All-sky Search for High-Energy Neutrinos from Gravitational Wave

Event GW170104 with the Antares Neutrino Telescope

A. Albert1, M. Andre2, M. Anghinolfi3, G. Anton4, M. Ardid5, J.-J. Aubert6, T. Avgitas7,B. Baret7, J. Barrios-Martı8, S. Basa9, B. Belhorma10, V. Bertin6, S. Biagi11,

R. Bormuth12,13, S. Bourret7, M.C. Bouwhuis12, H. Branzas14, R. Bruijn12,15, J. Brunner6,J. Busto6, A. Capone16,17, L. Caramete14, J. Carr6, S. Celli16,17,18, R. Cherkaoui El

Moursli19, T. Chiarusi20, M. Circella21, J.A.B. Coelho7, A. Coleiro7,8, R. Coniglione11,H. Costantini6, P. Coyle6, A. Creusot7, A. F. Dıaz22, A. Deschamps23, G. De Bonis17,

C. Distefano11, I. Di Palma16,17, A. Domi3,24, C. Donzaud7,25, D. Dornic6, D. Drouhin1,T. Eberl4, I. El Bojaddaini26, N. El Khayati19, D. Elsasser27, A. Enzenhofer6, A. Ettahiri19,F. Fassi19, I. Felis5, L.A. Fusco20,28, P. Gay29,7, V. Giordano30, H. Glotin31,32, T. Gregoire7,R. Gracia Ruiz7, K. Graf4, S. Hallmann4, H. van Haren33, A.J. Heijboer12, Y. Hello23, J.J.Hernandez-Rey8, J. Hoßl4, J. Hofestadt4, C. Hugon3,24, G. Illuminati8, C.W. James4, M.

de Jong12,13, M. Jongen12, M. Kadler27, O. Kalekin4, U. Katz4, D. Kießling4,A. Kouchner7,32, M. Kreter27, I. Kreykenbohm34, V. Kulikovskiy6,35, C. Lachaud7,

R. Lahmann4, D. Lefevre36, E. Leonora30,37, M. Lotze8, S. Loucatos38,7, M. Marcelin9,A. Margiotta20,28, A. Marinelli39,40, J.A. Martınez-Mora5, R. Mele41,42, K. Melis12,15,T. Michael12, P. Migliozzi41, A. Moussa26, S. Navas43, E. Nezri9, M. Organokov44,

G.E. Pavalas14, C. Pellegrino20,28, C. Perrina16,17, P. Piattelli11, V. Popa14, T. Pradier44,L. Quinn6, C. Racca1, G. Riccobene11, A. Sanchez-Losa21, M. Saldana5, I. Salvadori6, D. F.

E. Samtleben12,13, M. Sanguineti3,24, P. Sapienza11, F. Schussler38, C. Sieger4,M. Spurio20,28, Th. Stolarczyk38, M. Taiuti3,24, Y. Tayalati19, A. Trovato11, D. Turpin6,

C. Tonnis8, B. Vallage38,7, V. Van Elewyck7,32, F. Versari20,28, D. Vivolo41,42,A. Vizzoca16,17, J. Wilms34, J.D. Zornoza8, and J. Zuniga8

1GRPHE - Universite de Haute Alsace - Institut universitaire de technologie de Colmar, 34 rue du Grillenbreit BP 50568 -

68008 Colmar, France2Technical University of Catalonia, Laboratory of Applied Bioacoustics, Rambla Exposicio, 08800 Vilanova i la Geltru,

Barcelona, Spain3INFN - Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy

4Friedrich-Alexander-Universitat Erlangen-Nurnberg, Erlangen Centre for Astroparticle Physics, Erwin-Rommel-Str. 1, 91058Erlangen, Germany

5Institut d’Investigacio per a la Gestio Integrada de les Zones Costaneres (IGIC) - Universitat Politecnica de Valencia. C/Paranimf 1, 46730 Gandia, Spain

6Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France7APC, Univ Paris Diderot, CNRS/IN2P3, CEA/Irfu, Obs de Paris, Sorbonne Paris Cite, France

8IFIC - Instituto de Fısica Corpuscular (CSIC - Universitat de Valencia) c/ Catedratico Jose Beltran, 2 E-46980 Paterna,

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Valencia, Spain9LAM - Laboratoire d’Astrophysique de Marseille, Pole de l’Etoile Site de Chateau-Gombert, rue Frederic Joliot-Curie 38,

13388 Marseille Cedex 13, France10National Center for Energy Sciences and Nuclear Techniques, B.P.1382, R. P.10001 Rabat, Morocco

11INFN - Laboratori Nazionali del Sud (LNS), Via S. Sofia 62, 95123 Catania, Italy12Nikhef, Science Park, Amsterdam, The Netherlands

13Huygens-Kamerlingh Onnes Laboratorium, Universiteit Leiden, The Netherlands14Institute for Space Science, RO-077125 Bucharest, Magurele, Romania

15Universiteit van Amsterdam, Instituut voor Hoge-Energie Fysica, Science Park 105, 1098 XG Amsterdam, The Netherlands16INFN - Sezione di Roma, P.le Aldo Moro 2, 00185 Roma, Italy

17Dipartimento di Fisica dell’Universita La Sapienza, P.le Aldo Moro 2, 00185 Roma, Italy18Gran Sasso Science Institute, Viale Francesco Crispi 7, 00167 L’Aquila, Italy

19University Mohammed V in Rabat, Faculty of Sciences, 4 av. Ibn Battouta, B.P. 1014, R.P. 10000 Rabat, Morocco20INFN - Sezione di Bologna, Viale Berti-Pichat 6/2, 40127 Bologna, Italy

21INFN - Sezione di Bari, Via E. Orabona 4, 70126 Bari, Italy22Department of Computer Architecture and Technology/CITIC, University of Granada, 18071 Granada, Spain

23Geoazur, UCA, CNRS, IRD, Observatoire de la Cote d’Azur, Sophia Antipolis, France24Dipartimento di Fisica dell’Universita, Via Dodecaneso 33, 16146 Genova, Italy

25Universite Paris-Sud, 91405 Orsay Cedex, France26University Mohammed I, Laboratory of Physics of Matter and Radiations, B.P.717, Oujda 6000, Morocco

27Institut fur Theoretische Physik und Astrophysik, Universitat Wurzburg, Emil-Fischer Str. 31, 97074 Wurzburg, Germany28Dipartimento di Fisica e Astronomia dell’Universita, Viale Berti Pichat 6/2, 40127 Bologna, Italy

29Laboratoire de Physique Corpusculaire, Clermont Universite, Universite Blaise Pascal, CNRS/IN2P3, BP 10448, F-63000Clermont-Ferrand, France

30INFN - Sezione di Catania, Viale Andrea Doria 6, 95125 Catania, Italy3131, Aix Marseille Universite CNRS ENSAM LSIS UMR 7296 13397 Marseille, France; Universite de Toulon CNRS LSIS

UMR 7296, 83957 La Garde, France32Institut Universitaire de France, 75005 Paris, France

33Royal Netherlands Institute for Sea Research (NIOZ) and Utrecht University, Landsdiep 4, 1797 SZ ’t Horntje (Texel), theNetherlands

34Dr. Remeis-Sternwarte and ECAP, Universitat Erlangen-Nurnberg, Sternwartstr. 7, 96049 Bamberg, Germany35Moscow State University, Skobeltsyn Institute of Nuclear Physics, Leninskie gory, 119991 Moscow, Russia

36Mediterranean Institute of Oceanography (MIO), Aix-Marseille University, 13288, Marseille, Cedex 9, France; Universite duSud Toulon-Var, CNRS-INSU/IRD UM 110, 83957, La Garde Cedex, France

37Dipartimento di Fisica ed Astronomia dell’Universita, Viale Andrea Doria 6, 95125 Catania, Italy38Direction des Sciences de la Matiere - Institut de recherche sur les lois fondamentales de l’Univers - Service de Physique des

Particules, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France39INFN - Sezione di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy

40Dipartimento di Fisica dell’Universita, Largo B. Pontecorvo 3, 56127 Pisa, Italy41INFN - Sezione di Napoli, Via Cintia 80126 Napoli, Italy

42Dipartimento di Fisica dell’Universita Federico II di Napoli, Via Cintia 80126, Napoli, Italy43Dpto. de Fısica Teorica y del Cosmos & C.A.F.P.E., University of Granada, 18071 Granada, Spain

44Universite de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France

October 10, 2017

2

Abstract

Advanced LIGO detected a significant gravitational wave signal (GW170104) originatingfrom the coalescence of two black holes during the second observation run on January 4th,2017. An all-sky high-energy neutrino follow-up search has been made using data from theAntares neutrino telescope, including both upgoing and downgoing events in two separateanalyses. No neutrino candidates were found within ±500 s around the GW event time nor anytime clustering of events over an extended time window of ±3 months. The non-detection isused to constrain isotropic-equivalent high-energy neutrino emission from GW170104 to less than∼ 4× 1054 erg for a E−2 spectrum.

1 Introduction

The first two confirmed observations of gravita-tional waves (GWs) produced by the merger ofbinary black holes (BBHs) were recently madeby the Advanced LIGO interferometers duringtheir observation run O1 [1, 2]. The second ob-servation run of Advanced LIGO (O2) beganin November 2016 and stopped on August 25th,2017. A BBH signal, GW170104, was recordedduring O2 on January 4th, 2017 at 10:11:58.6UTC [3]. The false alarm rate corresponding tothe signal produced by this event is less thanone event over 70 000 years. The signal was pro-duced by the coalescence of two black holes ofinferred masses of 31.2+8.4

−6.0 M� and 19.4+5.3−5.9 M�

at a luminosity distance of 880+450−390 Mpc. The

GW source location was constrained to within1608 deg2 of the sky at 90% credible level (re-gion hereafter denoted as GW error box) by theLALInference reconstruction algorithm [3].

Black holes with accretion disks can triggerrelativistic outflows where high-energy (TeV–PeV) neutrinos (HENs) can be produced, ifhadronic particles are accelerated within the jets[4, 5, 6]. Such an acceleration process can takeplace if magnetic fields and a long-lived debrisdisk remain from the stellar evolution of the

black-hole progenitors or if the binary systemresides in a dense gaseous environment (see e.g.[7, 8, 9, 10]). Since the presence of an accretiondisk was not excluded in the case of GW170104,the search for muon HENs emitted before or af-ter the merger could bring valuable informationabout the formation of relativistic outflows.

The Antares Collaboration has joined thefollow-up program of LIGO/Virgo detectionsand has received GW alerts during the wholeO2 run period. The angular resolution of theAntares neutrino telescope (∼0.4◦ at ∼10 TeVfor muon neutrinos) compared to the size of theGW error box offers the possibility to drasticallyreduce the size of the region of interest in caseof a coincident muon neutrino detection.

The Antares field-of-view (FoV), when re-stricted to upgoing events, enclosed 51% of theGW170104 error box provided by LIGO/Virgoat the alert time. Coincidences in time and direc-tion between the GW signal and reconstructedmuon HEN candidates were searched for in adatastream of about 1.2 events per day, selectedfrom a total of O(100) upgoing neutrino trackcandidates triggered by ANTARES per day [11].No neutrino counterpart was found and the re-sults of this real-time analysis were transmittedvia the Gamma-ray Coordinates Network (GCN)

3

circular #20370 [12] to the LIGO/Virgo follow-up community in less than 24 hours after therelease of the alert. The results provided bythe Antares Collaboration were the only real-time neutrino follow-up related to this event.The absence of neutrino candidates both tem-porally and spatially coincident with GW170104allowed for deriving a preliminary upper limit onthe spectral fluence emitted in neutrinos by thesource at 90% confidence level (CL). This up-per limit is expressed as a function of the loca-tion of the source in equatorial coordinates andassuming a standard neutrino spectral modeldN/dE ∝ E−2. This result was transmittedto the LIGO/Virgo follow-up community in theGCN circular #20517 [12].

The results of an updated high-energy neu-trino follow-up of GW170104 using the Antaresneutrino telescope are presented in this paper.The search for a transient neutrino counterparthas been extended to the full sky with differentenergy thresholds for events originating from be-low and above the Antares horizon, and to alarger emission timescale. The search describedhereafter was performed with the most recentoffline-reconstructed dataset, incorporating ded-icated calibrations of positioning [13], timing [14]and efficiency [15]. The analysis has been op-timized to increase the sensitivity of the de-tector at the time of the alert. Two neutrinospectral models were assumed: a generic modeldN/dE = φ0E

−2 typically expected for Fermiacceleration and a model with a high-energy

cutoff dN/dE = φ0E−2exp

[−√

(E/100TeV)].

The second model is expected for sources withexponential cutoff in the primary proton spec-trum [16]. Finally, systematic errors affectingthe corresponding upper limits on neutrino emis-sion are accounted for.

The capabilities of the Antares detector andthe search procedures are summarized in Section2. The constraints on the neutrino fluence andtotal energy emitted in neutrinos derived fromthe non-detection of a neutrino counterpart forGW170104 are presented in Section 3. The con-clusions are reported in Section 4.

2 High energy neutrino search

Antares [17] is an underwater neutrino tele-scope located in the Mediterranean Sea, offshoreToulon (France). It is composed of an arrayof photomultiplier tubes (PMTs), anchored ata depth of 2475 m under the sea level. Neu-trinos with energies above ∼ 102 GeV are de-tected through the Cherenkov light induced byrelativistic particles created from the interactionof neutrinos with matter. In addition to as-trophysical neutrino signals, both atmosphericmuons and neutrinos can lead to detectable lightin the detector and are considered as backgroundevents. However, only neutrinos can traverse theEarth. Looking at upgoing particles in the detec-tor reference frame allows for removing a largepart of the downgoing atmospheric muon back-ground. Remaining mis-reconstructed downgo-ing muons are further rejected by applying cutson the reconstruction quality parameters. In ad-dition, the intense background of downward go-ing atmospheric muons is drastically reduced bythe requirement for a joint time and space coin-cidence with the GW time and spatial error box.This allows for searching for a neutrino counter-part for GW170104 in both upgoing and downgo-ing datasets, which consist of events originatingrespectively from below and above the Antareshorizon.

Considering the refined location probability

4

provided by the LIGO/Virgo LALInference soft-ware [18], there is a 52% chance that the GWemitter was below the Antares horizon whereany neutrino events from this part of the skywould be seen as upgoing in the detector frame.This corresponds to a 45% probability for thesource to be located inside the GW error box andbelow the Antares horizon (see Fig. 1). To ex-tend the overlap between the Antares FoV andthe GW error box, downgoing events have beenadded to the search in an independent analysis.

All-sky Antares data have been searched fortrack events produced by νµ and νµ charged cur-rent interactions coincident with GW170104 us-ing a time window of ±500 s around the GWtransient (Sections 2.1 and 2.2). This time win-dow was adopted as the standard search win-dow for previous joint GW-HEN searches [19],for instance in the case of GW150914 andGW151226 [20, 21]. A search for a neutrinocounterpart within an extended time window of±3 months has also been done using the onlinedatastream of Antares (Section 2.3).

2.1 Search below the Antares horizon

A binned search for coincident upgoing neu-trinos was performed following a blind proce-dure. The track reconstruction algorithm com-putes both the neutrino direction, together withan estimated error β, and a quality parameterΛ [22]. This sample is dominated by backgroundevents from mis-reconstructed downgoing atmo-spheric muons, which deposit energy in the de-tector through stochastic processes. The datasetwas reduced by adjusting Λ such that any eventpassing the search criteria and located withinthe GW error box, below the Antares hori-zon, would lead to a detection with a significancelevel of 3σ. This optimization was carried out on

Figure 1: Visibility map of GW170104 in equa-torial coordinates. The sky regions below andabove the Antares horizon at the alert timeare shown in blue and white respectively. Eventsthat originate from the blue (white) region willbe seen as upgoing (downgoing) in the detectorframe. The red and black contours show the re-constructed probability density contours of theGW event at 50% and 90% credible level respec-tively.

data outside the 1000 s time window used in thissearch. A Monte Carlo simulation of the detec-tor response [23, 24] at the alert time allows forestimating the relative contribution of the atmo-spheric neutrinos and the mis-reconstructed at-mospheric muons to the background rate belowthe Antares horizon and within ±500 s. A totalof 2.2×10−2 atmospheric neutrino candidates areexpected while the number of mis-reconstructeddowngoing muons amounts to 3.7× 10−2 eventsover 2π sr.

After unblinding of the dataset, no event tem-porally coincident with GW170104 was found.

5

2.2 Search above the Antares horizon

A search for coincident neutrino candidates de-tected above the Antares horizon was carriedout by selecting downgoing events with β smallerthan 1◦. The cuts are optimized on a com-bination of Λ and the number of hits used inthe reconstruction, where a hit corresponds toa PMT signal above a given threshold. Thenumber of hits can be considered as a proxyof the muon/neutrino energy. Indeed, downgo-ing atmospheric muons are less likely to producea number of hits as large as that produced byvery high-energy cosmic neutrinos. Anew, theselection criteria were optimized such that oneevent occurring within the signal time windowof 1000 s and located inside the GW error boxlocated above the Antares horizon would leadto a detection with a significance level of 3σ. Thefinal set of cuts is chosen as the one maximizingthe fraction of surviving signal events. The fi-nal sample is mostly composed of atmosphericmuons with a total of 8.2 × 10−2 backgroundevents expected above the Antares horizonwithin ±500 s. The median neutrino energy thatwould be detected by Antares for a E−2 signalspectrum is about a factor of 10 higher for thisanalysis compared to the search below the hori-zon described in Section 2.1.

After unblinding of the dataset, no event tem-porally coincident with GW170104 was found.

2.3 Extended time window search

The time window of ±500 s was chosen by as-suming that if compact binary mergers are re-lated to gamma-ray bursts then the neutrino sig-nal should occur close in time to the GW emis-sion. This time window is large enough to catchpotential precursor neutrino emission and time

offsets with respect to the GW signal [19]. Forcompleteness, to probe non-standard propaga-tion scenarios similar to those described in [25],a search for shifted and/or longer-lasting emis-sion over ±3 months around the GW alert wasperformed by looking for time clustering of up-going neutrino events.

The events selected from the online datas-tream used in the Antares real-time alert pro-gram [11] are investigated for time clustering.The spatial clustering of the events and their co-incidence with the GW error box were investi-gated a posteriori.

An unbinned likelihood search was performedfollowing the methodology applied in previousanalyses [26, 27]. For each combination of twoevents a and b, a signal probability for the ith

event is defined as:

Sa,bi =H(tb − ti)H(ti − ta)

tb − ta, (1)

with H the Heaviside function1 and ta and tb,the detection time of events a and b (with ta <tb). The background time probability for the ith

event, Bi, is derived directly from the probabilitydensity function (PDF) of the downgoing recon-structed events. In this way, the background dis-tribution reflects the evolution of the event ratedue to the variability of the data taking condi-tions.

Given a dataset of N events, the likelihoodfunction La,b(ns) for a given pair of events oc-curring at times ta and tb is defined as:

La,b(ns) =N∏i=1

[nsNSa,bi +

(1− ns

N

)Bi

], (2)

where ns is the unknown number of signal events.For each pair of events occurring at times ta and

1H(0) is defined as 1.

6

tb, the likelihood is maximized with respect to nsto provide the best-fit number of events ns. Thetest statistic (TSa,b) is computed from the likeli-hood ratio of the background-only (null) hypoth-esis over the signal-plus-background hypothesisas:

TSa,b = −2 · log

[T

tb − taL(ns = 0)

La,b(ns)

], (3)

where the term Ttb−ta in the square brackets

is a trial factor. This quantity is needed tocorrect for the fact that there are many moreindependent small time windows than largeones, which tend to favour very short flares.The parameter T corresponds to the datasetlivetime. Given a sample of N events, N(N−1)

2values of TS were computed (one for each pair ofevents a and b). The cluster that maximizes theTS is finally considered as the most significantone.

To compute the p-value of the most signifi-cant cluster, O(10 000) pseudo-experiments weregenerated, each of them consisting of N eventsdrawn randomly from the time PDF of the back-ground. The fraction of trials for which the TSvalue is larger than the one obtained from thedata is referred to as the p-value.

The most significant time cluster has beenfound to contain ns=8.3 fitted signal events, oc-curring between tmin(MJD)=57682.73398 andtmax(MJD)=57685.62900 (tmax − tmin =2.89days). It leads to a post-trial p-value of 70%and is thus consistent with the background-onlyhypothesis. In addition, the Antares eventscontained in this time window are not spatiallycompatible and do not overlap with the GW er-ror box.

3 Astrophysical constraints

The non-detection of joint GW and neutrino sig-nals is used to constrain neutrino emission fromthe GW source. Upper limits on both the flu-ence and the total energy emitted in neutrinosare presented in the form of skymaps since thesensitivity of Antares depends on the sourcedirection.

3.1 Constraints on the neutrino spec-tral fluence

Upper limits at 90% CL on the neutrino fluencefrom a point source within ∆t = ±500 s werecalculated using the null result and the detectoracceptance, estimated via a Monte Carlo simu-lation of the detector response at the time of theGW signal. This simulation is produced on arun-by-run basis [23, 24] to account for the vari-ation of the data taking conditions under the sea.The two spectral models described in Section 1were considered.

The number of neutrino events expected to beobserved by Antares from a point source atdeclination δ and with a neutrino flux dN/dE(in GeV−1 cm−2 s−1) in a time window ∆t isgiven by:

Nevents = ∆t

∫dN

dE(E)Aeff(E, δ)dE, (4)

where Aeff(E, δ) is the effective area of Antaresat the alert time which take into account the ab-sorption of neutrinos by the Earth and dependson the neutrino energy E, the source declinationδ and the applied cuts.

The upper limit on the fluence, φ90%0 , is de-

fined as the fluence value that on average wouldproduce 2.3 detected neutrino events. Assuming

7

a dN/dE = φ0E−2 neutrino spectral model, it is

derived as:

φ90%0 =

2.3

∆t∫E−2Aeff(Eν , δ)dE

, (5)

where the denominator refers to the instanta-neous acceptance of the Antares detector atthe time of the alert computed between 1 GeVand 100 PeV. Equation 5 also applies for the sec-ond spectral model considered in this study. Thesame methodology is used to derive φ90%

0 in thecase of the second considered spectral model andon the search above the horizon.

Fig. 2 shows the neutrino spectral fluence up-per limit (φ90%

0 ) for GW170104 as a functionof the source direction for both spectral mod-els. Computed from the Monte Carlo simula-tion, the energy range corresponding to the 5%–95% quantiles of the neutrino flux below theAntares horizon is equal to [3.2 TeV; 3.6 PeV]for the dN/dE = φ0E

−2 spectral model and[1.4 TeV; 270 TeV] for the model with exponen-tial cutoff at 100 TeV. Above the Antares hori-zon, the 5%–95% quantiles of the neutrino fluxare respectively equal to [120 TeV; 22 PeV] and[53 TeV; 950 TeV].

The systematic uncertainties on the fluenceupper limits have been estimated by summingquadratically i) the systematic error on the ac-ceptance of the detector and ii) the uncertaintyrelated to the ability of the Antares run-by-runMonte Carlo approach to accurately reproducethe variable data taking conditions on short timescales. This latter effect can become dominantwhen looking for transient neutrino sources.

The systematic error on the acceptance hasbeen computed by reducing the efficiency of eachoptical module by 15% in the detector simula-tions. This leads to a 15% uncertainty on theacceptance as detailed in [22].

30 ◦ 60 ◦ 90 ◦ 120 ◦ 150 ◦ 180 ◦ 210 ◦ 240 ◦ 270 ◦ 300 ◦ 330 ◦

-75°

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100 101 102

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30 ◦ 60 ◦ 90 ◦ 120 ◦ 150 ◦ 180 ◦ 210 ◦ 240 ◦ 270 ◦ 300 ◦ 330 ◦

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Figure 2: All-sky upper limit on the neu-trino spectral fluence (νµ + νµ) from GW170104as a function of source direction assum-ing dN/dE ∝ E−2 (top) and dN/dE ∝E−2exp

[−√

(E/100TeV)]

(bottom) neutrino

spectra. The red and black lines show the GWskymap contours at 50% and 90% credible levels,respectively. Skymaps are defined in equatorialcoordinates.

The second source of uncertainty has beenconstrained by quantifying the ability of the run-

8

by-run Monte Carlo to accurately reproduce theevolution of the event rate observed in the datafrom one run to another. Due to the low numberof events passing the optimized quality cuts, therun-by-run agreement between data and MonteCarlo can only be assessed by loosening the cuts,on a data sample dominated by atmosphericmuon events. The variations of the muon rateare well reproduced with a median relative varia-tion between data and Monte Carlo smaller than20%. In addition, the short-timescale fluctua-tions of the event rate are smaller for signal neu-trinos with a E−2 spectral model than for atmo-spheric muons. This was expected since the de-tector geometry is optimized for upgoing events.Thus, the systematic error of 20% is considereda conservative value.

The resulting total systematic uncertainty onthe fluence upper limits, which applies for bothupgoing and downgoing event searches, is 25%.

3.2 Constraints on the total energyemitted in neutrinos

The GW signal contains also information onthe source distance which can be reconstructedaround the GW error box [28]. This informationcan be used to derive an upper limit on the totalenergy radiated in neutrinos as a function of thedirection as performed in [21].

The most likely value D(~x) of the distancefor each direction ~x is used to calculate the up-per limit on the total isotropic-equivalent energyemitted in neutrinos by the source as:

EULν,iso (~x) = 4π [D(~x)]2

∫dN

dE(E, ~x)EdE. (6)

Upper limits on the total energy arecomputed for both dN/dE ∝ E−2 and

dN/dE ∝ E−2exp[−√

(E/100TeV)]

neutrino

spectral models. The spectrum is integrated overthe range [100 GeV; 100 PeV]. The upper limitsas a function of source direction are shown inFig. 3 for the region corresponding to upgoingevents for Antares. It can be seen in Fig. 3that the derived constraints depend on the posi-tion on the sky as both the fluence upper limitsand the distance constraints do. The 5%–95%range of values is [1 × 1054; 4 × 1054] erg and[6× 1053; 4× 1054] erg, for the E−2 and the 100TeV cutoff models respectively. The strongestconstraint is obtained at declination δ ∼ −17◦

with E < 5 × 1053 erg for a E−2 spectrum andE < 3 × 1053 erg for the spectral energy distri-bution with cutoff at 100 TeV. These values areabout 10% of the total energy of ∼ 3.6×1054 ergemitted from GW170104 in gravitational waves.The results obtained for downgoing events arenot provided since the neutrino fluence upperlimits are much weaker. The uncertainty on thetotal energy emitted in neutrinos is estimated byaccounting for both the systematic error on φ90%

0

(computed above) and the 1σ standard deviationon the distance provided by the LIGO/VirgoGW event reconstruction, leading to an averagevalue of ∼ 40%.

4 Conclusion

No neutrino emission associated with the thirdconfirmed binary black hole merger, GW170104was detected in the Antares data. Thisnon-detection was used to derive an upper limitto the total neutrino emission from GW170104of ∼ 4×1054 erg, for a generic E−2 neutrinospectrum and for a high-energy cutoff spectrum

E−2exp[−√

(E/100TeV)]

as expected for

sources with an exponential cutoff in the proton

9

30 ◦ 60 ◦ 90 ◦ 120 ◦ 150 ◦ 180 ◦ 210 ◦ 240 ◦ 270 ◦ 300 ◦ 330 ◦

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75°

0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4

U.L. on total energy (erg) 1e54

30 ◦ 60 ◦ 90 ◦ 120 ◦ 150 ◦ 180 ◦ 210 ◦ 240 ◦ 270 ◦ 300 ◦ 330 ◦

-75°

-60°

-45°

-30°

-15°

0°

15°

30°

45°

60°

75°

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

U.L. on total energy (erg) 1e54

Figure 3: Upper limits on the total energy ra-diated in νµ + νµ from GW170104 as a func-tion of source direction assuming dN/dE ∝ E−2

(top) and dN/dE ∝ E−2exp[−√

(E/100TeV)]

(bottom) neutrino spectra. The upper limits aregiven for the sky below the Antares horizon,where they are the most stringent. Skymaps aredefined in equatorial coordinates.

spectrum. These results are of the same order ofmagnitude as the ones previously published forGW150914, LVT151012 and GW151226. The

strongest constraint, obtained at a declinationδ ∼ −17◦, shows that if the GW source islocated at this position on the sky, the totalenergy emitted in neutrinos from GW170104 isnot more than 10% of the total energy emittedin gravitational waves.

The Antares Collaboration is grateful to theLIGO Scientific Collaboration and the VirgoCollaboration for the setting up of an impres-sive follow-up observation program, and for shar-ing invaluable scientific information for the ben-efit of the emerging multi-messenger astronomy.The authors acknowledge the financial supportof the funding agencies: Centre National de laRecherche Scientifique (CNRS), Commissariat al’energie atomique et aux energies alternatives(CEA), Commission Europeenne (FEDER fundand Marie Curie Program), Institut Universi-taire de France (IUF), IdEx program and Uni-vEarthS Labex program at Sorbonne Paris Cite(ANR-10-LABX-0023 and ANR-11-IDEX-0005-02), Labex OCEVU (ANR-11-LABX-0060) andthe A*MIDEX project (ANR-11-IDEX-0001-02), Region Ile-de-France (DIM-ACAV), RegionAlsace (contrat CPER), Region Provence-Alpes-Cote d’Azur, Departement du Var and Villede La Seyne-sur-Mer, France; Bundesminis-terium fur Bildung und Forschung (BMBF),Germany; Istituto Nazionale di Fisica Nu-cleare (INFN), Italy; Nederlandse organisatievoor Wetenschappelijk Onderzoek (NWO), theNetherlands; Council of the President of theRussian Federation for young scientists and lead-ing scientific schools supporting grants, Rus-sia; National Authority for Scientific Research(ANCS), Romania; Ministerio de Economıa yCompetitividad (MINECO): Plan Estatal de In-vestigacion (refs. FPA2015-65150-C3-1-P, -2-P

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and -3-P, (MINECO/FEDER)), Severo OchoaCentre of Excellence and MultiDark Consolider(MINECO), and Prometeo and Grisolıa pro-grams (Generalitat Valenciana), Spain; Ministryof Higher Education, Scientific Research andProfessional Training, Morocco. We also ac-knowledge the technical support of Ifremer, AIMand Foselev Marine for the sea operation and theCC-IN2P3 for the computing facilities.

References

[1] B. P. Abbott et al., Phys. Rev. Lett. 116,061102 (2016).

[2] B. P. Abbott et al., Phys. Rev. Lett. 116,241103 (2016).

[3] B. P. Abbott et al., Phys. Rev. Lett. 118,221101 (2017).

[4] P. Meszaros, Rep. Prog. Phys. 69, 2259(2006).

[5] E. Waxman and J. Bahcall, Phys. Rev. Lett.78, 2292 (1997).

[6] A. Beloborodov, Mon. Not. Roy. Astron. Soc.407, 1033 (2010).

[7] R. Perna et al., Astrophys. J. Lett. , 821,L18 (2016).

[8] K. Murase et al., Astrophys. J. Lett. , 822,L9 (2016).

[9] K. Kotera and J. Silk, Astrophys. J. Lett. ,823, L29 (2016).

[10] I. Bartos et al., Astrophys. J. , 835, 2(2017).

[11] S. Adrian-Martınez et al., JCAP 02, 062(2016).

[12] The GCN circulars published by the col-laborating astronomers related to GW170104are archived at gcn.gsfc.nasa.gov/other/

G268556.gcn3.

[13] S. Adrian-Martınez et al., J. Instrum. 7,T08002 (2012).

[14] J.A. Aguilar et al., Astropart. Phys. 34, 539(2011).

[15] J. Aguilar et al., Nucl. Instrum. Meth. A570, 107 (2007).

[16] A. Kappes et al., Journal of Physics Con-ference Series 60, 243 (2007).

[17] M. Ageron et al., Nucl. Instrum. Meth. A656, 11 (2011).

[18] J. Veitch et al., Phys. Rev. D. 91, 042003(2015).

[19] B. Baret et al., Astropart. Phys. 35, 1(2011).

[20] S. Adrian-Martınez et al., Phys. Rev. D.93, 122010 (2016).

[21] S. Adrian-Martınez et al., Phys. Rev. D.96, 022005 (2017).

[22] S. Adrian-Martınez et al., Astrophys.J. 760, 53 (2012).

[23] A. Margiotta, Nucl. Instrum. Meth. A 725,98 (2013).

[24] L. Fusco and A. Margiotta, Europ. Phys. J.Web Conf. 116, 02002 (2016).

11

[25] S. Adrian-Martınez et al., Eur. Phys. J. C77:20 (2017).

[26] J. Braun et al., Astropart. Phys. 29, 299(2008).

[27] M.G. Aartsen et al., Science 342, 1242856(2013).

[28] L. Singer et al., Astrophys. J. Lett. 829, 15(2016).

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