SEARCH FOR NEUTRINOS IN SUPER-KAMIOKANDE ASSOCIATED WITH GRAVITATIONAL-WAVE EVENTS GW150914 AND GW151226

On 2015 September 14 at 09:50:45 UT, LIGO identified the first evident signal of a gravitational wave as a coincidence of two chirp signals observed by two distant independent interferometers (Abbott et al. 2016c). It has been suggested that the gravitational-wave event, namely, GW150914, was due to a merger of two black holes having masses of approximately 30 to 60 solar mass. After the announcement of the discovery by the LIGO team on 2016 February 11, many efforts to search for coincidences in the observational data in complementary experiments have been made (Abbott et al. 2016b); no astronomical counterpart has been identified, except a weak coincident excess reported by Fermi GBM ∼0.4 s after GW159014 (Connaughton et al. 2016), although this result is controversial (Greiner et al. 2016). Because of the tremendous energies involved and the unknown nature of the region of the black hole merger, it is possible to imagine coincident production of neutrinos. For example, the possibility of high-energy neutrino emission from relativistic jets when an accretion disk is formed around the source has been discussed (Eichler et al. 1989; Woosley 1993). IceCube and ANTARES have searched for high-energy neutrinos above ∼100 GeV in a time window of ±500 s around the real-time alert for GW150914 issued by LIGO, but reported no positive evidence for coincident neutrino events (Adrián-Martínez et al. 2016).

Following this event the second gravitational-wave signal, GW151226, was reported (Abbott et al. 2016a). It was observed on 2015 December 26 at 03:38:53 UT and was predicted to be due to a merger of two black holes having masses of 14.2 and 7.5 solar mass. KamLAND reported no positive coincident neutrino events for both of these two gravitational-wave events (Gando et al. 2016).

We report the results of a search for neutrinos in coincidence with GW150914 and GW151226 in Super-Kamiokande (SK). It is a water Cherenkov detector located at 2700-meters-water-equivalent underground in Kamioka, Japan. A detailed description of the detector can be found elsewhere (Fukuda et al. 2003). In this detector, the Cherenkov ring pattern reconstruction identifies final state electron and muon direction and energy from which we infer the neutrino direction, flavor, and energy. Our search includes the neutrino energy region of 1–100 GeV, which is not covered by the previous searches with neutrino telescopes. Moreover, SK has unique sensitivity to MeV neutrinos either from a core-collapse supernova in the Local Group or from some other similarly efficient mechanism. The neutrino events with reconstructed energies above 100 MeV are categorized as the "high-energy data sample" in SK and are typically used to study atmospheric neutrinos and search for proton decay. Neutrino events with reconstructed energies down to 3.5 MeV are categorized as the "low-energy data sample" and are typically used to study solar neutrinos and to search for core-collapse supernova neutrinos. The background events in the search for astrophysical neutrinos for the high-energy data sample are almost entirely atmospheric neutrinos, while radioactive impurities, spallation products from cosmic-ray muons, atmospheric and solar neutrinos are the main backgrounds in the low-energy data sample.

2.1. High-energy Data Sample

2.2. Low-energy Data Sample

There are two neutrino event selection algorithms for the low-energy data sample: the supernova relic neutrino (SRN) search (Bays et al. 2012) and the solar neutrino analysis (Abe et al. 2016). The largest cross section in this energy region is the inverse beta decay of electron antineutrinos (${\bar{\nu }}_{e}+p\to {e}^{+}+n$). Neutrino elastic scattering ($\nu +{e}^{-}\to \nu +{e}^{-}$) is sensitive to all neutrino flavors, but dominated by electron neutrinos. The observable signal in the detector originates from the charged particle, i.e., positron or electron in these interactions. There are other charged-current and neutral-current interactions with ¹⁶O nuclei that are subdominant.

The target energy range for the SRN analysis is from 15.5 to 79.5 MeV. Backgrounds relevant to the SRN analysis are atmospheric neutrino interactions (decay electrons from invisible muons, neutral-current interactions, low-energy pions and muons), solar neutrino interactions, and spallation products from cosmic-ray muons. The detailed analysis method and the reduction criteria are described in Bays et al. (2012), which, as well as this analysis, does not require a neutron capture in delayed coincidence (Zhang et al. 2015). After all the reduction steps, no neutino events are observed for the SRN analysis in the ±500 s search window around both GW150914 and GW151226. The expected number of background events in a 1000 s time window is (1.45 ± 0.09) × 10⁻³ based on 1888.9 days of data. The absence of neutrino events in this energy region excludes the scenario of a coincidence between the gravitational-wave and a core-collapse supernova within a distance of 260 kpc at 90% C.L.

The energy region considered in the solar neutrino analysis is lower than that of the SRN search, from 3.5 to 19.5 MeV. The fluence calculation will be applied below 15.5 MeV to avoid double counting with the SRN sample. After applying all the reduction steps for the solar neutrino analysis, four neutrino event candidates remain within the ±500 s search window around the LIGO detection time of GW150914, while no neutrino event candidates remain around GW151226. Figure 1 shows the detection time and the energy of neutrino event candidates passing the reduction cuts for GW150914 (left) and the energy spectrum of the remaining events, which is consistent with the background spectrum (right). On 2015 May 1, the trigger threshold was changed from 34 observed PMT signals within 200 ns to 31 hits (Yamada et al. 2009; Nakano 2016). Using the data after that (306.6 days of livetime) we expect (2.90 ± 0.01) events due to random coincidence for each 1000 s time window centered around a gravitational-wave incident. For GW150914 the probability of seeing four or more events passing the reduction cuts is calculated to be 33.0%, the probability of seeing none for GW151226 is 5.5%. Therefore, our findings are consistent with all of these neutrino event candidates being background.

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The background events in the solar neutrino analysis consist mainly of radioactive impurities below 5.5 MeV and spallation products above 5.5 MeV. The first and second events are most likely remaining spallation events caused by ¹⁶N (Zhang et al. 2016). The transverse distance between each event and its preceding muon are 1.7 and 1.2 m, the timing differences between the event and the preceding muon are 10.77 and 17.38 s, and the energies are above 6 MeV, making these consistent with spallation production. Additionally, the likelihood value of the spallation product falls close to the cut value applied in the reduction steps. The expected number of background events above 5.5 MeV that survive the reduction cuts is (1.169 ± 0.007); therefore the probability of two or more events remaining in our sample is 32.6%. The third event is most likely a radioactive background event caused by the beta decay of ${}^{214}\mathrm{Bi}$ from the radon decay chain. This is the dominant background near this energy region (3.6 MeV; Nakano 2016). The expected number of background events below 5.5 MeV that survive the reduction cuts is (1.735 ± 0.008); therefore, the probability that one or more events remains in our sample is 82.4%. The fourth event is most likely a solar neutrino event because the reconstructed direction is close to the solar direction (cosine of the angle between them ($\cos {\theta }_{\mathrm{Sun}}$) is 0.96 with an angular resolution of 22.9°) and its recoil electron kinetic energy is 11.3 MeV, which is typical for solar neutrino event. The main background of this energy region is spallation events; however, the chance of accidental coincidence of these background events with the solar direction is quite small since the reduction of spallation events are already fairly efficient. The expected number of solar neutrino events is (0.229 ± 0.005) from the latest solar neutrino measurement in SK. The probability of one or more solar events remaining in our sample is 20.5%.

Figure 2 shows the sky map using the reconstructed direction of the charged particle in the remaining four events associated with GW150914, along with the 90% CL contour for the location of GW150914 according to LALInterference data (Abbott et al. 2016b). The angular resolution of the charged particle is calibrated by electron LINAC (Nakahata et al. 1999). Because the energy spectrum and species of the incoming neutrinos is not known, an estimate of the angular uncertainty on the direction of the incoming neutrino is difficult; however, the direction of the charged particle has a strong correlation with the incident neutrino direction for the case of neutrino–electron scattering, while a very weak anti-correlation exists in the case of inverse beta decay (Strumia & Vissani 2003).

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2.3. LVT151012

The number of neutrino candidate events observed in the search window can be converted to an upper limit on neutrino fluence for both of the gravitational-wave events. This is done separately for the low-energy, FC+PC, and UPMU data sets. The procedure used to extract the fluence limit will be described briefly here, but uses the same prescription laid out in Thrane et al. (2009), which follows from Swanson et al. (2006).

For the FC and PC data set, the neutrino fluence can be calculated using Equation (1):

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{\mathrm{FC},\mathrm{PC}}=\displaystyle \frac{{N}_{90}}{{N}_{T}\int {{dE}}_{\nu }\sigma ({E}_{\nu })\epsilon ({E}_{\nu })\lambda ({E}_{\nu }^{-2})},\end{eqnarray} \tag{ 1 }$$

where N₉₀ is the 90% C.L. limit on the number of neutrino events in the search window calculated using a Poisson distribution with a background, N_T is the number of target nuclei, σ is the combined cross section for all interactions particular to that neutrino flavor, is the efficiency for measuring the neutrino event in the detector, and λ is the number density of the events for a given energy spectrum with an index of −2. This spectral index is commonly used for astrophysical neutrinos accelerated by shocks (Gaisser et al. 1995). Since no neutrino candidate events pass cuts within the search window for the FC and PC data sets, we derive N₉₀ using ${N}_{90}=-\mathrm{ln}(0.1)=2.3.$ Fluence limits are calculated separately for each neutrino species by considering the cross section and detection efficiency specific to the neutrino type.

Cross sections from NEUT 5.3.5 (Hayato 2009) are used in the calculation of Equation (1). To determine the detector efficiency, mono-energetic neutrino interaction files produced with NEUT 5.3.5 are passed as inputs to the SK Monte Carlo detector simulation. The resulting output files then undergo the same reconstruction and reduction procedures that are applied to the data. The efficiency is determined by calculating the fraction of remaining events after reduction and selection cuts. The energy range of 100 MeV–10 GeV is considered.

For the UPMU data set, the neutrino fluence is calculated using Equation (2):

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{\mathrm{UPMU}}=\displaystyle \frac{{N}_{90}}{{A}_{\mathrm{eff}}(z)\int {{dE}}_{\nu }P({E}_{\nu })S(z,{E}_{\nu })\lambda ({E}_{\nu }^{-2})}.\end{eqnarray} \tag{ 2 }$$

Here, fluence depends on the zenith-dependent effective area (A_eff(z)), where z is the zenith angle of the incoming neutrino, the probability for a neutrino to create a muon with energy greater than ${E}_{\nu }^{\min }$ (P(E_ν)), the shadowing of the neutrinos due to interactions in the Earth ($S(z,{E}_{\nu })$), and the number density (λ) of the neutrino events for the given energy spectrum with an index of −2. Again, since there are no neutrino candidate events within the search window for the UPMU data set, we use N₉₀ = 2.3. The energy range considered for the UPMU fluence is 1.6 GeV–100 PeV.

For the low-energy data sample, the neutrino fluence calculation is similar to Equation (1); however, since there is no reason to assume a power spectrum nor any reliable theory of neutrino emission spectrum in this energy region, we set the neutrino energy spectrum to have an index of 0, which is flat. Therefore, the fluence limit is calculated with the assumption of flat spectrum of neutrino energy from 3.5 to 75 MeV as shown in Equation (3):

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{\mathrm{lowe}}=\displaystyle \frac{{N}_{90}}{{N}_{T}\int {{dE}}_{\nu }\lambda ({E}_{\nu })\sigma ({E}_{\nu })R({E}_{e},{E}_{\mathrm{vis}})\epsilon ({E}_{\mathrm{vis}})},\end{eqnarray} \tag{ 3 }$$

where R is the response function from electron or positron energy (E_e) to the kinetic energy in SK (E_vis). The response function and the detection efficiency () is calculated using the SK detector Monte Carlo simulation. N₉₀ is calculated to be 5.41 (2.30) from the remaining four (zero) neutrino candidate events compared to the expected 2.90 events in this data sample for GW150914 (GW151226). The accidental coincidence of solar neutrinos with a gravitational-wave signal are easily reduced by a factor of 0.9 with an angular cut on the recoil electron's direction ($\cos {\theta }_{\mathrm{Sun}}\gt 0.8$). In this case, the number of remaining neutrino candidate events is three (zero) compared to 2.46 expected events, and N₉₀ is 4.64 (2.30) for GW150914 (GW151226). In addition, since any emission models for low-energy neutrinos are not well motivated, we express the fluence limit that is calculated for monochromatic neutrino energy E_ν obtained by replacing λ(E_ν) with a delta function $\delta (E-{E}_{\nu })$. The fluence limits for both GW events are shown in Figure 3.

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Table 1 shows the fluence limit results for the FC+PC, UPMU, and low-energy data sets for both gravitational-wave events separately, as well as for both events combined. To calculate the combined neutrino fluence limit, the N₉₀ is calculated using the search windows around both gravitational-wave events and is then weighted by the number of gravitational-wave events, which in this case is two. For the UPMU events, fluence is dependent on zenith angle, and thus we show the upper limit of neutrino fluence from UPMU events as a sky map of possible fluence limits in Figure 4. Since the gravitational-wave events are not well localized, a combined fluence limit for the UPMU data set is not reported. The UPMU upper limit fluence values range from (14–37) cm⁻² for neutrinos and from (19–50) cm⁻² for antineutrinos, depending on the direction of the gravitational-wave event. We convert our UPMU fluence limit to an upper limit on total energy radiated in neutrinos by convolving Equation (2) by the energy spectrum and weighting by $4\pi {d}_{\mathrm{GW}}^{2}$ where d_GW is the distance between the detector and the gravitational-wave source. The resulting upper limit on total energy is ${E}_{\nu }^{\mathrm{tot}}\sim (1\mbox{--}6)\,\times \,{10}^{55}$ erg for GW150914 assuming the LIGO-determined distance of 410 Mpc and ${E}_{\nu }^{\mathrm{tot}}\sim (2\mbox{--}7)\,\times \,{10}^{55}$ erg for GW151226 assuming the LIGO-determined distance of 440 Mpc. For comparison, the total energy radiated in gravitational waves by GW150914 is ∼5 × 10⁵⁴ erg (Adrián-Martínez et al. 2016), and the total energy radiated in neutrinos from a typical supernova is ∼ a few ×10⁵³ erg (Bethe 1990).

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Table 1.  Limits at 90% C.L. on the Fluence of Neutrinos from GW150914 and GW151226 Given a Spectral Index of −2 and an Energy Range of 100 MeV–10 GeV for the FC+PC and 1.6 GeV−100 PeV for the UPMU Data Samples, and a Flat Spectrum for the Low-energy Data Sample whose Energy Region Is from 3.5 to 75 MeV

	GW150914 Φν (cm−2)	GW151226 ${{\rm{\Phi }}}_{\nu }$(cm−2)	Combined Φν (cm−2)
	From FC+PC only
νμ	5.6 × 104	5.6 × 104	2.8 × 104
${\bar{\nu }}_{\mu }$	1.3 × 105	1.3 × 105	6.5 × 104
νe	4.8 × 104	4.8 × 104	2.4 × 104
${\bar{\nu }}_{e}$	1.2 × 105	1.2 × 105	6.0 × 104
	From UPMU only
νμ	14–37	14–37	...
${\bar{\nu }}_{\mu }$	19–50	19–50	...
	From low-energy only
${\bar{\nu }}_{e}$	4.2/3.6 × 107	1.8/1.8 × 107	1.6/1.5 × 107
νe	3.0/2.6 × 109	1.3/1.3 × 109	1.2/1.1 × 109
νx	1.9/1.6 × 1010	8.1/8.1 × 109	7.0/7.0 × 109

Note. The values on the left/right in the low-energy sample show the fluence limit without/with the solar direction cut, respectively.

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We search for possible neutrino signals coincident with GW150914, GW151226, and LVT151012 in the SK detector using a wide energy range from 3.5 MeV to 100 PeV. In the high-energy data sample, three neutrino interaction categories are considered: FC, PC, and UPMU. No neutrino candidate events are found in the search window of ±500 s around the LIGO detection time for both gravitational-wave signals.

Low-energy neutrino events are also examined using the SRN and the solar neutrino data samples in the same search time window. No neutrino candidate events are found in the SRN data sample for both gravitational-wave signals. No neutrino candidate events are found in the solar neutrino data for GW151226; however, four neutrino candidate events are found for GW150914. These four events are consistent with the estimated background, with one of them possibly associated with solar neutrinos.

The obtained neutrino fluence limits give the most stringent limits for neutrino emission in the energy region below ∼100 GeV, assuming an E⁻² spectrum from GW150914 and GW151226. The absence of MeV neutrino emission in the solar neutrino and the SRN data samples is inconsistent with the source of the gravitational-wave signals being a nearby core-collapsed astronomical object.

We gratefully acknowledge the cooperation of the Kamioka Mining and Smelting Company. The Super-Kamiokande experiment has been built and operated from funding by the Japanese Ministry of Education, Culture, Sports, Science and Technology, the U.S. Department of Energy, and the U.S. National Science Foundation. Some of us have been supported by funds from the Korean Research Foundation (BK21 and KNRC), the National Research Foundation of Korea (NRF-20110024009), the European Union (H2020 RISE-GA641540-SKPLUS), the Japan Society for the Promotion of Science, the National Natural Science Foundation of China under grant No. 11235006, and the Scinet and Westgrid consortia of Compute Canada.