Search for Solar Flare Neutrinos with the KamLAND detector

Solar flares are the largest explosions in the solar system, releasing energy between $10^{28}$–$10^{33}$ erg in only tens of minutes (Schrijver et al., 2012). The mechanism of solar flares can be described as a rapid conversion of magnetic energy to thermal and kinetic energy of charged particles by reconnection of the magnetic field on the solar surface (Parker, 1957). Observations of electromagnetic signals, ranging from radio waves to $\gamma$-rays at 100 MeV, and neutrons emitted during solar flares contribute to the current understanding of this phenomenon (Benz, 2008).

In the standard flare model, solar flares accelerate protons to more than 300 MeV and then nuclear reactions of accelerated protons generate pions in the solar atmosphere (Hudson & Ryan, 1995). Decay of these pions produces high energy ($>$70 MeV) $\gamma$-rays and MeV-scale neutrinos. Thus, neutrino production is expected in the standard solar flare model and the properties of these solar flare neutrinos depend on the initial accelerated proton spectrum and flux (Kocharov et al., 1991).

In recent decades, neutrino emission models from solar flares have been developed and such models inform the feasibility of detecting solar flare neutrinos. Fargion (2004) predicted that detection of neutrinos from a large solar flare ($>10^{32}$ erg) was feasible with Super-Kamiokande and IceCube. Recent updates however, predict no possibility to detect solar flare neutrinos even with Hyper-Kamiokande (Takeishi et al., 2013). Another study (de Wasseige, 2016) predicts 398–770 $\mathrm{cm}^{-2}$ neutrino fluence at Earth in the 10–100 MeV range, which corresponds to $\ll 1$ electron scatterings in KamLAND. From these recent studies (Takeishi et al., 2013; de Wasseige, 2016), it is clear that MeV neutrino observation from a single flare is hardly feasible. However, by searching for a statistical excess in coincidence with a large number of solar flares, it may be possible to detect solar flare neutrinos. Such a detection can provide an additional probe to understand the particle acceleration on the solar surface.

There have been several efforts to experimentally search for solar flare neutrinos. The Homestake experiment reported a small excess of events correlated with a large solar flare in 1991 (Davis, 1994). On the other hand, KAMIOKANDE II and LSD observed no excess of events associated with different solar flares (Hirata et al., 1990; Aglietta et al., 1991). SNO has performed a coincidence search with 842 solar flares measured from radiation from 3 keV to 17 MeV with the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and found no correlations (Aharmim et al., 2014). In 2019, an analysis by Borexino improved the upper limits on neutrino fluence and excluded the Homestake parameter space (Agostini et al., 2021). In this analysis, the Borexino collaboration assumed that the neutrino flux is proportional to X-ray intensity and used 472 M- and X-class solar flares selected from the Geostationary Operational Environmental Satellite (GOES) database. The aforementioned studies are sensitive to neutrinos in the 1–100 MeV range. Recently, IceCube reported the first search for GeV-scale neutrinos related to intense $\gamma$-ray solar flares and constrained some of the parameter space associated with theoretical predictions for the neutrino flux (Abbasi et al., 2021).

In this paper, we present a search for solar flare neutrinos using the KamLAND data taken from 2002 March to 2019 September, which includes Solar cycle 23 and 24. KamLAND is a 1 kton liquid-scintillator detector which is sensitive to neutrinos in the energy range between 1 MeV and a few GeV. However, in this study we focus on 1–35 MeV neutrinos. For experimental studies of solar flare neutrinos, flare selection and the time window for coincidence studies are important. We discuss these in Sec. 2. Section 3 provides an overview of the KamLAND detector and the two detection channels for our solar flare neutrino search. The scheme of the coincidence analysis is presented in Sec. 4 and 5. The analysis results are converted to fluence upper limits in Sec. 6.

In a solar flare, neutrinos are generated from charged pion decay. Neutral pion decay emits 70–100 MeV $\gamma$-rays. It is natural to identify solar flares and set the coincidence time window from the $\gamma$-ray measurements (de Wasseige, 2016). IceCube applied this strategy with the $\gamma$-ray data taken by the Fermi-LAT satellite (Abbasi et al., 2021).

However, since the Fermi-LAT satellite was launched in 2008, solar $\gamma$-ray burst observations are not available for the 23rd solar cycle, including the largest (class X28) flare on record that occurred on 2003 Nov 4. For this reason, we apply another strategy to identify solar flares and the timing of particle acceleration in solar flares.

Hard X-ray is an alternative channel to identify flares and set the time windows. Hard X-ray emission is generated from bremsstrahlung of non-thermal electrons accelerated to relativistic velocity by a solar flare. Shih et al. (2009) reported that there is a close proportionality between line $\gamma$-ray and hard X-ray fluence from solar flares. The existence of line $\gamma$-rays is indirect evidence of hadronic interactions in a solar flare, which is one of potential sources of neutrino emission.

The light curve of solar flare X-rays differentiated by time is expected to be similar to the light curve of hard X-rays through the Neupert effect (Neupert, 1968; Dennis & Zarro, 1993). The Neupert effect is an experimentally known effect that the derivative of soft X-ray light curves from solar flare tend to have the same timing response as microwave emission. It can also be applied in the case of hard X-ray instead of the microwave emission. Thus, we can find the time window for the solar flare neutrino search using the differential soft X-ray lightcurves from GOES satellites.

The advantage of GOES soft X-ray profile compared to RHESSI hard X-ray/$\gamma$-ray profile or Fermi-LAT $\gamma$-ray profile is the length of the observation and the availability of stable data. With the method mentioned above, we can use the most abundant dataset of the solar flare since 1975, which covers the 23rd and 24th solar cycles, and set the flare time window even if the hard X-ray and $\gamma$-ray observation are not available during the solar flare. This method is suggested and validated in Okamoto et al. (2020).

Based on Okamoto et al. (2020), we determine the flare time window as follows: (i) calculate the differential X-ray light curve, (ii) search for the peak of the differential curves, (iii) define the time window starting from the nearest zero coefficient before the peak and ending at the nearest zero coefficient after the peak. The red curve in Figure 1 is one of the examples for our flare time window. The duration time of this example is 1,143 sec.

We obtain the flare list from the GOES X-ray database at National Oceanic and Atmospheric Administration. After the X- and M-class selection, which was also used in the Borexino analysis (Agostini et al., 2021), there were 1342 flares with a total X-ray intensity of $639.3\times 10^{-4}$ W/m² from 2002 March to 2019 September. For the coincidence analysis with the KamLAND data, all time windows were required to be in a period of operation in which the livetime to running time ratio of the detector was more than 95%. The KamLAND livetime is defined as the integrated period of time that the detector was sensitive to neutrinos and includes corrections for calibration periods, detector maintenance, daily run switch, etc. Applying these requirements, we found 614 solar flares remained. The distributions of the duration and intensity of these flares are shown in Figure 2 and Figure 3, respectively. The average length of the 614 time windows is 1,028 s. The duration time described in Figure 1 is almost the mean value. The integrated intensity is $303.0\times 10^{-4}$ W/m², which is 25 times larger than the flare coincident with the Homestake excess and 1.7 times larger than the flares used in the Borexino analysis (Agostini et al., 2021).

The KamLAND detector is a large-volume neutrino detector, which is located approximately 1 km underground under Mt. Ikenoyama in Kamioka, Japan. KamLAND consists of an outer water-Cherenkov detector and an inner scintillation detector. The water-filled outer detector (OD), housed in a 10 m-radius $\times$ 20 m-high cylindrical vessel, provides shielding from external $\gamma$-ray backgrounds and an active muon counter. The OD was instrumented with 225 20-inch Photo Multiplier Tubes (PMTs) before a refurbishment in 2016 and 140 20-inch PMTs after the refurbishment (Ozaki & Shirai, 2017). The inner detector is a 9 m-radius stainless steel spherical tank with 1325 17-inch PMTs and 554 20-inch PMTs mounted on the inner surface. The main volume of the inner detector is 1 kton liquid scintillator supported by a 6.5 m-radius nylon/EVOH balloon installed at the center of the stainless steel tank. This nylon/EVOH balloon is called the outer balloon. Outside the outer balloon is filled with non-scintillating buffer oil. Another smaller nylon balloon for KamLAND-Zen is called the inner balloon and is described later. The details of the KamLAND detector are described in Suzuki (2014).

KamLAND began data taking in March 2002. From August 2011, KamLAND started the KamLAND-Zen phase to search for the neutrinoless double-beta decay of ¹³⁶Xe using a nylon balloon (inner balloon) installed at the center of the detector; this inner balloon is filled with xenon-loaded liquid scintillator (Gando et al., 2016). During the initial phase, known as KamLAND-Zen 400, which ran from August 2011 to September 2015, the inner balloon radius was 1.5 m and the mass of xenon was about 400 kg. In 2018 May, the KamLAND-Zen experiment was upgraded to the so-called KamLAND-Zen 800 phase, with an enlarged inner balloon of radius 1.9 m and double the amount of xenon (about 800 kg) for a higher sensitivity search (Gando, 2020; Gando et al., 2021). For the KamLAND-Zen periods, the regions with xenon-loaded scintillator were excluded from the effective volume for the neutrino search to suppress backgrounds from the xenon nuclei, nylon balloon, and supporting structures.

KamLAND has multiple reaction channels to detect neutrinos. We use the following two channels, neutrino-electron elastic scattering (ES), $\nu+e^{-}\to\nu+e^{-}$, and inverse-beta decay (IBD), $\bar{\nu}_{e}+p\to e^{+}+n$. ES is sensitive to all flavor of neutrinos, though the cross section depends on the neutrino flavor. This channel does not provide a measurement of the neutrino energy, though the energy of the scattered electron provides a lower bound. IBD is sensitive only to electron anti-neutrinos above 1.8 MeV. The IBD cross section is roughly ten times larger than the ES cross section. In addition, the IBD signal has advantages to suppress backgrounds thanks to a delayed coincidence measurement. The positron annihilates with an electron, emitting two 511 keV $\gamma$-rays. The positron and two $\gamma$-rays are observed as one event called the prompt event. The incident electron anti-neutrino energy, $E_{\nu}$, can be reconstructed from the prompt scintillation as $E_{\nu}\simeq E_{\mathrm{p}}+0.8\,\mathrm{MeV}$, where $E_{\mathrm{p}}$ is the energy of the prompt signal. With the mean capture time about 207 $\mu$s, the neutron captures on a proton (carbon) emitting a 2.2 (4.9) MeV $\gamma$-ray, which is called the delayed event. Exploiting time-spatial correlation between the prompt and delayed events, we can observe electron type anti-neutrinos in an almost background free condition.

Although there are some theoretical predictions of the spectrum of solar flare neutrinos (Kocharov et al., 1991; Fargion, 2004), it has not been experimentally measured. Keeping the assumption of the monochromatic signal, we converted $\alpha^{\mathrm{ES}}_{90}$ into an upper limit on neutrino fluence, $\Phi^{\rm ES}(E_{\nu})$, as

for the ES studies, where $N_{\mathrm{e}}$ is the number of electrons in the 6 m-radius spherical volume: $2.4\times 10^{32}$, $E_{\mathrm{e}}$ is the kinetic energy of recoil electron, $\sigma(E_{\nu},E_{\mathrm{e}})$ is the cross section of electron scattering with the incident neutrino of energy $E_{\nu}$, and $T_{\rm max}$ is the maximum $E_{\mathrm{e}}$. For the IBD studies, the upper limit on neutrino fluence, $\Phi^{\rm IBD}(E_{\nu})$, was obtained from

where $N_{p}$ is the number of protons in the 6 m-radius spherical volume: $(5.98\pm 0.13)\times 10^{31}$, $\sigma(E_{\nu})$ is the total cross section of IBD from Strumia & Vissani (2003).

The fluence upper limit per flare is shown in Figure 9 with the assumption that all the flares have the same neutrino luminosity, which is discussed in SNO analysis (Aharmim et al., 2014). The allowed fluence region from the Homestake excess (Aharmim et al., 2014) is shown in the purple band. The upper limit by SNO (Aharmim et al., 2014) and Borexino (Agostini et al., 2021) are shown as purple and green curves, respectively.

Adopting another normalization that the solar flare neutrino luminosity is proportional to the X-ray intensity, the fluence upper limits were scaled to the Homestake flare’s intensity (X12) as

and shown in Figure 10. The last term in Equation (7) represents the scaling factor from the flares analyzed in this work to the Homestake flare. The upper limit by Borexino (Agostini et al., 2021) is shown as green curve after scaling to the X12 flare. Here, it is difficult to directly compare the results from KAMIOKANDE II (Hirata et al., 1990) and SNO (Aharmim et al., 2014) in this normalization because the flare catalogue of those studies are different from this study and we do not have sufficient X-ray measurements for the corresponding flares.

In both normalizations, the 90% C.L. upper limits from this work exclude the entire region of the parameter space associated with the Homestake event excess for the large solar flare in 1991, and are the strictest upper limits on the solar flare neutrino fluence of all flavors in the neutrino energy range of 0.4–35 MeV.

We observe no evidence for neutrinos associated with solar flares in KamLAND. This work places the strictest upper limits on fluence normalized to the X12 flare with the assumption that neutrino fluence is proportional to the X-ray intensity. At 20 MeV, the obtained 90% C.L limits are $8.4\times 10^{7}$ cm^-2 for electron anti-neutrinos and $3.0\times 10^{9}$ cm^-2 for electron neutrinos. The Homestake region is independently rejected by this result. To our knowledge, this is the first time to present the upper limit normalized to the flare intensity. We believe that this approach is useful to compare to results from other experiments and theoretical predictions.