Stacked search for time shifted high energy neutrinos from gamma ray bursts with the ANTARES neutrino telescope
ANTARES Collaboration, S. Adrian-Martínez, A. Albert, M. André, M. Anghinolfi, G. Anton, M. Ardid, J.-J. Aubert, B. Baret, J. Barrios-Marti, S. Basa, V. Bertin, S. Biagi, R. Bormuth, M. C. Bouwhuis, R. Bruijn, J. Brunner, J. Busto, A. Capone, L. Caramete, J. Carr, T. Chiarusi, M. Circella, R. Coniglione, H. Costantini, P. Coyle, A. Creusot, I. Dekeyser, A. Deschamps, G. De Bonis, C. Distefano, C. Donzaud, D. Dornic, D. Drouhin, A. Dumas, T. Eberl, D. Elsasser, A. Enzenhofer, K. Fehn, I. Felis, P. Fermani, F. Folger, L. A. Fusco, S. Galatà, P. Gay, S. Geisselsoeder, K. Geyer, V. Giordano, A. Gleixner, R. Gracia-Ruiz, K. Graf, S. Hallmann, H. van Haren, A. J. Heijboer, Y. Hello, J. J. Hernàndez-Rey, J. Hoessl, J. Hofestadt, C. Hugon, C. W. James, M. de Jong, M. Kadler, M. Kadler, O. Kalekin, U. Katz, D. Kiessling, P. Kooijman, A. Kouchner, M. Kreter, I. Kreykenbohm, V. Kulikovskiy, R. Lahmann, D. Lefèvre, E. Leonora, S. Loucatos, M. Marcelin, A. Margiotta, A. Marinelli, J. A. Martínez-Mora, A. Mathieu, T. Michael, P. Migliozzi, A. Moussa, C. Muller, E. Nezri, G. E. Pavalas, C. Pellegrino, C. Perrina, P. Piattelli, V. Popa, T. Pradier, C. Racca, G. Riccobene, R. Richter, K. Roensch, M. Saldaña, D. F. E. Samtleben, A. Sánchez-Losa, M. Sanguineti, P. Sapienza, et al. (22 additional authors not shown)
SStacked search for time shifted high energy neutrinos from gammaray bursts with the
Antares neutrino telescope.
S. Adri´an-Mart´ınez , A. Albert , M. Andr´e , M. Anghinolfi , G. Anton , M. Ardid ,J.-J. Aubert , B. Baret ∗ , J. Barrios-Marti , S. Basa , V. Bertin , S. Biagi ,R. Bormuth , M. C. Bouwhuis , R. Bruijn , J. Brunner , J. Busto , A. Capone ,L. Caramete , J. Carr , T. Chiarusi , M. Circella , R. Coniglione , H. Costantini ,P. Coyle , A. Creusot , I. Dekeyser , A. Deschamps , G. De Bonis , C. Distefano ,C. Donzaud , D. Dornic , D. Drouhin , A. Dumas , T. Eberl , D. Els¨asser ,A. Enzenh¨ofer , K. Fehn , I. Felis , P. Fermani , F. Folger , L. A. Fusco , S. Galat`a , P. Gay , S. Geißels¨oder , K. Geyer , V. Giordano , A. Gleixner , R. Gracia-Ruiz ,K. Graf , S. Hallmann , H. van Haren , A. J. Heijboer , Y. Hello , J. J.Hern´andez-Rey , J. H¨oßl , J. Hofest¨adt , C. Hugon , C. W. James , M. de Jong , M.Kadler , M. Kadler , O. Kalekin , U. Katz , D. Kießling , P. Kooijman ,A. Kouchner , M. Kreter , I. Kreykenbohm , V. Kulikovskiy , R. Lahmann , D.Lef`evre , E. Leonora , S. Loucatos , M. Marcelin , A. Margiotta , A. Marinelli ,J. A. Mart´ınez-Mora , A. Mathieu , T. Michael , P. Migliozzi , A. Moussa , C. M¨uller , E. Nezri , G. E. P˘av˘ala¸s , C. Pellegrino , C. Perrina , P. Piattelli , V. Popa ,T. Pradier , C. Racca , G. Riccobene , R. Richter , K. Roensch , M. Salda˜na ,D. F. E. Samtleben , A. S´anchez-Losa , M. Sanguineti , P. Sapienza , J. Schmid ∗ ,J. Schnabel , F. Sch¨ussler , T. Seitz , C. Sieger , M. Spurio , J. J. M. Steijger ,Th. Stolarczyk , M. Taiuti , C. Tamburini , A. Trovato , M. Tselengidou , C. T¨onnis , B. Vallage , C. Vall´ee , V. Van Elewyck , E. Visser , D. Vivolo , S. Wagner ,J. Wilms , J. D. Zornoza , and J. Z´u˜niga GRPHE - Institut universitaire de technologie de Colmar, 34 rue du Grillenbreit BP 50568 - 68008 Colmar, France CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, Marseille, France Technical University of Catalonia, Laboratory of Applied Bioacoustics, Rambla Exposici´o,08800 Vilanova i laGeltr´u,Barcelona, Spain INFN - Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy Friedrich-Alexander-Universit¨at Erlangen-N¨urnberg, Erlangen Centre for Astroparticle Physics, Erwin-Rommel-Str. 1, 91058Erlangen, Germany Direction des Sciences de la Mati`ere - Institut de recherche sur les lois fondamentales de l’Univers - Service d’Electroniquedes D´etecteurs et d’Informatique, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France Nikhef, Science Park, Amsterdam, The Netherlands APC, Universit´e Paris Diderot, CNRS/IN2P3, CEA/IRFU, Observatoire de Paris, Sorbonne Paris Cit´e, 75205 Paris, France IFIC - Instituto de F´ısica Corpuscular, Edificios Investigaci´on de Paterna, CSIC - Universitat de Val`encia, c/ Catedr´atico a r X i v : . [ a s t r o - ph . H E ] O c t os´e Beltr´an, 2, Paterna 46980, Valencia, Spain LAM - Laboratoire d’Astrophysique de Marseille, Pˆole de l’´Etoile Site de Chˆateau-Gombert, rue Fr´ed´eric Joliot-Curie 38,13388 Marseille Cedex 13, France INFN - Sezione di Bologna, Viale Berti-Pichat 6/2, 40127 Bologna, Italy Dipartimento di Fisica dell’Universit`a, Viale Berti Pichat 6/2, 40127 Bologna, Italy INFN -Sezione di Roma, P.le Aldo Moro 2, 00185 Roma, Italy Dipartimento di Fisica dell’Universit`a La Sapienza, P.le Aldo Moro 2, 00185 Roma, Italy Institute for Space Sciences, R-77125 Bucharest, M˘agurele, Romania Clermont Universit´e, Universit´e Blaise Pascal, CNRS/IN2P3, Laboratoire de Physique Corpusculaire, BP 10448, 63000Clermont-Ferrand, France G´eoazur, Universit´e Nice Sophia-Antipolis, CNRS/INSU, IRD, Observatoire de la Cˆote d’Azur, Sophia Antipolis, France INFN - Sezione di Bari, Via E. Orabona 4, 70126 Bari, Italy INFN - Laboratori Nazionali del Sud (LNS), Via S. Sofia 62, 95123 Catania, Italy Mediterranean Institute of Oceanography (MIO), Aix-Marseille University, 13288, Marseille, Cedex 9, France; Universit´e duSud Toulon-Var, 83957, La Garde Cedex, France CNRS-INSU/IRD UM 110 Universit´e Paris-Sud, 91405 Orsay Cedex, France Kernfysisch Versneller Instituut (KVI), University of Groningen, Zernikelaan 25, 9747 AA Groningen, The Netherlands INFN - Sezione di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy Dipartimento di Fisica dell’Universit`a, Largo B. Pontecorvo 3, 56127 Pisa, Italy Royal Netherlands Institute for Sea Research (NIOZ), Landsdiep 4,1797 SZ ’t Horntje (Texel), The Netherlands Institut f¨ur Theoretische Physik und Astrophysik, Universit¨at W¨urzburg, Am Hubland, 97074 W¨urzburg, Germany Universiteit Utrecht, Faculteit Betawetenschappen, Princetonplein 5, 3584 CC Utrecht, The Netherlands Universiteit van Amsterdam, Instituut voor Hoge-Energie Fysica, Science Park 105, 1098 XG Amsterdam, The Netherlands Dr. Remeis-Sternwarte and ECAP, Universit¨at Erlangen-N¨urnberg, Sternwartstr. 7, 96049 Bamberg, Germany Moscow State University, Skobeltsyn Institute of Nuclear Physics, Leninskie gory, 119991 Moscow, Russia INFN - Sezione di Catania, Viale Andrea Doria 6, 95125 Catania, Italy Dipartimento di Fisica ed Astronomia dell’Universit`a, Viale Andrea Doria 6, 95125 Catania, Italy Direction des Sciences de la Mati`ere - Institut de recherche sur les lois fondamentales de l’Univers - Service de Physique desParticules, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France D´epartement de Physique Nucl´eaire et Corpusculaire, Universit´e de Gen`eve, 1211, Geneva, Switzerland IPHC-Institut Pluridisciplinaire Hubert Curien - Universit´e de Strasbourg et CNRS/IN2P3 23 rue du Loess, BP 28, 67037Strasbourg Cedex 2, France ITEP - Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, 117218 Moscow, Russia Universiteit Leiden, Leids Instituut voor Onderzoek in Natuurkunde, 2333 CA Leiden, The Netherlands Dipartimento di Fisica dell’Universit`a, Via Dodecaneso 33, 16146 Genova, Italy University Mohammed I, Laboratory of Physics of Matter and Radiations, B.P.717, Oujda 6000, Morocco INFN -Sezione di Napoli, Via Cintia 80126 Napoli, Italy Dipartimento di Fisica dell’Universit`a Federico II di Napoli, Via Cintia 80126, Napoli, Italy Institut Universitaire de France, 75005 Paris, France
October 18, 2018 ∗ Corresponding authors. Email addresses: [email protected] (J. Schmid) & [email protected] (B. Baret) bstract A search for high-energy neutrino emission correlated with gamma-ray bursts outside the elec-tromagnetic prompt-emission time window is presented. Using a stacking approach of the timedelays between reported gamma-ray burst alerts and spatially coincident muon-neutrino signa-tures, data from the
Antares neutrino telescope recorded between 2007 and 2012 are analysed.One year of public data from the
IceCube detector between 2008 and 2009 have been also investi-gated. The respective timing profiles are scanned for statistically significant accumulations within40 days of the Gamma Ray Burst, as expected from Lorentz Invariance Violation effects and someastrophysical models. No significant excess over the expected accidental coincidence rate could befound in either of the two data sets. The average strength of the neutrino signal is found to befainter than one detectable neutrino signal per hundred gamma-ray bursts in the
Antares dataat 90% confidence level.
Gamma-ray bursts (GRBs) are among the mostpowerful sources in the universe, which makesthem suitable candidates for the acceleration ofthe highest-energy cosmic rays. Unambiguousevidence for the acceleration of hadrons in as-trophysical environments can be provided by thedetection of neutrinos that would be coincidentlyproduced when accelerated protons interact withthe ambient photon field (see, e.g. [1],[2],[3] andreferences therein). Searches for the emissionof neutrinos from GRBs have been performedby a variety of experiments, for instance Super-Kamiokande [4], AMANDA [5], Baikal [6], RICE[7], ANITA [8], IceCube [9, 10] and
Antares [11, 12]. While covering a wide range of neutrinoenergies these studies have so far focussed mainlyon the time window coincident with the electro-magnetic signal of GRBs. Up to now no neutrinosignal could be identified by any neutrino detec-tor during the prompt emission phases, and ana-lytical models from [13] based on [2] have alreadybeen excluded by the IceCube collaboration [10].There has also been some effort to successivelyextend the search time windows in the IceCubedata from [-1h,+3h] up to ± ±
15 days [14], to account for prolonged neu-trino emission. However none of these searchescould bring compelling evidence for a GRB sig-nal, since all detected events have been identifiedwith cosmic-ray induced air showers or were oflow significance because of the large time win-dows.While the search for a signal of neutrinos coinci-dent with the emission of high-energy photons isthe most common ansatz, there are many modelsthat predict time-shifted neutrino signals, suchas neutrino precursors [15], afterglows (e.g. [16]),or different Lorentz Invariance Violation (LIV)effects for photons and neutrinos on their wayto Earth [17, 18]. For instance, the possibilitythat three low significance neutrino-like eventsfound in the IceCube data [10] could have beenproduced by GRBs but arrived before the pho-ton signal due to LIV effects is discussed in [19].Probing such scenarios requires a new approachto the search for correlated emission. Moreover,in all aforementioned scenarios, the neutrino sig-nal is simply shifted in time with respect to theelectromagnetic signal, and none of these mod-els predict any considerably prolonged neutrinoemission. Hence the approach used in this paperand described in section 3 aims at identifying a3resumably faint neutrino signal that is shiftedwith respect to the electromagnetic GRB emis-sion by an unknown time offset, while making noassumption about the origin of such an offset.
Neutrino telescopes are arrays of photomultipli-ers deployed in a very large volume of trans-parent medium like Antarctic ice or deep-seawater. They detect the Cherenkov light gen-erated by the products of the interaction of ahigh-energy neutrino in the vicinity of the de-tector. The direction of the impinging neutrinois reconstructed using the timing of signals fromphotomultipliers, while the detected amount oflight gives an estimate of the neutrino energy.The
Antares telescope [21] is located at a depthof 2475 m in the French Mediterranean Sea offthe coast of Toulon, at 42 ◦ (cid:48) N, 6 ◦ (cid:48) E. It com-prises 885 optical modules housing 10” photo-multipliers in 17” glass spheres installed on 12strings, representing an instrumented volume of0 .
02 km .The following analysis focuses on the detection ofmuon trajectories from below the horizon, whichare produced by muon-neutrino charged-currentinteractions. This channel provides significantlybetter directional reconstruction than neutral-current interactions and charged current inter-actions from the other neutrino flavors. In thischannel, Antares is the most sensitive detectorfor sources in a large part of the southern sky upto a few 100 TeV [22].The sample of
Antares events used in thisanalysis consists of 5516 neutrino candidates se-lected from data collected between March 2007and the end of 2012 [23]. From Monte Carlo simulations the angular resolution, defined asthe median of the space angle δ err between thetrue and reconstructed direction of neutrinos foran E − differential spectrum, is 0 . ◦ , with acontamination from atmospheric muons of 10%.The right-ascension distribution of the neutrinocandidates is shown in Figure 1.A suitable GRB sample was consolidated simi-larly to the one used in [12]. It was built us-ing catalogs from the Swift [24] and
Fermi satel-lites [25, 26], and supplemented by a table fromthe
IceCube
Collaboration [27], with informa-tion parsed from the GRB Coordinates Network(GCN) notices. Since only the time and posi-tion information (and the measured redshift, ifavailable) of each announced GRB was used, nofurther selection on e.g. the quality of the spec-tral measurements was required, leading to 1488GRBs. Only GRB alerts were taken into accountthat occurred both below the horizon of the neu-trino telescope and during the covered neutrinodata collection period. The upper panel of Fig-ure 2 shows the distribution of the selected neu-trino candidates, which are homogeneously dis-tributed in time. The lower panel displays theaccordingly selected GRBs in equatorial coordi-nates and their measured fluence. Neutrino signatures are searched-for in an an-gular cone around the direction of, and withina maximum time offset from the time of eachGRB. For any such space and time coincidence,the time difference with respect to the GRBalert is recorded. In order to avoid any bound-ary effect such as an artificial asymetry of neu- available on-line at http://grbweb.icecube.wisc.edu/ α of the Antares neutrino event sample (March2007 – December 2012). The respective cumula-tive distribution is shown in black.trino candidates around a GRB alert close tothe beginning or end of neutrino telescope datataking, GRBs detected during a period of halfthe considered maximum time offset at the be-ginning and end of the neutrino data sampleare excluded. The collected time differences arestacked in a common timing profile. In the caseof no signal, only purely accidental spatial co-incidences of the neutrino candidates with thedefined search cones around the GRB positionswould be expected. The observed time shiftsshould then be distributed randomly, yieldinga flat stacked distribution where all shifts areequally likely. Any neutrino emission associatedwith the GRBs, even if faint, can give rise to acumulative effect in these stacked profiles, whichcan then be identified by its discrepancy from thebackground hypothesis. An optimal choice of thesearch cone size δ max naturally depends on theGRB’s position accuracy and the neutrino direc- Figure 2: Distributions in equatorial coor-dinates of selected GRBs (upper panel) andrecorded neutrino candidates (lower panel) forthe Antares event sample. Each GRB’s loca-tion is color-coded with the photon fluence F γ ;those with no measurement are coloured in gray.The color of neutrino events represents their de-tection time.5ion reconstruction uncertainty. The size of theprobed time window τ max should be defined asthe largest shift predicted by any of the modelsunder consideration. Such a procedure had al-ready been proposed [28], where windows of ± IceCube
Col-laboration [10][14], which focused on successivelywidening symmetric search time windows aroundthe GRB alerts considering a flat temporal sig-nal probability density function. In the case of atime-shifted signal, these methods suffer from re-duced significance due to the accumulated back-ground in the increasingly large time windows.In contrast, the technique presented here aimsat identifying a time-shifted signal as a peak ontop of flat background.
For maximum generality we perform a test fora constant offset ( τ = t ν − t GRB ) between the(first) detected photon signal t GRB and the timeof a possibly associated neutrino candidate t ν ,for maximum generality. In the case of a con-stant shift τ em of the emission times of the neu-trino with respect to photons at the source, ittranslates into observed time delays at Earth τ obs that depend on the cosmological redshift z of theGRB as: τ em = τ obs / (1 + z ) . (1)To test for these intrinsic time shifts, the dis-tribution of τ z = τ / (1 + z ) will be investigated. Note that the redshift is only measured for ap-proximately 10% of all GRBs, significantly re-ducing the statistics of the stacked profile whenomitting all GRBs without determined redshift.Effects due to LIV (see e.g. [17], [18] and [19])can also yield different arrival times at Earth forphotons and neutrinos of high energy producedby a GRB. In a variety of quantum spacetimemodels, the velocity dispersion relation linkingthe energy of the particle E and its momentum p is modified by an additional term proportionalto an integer power of the ratio of the energy tothe Planck scale: E − p c = ± E · ( E/M
LIV ) n , (2)where M LIV is the scale at which the symmetryis broken. The mass term m c can be neglectedfor neutrinos [18]. First-order terms with n =1will be considered here as these exhibit the mostsizeable effects. Within this framework, the timeshift observed at Earth will depend on the energyof the neutrino, the distance of the source D ( z )and the energy scale M LIV :∆ t LIV = ( ± · E/M
LIV · D ( z ) /c , (3)where D ( z ) is the effective distance travelled bythe particles taking into account the expansionof the Universe, and is defined according to [19]as: D ( z ) = cH (cid:90) z (1 + z (cid:48) ) dz (cid:48) (cid:112) Ω m (1 + z (cid:48) ) + Ω Λ , (4)where z is the redshift, H is the Hubble con-stant, and Ω m and Ω Λ are the relative matterand dark energy densities of the Universe [20].These effects are expected to appear in a stackedhistogram that accounts for both the estimatedneutrino energy E est and the distance of the6ource. Consequently, the variable to be probedis defined as: τ LIV = τE est · D ( z ) , (5)In case of a sizeable LIV effect, with a given valueof M LIV this yields τ LIV ∝ ± EE est · M LIV · c , (6)and the time-stacked neutrino observations willaccumulate around a single value of τ LIV . Incontrast, the distribution of events due to purelyaccidental coincidences will peak around zero.The ratio r = n + /n − of spatially coincidentevents before and after the respective GRB alertis a very simple measure to probe the distribu-tions while making the fewest assumptions onany model. Any effect leading to different arrivaltimes of neutrinos and gamma-rays from GRBsis expected to yield either positive or negativetime shifts. This ratio is calculated if both n + and n − are non-zero.Consequently, in the search for an associatedneutrino signal from GRBs, three stacked timeprofiles for the measures τ , τ z and τ LIV were gen-erated for all neutrino candidates which matchedthe coordinates of a reported GRB alert, and theratio r for the whole sample was computed. The expected number of background events µ b increases with the solid angle of the searchcones Ω( δ max ) around each GRB’s position andwith the considered maximum time delay τ max .Hence, the choice of the search cone size and the probed time window should be optimised underreasonable physical considerations. The determination of an optimally-sized searchcone for spatially coincident neutrino candidateswith a GRB alert was based on the maximi-sation of the ratio of signal to square root ofbackground. Assuming a point-source-like sig-nal at the GRB’s location, the reconstructedneutrino directions approximately follow a two-dimensional Gaussian profile of standard devi-ation σ ν around this position. This approachyields an optimum search cone size of 1 . · σ ν as derived for example in [30]. Note that theneutrino telescope resolution is usually stated asthe median of the reconstructed direction error m ( δ err ) (see for instance [31]). For angles in con-sideration here, the relation m ( δ err ) ∼ . σ ν holds.The effects of uncertainty in GRB location∆ err (sub-arc second for Swift /UVOT or groundbased telescopes, up to several degrees for
Fermi /GBM) is accounted for by extending thesearch window whenever ∆ err > σ ν . As the con-tribution of random coincidences scales quadrat-ically with ∆ err , the background in the cumula-tive profile might be dominated considerably bya few bursts with very large satellite error boxes.Consequently, a reasonable trade-off should befound. On the one hand, the statistics shouldnot be reduced too much by excluding a largenumber of badly-localised bursts. On the otherhand, the stacked timing profiles should not bedominated by one burst with a large error box,which naturally leads to many accidental spatialcoincidences. In order to limit this effect withoutsignificantly reducing the data sample, a maxi-mum search-cone size was chosen – based on the7igure 3: Number of GRBs with a given errorbox ∆ err (orange). The cumulative distributionis shown by the grey line. For GRBs with mea-sured redshift, the distribution is shown in violet.distribution of ∆ maxerr shown in Figure 3 – suchthat no GRB contributed more than an orderof magnitude more of uncorrelated backgroundthan any other.The search-cone size is consequently definedas: δ cut = 1 . · max( σ ν , min (∆ err , ∆ maxerr )) . (7)Using the Antares pointing resolution of 0 . ◦ ,all bursts with error boxes larger than ∆ maxerr = 1 ◦ were consequently discarded from the search,which reduced the sample by ∼
54% while keep-ing 74% of the total gamma-ray fluence of thesample, yielding search-cone sizes in the range[0 . ◦ , . ◦ ]. Note that Fermi-detected burstswith a resolution of 1 ◦ are included. The approach presented in this paper aims at be-ing as model independent as possible. The max- imum time shift anticipated from the astrophysi-cal processes mentionned in section 3.1 is used toset the time coincidence window. Intrinsic shiftsin the emission times of neutrinos were predictedin [15] with neutrinos ∼
100 s before the electro-magnetic GRB signal. A precursor neutrino sig-nal that might be emitted even tens of years be-fore the actual GRB is derived in [32]. Since thelatter time scale exceeds the operational timesof the current neutrino telescopes, we will omitthis scenario. Early afterglow emission of neu-trinos ∼
10 s after the burst are predicted in[16] and [33] and extended neutrino fluxes upto 1 day after the prompt emission are derivedin [34]. These intrinsic time shifts between neu-trino and photon signals are still well within thetime scopes that have already been probed, forexample in [10],[14] – without positive result.Differences in arrival times induced by LIV ef-fects would depend not only on M LIV , but alsoon the energy of the particles and the distanceof the source. However, a maximum expectedtime shift of neutrinos and photons can be in-ferred from Equation 3 using the existing limiton the LIV energy scale. The most stringentlimit within the theoretical framework used herehas been set to M LIV = 7 . · M Planck based on the
Fermi /LAT data [35]. Using the distance D ( z )at a redshift of z = 8 .
5, which is the highest mea-sured redshift in the selected GRB catalog, and amaximum energy of ∼ E max = 10 GeV account-ing for the energy range at which a signal mightbe observed, a maximum time shift of τ max = 40days was derived. Even though the upper boundwas derived from quantum space-time models,the search itself remains model independent.A discretisation of the cumulative timing pro-files into 150 bins was chosen, which allows timescales down to 13 hours to be probed. Giventhe low number of expected coincidences within8he allowed time window (see section 4.5), thischoice ensures that there will be much less coin-cidences than bins, leading to a quasi-unbinnedapproach [29]. Having chosen the maximal search time windowand the largest angular search cone that shouldbe taken into account, the final samples associ-ated with the neutrino telescope data set weredetermined. The initially selected GRB cata-log comprised 1488 bursts that had occurred be-tween 2007 to 2012, which gives a detection rateof 0.68 bursts per day. Out of these, 563 havebeen selected for the search of associated neutri-nos in the
Antares data using the criteria out-lined above, of which 150 have a measured red-shift z . From the stacked histograms of τ , τ z and τ LIV ,test statistics are calculated that distinguish asystematically time-shifted neutrino signal asso-ciated with GRBs from the background-only hy-pothesis of purely accidental coincidences. Alarge number of background realisations pre-serving the telescope’s acceptance are generatedfrom the existing data sets by scrambling thetime from the corresponding distribution of Fig.1 and randomising the right ascension of de-tected neutrino candidate events in accordancewith the flatness of the data distribution. Thesignificance, of an excess in the data is then givenby the p -value which is the probability to mea-sure the test statistic in question (or more ex-treme values) from the background-only distri-bution.The test statistic associated to the ratio r will be the variable itself. For the stacked his-tograms, the Bayesian observable ψ to estimatethe compatibility of a given stacked (and binned)time profile with the expectations from back-ground has been proposed in [28] and [29]. Thistest statistic is proportional to the logarithm ofthe probability p of an observation D under anhypothesis H defined by a set of information I (here that the stacked profile bins are filledfollowing a multinomial law of known probabili-ties): ψ = −
10 log p ( D | H, I )= − (cid:34) log n ! + m (cid:88) k =1 n k log p k − log n k ! (cid:35) , (8)with n events in the histogram in total, dis-tributed in k ∈ [1 . . . m ] bins. The probability tofall within bin k is p k ; for a uniform backgrounddistribution (i.e. in the case of the τ profile), p k = 1 /m is simply given by the total number ofbins m .For the non-uniform profiles τ z and τ LIV ,these probabilities have to be determined by alarge number of pseudo-experiments simulatingthe background, of the order of 10 to estimatethe significance of a potential excess up to the 5 σ level. The value of ψ is calculated for each of the τ , τ z and τ LIV profiles, correspondingly denoted ψ , ψ z and ψ LIV . Around 1 . · pseudo experiments yieldingsky-maps of uncorrelated neutrino events weregenerated to simulate the case of purely acci-dental coincidences (background-only) betweenthe Antares neutrino data and the GRB cata-logue. On average, 3.9 of the neutrino candi-dates are expected to match the bursts’ search9indows in time and space, with 0.7 of them co-inciding accidentally with the bursts with mea-sured redshift.To illustrate the performance of the pro-posed technique to identify hypothetical neutri-nos from GRBs, a test signal was generated byassociating neutrino candidates artificially witha fraction of the GRBs at a hypothetical intrin-sic time shift of t in with t in = 1 , ,
10 or 20days. That is, taking into account the cosmo-logical redshift z , a simulated signal delayed by t ν = t GRB + t in · (1 + z ). Its strength was quan-tified by the probability f ∈ [0 ,
1] that a GRBproduced a signal in the neutrino telescope. Thesignal was consequently only simulated for thosebursts for which the redshift could be deter-mined, and the variable which has the best sensi-tivity to it will be τ z since signal will accumulatein one bin.Figure 4: Detection efficiency (color scale) atthe 3 σ level using the ψ z test statistic as a func-tion of the signal strength f (see text) and in-trinsic time delay at the source for a signal asdescribed in section 4.5.The discovery probability MDP at nσ signifi-cance level for a given signal strength is given by Figure 5: Detection probability MDP at 3 σ (solid) and 5 σ (dashed lines) for the test statis-tics ψ , ψ z , ψ LIV and r as a function of the meanfraction f of GRBs with one associated signalneutrino at t ν = t GRB + 5 d · (1 + z ). The fraction f z denotes the fraction of GRBs in the samplewith determined redshift z , whereas f all gives thefraction of the whole sample.the fraction of realisations that lead to values ofthe test statistics (here r , ψ , ψ z or ψ LIV ) abovea threshold corresponding to a p-value at the nσ level on the background-only realisations. Itrepresents the efficiency of the analysis and thespecific test statistic to identify a signal being as-sociated with a fraction of GRBs. The detectionefficiency of the ψ z test statistic is independentof the time shift of signal for delays up to 10days, as can be seen in Figure 4. The evolu-tion of the efficiencies for an example signal atan intrinsic time shift of 5 days as a functionof the signal strength f is shown in Figure 5,10igure 6: Probabilities P to measure values ofthe test statistics above the median value fromthe background-only realisations as a functionof f z or f all (as in Figure 5). The sensitiv-ity is given by the signal fraction f where thecurves reach 90% probability (grey dashed line).Note that the curves for ψ z and ψ LIV lie on topof each other. Probabilities were derived usingthe
Antares data from 2007-2012.and is hence representative of shifts from 0 to 10days. Signal strength corresponding to discoveryprobabilities are summarized in Table 1, for thewhole sample and for GRBs with measured red-shift. For instance, using the ψ test statistics, ifonly f = 1 .
3% of the GRBs would give rise to anassociated signal neutrino, it would produce anexcess of 3 σ significance with 50% probability,whereas a stronger signal in 2 .
4% of the burstswould be identified at the 5 σ level. For the sam-ple of GRBs with measured redshift, the ψ z teststatistic only needs a fraction f z = 4 .
5% which is half of the signal fraction necessary with the ψ test statistic for the same detection efficiency.The introduced time-stacking technique isconsequently capable of robustly finding at the3 σ level an intrinsically delayed neutrino emis-sion from GRBs as long as it is associated withat least 3 of the 563 bursts.The probability of measuring values of thetest statistics exceeding the median backgroundvalue for different signal strengths is shownin Figure 6.The sensitivity at 90% (99%)confidence-level (CL) is defined as the 90%(99%) CL upper limit that can be placed on thesignal strength when observing the median back-ground (see gray dashed line marking 90%). Thesensitivities at 90% and 99% CL of the proposedanalysis for the given test signal simulating neu-trino emission delayed by five days at the sourcein a mean fraction of all bursts are summarisedin Table 1. For instance, at 90% CL, consideringonly the sub-sample of bursts with determinedredshift and the test statistics ψ z and ψ LIV , themethod is sensitive to a signal in only 1 .
1% ofthe bursts.
The data collected by the
Antares telescopefrom the years 2007 to 2012 were analysed tosearch for neutrinos within the predefined angu-lar and timing search windows associated withthe GRB catalogue. None of the neutrino candi-dates in the data matched these search windows,where 3.9 would have been expected from back-ground (0.7 coincidences were expected for theGRBs with measured redshift z ). The measuredvalues of the test statistics are thus zero, and theratio r = n + /n − is undefined. The probabilityto observe no events coinciding with all GRBs11est Statistic Sensitivity at 90% CL Sensitivity at 99% CL MDP σ MDP σf all f z f all f z f all f z f all f z r ψ ψ z ψ LIV σ and 5 σ with 50% statistical power for a signal delayed by 5 days at the source (see text) for the differenttest statistics expressed in terms of the fraction f all of the GRB sample with detectable signal andthe fraction f z of the GRB sample with measured redshift f z . ν data sample τ tot N events m ( δ ) δ max τ max N GRB N GRB ,z n coinc n coinc ,z [d] [ ◦ ] [ ◦ ] [d] (uncorrelated) Antares (07-12) 2154 5516 0.38 0.51 – 1.59 40 563 150 3.9 0.7IC40 (08-09) 408 12876 0.70 0.95 – 2.99 40 60 12 35.0 4.0Table 2: Total live-time of the considered neutrino telescope data sets τ tot , respective number ofneutrino candidate events N events and respective median angular resolution m ( δ ). Samples of N GRB
GRBs are identified (out of which N GRB ,z have measured redshifts) for the search of correlations.Assuming totally uncorrelated neutrino data, the mean numbers of coincident events that wouldbe expected within the GRB’s search windows n coinc are also given.12s relatively small, with P (0 | .
9) = 1 .
2% (and51 .
4% for GRBs with measured z ).We verified the under-fluctuation to be of sta-tistical origin instead of intrinsic systematic ef-fects in the search methodology or the software.In particular, we derived the number of coinci-dences when increasing independently τ max and δ max . Using these enlarged coincidence windows,the number of coincident data events is close tothe expected number of coincidences from ran-domized data.In Table 3, the probabilities P to measure teststatistics above the measurements and the ex-pected values from the median background real-isations are given. This results in 99% CL limitsof f all = 0 .
04% and f z = 2 . f z of 1 . f all defined according to section 4.5is not possible. A conservative option would beto set the limit equal to the sensitivity as in [36].Since this method does not make use of the infor-mation contained in the actual nonobservation,the resulting 90% CL of f all = 0 .
6% is weakerthan the standard 99% CL of 0 . .
04% should be used for both 90% and 99%CL.We can state a sensitivity of m ( f ) =0 .
6% of all GRBs (2 .
2% for those with measured z ), which is the median upper limit on the frac-tion of bursts that contain a signal of the form τ s = 5 d · (1+ z ). Furthermore, we see that 99% ofall realisations with a signal fraction f all = 0 . ψ than observed, so we canexclude such a signal with 99% confidence. Re-garding the sample of bursts with measured red-shift z , the observation of zero events matchedthe median expectation from background, so wecould exclude that 1 .
1% of them produced a sig-nal neutrino with a delay shape τ s = 5 d · (1 + z ) with 90% confidence, in accordance with the sen-sitivity that had previously been derived. The same parameter optimisation and search hasbeen performed with the public data sample from an analysis searching for neutrino pointlikesources [37] of the IceCube observatory in its40-string configuration. These data cover April2008 to May 2009 and comprise 12877 neutrinocandidates. The selection procedure of neutrinosand GRBs is the same as in 4. With a resolutionof 0 . ◦ [38] it leads to 60 GRBs ( respectively12 with measured z ) 35 of which are expectedto be in coincidence with neutrinos (respectively4). The different parameters summarising the Antares and
IceCube samples, including thenumber of coincident events n coinc that wouldbe expected if the neutrino data was completelyuncorrelated with the chosen GRBs (i.e., thebackground-only hypothesis) are given in Table2.The IceCube
GRB sample shows significantlylower statistics, due to the fact that the pub-lished data spans only around one year comparedto almost six years in the
Antares sample. Inaddition, because of the location of the detec-tors on Earth, 87% of the sky is visible for the
Antares detector with unequal coverage, whilstthe
IceCube experiment covers the northern skybut at all times. It is also worth noting that, dueto the larger instrumented volume of the detec-tor, the
IceCube data set contains more neu-trino candidates than the
Antares one, whilecovering a smaller time period in which less GRBalerts were recorded. Both samples therefore ex- IceCube
IC40 neutrino candidates are available at http://icecube.wisc.edu/science/data/ic40/ all P ( > ψ meas ) P ( > m ( ψ )) f z P ( > ψ z , meas ) P ( > m ( ψ z )) P ( > ψ LIV , meas ) P ( > m ( ψ LIV )) ψ meas = 0 m ( ψ ) = 73 . z ) ψ z , meas = 0 m ( ψ z ) = 0 ψ LIV , meas = 0 m ( ψ LIV ) = 00.0% 98% 50% 0.0% 48.5% 48.5% 48.2% 48.2%0.04% 99% 54% 0.15% 59% 59% 59% 59%0.29% 99% 75% 1.1% 90% 90% 90% 90%0.60% 100% 90% 2.3% 98% 98% 98% 98%0.69% 100% 93% 2.6% 99% 99% 99% 99%1.07% 100% 98% 4.0% 100% 100% 100% 100%1.33% 100% 99% 5.0% 100% 100% 100% 100%2.10% 100% 100% 8.0% 100% 100% 100% 100%Table 3: Probabilities P to yield values of the test statistic Q ∈ [ ψ, ψ z , ψ LIV ] above the measurement Q meas and above the median value m ( Q ) as expected from pure background realisations for differentfractions f all ( f z ) of all GRBs (with measured redshift z ) with one associated signal neutrinointrinsically shifter by 5 days at the source.plore different statistical regimes. In the end, 42of the neutrino candidates fall within the searchwindows, with 8 for the bursts with measured z . This is a slight fluctuation above the expec-tations from background, with p -values of 13.5%(whole sample) and 5.1% (GRBs with measuredredshift), yielding excesses of moderate 1.5 σ and1.9 σ significances, respectively. The observationis compatible with no correlation of the Ice-Cube data with the chosen GRB sample. More-over, the timing profiles show no indication forany preferred time delay. The measured and ex-pected values as well as the corresponding signif-icance of the different test statistics for the twostudied samples, are summarised in Table 4.
A powerful method has been presented to iden-tify a neutrino signal associated with GRBs if itis shifted in time with respect to the photon sig-nal. The signal is distinguished from randomlydistributed data as a cumulative effect in stacked timing profiles of spatially coincident neutrinosin the data from the
Antares and
IceCube neutrino telescopes.Estimating the behaviour of the search for alarge number of simulated measurements usingrandomised sky maps of the neutrino events, andcomparing these with the actual neutrino tele-scope data, significances of the observations werederived. Using data from the
Antares neu-trino telescope between the years 2007 and 2012,a deficit of spatially coincident neutrinos withthe selected gamma-ray-burst catalogue was re-ported, with 98 .
8% of the randomised data lead-ing to more coincidences between the neutrinodata and the GRBs. The application of themethod to the public
IceCube data in its 40line configuration gives results compatible withthe expectation from background.The presented approach could have identifiedan intrinsically time-shifted signal even if onlyof the order of one in a hundred GRBs wouldhave given rise to a single associated neutrinoin the
Antares data. This is above the de-14NTARES 07-12
IceCube
IC40 08-09all GRBs GRBs w/ z all GRBs GRBs w/ zn coinc ψ n coinc ψ z ψ LIV n coinc r ψ n coinc ψ z ψ LIV (dB) (dB) (dB) (dB) (dB) (dB)Bgd mean 4.4 77.4 0.7 11.9 4.5 1.1 35.0 371.3 4.0 56.6 10.4Bgd median 4 73.3 0 0 0 35 1.0 371.8 4 56.3 7.9Measurement 0 0 0 0 0 42 0.4 416.0 8 1.1 93.9 8.8 P ( > meas . ) 98.8% 98.8% 48% 48.6% 48.6% 10.4% 0.4 14.0% 2.1% 6.1% 45.1% P ( ≥ meas . ) 100% 100% 100% 100% 100% 13.5% 14.0% 5.1% 6.1% 45.1%Table 4: Mean and median values of the different test statistics used in this analysis as derivedin the pseudo experiments of background and in the measurement using the neutrino candidatesas selected in the Antares data from 2007 to 2012 and
IceCube data from the IC40-period fromApril 2008 to May 2009. The number of data events coinciding spatially with the respective GRBsamples n coinc are also given. The probabilities P ( > meas) and the p -value, P ( ≥ meas) give thefraction of background-only pseudo experiments that yield test statistics above and at and abovethe measurement. Being 10 times the logarithm of two definite positive quantities, the ψ typetest statistics are usually expressed in dB [29]. Note that since there are no coincidences in the Antares data sample, r is not definedtectable neutrino signal predicted by the Neu-CosmA model [39] that is on average only of theorder of ∼ · − in the Antares detector, andonly the strongest individual burst yields a neu-trino detection rate exceeding 0.01 [12].In conclusion, novel analysis techniques havebeen developed that increase the sensitivity ofexisting neutrino searches from GRBs to mod-els of delayed neutrino emission and Lorentz In-variance Violation. They allow extending thesearch for neutrinos from GRBs with time dis-placements of up to 40 days. It confirms the ab-sence of a significant neutrino signal being asso-ciated with GRBs that has so far been measuredin the simultaneous time windows.
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 Europ´eenne (FEDER fundand Marie Curie Program), Institut Universi-taire de France (IUF), IdEx program and Uni-vEarthS Labex program at Sorbonne Paris Cit´e(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), R´egion ˆIle-de-France (DIM-ACAV), R´egionAlsace (contrat CPER), R´egion Provence-Alpes-Cˆote d’Azur, D´epartement du Var and Ville deLa Seyne-sur-Mer, France; Bundesministeriumf¨ur Bildung und Forschung (BMBF), Germany;Istituto Nazionale di Fisica Nucleare (INFN),15taly; Stichting voor Fundamenteel Onderzoekder Materie (FOM), 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 Econom´ıa yCompetitividad (MINECO): Plan Estatal de In-vestigaci´on (refs. FPA2015-65150-C3-1-P, -2-Pand -3-P, (MINECO/FEDER)), Severo OchoaCentre of Excellence and MultiDark Consolider(MINECO), and Prometeo and Grisol´ıa pro-grams (Generalitat Valenciana), Spain; Agencede l’Oriental and CNRST, Morocco. We also ac-knowledge the technical support of Ifremer, AIMand Foselev Marine for the sea operation and theCC-IN2P3 for the computing facilities.
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