Search for Neutrinos in Super-Kamiokande Associated with Gravitational Wave Events ^†

Abstract

We report the results from a search in Super-Kamiokande for neutrino signals coincident with gravitational-wave events using a neutrino energy range from $3.5$ MeV–100 PeV. We searched for coincident neutrino events within a time window of $\pm 500$ s around the gravitational-wave detection time. In this work, we report the number of events within the search-window and the $90\%$ confidence level upper limits on the neutrino fluence for each gravitational-wave event.

1. Introduction

1.1. Era of Multi-Messenger Astronomy

After the discovery of the gravitational wave from the black hole (BH) merger of GW150914 [1,2] by Advanced LIGO [3], the era of multi-messenger astronomy has started. The goals of multi-messenger observations are to understand an evolution of cosmic processes through a combination of observed signals. For this purpose, many efforts to search for coincidences in the observational data in complementary experiments have been made.

Since then, other BH-BH mergers (GW151226 [4], GW170104 [5], GW170814 [6], GW170608 [7]), as well as a neutron star (NS) merger (GW170817 [8]) have been observed by both Advanced LIGO and Advanced Virgo [9]. Currently, eleven GW events in total have been reported (including GW151012, GW170729, GW170809, GW170818, and GW170823) [10]. In the case of GW170817, the first joint detection of gravitational waves and electromagnetic radiation from a single source has been performed [11,12]. Soon after the observation of GW170817, a short gamma-ray burst (GRB170817A) that followed the merger of this binary was also detected by the Fermi GBM [13] and INTEGRAL [14]. In addition, many observations have been reported by X-ray [15,16] and radio bands [17,18], while no neutrino signal [19] consistent with the source has been found in follow-up searches.

1.2. Neutrino Detectors

Neutrinos from a binary merger (BH-BH or NS-NS) can open a new window for multi-messenger research since a mechanism for the neutrino emission from such mergers is unclear. Currently, several neutrino detectors have accumulated neutrino signals with various techniques. They can search for neutrino signals at any time around a gravitational event because they continuously take data observing the whole sky.

Several searches have been performed for the neutrino counterparts of either binary BH-BH merges or the binary NS-NS merger [19,20,21,22,23,24,25,26,27,28], as summarized in

Table 1. Summary of neutrino detectors and references for their searches.

Experiment	Typical Energy Range	Reference
Borexino	250 keV–15 MeV	[20]
KamLAND	$1.8$ MeV–111 MeV	[21]
Super-Kamiokande (SK)	$3.5$ MeV–100 PeV	[22,23]
Baikal-GVD	5 TeV–10 PeV	[24]
ANTARES	100 GeV–100 TeV	[19,25,26,27]
IceCube	100 GeV–100 TeV	[19,25,26,27]
Peirre Auger	100 PeV–25 EeV	[19,28]

. However, no significant neutrino signal has been observed by the neutrino telescopes, so far.

In this work, we report the results of a search in the Super-Kamiokande (SK) detector for neutrino signals associated with the gravitational events based on [22,23].

2. Super-Kamiokande Detector and Analysis Method

2.1. Detector

The Super-Kamiokande (SK) is a water Cherenkov detector located at 1000 m (2700 m water equivalent) below the top of Mt. Ikenoyama in Gifu prefecture, Japan [29]. It is a cylindrical stainless tank structure and contains 50 ktons of ultra-pure water. The detector is divided into two regions of its structure to separate them optically with a Tyvek sheet [30]; one is an inner detector (ID), and the other is an outer detector (OD). The ID serves as the target of interactions, and the OD is used to veto external cosmic ray muons. In the ID detector, 11,129 20-inch photomultipliers (PMTs) [31] are placed to observe the Cherenkov light produced by penetrating charged particles. On the other hand, 1885 8-inch PMTs are placed to detect cosmic ray muons. The configuration of the detector and its performance are described [29,30].

The first phase of the SK experiment (SK-I) began with the original configuration in April 1996. The later phases are described in

Table 2. Experimental phases of the Super-Kamiokande detector. ID, inner detector; OD, outer detector; PMT, photomultiplier.

Phase	SK-I	SK-II	SK-III	SK-IV
Period	April 1996–July 2001	October 2002–October 2005	July 2006–August 2008	September 2008–May 2018
ID PMTs [31]	11,149	5182	11,129	11,129
OD PMTs	1885	791	1885	1885
Photo coverage	$40\%$	$19\%$	$40\%$	$40\%$
Electronics	ATM [32,33]	ATM	ATM	Qbee [34,35]

. In May 2018, the forth phase of SK (SK-IV) ended the physics data taking to refurbish the detector for the next project of SK (SK-Gd).

The ring pattern of the observed Cherenkov light produced by charged particles enables the detector to reconstruct the initial interaction vertex and the energy. With this water Cherenkov technique, SK can study many interactions between neutrinos and nuclei, as well as proton decay in the energy range from a few MeV to tens of GeV inside the detector.

2.2. Analysis to Search for Neutrino Candidates

SK has sensitivity to a wide range of neutrino energies from a few MeV to $\sim 100$ PeV. Neutrino events below 100 MeV in SK are categorized as the “low energy sample” and typically used to study solar neutrinos [36] and to search for core-collapse supernova neutrinos [37]. In this energy range, radioactive impurities [38], spallation products from cosmic ray muons [39], atmospheric and solar neutrinos are the main background for the coincidence search. Above 100 MeV, neutrino events are categorized as “high energy samples” and typically used to study atmospheric neutrinos [40] and to search for proton decays. This sample consists of three distinct topologies [41]: fully-contained (FC), partially-contained (PC), and upward-going muon (UPMU). In this energy range, only atmospheric neutrinos are the main background. The details of these analyses can be found in [36,37,40,41].

In order to search for a neutrino candidate event, we selected a search window of $\pm 500$ s around the detection time of each gravitational wave event. The expected background rate within this search window, as well as the typical energy range of each sample are summarized in

Table 3. Number of expected background events within a search window of 1000 s for all samples. In order to estimate the rate, we used $306.1$ days of SK data for the solar sample, 2887 days for the relic sample, and 2976 days for the fully-contained (FC), partially-contained (PC), and upward-going muon (UPMU) samples [23].

Sample Name	Typical Energy Range	Expected Background Rate (Event/(1000 s))
Solar	$3.5$–$15.5$ MeV	$2.90\pm 0.01$
Relic	$15.5$–$100.0$ MeV	$(1.93\pm 0.08)\times {10}^{-3}$
FC	100 MeV–10 GeV	$(9.36\pm 0.06)\times {10}^{-2}$
PC	100 MeV–10 GeV	$(7.52\pm 0.23)\times {10}^{-3}$
UPMU	$1.6$ GeV–100 PeV	$(1.64\pm 0.02)\times {10}^{-2}$

.

3. Neutrinos from Black Hole-Black Hole Mergers

3.1. Introduction

Searching for an electromagnetic counterpart is critically important for a gravitational wave event. In the case of GW150914, many searches for coincidence signals have been performed around the detection time of GW150914. Eventually, no astronomical counterpart with a BH-BH merger event has been observed except for a weak coincident excess reported by Fermi GBM of about $0.4$ s after GW150914 [42].

In general, there is no theory of neutrino generation associated with a BH-BH merger. However, some possibilities of high energy neutrino emission have been discussed; for example, relativistic jets when an accretion disk is formed around the source [43,44], or the synthesis of heavy elements with the accretion disk [45,46]. A search for neutrinos from BH-BH mergers gives the opportunity to obtain a more complete picture of emission processes.

3.2. Search for Neutrinos around GW150914/GW151226

We have carried out the search for neutrinos from both GW150914 and GW151226. After the reduction cuts, four events were found in the solar sample, while no event was found in either the atmospheric or relic samples within $\pm 500$ s around GW150914. Figure 1a shows the energy distribution as a function of time, and Figure 1b shows the energy distribution of remaining events together with the expected background spectrum. According to the background rate for the solar sample described in Table 3, the probability of finding four or more events passing the reduction cuts is calculated to be $33.0\%$.

Figure 2 shows the sky map using the reconstructed direction of the charged particle in the remaining four events, as well as the $90\%$ C.L. contour for the location of GW150914 [1]. In this analysis, we assumed all interaction occurred via electron-neutrino elastic scattering because of its strong correlation with the incident neutrino direction (very weak anti-correlation exists in the case of the inverse beta decay [47]). The angular resolution of the charged particle below $18.0$ MeV is calibrated by the electron LINAC [48].

For GW151226 [4], we did not find any event within $\pm 500$ s after the reduction cuts in any sample. The probability of finding no event passing the reduction cuts is $5.5\%$.

3.3. Neutrino Fluence Limit

The number of neutrino candidate events observed in the search window can be converted into an upper limit on neutrino fluence. In this analysis, the method developed in [49,50] was used. For the calculation, the $90\%$ C.L. limit on the number of neutrino events in the search window calculated using a Poisson distribution with a background, the number of events after the reduction cuts, the number of target nuclei in the detector, the total cross-section for all interaction based on NEUT 5.3.5 [51], the reduction efficiencies for each analysis sample and the detector response were considered. For both solar and relic samples, we used the energy spectrum with an index of zero since there was no reason to assume a power spectrum of neutrino emission in this energy region. For FC/PC/UPMU samples, we used the energy spectrum with an index of $-2$ because this index is commonly assumed for astrophysical neutrinos accelerated by shocks [52]. Only for the UPMU sample, the shadowing effect of neutrinos due to the Earth, as well as the dependence of the zenith angle of incoming neutrinos were additionally considered.

Table 4. Neutrino fluence limits at $90\%$ C.L. from GW150914, GW151226, and GW170817. The unit for the neutrino fluence is ${\mathrm{cm}}^{-2}$. For GW170817 (NS-NS merger), two energy spectrum of neutrino emission is used; one is the flat spectrum with an index of zero, and the other is the Fermi–Dirac distribution with an average energy of 20 MeV. The latter is described in round brackets.

Neutrino (Sample)	GW150914	GW151226	GW170817
${\nu }_{\mu }$ (FC +P C)	$5.6\times {10}^4$	$5.6\times {10}^4$	$5.6\times {10}^4$
${\overline{\nu }}_{\mu }$ (FC + PC)	$1.3\times {10}^4$	$1.3\times {10}^4$	$1.3\times {10}^4$
${\nu }_e$ (FC + PC)	$4.8\times {10}^4$	$4.8\times {10}^4$	$4.8\times {10}^4$
${\overline{\nu }}_e$ (FC + PC)	$1.2\times {10}^4$	$1.2\times {10}^4$	$1.2\times {10}^4$
${\nu }_{\mu }$ (UPMU)	14–37	14–37	${16.0}_{-0.6}^{+0.7}$
${\overline{\nu }}_{\mu }$ (UPMU)	19–50	19–50	${21.3}_{-0.8}^{+1.1}$
${\nu }_e$ (solar + relic)	$3.0\times {10}^9$	$1.3\times {10}^9$	$1.0\times {10}^9(3.4\times {10}^9)$
${\overline{\nu }}_e$ (solar + relic)	$4.2\times {10}^7$	$1.8\times {10}^7$	$1.2\times {10}^7(6.6\times {10}^7)$
${\nu }_x$ (solar + relic)	$1.9\times {10}^{10}$	$8.1\times {10}^9$	$6.3\times {10}^9(2.1\times {10}^{10})$

summarizes the $90\%$ C.L. limit on neutrino fluence obtained in this analysis. The obtained results gave the most stringent limits for neutrino emission in the energy range between $\sim 10$ MeV and 100 GeV (a comparison of fluence limits below 100 MeV was discussed in [53]).

4. Neutrinos from a Neutron Star Merger

4.1. Introduction

The electromagnetic counterparts for binaries of NS-NS or NS-BH have actively been discussed; for example, short gamma-ray burst [45,54], kilonova/micronova [55], and so on. Some theoretical predictions of neutrino emission via an NS merger have been proposed. A similar mechanism as for core-collapse supernova can produce neutrinos whose average energy is typically a few tens of MeV based on the recent numerical simulations [56,57,58].

Since the two-week-long electromagnetic counterpart after GW170817 was observed [59], ANTARES, IceCube, the Pierre Auger Observatory, and Baikal-GVDhave searched for neutrino signals with two different time windows [19,24]; one is $\pm 500$ s around the merger to search for neutrinos associated with prompt and extended gamma-ray emissions [60,61,62], and the other is 14 days after the merger to search for longer-lived emission processes [63].

4.2. Search for Neutrinos within ±500 s around GW170817

We searched for neutrinos within the window of $\pm 500$ s and found no event in relic/FC/PC/UPMU samples. For the solar sample, we note that we have performed the calibration of LINAC [48] from 3–22 August 2017. Fortunately, the physics run was operated at the time of GW170817. However, many low-energy events occurring near the surface of the LINAC pipes have been observed because radioactive impurities existed on the pipes in the water tank. In order to remove such additional background events occurring on the surface of the pipe, we additionally applied the calibration source cut to the solar sample [36]. Ultimately, no event was found in the solar sample. The probability of no event after the reduction cut is $5.5\%$. Using the null number for each sample, we obtained the neutrino fluence limits within $\pm 500$ s around GW170817. The results are summarized in Table 4. In addition to the energy spectrum of neutrino emission with an index of zero in the low energy sample, we also used another spectrum assuming a Fermi–Dirac distribution with an average energy of 20 MeV since such models are well studied based on the simulation [56,57].

4.3. The Following 14-Day Time Window

In order to search for longer-lived emission process, we searched for neutrinos in the 14-day window after GW170817. The effective lifetime of the window for each sample and the observed event, as well as the expected background event are summarized in

Table 5. Analysis results of the 14-day window search. Lifetime for each sample, the observed events within the lifetime, and the expected background event within the lifetime are described. As mentioned in the main text, we did not carry out the search in the solar sample due to the large amount of background due to radioactive impurities.

Sample Name	Lifetime	Observed Event (Event/Lifetime)	Expected Event (Event/Lifetime)
Solar	–	Many radioactive impurities	–
Relic	9.15	2	$1.53\pm 0.06$
FC	11.30	76	$91.44\pm 0.57$
PC	11.30	8	$7.35\pm 0.23$
UPMU	11.30	13	$16.05\pm 0.23$
UPMU (≤5${}^{\circ }$)	11.30	0	$(6.11\pm 0.04)\times {10}^{-2}$

.

As explained before, we observed many background events due to radioactive impurities in the water tank. Because of this, the quality of the event selection and reconstruction in the solar sample was not stable. Therefore, we did not use the solar sample in the 14-day time window. In the relic sample, we found two events on 24 August 2017 10:33:04 UTC and on 28 August 2017 14:36:34 UTC, where the expected background rate was $1.53\pm 0.06$. The probability of observing two or more events is $45.1\%$. In the FC/PC/PUMU samples, we found 76, 8, and 13 events within the 14-day time window, where their expected backgrounds were $91.44\pm 0.57$, $7.35\pm 0.23$, and $16.05\pm 0.23$, respectively. Therefore, no excess over the background was observed in any sample.

Figure 3 shows the sky map of the observed event within the following 14-day time window. Since the UPMU events were higher in energy than the other topologies, their angular resolution was better. Therefore, the detected lepton pointed back to the incoming neutrino with more accuracy, allowing for a smaller search cone [64]. With this method, we concentrated on a $\pm 5^{\circ }$ cone around the location of GW170817 and found no event in this cone in the 14-day time window.

5. Conclusions

We carried out coincidence searches in SK for neutrino signals with gravitational waves GW150914, GW151226, and GW170817 using a wide energy range from $3.5$ MeV–100 PeV. The analysis was performed within a time window of $\pm 500$ s, as well as 14 days after the merger. Four neutrino candidates were found within the $\pm 500$ s time window for GW150914. These were consistent with the estimated background. For GW151226 and GW170817, no event was observed in the $\pm 500$ s window. For the 14-day time window of GW170817, no significant neutrino signal was observed over the expected background. The $90\%$ C.L. limits on neutrino fluence were determined considering the detector performance. As mentioned, more details about this study can be found in [22,23].