γ-rays, so called line γ-rays, whenthey are captured on hydrogen nuclei. A line γ-ray is an indirect evidence ofhadronic interactions including neutrons and high energy protons in a solarflare. Therefore, the determination of the search window should include analysisof the timing of line γ-rays, as their appearance indicates the acceleration ofprotons. However, in so doing we must take into account the delay time of about100 s from the generation of line γ-rays to the capture of produced neutrons onhydrogen (Gan, 1998).

As explained above, hard X-rays are produced by the acceleration of electrons,and line γ-rays are produced by hadronic interactions after the acceleration ofprotons (i.e. ions). Shih et al., 2009 found a linear correlation between the fluenceof the 2.223 MeV γ-ray and the fluence of the hard X-ray above 300 keV in alarge solar flare. Although it is unclear whether each acceleration happens at thesame time and at the same location, this correlation implies a close relationshipbetween the acceleration process of electrons and that of protons. Assuming thiscorrelation, a timing delay due to neutron capture is expected in the line γ-rayflux in comparison with the hard X-ray flux.

2.3.2. γ-rays from Pions

Neutral pions (π0) appear in proton-proton collisions when their energies exceed300 MeV. The observation of γ-ray between 70 MeV and 100 MeV producedvia neutral pion decays (π0 → 2γ) implies the production of neutrinos duringsolar flares because neutral pions are produced simultaneously with the chargedpions (Kurt, Yushkov, and Grechnev, 2013). In fact, the Fermi-LAT satelliteand Coronal-F satellite’s SONG detector have both provided examples of γ-rayobservations from neutral pions. In the case of the solar flare on October 28, 2003,SONG recorded a sharp γ-ray increase due to γ-ray emission from neutral pions.In this case, the emission lasted for at least 8–9 min (Kurt et al., 2010; Kuznetsovet al., 2011). On the contrary, Fermi-LAT reported that the π0 emission afterthe solar flare on September 10, 2017 lasted for about 12 h (Omodei et al.,2018). On the basis of these observations, the expected solar flare neutrino rateat the Earth’s surface may be estimated by numerical calculation. However, thisestimation is beyond the scope of this paper, because the time profile of γ-rayemission remains unclear.

3. Analysis Method

To search for solar flare neutrinos, we used public data from solar satellitesand computational resources of the Center for Integrated Data Science (CIDAS)at Nagoya University. In this study, we analyzed the data recorded by threesatellites; GOES, RHESSI and GEOTAIL. The main (sub) targets for eachsatellite are summarized in Table 1.



Table 1. Observation targets for each solar satellite. Circles (©) show the main targetwhose energy and timing can be measured by the satellite’s devices. Triangles (△) indicatesecondary target, hardly detectable by the satellite as direct measurements; the counting ratealone can indirectly imply target existence. Details are described in the later sections.

Satellite Launch year End year Soft X-ray Hard X-ray Line γ-ray γ-ray

GOES 1975 – © △ – –

RHESSI 2002 2018 © © © ©

GEOTAIL 1992 – – △ △ △

Table 2. Summary of satellites and energy ranges in this study. As de-scribed in the main text, GEOTAIL cannot measure the energy of neutralcharged particles above 50 keV.

Type Satellite Energy range (wave length)

Soft X-ray GOES 1.5–12 keV (1–8 Å)

Hard X-ray RHESSI 100–800 keV

Line γ-ray RHESSI 2.218–2.228 MeV

Hard X-ray and soft γ-ray GEOTAIL Above 50 keV

Using CIDAS, we analyzed the GOES satellite’s soft X-ray data, as well asthe RHESSI satellite’s hard X-ray and γ-ray data, as summarized in Table 2.For the analysis of GEOTAIL data, we checked the public data in CIDAS andthen analyzed the corresponding raw data in order to recover hard X-rays above50 keV including soft γ-rays.

3.1. Soft X-rays (GOES)

We used data obtained by the GOES satellite to determine the search window,because the GOES satellite series have continually monitored solar flares since1975. Its long operation permits the use of the same indicator in comparisonsbetween older and more recent flares.

For this study, we first registered all solar flares occurring from 1996 to 2018in the NOAA list. Then, we selected the 23 solar flares whose peak soft X-rayintensity exceeds 5.0 × 10−4 W/m2 (X5.0 class). The date, class, and locationon the Sun (active region, so called AR) for each selected flare are summarizedin Table 3.

A typical soft X-ray light curve observed by the GOES satellite is shown inthe top panel of Figure 1. In the NOAA list, the timing at which four consecutiveflux increases occur was determined as the start time of each solar flare. Theflare end time was typically determined as the timing at which the event’s fluxdecline to half the value of its peak. However, this end time depends on the flareclass which make unsuitable for our analysis. We therefore set the flare end timeas the timing at which the flux declines to 1.0× 10−4 W/m2 (X1.0 class).


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Table 3. List of solar flares selected forthis study. The data, class and activeregion (AR) location are taken froma National Oceanic and AtmosphericAdministration source (NOAA, https://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solar-flares/x-rays/goes/xrs/).

Date Class AR location

1997 Nov. 6 X9.5 S18W63

2000 Jul. 14 X5.7 N22W07

2001 Apr. 2 X20.0 S21E83

2001 Apr. 6 X5.6 S21E31

2001 Apr. 15 X14.4 S20W85

2001 Aug. 25 X5.8 S17E34

2001 Dec. 13 X5.3 N16E09

2002 Jul. 23 X5.1 S13E72

2003 Oct. 23 X5.4 S21E88

2003 Oct. 28 X17.2 S16E08

2003 Oct. 29 X10.0 S15W02

2003 Nov. 2 X9.2 S14W56

2003 Nov. 4 X28.0 S19W83

2005 Jan. 20 X7.1 N14W61

2005 Sep. 7 X18.2 S11E77

2005 Sep. 8 X5.4 S12E75

2005 Sep. 9 X6.2 S12E67

2006 Dec. 5 X9.0 S07E68

2006 Dec. 6 X6.5 S05E64

2011 Aug. 9 X7.4 N14W69

2012 Mar. 7 X5.4 N22E12

2017 Sep. 6 X9.4 S09W34

2017 Sep. 10 X8.3 S08W88

To extract information about light curve brightening correlated with particleacceleration, we took a calculation of the time derivative of the light curve asshown in the bottom panel of Figure 1. In this analysis, we used the 1–8 Åband the same as used by Kurt, Yushkov, and Grechnev, 2013. For setting thetime window, we first fitted the light curve with a Gauss function (A exp{(t −tpeak)

2/σ2}). We then selected the region of [tpeak−3σ, tpeak+3σ] as the searchwindow.

3.2. Hard X-ray (RHESSI)

The RHESSI satellite was launched on February 2002 to monitor solar flares. Itrecords electromagnetic waves in the range of 3 keV to 17 MeV and measurescontinuous spectra from bremsstrahlung of high energy electrons, line γ-rays of2.223 MeV, and γ-rays from 12C and 16O nuclei (Lin et al., 2002). Owing to



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Figure 1. An example solar flare occurring on October 28, 2003, showing the soft X-ray lightcurve (top) observed by the GOES satellite and the derivative of the flux of soft X-rays (bot-tom). In the top panel, the horizontal axis is universal time and the vertical axis is the flux ofsoft X-rays. The black dotted horizontal (vertical) line shows the flux of 1.0×10−4 W/m2 (thepeak timing of this channel). The region drawn in gray shows the time window selected in thisstudy. In the bottom panel, the horizontal axis is universal time and the vertical axis is thederivative of the flux of soft X-rays with respect to time. The blue dots and the green regiondepict the data and their error, respectively. The red curve is the result of the Gaussian fittingand the vertical dotted line shows the peak timing of this channel. The gray region shows thetime window selected by this study.

its wide energy range, the RHESSI satellite provides important information forextracting acceleration time scales for electrons, protons, and ions.

In this study, we integrated the energy spectrum in the range of 100–800 keVfor hard X-ray analysis as shown in the top panel of Figure 2a. We then deter-mined the count rate within this energy range using the front detector on theRHESSI because the front detectors are sensitive to 100–300 keV emission andthey are dominant in the range of 100–800 keV. To set the search window, wefitted the light curve via a combination of basic functions. For the fitting, weused constant value for the background before the brightening, a linear functionfor the impulsive phase of the light curve, and an exponential function for thegradual phase. The start time (tstart) is defined as the time when the linerfunction intersects the background constant. The time window was determinedby selecting the region where the exponential function is 2σ above the back-ground constant. The standard deviation (σ) is obtained as standard deviationof constant background fitting. The end time (tend) is the last point satisfyingthis condition. In this way, the search window by hard X-ray is determined as[tstart, tend].


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Figure 2. (a) Energy spectra of γ-rays associated with the solar flare occurring on Novem-ber 2, 2003 as recorded by the RHESSI detectors (front 4–8 and rear 1–9). The bluesolid and pink dotted lines shows the energy spectrum in quiet period and during solarflare (17 : 03 : 00–18 : 07 : 03 UTC). The horizontal axis shows energy in keV and the verticalaxis in the top panel shows the flux of γ-rays in units of cm−2sec−1keV−1. The vertical axis inthe bottom panel shows the ratio between fluxes. The vertical dashed line in top and bottompanel indicates 800 keV. For hard X-ray analysis, we used 100–800 keV. Above this energyregion, we searched for line γ-rays due to neutron captures. (b) Light curve of the line γ-raysin this solar flare shown in (a). The horizontal axis shows universal time and the vertical axisshows the count rate in units of count per 4 s. The blue points and green bars depict the dataand their error, respectively. The red lines show the fitting results and the shaded region showsthe time window determined by this method.

3.3. Line γ-rays (RHESSI)

For line γ-ray analysis, we first scanned the energy spectrum recorded by therear detector of RHESSI in quiet period of the Sun and during each solar flare asexampled in the top panel of Figure 2a. During solar flare, we selected the timeinterval corresponding to the time window determined by GOES soft X-rays. Onthe other hand, we selected the time interval of quiet period one month beforea solar flare and then removed the time period when C (or larger) class flareoccurred. Then, we took a ratio between them as shown in the bottom panelof Figure 2a. When we confirmed an excess of the line γ-ray in the spectrumduring the solar flare, we plotted the light curve using the energy range of 2.218–2.228 MeV after subtracting its sideband of both 2.213–2.218 keV and 2.228–2.233 keV in order to remove bremsstrahlung from high energy electrons asshown in Figure 2b. To determine the search window, we used the same methoddescribed above for hard X-rays. However, because of the neutron capture timedelay (Gan, 1998), we ultimately selected the region of [tstart − 100 sec, tend] asthe time window for line γ-ray.

3.4. GEOTAIL Satellite Hard X-ray Events

The GEOTAIL satellite was launched in July 1992 to observe the Earth’s mag-netosphere. Its main targets are electrical field, magnetic field, plasma and highenergy particles in the magnetosphere. The LEP (low energy particle) instrument



mounted on the satellite, can measure counts of ions and electrons independentlybased on energy-per-charge separation (Mukai et al., 1994). The LEP detectorconsists of an electrostatic analyzer and particle counters: microchannel platesfor ions, and channel electron multipliers for electrons.

GEOTAIL has occasionally been exposed to the intense fluxes of energeticions >50 MeV and photons of >50 keV after strong solar flares or giant flaresof magnetars (Terasawa et al., 2005; Tanaka et al., 2007; Tanaka et al., 2007).These energetic ions and photons do not follow the the electrostatic analyzer’senergy-per-charge regulation, but rather penetrate through the satellite walland hit the particle counters directly. For the solar flare case, energetic photonsinclude hard X-ray photons from bremsstrahlung by high energy electrons, aswell as line γ-ray photons from nuclear interactions. Figure 3 shows an exampleof this situation. During the interval 10:35:00–11:35:00 UTC on October 28,2003, GEOTAIL was in the solar wind upstream of the Earth’s bow shock andcontinued to measure solar wind particles as well as nonthermal ions (10–40keV/q) accelerated by the bow shock. However, during the interval 11:01:40–11:15:30 UTC, GEOTAIL was hit the solar flare hard X-ray photons, whichproduced the energy-independent stripes in the first to three panels of Figure 3.It is noted that tailward-flowing solar wind ions (less than ∼20 keV/q coloredwith yellow-red-black) overwrapped with the hard X-ray stripes as shown in thefourth panel of Figure 3. The penetration depth for hard X-ray photons fromthe satellite wall to the counter depends on the satellite spin phase, so thatthe colors of the energy-independent differ stripes slightly sector by sector. Theelectron detector (not shown) responded to the solar flare hard X-ray photonssimilarly. However, because the form factor of the electron detectors is two ordersof magnitude smaller than that of the ion detectors, the apparent contributionof solar flare hard X-ray photons is much weaker.

In the present study, we estimated the time profiles of particle accelerationby selecting data from the four sectors and the energy range that was not“contaminated” by ions, taking count averages every 12 s. Figure 4 shows thephoton counts from 10:50:00 to 11:20:00 UTC, as calculated from the data inthe dawnward, sunward, and duskward sectors in Figure 3. Finally, the timewindow for GEOTAIL was determined using the same method as that used inthe analysis for line γ-ray above, because a component of the GEOTAIL signalcontains line γ-rays.

In order to avoid confusion with the term hard X-ray by RHESSI, we use theterm hard X-ray (>50 keV, or above 50 keV) to refer this channel by GEOTAILeven if the actual signals contain soft γ-ray as listed in Table 2.

4. Results and Discussion

4.1. Results

Because all satellite data are available for the solar flare occurring on November2, 2003, we used this example to illustrate the method for the time windowdetermination developed in this study as shown in Figure 5.


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Figure 3. Count rates recorded by the LEP detector when this solar flare occurred on October,28, 2003 are color-coded (white-blue-green-yellow-red-black). The horizontal axis shows theuniversal time (HH:MM) of particle detection. The vertical axis shows the energy of nonthermalions in unis of energy-per-charge (5–40 keV/q). Four panels, top to bottom, show ion countsin the four sectors pointed dawnward, sunward, duskward, and tailward, respectively, wherethe ion flow directions are defined with respect to the relative magnetosphere geometry of theSun and Earth.

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Figure 4. Light curve associated with the solar flare occurring on October, 28, 2003 asrecorded by the GEOTAIL satellite. The horizontal axis shows the universal time, and thevertical axis shows count rate in units of counts/detector/12 s). Red points show the data, andblue lines show the fitting results. This flare is the same flare shown in Figure 3.



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Figure 5. Light curves of the solar flare occurring on November 2, 2003. Gray regions showthe time windows extracted by the analysis methods developed in this study. From top tobottom, the panels show the light curves for soft X-rays, derivative of soft X-rays, hardX-rays (100–800 keV), line γ-rays (2.223 MeV), and hard X-rays (GEOTAIL, above 50 keV),respectively. The vertical lines show the peak timing of each channel. For the hard X-ray lightcurve (above 50 keV), the count rate gradually increased from 17:40 onward because protonsin the range of 30–50 MeV were observed. These protons masked other counts due to plasmaparticles and hard X-ray photons.

The analysis results for 23 solar flares selected in this study are summarized inTables 4 and 5. It is noted that we failed to obtain the time window determined

by derivative of soft X-ray for the solar flare occurred on September 9, 2005,because the brightening of its soft X-ray light curve was relatively slow andderivative of soft X-ray was not large enough. Except for this flare, we determined

the time window for 22 of 23 solar flares by using derivative of the soft X-ray.In addition to this, we also determined the time window for five flares by hardX-ray (100–800 keV), three flares by line γ-ray, and seven flares by hard X-

ray (>50 keV). It is noted that the time profile of the flare occurring on October29, 2003 is not similar to those of the other flares, because a signal whose originis not solar flare contaminated the solar flare signal. We did not determine the

time windows for this flare by hard X–ray and line γ–ray channel. An alternativemethod, imaging method developed in Liu et al., 2009, allows us to confirm non-solar flare signal causes this contamination. The hard X-ray light curve of this

solar flare measured by this imaging method is shown in appendix. It is notedthat there is not the line γ–ray light curve with the imaging method, because

its flux was not large ehough. The line γ–ray time profile of this solar flare wasinvestigated in Kurt et al., 2017.


K. Okamoto et al.

Figure 6 summarizes the distribution of timing window duration for eachchannel. On the basis of these results, the average time duration for each channelis as follows; 4, 178 s for soft X-rays, 700 s for derivative of soft X-rays, 944 s forhard X-rays (100–800 keV), 1, 586 s for line γ-rays from neutron capture, and776 s for hard X-rays (>50 keV). The shortest time window among these is thederivative of soft X-rays.


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Date Soft X-rays (GOES) Derivative of soft X-rays (GOES) Hard X-rays (RHESSI)

tstart tend ∆t [s] tstart tend ∆t [s] tstart tend ∆t [s]

1997 Nov. 6 11:49:00 12:12:21 1,401 11:52:13 11:54:58 165 – – –

2000 Jul. 14 10:03:00 11:05:03 3,723 10:08:44 10:28:31 1,187 – – –

2001 Apr. 2 21:32:00 22:56:12 5,052 21:35:10 21:52:57 1,067 – – –

2001 Apr. 6 19:10:00 19:43:15 1,995 19:12:32 19:21:31 539 – – –

2001 Apr. 15 13:19:00 14:23:39 3,879 13:43:48 13:51:03 435 – – –

2001 Aug. 25 16:23:00 17:36:18 4,398 16:28:36 16:33:38 302 – – –

2001 Dec. 13 14:20:00 14:41:57 1,317 14:24:25 14:31:05 400 – – –

2002 Jul. 23 00:18:00 01:08:27 3,027 00:25:08 00:31:36 388 00:25:44 00:36:46 562

2003 Oct. 23 08:19:00 09:13:9 3,249 08:20:32 08:36:03 931 – – –

2003 Oct. 28 09:51:00 12:36:54 9,954 10:59:30 11:10:57 687 – – –

2003 Oct. 29 20:37:00 21:23:39 2,799 20:38:46 20:50:07 681 – – –

2003 Nov. 2 17:03:00 18:07:03 3,843 17:12:01 17:26:03 842 17:15:41 17:39:22 1421

2003 Nov. 4 19:29:00 21:10:12 6,072 19:36:59 19:56:03 1,144 – – –

2005 Jan. 20 06:36:00 08:05:48 5,388 06:39:22 06:57:12 1,070 06:43:27 06:57:57 870

2005 Sep. 7 17:17:00 18:48:57 5,517 17:23:34 17:39:48 974 – – –

2005 Sep. 8 20:52:00 21:31:48 2,388 21:00:27 21:08:05 458 – – –

2005 Sep. 9 19:13:00 21:20:36 7,656 – – – – – –

2006 Dec. 5 10:18:00 10:56:09 2,289 10:24:18 10:35:43 685 – – –

2006 Dec. 6 18:29:00 19:16:30 2,850 18:41:29 18:47:06 337 18:42:33 18:49:19 406

2011 Aug. 9 07:48:00 08:11:47 1,427 08:00:50 08:05:40 290 – – –

2012 Mar. 7 00:02:00 01:31:34 5,374 00:04:21 00:25:16 1,255 – – –

2017 Sep. 6 11:53:00 13:30:00 5,820 11:54:39 12:03:20 521 – – –

2017 Sep. 10 15:35:00 17:26:06 6,666 15:49:12 16:06:32 1,040 15:54:42 16:19:03 1,461

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Table 5. Time windows determined for line γ-rays (RHESSI) and hardX-rays (GEOTAIL). Time is described in units of UTC ([HH:MM:SS]).

Date Line γ-ray (RHESSI) Hard X-ray (GEOTAIL)

tstart tend ∆t [s] tstart tend ∆t [s]

1997 Nov. 6 – – – 11:50:55 11:57:04 369

2000 Jul. 14 – – – – – –

2001 Apr. 2 – – – – – –

2001 Apr. 6 – – – – – –

2001 Apr. 15 – – – 13:43:42 13:51:58 469

2001 Aug. 25 – – – 16:28:29 16:34:54 385

2001 Dec. 13 – – – – – –

2002 Jul. 23 00:26:28 00:56:22 1,794 – – –

2003 Oct. 23 – – – – – –

2003 Oct. 28 – – – 10:59:45 11:17:36 1,071

2003 Oct. 29 – – – – – –

2003 Nov. 2 17:14:14 17:36:41 1,347 17:13:08 17:37:11 1,443

2003 Nov. 4 – – – 19:38:35 19:53:32 897

2005 Jan. 20 06:42:54 07:09:52 1,618 – – –

2005 Sep. 7 – – – 17:32:44 17:45:32 7678

2005 Sep. 8 – – – – – –

2005 Sep. 9 – – – – – –

2006 Dec. 5 – – – – – –

2006 Dec. 6 – – – – – –

2011 Aug. 9 – – – – – –

2012 Mar. 7 – – – – – –

2017 Sep. 6 – – – – – –

2017 Sep. 10 – – – – – –

Figure 7 shows the time duration of search windows as a function of themaximum value of the soft X-ray peak. The correlation coefficients between themaximum value of the soft X-ray peak and the time duration of search windowsare 0.436 for soft X-rays, 0.341 for soft X-rays (derivative), 0.236 for hard X-rays (100–800 keV), −0.344 for line γ-rays, and 0.307 for hard X-rays (>50 keV).Therefore, no strong correlation is found among them, as summarized in Table 6.

To investigate the difference in time profile between channels, we calculatedthe time elapsed between the peak timing of a given channel and the peak timingof soft X-rays as shown in Figure 8, because the peak timing of each channelis earlier than that of soft X-rays. The mean differences are −320 s for thederivative of soft X-rays, −482 s for hard X-rays (100–800 keV), −471 s for lineγ-rays, and −342 s for hard X-rays (>50 keV).

Each panel in Figure 9 shows the time correlation between two variables: onthe x-axis, the peak timing of soft X-rays; on the y-axis, a given channel aftersubtracting the peak timing of soft X-rays. To extract the difference betweenpeak timings, the plots are fitted with a linear function; the fitting results aresummarized in Table 7. The y-intercept of the linear function gives the differencein peak timings.



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Figure 6. Distributions of the time window determined by each method: (a) light curve ofsoft X-rays, (b) derivative of the light curve of soft X-rays, (c) hard X-rays (100–800 keV),(d) line γ-rays, and (e) hard X-rays (>50 keV). The horizontal axis shows duration of the timewindow and the vertical axis shows the number of entry.

In Figure 9c, the fitting results are 0.9 ± 0.1 for the slope and 7 ± 55 s for

the y-intercept. We found a good timing correlation between the derivative of

soft X-rays and hard X-rays because the y-intercept is close to the origin of

coordinates (0, 0), thus confirming the Neupert effect between them. Notably,

this confirmation takes place by comparing the peak timing without considering

the shape of light curves.

In Figure 9d, the y-intercept is 141±285 s, suggesting that the peak timing of

line γ-rays is delayed from that of hard X-rays (100–800 keV). If the acceleration

of both electrons and ions occurs simultaneously, this difference between their


K. Okamoto et al.

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Figure 7. Time duration as a function of the peak intensity of soft X-ray. Black dot, redsquare, green up-triangle, blue down-triangle, and light blue star show soft X-ray, derivativeof soft X-ray, hard X-ray (100–800 keV), line γ-ray, and hard X-ray (>50 keV), respectively.

Table 6. Summary of timing information obtained in this study. Average time durations arecalculated from the distributions shown in Figure 6. Correlation coefficients are calculatedfrom the distribution shown in Figure 7. The differences in peak timing are calculated at asoft X-ray peak time of 0 (Figure 8).

Entries Average duration Correlation Peak timing

[s] coefficient difference [s]

Soft X-ray 23 4, 178 0.436 –

Soft X-ray (derivative) 22 700 0.341 −320

Hard X-ray (100–800 keV) 5 944 0.236 −482

Line γ-ray 3 1, 586 −0.344 −471

Hard X-ray (>50 keV) 7 776 0.307 −342

timings is explained by considering neutron capture (Gan, 1998; Shih, Lin, andSmith, 2009).

Figure 9e overlays the plots shown in Figure 9a and Figure 9b. We found thatthe peak timing of hard X-rays is earlier than that of line γ-rays, where theirdifference is about 100 s.

4.2. Applications to Neutrino Detectors

On the basis of our results, the longest time window, averaging 4, 178 s, can beset using soft X-rays. It is expected that all processes (acceleration of chargedparticles, energy release of (non) thermal electrons, etc) occurring during a solarflare complete within this time window. Therefore, this window is advantageousfor estimating the time scale of physics processes during solar flares. Despite



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Figure 8. Time difference distribution after subtracting the peak timing of soft X-rays. Thehorizontal axis shows the time difference in units of seconds and the vertical axis shows theentry per 50 s.

Table 7. Summary of results from fits in Figure 9. Each axis in Figure 9represents the time elapsed between the peak timing of a given channel andthat of soft X-rays.

Figure 9 x-axis y-axis Fitting result χ2/d.o.f

(a) Soft X-ray Hard X-ray (1.1± 0.4)x 1.0/3

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(100–800 keV) (141 ± 286)

its uselessness for identifying the time of solar flare neutrinos, the continuous

monitoring by GOES allows us to set the search window for every solar flareeven if other satellites miss the signals.

The time derivative of soft X-rays allows the setting of the shortest timewindow, with an average of 700 s. This time window is advantageous for searching

for solar flare neutrinos, because it has the best chance of improving the signal-


K. Okamoto et al.

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to-noise ratio. In the case of Super-K, the average observing rate of atmospheric

neutrinos is 8.3 events/day (Richard et al., 2016). Assuming this time window,

the expected background rate can be reduced to 0.067 events/flare. If three

events are observed within this time window, the Super-K detector can reject

the null hypothesis of neutrinos not from solar flares at 95% confidence level



(C.L.). On the contrary, the derivative of soft X-rays does not provide us withinformation on the acceleration of protons or ionized particles, which producesneutrinos via hadronic interactions. Therefore, it is questionable whether thiswindow is entirely appropriate for a comprehensive solar flare neutrino search.

The line γ-ray observation is crucial in this study because such signals in-dicate the acceleration of protons and hadronic interactions including chargedpions that produce neutrinos. The search window for solar flare neutrinos shouldtherefore be determined by this channel. In the present study, four solar flaresinclude γ-ray observation by RHESSI. One of these is shown in Figure 5. Thelight curves of the other three flares are shown in Figures 10–12 in the appendix.According to our study, hard X-ray (100–800 keV) light curve shape looks similarto that of line γ-rays. Their time profiles are also similar after subtracting thepeak timing of soft X-rays in Figure 9c. Therefore, we suggest that the searchwindow determined by hard X-ray (100–800 keV) information is useful in thesearch for solar flare neutrinos even if no line γ-ray data are available.

5. Conclusions and Future Prospects

Solar flare neutrinos attract significant attention because the detection of suchneutrinos can extract information about particle acceleration during solar flares.Hence, we have developed a method for determining the search window for solarflare neutrinos. The longest search window, based on soft X-ray light curve, isestimated to last for 4, 178 s. On the contrary, the shortest search window, basedon the derivative of soft X-rays, is estimated to last for 700 s.

The method developed in this study is useful for adoption by other spacesatellites, such as HINOTORI, Yohkoh, Hinode (Kosugi et al., 2007), and severalfuture planned satellites, for example the Spectrometer/Telescope for Imaging X-rays on board the ESA Solar Orbiter (Müller et al., 2013; Massa et al., 2019),the Focusing Optics X-ray Solar Imager (Krucker et al., 2014), and Physics ofEnergetic and Nonthermal plasmas in the X region (PhoENiX), proposed inJapan. This adoption will permit the extraction of information about both theneutrino production timing and particle acceleration during solar flares.

Using the method in this study, a search for solar flare neutrinos above theX5 class undertaken from 1996 to 2018 by neutrino detectors, such as Super-K,SNO (Boger et al., 2000), IceCube, ANTARES (Ageron et al., 2011), Kam-LAND (Gando et al., 2012) and Borexino (Alimonti et al., 2009). Assumingthe shortest time window of derivative of soft X-ray, the expected backgroundrate can be reduced to 0.067 events/flare in the case of Super-K. If three eventsare observed within this time window, the Super-K detector can reject the nullhypothesis of neutrinos not from solar flares at 95% C.L.

This method can also be used for future large solar flares and can improve sen-sitivity in the next generation of neutrino experiments, such as Hyper-Kamiokande,IceCube-Gen2 (Aartsen et al., 2014), SNO+ (Andringa et al., 2016), DUNE (Ac-ciarri et al., 2015), LENA (Wurm et al., 2012), and JUNO (An et al., 2016).


K. Okamoto et al.

Acknowledgments This work was carried out by the joint research program of the Institute

for Space-Earth Environmental Research (ISEE), Nagoya University. A part of this study was

carried using the computational resources of the Center for Integrated Data Science, Institute

for Space-Earth Environmental Research, Nagoya University, through the joint research pro-

gram. We thank Y. Saito from JAXA and I. Shinohara from JAXA for reproducing GEOTAIL

satellite data. We thank S. Krucker for his careful reading of this manuscript and for his

insightful comments and suggestions. This work is supported by MEXT KAKENHI Grant

Numbers 17K17880, 18H05536, 18J00049 and 19J21344.

Disclosure of Potential Conflicts of Interest

The authors declare that they have no conflicts of interest.

Appendix

A. Line γ-ray Light Curves for Solar Flares

As mentioned in section 2, the observation of γ-rays indicates the production ofneutrinos via hadronic interactions, thus constituting the most important chan-nel in this analysis. The present study captures four solar flares that include lineγ-rays. In the main text, light curves for the solar flare occurring on November2, 2003 are shown, because all channels are available for this event. Light curvesof the other three flares are shown as follows: July 23, 2002 (Figure 10), October29, 2003 (Figure 11), and January 20, 2005 (Figure 12).

B. Comment on the Solar Flare Occurring on October 29,2003

The time profile of the flare occurring on October 29, 2003 is not similar to thoseof the other flares, because signal is contaminated with non-solar hard X-raysfrom magnetospheric origin. For only this flare, the peak timings of both hardX-rays and line γ-rays are delayed relative to that of soft X-ray as shown inFigure 11. The light curve of hard X-rays shows several minor peaks. To confirmthe contaimination was caused by non-solar flare origin signal, we used spacialinformation from the imaging method to see the flare region on the surface ofthe Sun. The light curve with imaging method is shown in the third panel ofFigure 11. The line γ–ray light curves shown in Kurt et al., 2017 is overlaid inthe fourth panel of Figure 11.

C. Light Curves for the Largest Solar Flare; November 4, 2003

The largest solar flare on record occurred on November 4, 2003, with class X28.0.This flare attracts significant attention because of the presumably chance of solarflare neutrino detection. Figure 13 shows the light curves for this solar flare.



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Figure 10. Light curves of the solar flare occurring on July 23, 2002. Gray bands show thesearch windows as same in Figure 5. The vertical dotted lines show the peak timing for eachchannel.

The GOES satellite instrument was saturated due to the high intensity ofsoft X-rays, and did not continue to record data for more than 15 min around19:45–20:00. Because of this situation, we set the peak timing of soft X-ray forthis flare at the middle point of the saturation phase, instead of the way outlinedin the body of this paper. On the other hand, we could not set the peak timing ofthe derivative of soft X-rays due to the saturation. For this reason, we excludedthis flare from comparison of peak timing with soft X-rays shown in Figure 8.Moreover, we made a special treatment to set the end time of the derivative ofsoft X-rays at the end time of the saturation of soft X-rays.

Unfortunately, the RHESSI satellite did not record data related to this solarflare because it entered the Earth’s shadow soon after the flare occurred.

References

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Aartsen, M.G., Ackermann, M., Adams, J., Aguilar, J.A., Ahlers, M., Ahrens, M., Altmann,D., Andeen, K., Anderson, T., Ansseau, I., et al.: 2017, The IceCube Neutrino Observatory:instrumentation and online systems. Journal of Instrumentation 12, P03012. DOI. ADS.

Abe, K., Abe, K.E., Aihara, H., Aimi, A., Akutsu, R., Andreopoulos, C., Anghel, I., Anthony,L.H.V., Antonova, M., Ashida, Y., et al.: 2018, Hyper-Kamiokande Design Report. ADS.arXiv.

Acciarri, R., Acero, M.A., Adamowski, M., Adams, C., Adamson, P., Adhikari, S., Ahmad,Z., Albright, C.H., Alion, T., Amador, E., et al.: 2015, Long-Baseline Neutrino Facility


https://ui.adsabs.harvard.edu/#abs/2014arXiv1412.5106I/abstracthttp://arxiv.org/abs/1412.5106https://doi.org/10.1088/1748-0221/12/03/P03012https://ui.adsabs.harvard.edu/#abs/2017JInst..12P3012A/abstracthttps://ui.adsabs.harvard.edu/#abs/2018arXiv180504163H/abstracthttp://arxiv.org/abs/1805.04163

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Figure 11. Light curves of the solar flare occurring on October 29, 2003. Gray bands showthe search windows as same in Figure 5. The vertical dotted lines show the peak timing foreach channel. As described in the appendix text, both hard X-ray and line γ-ray are not usedto determine the time window since their light curves were contaminated. The solid black lineon third panel from top shows hard X-ray light curve using imaging method. The solid blackline on fourth panel from top shows time profile of line γ-ray flux which is same as Fig.6(c) inKurt et al., 2017.

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Figure 12. Light curves of the solar flare occurred on January 20, 2005. Gray bands showthe search windows as same in Figure 5. The vertical dotted lines show the peak timing foreach channel.

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Figure 13. Light curves of the solar flare occurring on November 4, 2003. Gray bands showthe search windows as same in Figure 5. The vertical dotted lines show the peak timing foreach channel. Because of high intensity, the soft X-ray flux was saturated.


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https://doi.org/10.1016/j.astropartphys.2012.02.011https://ui.adsabs.harvard.edu/#abs/2012APh....35..685W/abstract

1 Introduction1.1 Neutrino Production in Solar Flare1.2 Brief History of Neutrinos Associated with Solar Flare1.3 Time Window for Neutrino Search

2 Overview of Electromagnetic Observations Related to Accelerated Particles2.1 Soft X-rays2.2 Hard X-rays2.3 -rays

3 Analysis Method3.1 Soft X-rays (GOES)3.2 Hard X-ray (RHESSI)3.3 Line -rays (RHESSI)3.4 GEOTAIL Satellite Hard X-ray Events

4 Results and Discussion4.1 Results4.2 Applications to Neutrino Detectors

5 Conclusions and Future ProspectsA Line -ray Light Curves for Solar FlaresB Comment on the Solar Flare Occurring on October 29, 2003C Light Curves for the Largest Solar Flare; November 4, 2003

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