AampA 559 A9 (2013)DOI 1010510004-6361201322169ccopy ESO 2013

Astronomyamp

Astrophysics

Search for muon neutrinos from gamma-ray burstswith the ANTARES neutrino telescope using 2008 to 2011 data

S Adriaacuten-Martiacutenez1 A Albert2 I Al Samarai3 M Andreacute4 M Anghinolfi5 G Anton6 S Anvar7 M Ardid1T Astraatmadja8 J-J Aubert3 B Baret9 J Barrios-Marti10 S Basa11 V Bertin3 S Biagi1213 C Bigongiari10C Bogazzi8 B Bouhou9 M C Bouwhuis8 J Brunner3 J Busto3 A Capone1415 L Caramete16 C Carloganu17

J Carr3 S Cecchini12 Z Charif3 Ph Charvis18 T Chiarusi12 M Circella19 F Classen6 R Coniglione20 L Core3H Costantini3 P Coyle3 A Creusot9 C Curtil3 G De Bonis1415 I Dekeyser2141 A Deschamps18 C Distefano20

C Donzaud922 D Dornic3 Q Dorosti23 D Drouhin2 A Dumas17 T Eberl6 U Emanuele10 A Enzenhoumlfer6J-P Ernenwein3 S Escoffier3 K Fehn6 P Fermani1415 V Flaminio2425 F Folger6 U Fritsch6 L A Fusco1213

S Galatagrave9 P Gay17 S Geiszligelsoumlder6 K Geyer6 G Giacomelli1213 V Giordano32 A Gleixner6J P Goacutemez-Gonzaacutelez10 K Graf6 G Guillard17 H van Haren26 A J Heijboer8 Y Hello18 J J Hernaacutendez-Rey10

B Herold6 J Houmlszligl6 C W James6 M de Jong8 M Kadler27 O Kalekin6 A Kappes6 U Katz6P Kooijman82829 A Kouchner9 I Kreykenbohm30 V Kulikovskiy315 R Lahmann6 E Lambard3 G Lambard10

G Larosa1 D Lefegravevre2141 E Leonora3233 D Lo Presti3233 H Loehner23 S Loucatos349 F Louis7 S Mangano10M Marcelin11 A Margiotta1213 J A Martiacutenez-Mora1 S Martini2141 T Michael8 T Montaruli1935

M Morganti24dagger C Muumlller30 M Neff6 E Nezri11 D Palioselitis8 G E Pavalas16 C Perrina1415 P Piattelli20V Popa16 T Pradier36 C Racca2 G Riccobene20 R Richter6 C Riviegravere3Dagger A Robert2141 K Roensch6

A Rostovtsev37 D F E Samtleben838 M Sanguineti39 J Schmid6Dagger J Schnabel6 S Schulte8 F Schuumlssler34T Seitz6 R Shanidze6 C Sieger6 F Simeone1415 A Spies6 M Spurio1213 J J M Steijger8 Th Stolarczyk34

A Saacutenchez-Losa10 M Taiuti539 C Tamburini2141 Y Tayalati40 A Trovato20 B Vallage34 C Valleacutee3V Van Elewyck9 P Vernin34 E Visser8 S Wagner6 J Wilms30 E de Wolf829 K Yatkin3 H Yepes10

J D Zornoza10 J Zuacutentildeiga10 and P Baerwald27

(Affiliations can be found after the references)

Received 28 June 2013 Accepted 20 August 2013

ABSTRACT

Aims We search for muon neutrinos in coincidence with GRBs with the ANTARES neutrino detector using data from the end of 2007 to 2011Methods Expected neutrino fluxes were calculated for each burst individually The most recent numerical calculations of the spectra using theNeuCosmA code were employed which include Monte Carlo simulations of the full underlying photohadronic interaction processes The discoveryprobability for a selection of 296 GRBs in the given period was optimised using an extended maximum-likelihood strategyResults No significant excess over background is found in the data and 90 confidence level upper limits are placed on the total expected fluxaccording to the model

Key words neutrinos ndash gamma-ray burst general ndash methods numerical

1 Introduction

Gamma-ray bursts (GRBs) are short and very intense flashesof high-energy gamma rays which occur unpredictably andisotropically over the sky (Meegan et al 1992) Over timescales

Appendices are available in electronic form athttpwwwaandaorg Full Table 2 is only available at the CDS via anonymous ftp tocdsarcu-strasbgfr (130791285) or viahttpcdsarcu-strasbgfrviz-binqcatJA+A559A9 Also at University of Leiden the Netherlands

On leave of absence at the Humboldt-Universitaumlt zu Berlindagger Also at Accademia Navale di Livorno Livorno ItalyDagger Corresponding authors

J Schmid (e-mail juliaschmidphysikuni-erlangende)C Riviegravere (e-mail crivierecppmin2p3fr)

of the order of a few seconds they release as much energy asthe Sun in its entire lifetime (see Woosley amp Bloom 2006 for areview) The doubly peaked distribution of burst durations mea-sured by the BATSE satellite led Kouveliotou et al (1993) to theclassification of GRBs into two types (see also Paciesas et al1999) The sub-class of long bursts (with durations gtsim2 s) hasbeen shown to be associated with supernovae of type I bc (seeeg Galama et al 1998) For the short bursts (ltsim2 s duration) it ismuch harder to measure the fast-fading afterglow emission andthereby obtain information about their origin However they arenow widely accepted to originate from the merging of two com-pact objects for example neutron stars and black holes (Eichleret al 1989 Nakar 2007)

In the fireball model (as proposed by Meacuteszaacuteros amp Rees1993) the observed electromagnetic radiation is explained byhighly relativistic outflows of material most likely collimated

Article published by EDP Sciences A9 page 1 of 11

AampA 559 A9 (2013)

in jets pointed towards the Earth Shock fronts emerge in theseoutflows in which electrons are accelerated (Rees amp Meacuteszaacuteros1992) The synchrotron emission of these relativistic electronsand subsequent inverse Compton-scattering of the emitted pho-ton field causes the observed gamma-ray radiation (Meacuteszaacuteros2006) Within the framework of the fireball model protons canalso be shock-accelerated which yields emission of high-energyneutrinos accompanying the electromagnetic signal of the burst(Waxman 1995a 2000 Waxman amp Bahcall 1997) The detec-tion of neutrinos from GRBs would be unambiguous proof forhadronic acceleration in cosmic sources and could also serve toexplain the origin of the cosmic-ray flux at ultra-high energies(Waxman 1995b)

Several limits over a wide range of energies have beenplaced on the neutrino emission from GRBs for instance fromexperiments such as Super-Kamiokande (Fukuda et al 2002)AMANDA (Achterberg et al 2008) Baikal (Avrorin et al 2011)RICE (Besson et al 2007) and ANITA (Vieregg et al 2011)Very-large-volume neutrino telescopes such as ANTARES andIceCube are sensitive to neutrino fluxes above approximately100 GeV since they simultaneously observe at least half thesky they are ideal instruments to search for any high-energyneutrino flux from GRBs The data from ANTARES in its con-struction phase in 2007 with the first five detection lines de-ployed (Adriaacuten-Martiacutenez et al 2013) and from IceCube in itsIC 22 IC 40 and IC 59 detector phases from 2007 to 2010(Abbasi et al 2010 2011 2012) have previously been analysedin searches for this emission with corresponding limits set in theTeV to PeV energy range Due to its location at the South Polethe IceCube detector has sensitivity for Northern Hemispheresources whereas the ANTARES detector being situated at a lat-itude of 43 has sensitivity for Southern Hemisphere sources

In this paper we present a search for prompt GRB neutrinoemission in the period from the end of 2007 to 2011 with theANTARES telescope using 296 bursts out of which 90 havenot been included in the previously mentioned references Incontrast to previous analyses this search has for the first timebeen optimised for a fully numerical neutrino-emission modelbased on Huumlmmer et al (2010 2012)

This paper is organised as follows in Sect 2 the ANTARESneutrino telescope is briefly introduced A description of howthe burst parameters are obtained and how the final sample isselected is given in Sect 3 Models for the expected neutrinospectra within the fireball paradigm are described in Sect 4including the numerical model NeuCosmA which is used forthe optimisation of the analysis In Sect 5 we describe MonteCarlo simulations of GRB neutrino events that yield the detec-tor response to the signal The background distribution is esti-mated from data as reported in Sect 6 From these distribu-tions pseudo-experiments were generated that by exploiting anextended maximum-likelihood ratio method were used to opti-mise the search to obtain the highest discovery potential for theneutrino flux ndash this is presented in Sect 7 In Sect 8 we investi-gate whether the discovery potential can be improved by limitingthe analysis to an optimised sub-sample of the bursts Results ofthe analysis and the derived limits are provided in Sect 9

2 ANTARES detector and data taking

The underwater neutrino telescope ANTARES (see Ageron et al2011) is primarily designed for detecting relativistic muons from

charged-current interactions of cosmic muon neutrinos1 withmatter in or close-by to the detector The passage of thesemuons through the seawater induces the emission of Cherenkovlight that is then detected by an array of photo-multiplier tubes(PMTs) Using the time and position information of the photonsthe muon trajectory is reconstructed The original neutrino direc-tion is then inferred from the measured muon direction ndash at theenergies considered here the uncertainty introduced by the scat-tering angle is negligible compared to the detectorrsquos resolution

The ANTARES telescope is located in the MediterraneanSea at a depth of 24 km The detector consists of twelve ver-tical ldquostringsrdquo anchored to the seabed each of which is held up-right by a buoy at the top They are separated from each otherby a typical distance of 70 m The twelve strings each with alength of 450 m are equipped with 25 triplets of PMTs build-ing a three-dimensional array of 885 PMTs in total2 The tripletshave a vertical spacing of 145 m between them whereas thefirst triplet is placed at a height of 100 m above the seabed

Bioluminescence and radioactive decay of 40K producea random optical background that can vary between 50 and300 kHz per PMT depending for example on the time of theyear or the sea current A multi-level online triggering proce-dure is applied to select possible particle signatures ndash see Aguilaret al (2007) for a more detailed description

In addition to the cosmic neutrino signal that the ANTARESexperiment is searching for there are other processes that canproduce muon tracks in the detector that are considered as back-ground events Air showers are generated when high-energycosmic rays hit the Earthrsquos atmosphere Among other particlesmuons and neutrinos are produced in these showers Since onlythe (weakly interacting) neutrinos are capable of traversing theEarth it can effectively be used as a ldquoshieldrdquo against all particlesbut neutrinos By searching only for upgoing particles thereforethe atmospheric downgoing muon background can be rejectedNevertheless muons from above can also produce signals in thedetector that appear as upgoing events Using quality cuts onthe reconstruction parameters these falsely reconstructed atmo-spheric muon tracks can be suppressed to a rate of 04 events perday

Atmospheric neutrinos produced by cosmic rays below thehorizon can also traverse the Earth and represent the main back-ground component (simthree events per day after quality cuts seeAdriaacuten-Martiacutenez et al 2012) to the cosmic neutrinos

In the analysis presented in the following the requirementof temporal and spatial coincidence with a recorded GRB re-duces the number of expected background events to simO(10minus4)per GRB (see Sect 6) and an extended likelihood method isfurthermore used to distinguish between signal and backgroundevents Data collected between December 6 2007 and the endof 2011 were analysed The first six months of this period com-prised the last phase of construction of the apparatus after thedeployment of detection lines 6 to 10 with the last two linesinstalled in May 2008 In that period the instrumented volumeof the detector increased from 0008 to 0011 km3 at full sizeThe corresponding average effective area to muon neutrinos asa function of the energy is shown in Fig 1 for different decli-nation bands The huge increase of effective area with energy acommon feature of neutrino telescopes is due not only to theincrease of the neutrino cross-section but also to that of themuon range which can reach several kilometres at the highest

1 Throughout the paper ldquoneutrinordquo will denote both ν and ν andldquomuonrdquo will denote both microminus and micro+2 One string is equipped with 60 instead of 75 PMTs

A9 page 2 of 11

The ANTARES Collaboration Search for muon neutrinos from GRBs with ANTARES

Fig 1 Time-averaged muon-neutrino effective area of the ANTARESneutrino telescope as a function of energy for different declinationbands δ for the considered data-taking period Typical quality cuts asderived in this analysis (Λ gt minus535 β lt 1) are applied

Table 1 Selection of GRBs

Criterion Selected

All GRBs (end of 2007ndash2011) 1110Long GRBs 942Measured spectrum 930Below ANTARES horizon 508Detector running and stable data-taking conditions 296

energies The total integrated livetime of the data in coincidencewith the selected 296 GRB search-time windows is 66 h

3 GRB selection and parameters

The GRB parameters needed for the search and the simulationof expected neutrino fluxes are primarily obtained from differ-ent tables provided by the Swift (Gehrels et al 2004) and Fermi(Atwood et al 2009 Meegan et al 2009) collaborations Thisinformation is then supplemented using a table supplied by theIceCube Collaboration (Aguilar 2011) which is created by pars-ing the Gamma-ray Coordinates Network (GCN) notices3 InAppendix A we specify how these tables are merged how of-ten burst parameters are taken from each of them and how thesearch-time windows are defined

For the final sample GRBs are required to meet certain cri-teria as specified in Table 1 ndash short bursts for instance are ex-cluded as this class is much less understood A total of 296 burstspass these selection cuts of which 10 are also included inthe most recent gamma-ray-burst search from IceCube (Abbasiet al 2012) The distribution of the selected bursts in equa-torial coordinates is shown in Fig 2 Out of this selectionGRB 110918 outshines all others by at least half an order ofmagnitude in the expected neutrino flux (see Sect 4) It is atthe same time one of the most intense bursts ever observed bythe Konus-Wind instrument (Aptekar et al 1995 Golenetskiiet al 2011) Unfortunately both Swift and Fermi satellites wereEarth-occulted at the time of the burst (Krimm et al 2011) butSwift could still observe the afterglow emission after sim30 hThe measured parameters for this exceptional burst are given inTable A2

3 GCN httpgcngsfcnasagovgcn3_archivehtml

Fig 2 Sky distribution of the selected 296 GRBs in equatorial coordi-nates The gamma-ray fluence of each burst is colour-coded The in-stantaneous field of view of the ANTARES detector is 2π sr within aperiod of 24 h the sky up to a declination of 47 is visible

4 Calculation of neutrino spectra

To calculate the expected neutrino spectra we focused on therecently developed fully numerical NeuCosmA model (Huumlmmeret al 2010 2012) In addition we also present the widely usedanalytical approach of Guetta et al (2004) in the following

41 Analytic approaches

Waxman amp Bahcall (1997) were the first to calculate the ex-pected neutrino flux in coincidence with the electromagneticGRB in the framework of the standard fireball internal shockmodel using averaged burst parameters as measured by theBATSE instrument on board the CGRO satellite (Band et al1993) Their calculation was based on the assumption of Fermi-accelerated protons in the relativistic ejecta of the burst inter-acting with the associated photon field to produce pions via the∆-resonance The subsequent decay of charged pions and muonsleads to the emission of high-energy neutrinos The authors de-rived a doubly broken power-law spectrum for the neutrinosTheir model is referred to as the standard Waxman-Bahcall GRBneutrino flux and is for instance used to set limits with theBAIKAL (Avrorin et al 2011) and AMANDA (Achterberg et al2008) experiments Guetta et al (2004) modified the formulae ofWaxman and Bahcall to calculate individual neutrino fluxes forthe bursts Such individual burst predictions are used in recentsearches with IceCube (Abbasi et al 2010 2011 2012) RICE(Besson et al 2007) and ANITA (Vieregg et al 2011) Note inparticular that the most recent IceCube limit was a factor of 37below predictions made using this model This could either in-dicate the need for rejection of the model a modification of theparameters upon which it is based or for more detailed mod-elling of the neutrino emission within the fireball paradigm

To calculate the analytic spectrum as shown in Fig 3ablue solid line the formulae given in Abbasi et al (2010Appendix A) were applied

In principle Guetta et al (2004) predicted different breakenergies for νmicro and νmicro (see Guetta et al 2004 Eqs (A10)and (A11)) yielding three breaks in the combined νmicro + νmicro spec-trum (or in the single νmicro spectrum when taking oscillations intoaccount) as shown in Fig 3a blue dashed ndash in the previousANTARES analysis (Adriaacuten-Martiacutenez et al 2013) this effecthas been accounted for

A9 page 3 of 11

The ANTARES Collaboration Search for muon neutrinos from GRBs with ANTARES

Fig 1 Time-averaged muon-neutrino effective area of the ANTARESneutrino telescope as a function of energy for different declinationbands δ for the considered data-taking period Typical quality cuts asderived in this analysis (Λ gt minus535 β lt 1) are applied

Table 1 Selection of GRBs

Criterion Selected

All GRBs (end of 2007ndash2011) 1110Long GRBs 942Measured spectrum 930Below ANTARES horizon 508Detector running and stable data-taking conditions 296

energies The total integrated livetime of the data in coincidencewith the selected 296 GRB search-time windows is 66 h

3 GRB selection and parameters

The GRB parameters needed for the search and the simulationof expected neutrino fluxes are primarily obtained from differ-ent tables provided by the Swift (Gehrels et al 2004) and Fermi(Atwood et al 2009 Meegan et al 2009) collaborations Thisinformation is then supplemented using a table supplied by theIceCube Collaboration (Aguilar 2011) which is created by pars-ing the Gamma-ray Coordinates Network (GCN) notices3 InAppendix A we specify how these tables are merged how of-ten burst parameters are taken from each of them and how thesearch-time windows are defined

For the final sample GRBs are required to meet certain cri-teria as specified in Table 1 ndash short bursts for instance are ex-cluded as this class is much less understood A total of 296 burstspass these selection cuts of which 10 are also included inthe most recent gamma-ray-burst search from IceCube (Abbasiet al 2012) The distribution of the selected bursts in equa-torial coordinates is shown in Fig 2 Out of this selectionGRB 110918 outshines all others by at least half an order ofmagnitude in the expected neutrino flux (see Sect 4) It is atthe same time one of the most intense bursts ever observed bythe Konus-Wind instrument (Aptekar et al 1995 Golenetskiiet al 2011) Unfortunately both Swift and Fermi satellites wereEarth-occulted at the time of the burst (Krimm et al 2011) butSwift could still observe the afterglow emission after sim30 hThe measured parameters for this exceptional burst are given inTable A2

3 GCN httpgcngsfcnasagovgcn3_archivehtml

Fig 2 Sky distribution of the selected 296 GRBs in equatorial coordi-nates The gamma-ray fluence of each burst is colour-coded The in-stantaneous field of view of the ANTARES detector is 2π sr within aperiod of 24 h the sky up to a declination of 47 is visible

4 Calculation of neutrino spectra

To calculate the expected neutrino spectra we focused on therecently developed fully numerical NeuCosmA model (Huumlmmeret al 2010 2012) In addition we also present the widely usedanalytical approach of Guetta et al (2004) in the following

41 Analytic approaches

Waxman amp Bahcall (1997) were the first to calculate the ex-pected neutrino flux in coincidence with the electromagneticGRB in the framework of the standard fireball internal shockmodel using averaged burst parameters as measured by theBATSE instrument on board the CGRO satellite (Band et al1993) Their calculation was based on the assumption of Fermi-accelerated protons in the relativistic ejecta of the burst inter-acting with the associated photon field to produce pions via the∆-resonance The subsequent decay of charged pions and muonsleads to the emission of high-energy neutrinos The authors de-rived a doubly broken power-law spectrum for the neutrinosTheir model is referred to as the standard Waxman-Bahcall GRBneutrino flux and is for instance used to set limits with theBAIKAL (Avrorin et al 2011) and AMANDA (Achterberg et al2008) experiments Guetta et al (2004) modified the formulae ofWaxman and Bahcall to calculate individual neutrino fluxes forthe bursts Such individual burst predictions are used in recentsearches with IceCube (Abbasi et al 2010 2011 2012) RICE(Besson et al 2007) and ANITA (Vieregg et al 2011) Note inparticular that the most recent IceCube limit was a factor of 37below predictions made using this model This could either in-dicate the need for rejection of the model a modification of theparameters upon which it is based or for more detailed mod-elling of the neutrino emission within the fireball paradigm

To calculate the analytic spectrum as shown in Fig 3ablue solid line the formulae given in Abbasi et al (2010Appendix A) were applied

In principle Guetta et al (2004) predicted different breakenergies for νmicro and νmicro (see Guetta et al 2004 Eqs (A10)and (A11)) yielding three breaks in the combined νmicro + νmicro spec-trum (or in the single νmicro spectrum when taking oscillations intoaccount) as shown in Fig 3a blue dashed ndash in the previousANTARES analysis (Adriaacuten-Martiacutenez et al 2013) this effecthas been accounted for

A9 page 3 of 11

AampA 559 A9 (2013)

E [GeV]310 410 510 610 710 810 910

]-2

[G

eV c

mν

F2 E

-510

-410

-310

-210

-110

E [GeV]310 410 510 610 710 810 910

]-2

[G

eV c

m F2 E

-510

-410

-310

-210

-110

(b)

Fig 3 a) Expected νmicro + νmicro spectra of GRB 110918 The analytic modelof Guetta et al (2004) (blue) is shown with the usual simple treatment(blue solid) and accounting for different break energies of νmicro and νmicro(blue dashed) The numerical NeuCosmA prediction is presented in redb) Individual νmicro + νmicro NeuCosmA spectra of the 296 GRBs (thin lines)and their sum (thick line)

42 NeuCosmA model

Monte Carlo algorithms such as SOPHIA (see Muumlcke et al2000) have improved the calculations of photohadronic interac-tions in astrophysical processes Huumlmmer et al (2012) showedthat a more detailed treatment of the particle physics involvedin calculating the neutrino spectra greatly changes the result-ing neutrino flux predictions compared with those describedin Sect 41 Using their neutrinos from cosmic accelerators(NeuCosmA) code the authors pointed out how the full photo-hadronic interaction cross-section individual treatment of sec-ondary particles (including energy losses) and neutrino mixingaffect the predicted neutrino flux (Huumlmmer et al 2010 2012Baerwald et al 2012) Owing to these effects the doubly peakedstructure of the spectrum from muon and pion decays now fea-tures an additional high-energy component from K+ decaysMoreover the authors discussed several problems with the olderneutrino flux estimations such as using the real average pho-ton energy instead of the peak energy of the photon distributiontaking the full width of the ∆-resonance into account and sim-ulating the energy losses of secondary particles as well as theenergy dependence of the mean free path of protons (see alsoHe et al 2012) The combination of all these effects gives riseto a prediction for the neutrino yield that is about one order ofmagnitude below the result of Guetta et al (2004)

Note that the NeuCosmA model however does not intro-duce any new assumptions on the nature of GRBs in general butapplies known physics in greater detail within the paradigm ofthe fireball model Hence limits on these predictions will firstof all constrain parameters governing the fireball model (such as

the boost factor Γ of the jet) and might later on probe the fireballparadigm itself

Predictions made by the NeuCosmA model are used to op-timise this analysis In Fig 3a a comparison between the pre-dicted neutrino spectra from Guetta et al (2004) and fromNeuCosmA is shown exemplarily for GRB 110918 Figure 3bshows all individual numerical neutrino spectra and their sum

5 Simulation and signal probability densityfunction

For each GRB in the selection neutrino events were generatedwith high statistics to simulate the predicted NeuCosmA spec-trum They were then reconstructed to compute the acceptanceof the detector Their distribution gives the signal probabilitydensity function (PDF) labelled S(α) = dN(α)dΩ with α beingthe space angle between the reconstructed track direction and thegamma-ray-burstrsquos coordinates

Firstly the passage of neutrinos from the direction of a GRBthrough the Earth was simulated If they interacted with mat-ter sufficiently close to or in the detector the resulting hadronicshower from the break-up of the target nucleon was gener-ated The secondary particles were then propagated through themedium inducing the emission of Cherenkov photons on theirtrajectory The response of the PMTs to the emitted Cherenkovlight was then simulated taking into account the detector andenvironmental conditions at the time of the GRB occurrenceFor a more detailed description of the simulation scheme seeAdriaacuten-Martiacutenez et al (2012)

For each GRB 4 times 109 muon neutrinos were simulated Nobackground events were generated as the background rate wasestimated using the data themselves (see Sect 6)

The applied track reconstruction algorithm is the same asused in Adriaacuten-Martiacutenez et al (2012) It is based on a multi-step algorithm to maximise the likelihood of an assumed trackhypothesis The reconstruction returns two quality parametersnamely the track-fit quality parameter Λ and the estimated an-gular uncertainty on the muon track direction β Cuts on theseparameters can be used to improve the signal-to-noise ratio Toensure a good directional reconstruction of the selected neutrinocandidates we required β lt 1 For a sample of track candidateswith high reconstruction quality (Λ gt minus52) this cut has beenshown to remove most of the remaining atmospheric muons thatwere falsely reconstructed as upgoing without significantly af-fecting the neutrino signal atmospheric muons are reduced bya factor of 12 times 10minus5 while atmospheric neutrinos are reducedby 019 The total background due to atmospheric events is de-creased by 10minus6 (Adriaacuten-Martiacutenez et al 2012) In this analysisthe same cut combination would leave sim60 70 of a typicalGRB signal However the narrow time windows (typically a fewtens of seconds see Table 2 for per-GRB values) yield intrinsi-cally low background in coincidence with each GRB allowingone to loosen the cuts on the Λ parameter These were then opti-mised for each burst individually

To account for the satellitersquos uncertainty on the directionof the GRB the reconstructed space angle was additionallysmeared with a Gaussian of the appropriate width

The resulting distribution of events relative to the GRB di-rection for each cut on Λ was then fitted with the function

logS(α) = logdN(α)

dΩ

=

A if α le α0

A minus B middot(1 minus exp

(minus(logαminus logα0)2

2σ2

))if α gt α0

(1)

A9 page 4 of 11

The ANTARES Collaboration Search for muon neutrinos from GRBs with ANTARES

Table 2 Optimisation results for the ten most promising GRBs

GRB Λcut microb microNeuCosmAs microGuetta

s 〈α〉 Tsearch σtot

() (s)

11091889 ndash53 11times 10minus4 30times 10minus2 15times 10minus1 030 734 5σ11091889 ndash55 37 times 10minus4 35 times 10minus2 17 times 10minus1 032 73408060725 ndash54 55 times 10minus4 65 times 10minus3 14 times 10minus2 033 164311100892 ndash55 36 times 10minus4 22 times 10minus3 26 times 10minus3 035 75410101417 ndash51 41 times 10minus4 12 times 10minus3 17 times 10minus2 089 723110072809 ndash56 20 times 10minus4 96 times 10minus4 14 times 10minus2 049 268609020174 ndash54 54 times 10minus4 70 times 10minus4 24 times 10minus2 039 126611122048 ndash52 14 times 10minus4 62 times 10minus4 12 times 10minus2 113 66509082967 ndash54 17 times 10minus4 39 times 10minus4 57 times 10minus3 102 112111062215 ndash54 17 times 10minus4 43 times 10minus4 95 times 10minus3 142 116608100914 ndash55 13 times 10minus4 35 times 10minus4 19 times 10minus3 094 702all GRBs 3σmean ndash54 17 times 10minus4 20 times 10minus4 16 times 10minus3 285 804sum 51 times 10minus2 61 times 10minus2 48 times 10minus1 24times 104

Notes Optimised Λcut values for the ten GRBs with the highest discov-ery probabilities and the resulting expected number of background andsignal events microb and micros at the significance level σtot The consequentmedian angular spread of events 〈α〉 is also provided In the last rowsthe sum and mean of the values for all 296 GRBs at 3σ is given Thenaming convention for the GRBs is similar to that used by Fermi thelast two digits of the GRB name correspond to the fraction of the day atwhich the burst occurred The full table is available at the CDS

Fig 4 Simulated and reconstructed signal events per solid angle Ωversus the logarithm of the space angle α in degrees for the burstGRB 110918 muon tracks are plotted in black shower-like events aredrawn in green The corresponding fit is shown in red (see Eq (1))The grey dotted line indicates the median angular spread of events〈α〉 = 032 The blue dashed line shows the flat background distri-bution B(α) as calculated in Sect 6 Cut values Λ gt minus55 and β lt 1are applied here

with the free parameters A B α0 andσ as shown in Fig 4 In thefinal analysis events with an angular distance of up to 10 fromthe burst positions were included in the maximum-likelihoodsearch

An investigation of shower-like events (eg from neutral cur-rent interactions of νmicro) revealed that these contribute only negli-gibly to the signal PDF up to 10 as the original neutrino direc-tion cannot be adequately reconstructed because of the sphericalsignatures of these interactions

6 Background estimation

Upgoing atmospheric neutrinos constitute the main backgroundcomponent for each GRB with a smaller contribution comingfrom misreconstructed downgoing atmospheric muons To es-timate the mean number of background events microb for each Λcut for each burst as realistically as possible data were usedHowever as the number of upgoing events is very low (simfourper day see Adriaacuten-Martiacutenez et al 2012 Table 1) long timeperiods are needed to yield sufficient statistics which in turn re-quires averaging over different data-taking conditions (in partic-ular because of seasonal variations of the optical background)To compensate for this we first estimated the average rate of re-constructed events in the GRBrsquos direction 〈n(θ φ)GRB〉all runs inlocal coordinates zenith θ and azimuth φ using data from the en-tire 2007 to 2011 period then adjusted it for varying data-takingconditions (for a detailed description see Appendix B)

For the final search the number of background events in co-incidence with each burst and within a search cone of 10 aroundits position was evaluated to be of the order of 10minus4 The back-ground PDF B(α) was considered to be flat in Ω within thiscone as shown in Fig 4 for GRB 110918

7 Pseudo-experiments and extendedmaximum-likelihood ratio

In the following we show how pseudo-experiments were gener-ated to compute the significance of a measurement then how thecut on the reconstruction quality parameter Λ was optimised foreach GRB to yield the highest discovery probability for a signalaccording to the NeuCosmA model

For the pseudo-experiments signal and background events iwith space angle αi were drawn randomly from the normalisedsignal S(α) and background B(α) PDFs corresponding to eachchosen cut on Λ For each pseudo-experiment with a total num-ber of events ntot the test statistic Q was calculated as follows

Q = maxmicroprimesisin[0ntot]

ntotsumi = 1

logmicroprimesS(αi) + microbB(αi)

microbB(αi)minus (microprimes + microb)

(2)

This is the so-called extended maximum-likelihood ratio(Barlow 1990) with an a priori knowledge of the expectednumber of background events microb (as evaluated in Sect 6 andAppendix B) Higher values of Q indicate that the measurementis more compatible with the signal hypothesis The signal con-tribution microprimes is scanned between 0 and ntot its value correspond-ing to the maximum of the sum in Eq (2) returns the estimatedsignal microest

s In the following hns (Q) denotes the distribution of Q-values

for ns injected signal events with a Poisson-distributed numberof background events with expectation value microb The signifi-cance of a measurement is determined by its p-value4 whichis given by the probability to yield Q-values at least as highas that observed if the background-only hypothesis were trueHence using the background-only distribution h0(Q) the low-est Q-value Qthres

p that is necessary to claim a discovery with acertain p-value can be calculated with

P(Q ge Qthresp | microb) =

int infin

Qthresp

h0(Q) dQ = p (3)

The probability distributions hns (Q) for different ns are shown inFig 5 with the threshold Q-values indicated by the grey dashed4 We used the two-sided convention that is p3σ = 27 times 10minus3 p5σ =57 times 10minus7

A9 page 5 of 11

AampA 559 A9 (2013)

Q0 10 20 30 40

snh

-1010

-910

-810

-710

-610

-510

-410

-310

-210

-110

13 4 5

Q0 10 20 30 40

snh

-1010

-910

-810

-710

-610

-510

-410

-310

-210

-110

1

Fig 5 Probability distributions of Q-values hns (Q) for different num-bers of injected signal events ns Black background only h0(Q) redgreen blue ns = 1 2 3 injected signal events Grey verticallines indicate the threshold values Qthres

p for different significances af-ter accounting for a trial factor of 296 (see Sect 8) as calculatedfrom h0(Q) This example shows GRB 110918 with Λ gt minus55 andmicrob = 37 times 10minus4 background events

lines The probability distribution of Q values for any number ofexpected signal events micros is calculated via

P(Q| micros) =

infinsumns = 0

P(ns| micros)hns (Q) (4)

with the Poisson distribution P(ns| micros) giving the probabil-ity of observing ns events from a mean number of expectedevents micros The integral of P(Q| micros) gives the model discovery po-tentialMDP it is the probability to make a discovery assumingthat the model was correct

MDP = P(Q ge Qthresp | micros) =

int infin

Qthresp

P(Q| micros) dQ (5)

=

infinsumns = 0

P(ns| micros)int infin

Qthresp

hns (Q) dQ

The value of the Λ cut at a given significance level is then cho-sen as that which maximises theMDP for the value of micros pre-dicted by the NeuCosmA model (see Sect 42) Figure 6 showsMDP(micros) of GRB 110918 for 3σ 4σ and 5σ versus an arbi-trary number of signal events The distribution P(Q| micros) fromEq (4) was also used to set upper limits on the number of signalevents when no discovery is made For example when the fi-nal analysis returns Qmeas we set a 90 confidence level (CL)upper limit micro90

s on the signal by rejecting all event expecta-tions micros that would lead to values Q gt Qmeas in 90 of allpseudo-experiments

P(Q ge Qmeas| micro90s ) =

int infin

Qmeas

P(Q| micro90s ) dQ = 09 (6)

When no event was measured (Qmeas = 0) a 90 CL upperlimit was set at 23 the lowest possible value5

For each number of injected signal events ns 105 pseudo-experiments were generated6 to derive the signal distributionshns (Q) Using this procedure the model discovery potential wascalculated for any given micros and the final cut on Λ for each GRBwas found5 The value derives from Poisson statistics since the probability todetect at least one event at a mean rate of 23 is exactly 906 Far more background-only pseudo-experiments are required to allowdetermining Qthres

p at p-values as low as p5σ296 sim 2 times 10minus9

s

0 1 2 3 4 5 6

MD

P

0

025

05

075

1

345

s

0 1 2 3 4 5 6

MD

P

0

025

05

075

1

Fig 6 Model discovery potential MDP versus number of signalevents micros for 3σ (red solid line) 4σ (black dotted) and 5σ (blue dashed)for GRB 110918

8 Search optimisation

In the following the best trade-off between an increased sampleand the associated statistical penalty is investigated In generala weighting factor wi could be assigned to each GRB accord-ing to the predicted flux from the model However this wouldresult in the search being very sensitive to the combined uncer-tainty from the NeuCosmA model and especially to the parame-ters upon which it is based An alternative approach is to includeonly the NGRB most promising candidates where to maintain thesame overall probability of making a false discovery the p-valuefor each burst must be divided by the total trial factor NGRBBy ordering the bursts from highest to lowestMDPi the mostpromising NGRB can be chosen to maximise the combined prob-ability of making a significant discovery from any of them Thetotal model discovery potential is then calculated via

MDP(NGRB) = 1 minusNGRBprodi = 1

(1 minusMDPi) (7)

The resulting distributions ofMDP(NGRB) as a function of thesize of the considered sub-sample of GRBs are shown in Fig 7for 3σ 4σ and 5σ (thick lines) The 3σMDP distribution risesto a maximum of 0059 at a sample size of 106 GRBs but is rel-atively flat around its highest value For a search optimised for3σ it is therefore reasonable to take the whole set of GRBs as itdoes not decrease theMDP significantly (around 34) and thesearch remains less model-dependent The 5σ MDP distribu-tion on the other hand is prominently peaked at NGRB = 1 withNGRB = 2 being almost equivalent (MDP(1) = MDP(2) =0025) ndash the model discovery potential then decreases for largersamples Even for NGRB = 2 the second strongest GRB con-tributes only a small fraction to the discovery potential

For comparison the distributions for a simple countingsearch (in which all events passing the cut criteria carry equalweighting) are also shown in Fig 7 (thin lines) To mimic thissearch a radius cut αcut for each GRB was calculated from theknown background microb at fixed reasonable quality cuts (Λ gtminus55 β lt 1) and the given significance level pNGRB Applyingthis search radius cut on the signal PDF S(α) the expected num-ber of signal events micros can be estimated and consequently theMDPi evaluated as the probability of detecting more than zeroevents

As expected the MDP curves for a counting analysis arewell below those for the likelihood method showing the advan-tage of the search method used in this analysis The shapes of the

A9 page 6 of 11

The ANTARES Collaboration Search for muon neutrinos from GRBs with ANTARES

GRB N1 10 210

MD

P

0

001

002

003

004

005

006

3

4

5

GRB N1 10 210

MD

P

0

001

002

003

004

005

006

Fig 7 Model discovery potential MDP versus the number of GRBsin an optimised sub-sample NGRB for 3σ 4σ and 5σ in red solidblack dotted and blue dashed lines For each sub-sample only the NGRBbursts with the best MDPi at the given trial factor NGRB are chosenThe thick lines show theMDP distributions of the likelihood methodused in this analysis the thin lines show the distributions for a simplecounting search with fixed quality cuts Λ gt minus55 β lt 1 (see text)

curves on the other hand are quite similar and the same con-clusions can be drawn from them namely that using the wholesample gives the best discovery probability at 3σ and using onlythe individual GRB 110918 at 5σ

Based on these results we decided to optimise the quality cuton Λ for a likelihood search on the whole sample of 296 GRBsat the 3σ significance level Because 3σ is not enough to claima discovery we predefined a cut on Λ that was optimised for a5σ discovery which was then used for a separate search for theemission from GRB 110918 only

Optimised cuts Λcut for the final analysis as well as the ac-cordingly expected number of background and signal eventsthe median angular resolution and the search-time window areshown in Table 2 for the ten most promising GRBs A full listfor the 296 selected bursts can be found at the CDS

9 Results and discussion

Using the strategy outlined above we analysed ANTARES datafrom the end of 2007 to 2011 searching for neutrino events in co-incidence with the search-time windows and within 10 aroundeach GRB No data events passed this selection within the accu-mulated search duration of 66 h Hence the measured Q-valueis zero

In total 006 neutrino events from GRBs are expected fromthe NeuCosmA model where only a small contribution of 46 times10minus5 events is not due to particle tracks produced by muon neu-trinos ndash the Guetta model predicts 05 signals from muon neu-trinos The overall background in the 10 cones is 005 eventsThe 90 CL upper limits on the expected number of sig-nal events micros from each model are thus set to 23 events andthe corresponding limits on the muon neutrino flux Fν fromGRB 110918 as well as on the cumulative flux from the wholesample are shown in Fig 8 The simple treatment of the Guettamodel is represented here (see Fig 3 a solid line) For theNeuCosmA model the limit on the total flux lies a factor of 38above the expected spectrum (44 for Guetta) The right-handaxis of Fig 8b represents the limits translated into limits on theinferred quasi-diffuse neutrino flux

E2Φν =sum

E2Fν times1

4π1

NGRB667 yminus1 (8)

E [GeV]510 610 710 810

]-2

[G

eV c

mν

F2 E

-310

-210

-110

1

10

210

]-1

sr

-1 s

-2 [

GeV

cm

ν2 E

-1110

-1010

-910

-810

-710

-610

E [GeV]510 610 710 810

]-2

[G

eV c

m F2 E

-310

-210

-110

1

10

210

ANTARES 2007ANTARES NeuCosmAANTARES GuettaIceCube IC40+59

(b)

Fig 8 a) Expected muon neutrino spectra of the most promising burstGRB 110918 (solid lines) from NeuCosmA (Huumlmmer et al 2010) (red)and Guetta et al (2004) (blue) Limits on these predictions are shownin the energy ranges where we expect 90 of the flux (dashed lines)b) Sum of the 296 individual gamma-ray-burst muon neutrino spectra(red and blue solid lines) and limits set by this analysis on the total fluxexpected from the sample (red and blue dashed lines) The IceCubeIC 40+IC 59 limit (Abbasi et al 2012) on the neutrino emission from300 GRBs and the first ANTARES limit from 2007 using 40 GRBs(Adriaacuten-Martiacutenez et al 2013) are also shown in black (dashed) and grey(dash-dotted) respectively The right-hand axis represents the inferredquasi-diffuse flux limit E2Φν (Eq (8))

where ν = νmicro + νmicro assuming that each analysed sample rep-resents an average burst distribution and that the annual rate oflong bursts is 667 per year

The first ANTARES limit (Adriaacuten-Martiacutenez et al 2013) ob-tained for 40 GRBs during the construction phase of the detec-tor in the year 2007 is also shown in Fig 8b That analysis wasbased on the Guetta model (accounting for different break ener-gies of νmicro and νmicro) and employed a counting method searching forneutrino events in a two-degree cone around each burst Usingthe data from the IC 40 and IC 59 detector phases in 2008 to2010 IceCube recently published a more stringent limit on theneutrino emission as predicted by the ldquosimplerdquo Guetta model(Abbasi et al 2012) which is also shown in Fig 8b

Because of the larger effective area of the IceCube detec-tor the new ANTARES limit presented in this paper does notset additional constraints on the Guetta emission model Notehowever that both detectors have complementary sky coverageand therefore the analysed sample of GRBs differs significantly90 of the analysed bursts have not previously had their neu-trino emission constrained When comparing limits obtained indifferent analyses however one should keep in mind that theprecise shapes of the spectra ndash and thus of the limits ndash dependon the actual selected sample the measured parameters of theindividual bursts and their uncertainty the set of default param-eters and on the chosen model

A9 page 7 of 11

AampA 559 A9 (2013)

10 Conclusion

Using data from the ANTARES detector a search for muon neu-trinos in coincidence with 296 GRBs occurring between the endof 2007 and 2011 has been performed No events passed the se-lection criteria and limits on the neutrino flux were derived Forthe NeuCosmA model a limit on E2Fν of 035minus56 GeV cmminus2

in the energy range from 75 times 104 GeV to 10 times 107 GeV wasderived and compared with limits obtained in previous analyses

This work is the first analysis based on an advanced numeri-cal calculation of GRB neutrinos the NeuCosmA code includesfull photohadronic interaction cross-sections energy losses ofsecondary particles and flavour mixing The neutrino flux hasbeen shown to be an order of magnitude below that predicted byprevious analytic approaches This helps to resolve the tensionbetween the non-observation of a neutrino signal and the moststringent experimental constraint currently available (Abbasiet al 2012) which was a factor of 37 below the predictionsmade by the Guetta model

Hence existing limits do not yet constrain realistic neu-trino emission models based on an internal shock scenarioNevertheless the collection of more data with active experi-ments such as ANTARES and IceCube as well as with theplanned neutrino telescope KM3NeT will certainly allow thewidely established fireball paradigm for GRBs to be probed inthe near future

Acknowledgements The authors acknowledge the financial support of thefunding agencies Centre National de la Recherche Scientifique (CNRS)Commissariat agrave lrsquoeacutenergie atomique et aux eacutenergies alternatives (CEA) AgenceNational de la Recherche (ANR) Commission Europeacuteenne (FEDER fund andMarie Curie Program) Reacutegion Alsace (contrat CPER) Reacutegion Provence-Alpes-Cocircte drsquoAzur Deacutepartement du Var and Ville de La Seyne-sur-Mer FranceBundesministerium fuumlr Bildung und Forschung (BMBF) Germany IstitutoNazionale di Fisica Nucleare (INFN) Italy Stichting voor FundamenteelOnderzoek der Materie (FOM) Nederlandse organisatie voor WetenschappelijkOnderzoek (NWO) the Netherlands Council of the President of the RussianFederation for young scientists and leading scientific schools supportinggrants Russia National Authority for Scientific Research (ANCS) RomaniaMinisterio de Ciencia e Innovacioacuten (MICINN) Prometeo of GeneralitatValenciana and MultiDark Spain Agence de lrsquoOriental and CNRST MoroccoWe also acknowledge the technical support of Ifremer AIM and Foselev Marinefor the sea operation and the CC-IN2P3 for the computing facilities We wouldlike to thank Walter Winter for helpful discussions and making it possible to usethe NeuCosmA model

ReferencesAbbasi R Abdou Y Abu-Zayyad T et al 2010 ApJ 710 346Abbasi R Abdou Y Abu-Zayyad T et al 2011 Phys Rev Lett 106 141101Abbasi R Abdou Y Abu-Zayyad T et al 2012 Nature 484 351Achterberg A Ackermann M Adams J et al 2008 ApJ 674 357Adriaacuten-Martiacutenez S Al Samarai I Albert A et al 2012 ApJ 760 53Adriaacuten-Martiacutenez S Samarai I Al Albert A et al 2013 J Cosmology

Astropart Phys 2013 006Ageron M Aguilar J A Al Samarai I et al 2011 Nucl Instr Meth A 656

11Aguilar J A 2011 in Proc of the 32nd International Cosmic Ray Conf 8

ICRC ed IUPAP (Institute of High Energy Physics Beijing) 232Aguilar J A Albert A Ameli F et al 2007 Nucl Instr Meth A 570 107Aptekar R Frederiks D Golenetskii S et al 1995 Space Sci Rev 71 265Atwood W B Abdo A A Ackermann M et al 2009 ApJ 697 1071Avrorin A Aynutdinov V Belolaptikov I et al 2011 Astron Lett 37 692Baerwald P Huumlmmer S amp Winter W 2012 Astropart Phys 35 508Band D Matteson J Ford L et al 1993 ApJ 413 281Barlow R 1990 Nucl Instr Meth A 297 496Besson D Razzaque S Adams J amp Harris P 2007 Astropart Phys 26

367de Ugarte Postigo A Gorosabel J Castro-Tirado A J amp Thoene C C 2011

GCN Circ 12375 1Eichler D Livio M Piran T amp Schramm D N 1989 Nature 340 126Fukuda S Fukuda Y Ishitsuka M et al 2002 ApJ 578 317

Galama T J Vreeswijk P M van Paradijs J et al 1998 Nature 395 670Gehrels N Chincarini G Giommi P et al 2004 ApJ 611 1005Goldstein A Burgess J M Preece R D et al 2012 ApJS 199 19Golenetskii S Aptekar R Frederiks D et al 2011 GCN Circ 12362 1Guetta D Hooper D Alvarez-Muntildeiz J Halzen F amp Reuveni E 2004

Astropart Phys 20 429He H-N Liu R-Y Wang X-Y et al 2012 ApJ 752 29Huumlmmer S Ruumlger M Spanier F amp Winter W 2010 ApJ 721 630Huumlmmer S Baerwald P amp Winter W 2012 Phys Rev Lett 108 231101Kouveliotou C Meegan C A Fishman G J et al 1993 ApJ Lett 413

L101Krimm H A Mangano V amp Siegel M H 2011 GCN Report 350 1Levan A J Tanvir N R Wiersema K Berger E amp Fox D 2011 GCN

Circ 12368 1Meegan C A Fishman G J Wilson R B et al 1992 Nature 355 143Meegan C Lichti G Bhat P N et al 2009 ApJ 702 791Meacuteszaacuteros P 2006 Rep Prog Phys 69 2259Meacuteszaacuteros P amp Rees M J 1993 ApJ 405 278Muumlcke A Engel R Rachen J P Protheroe R J amp Stanev T 2000 Comput

Phys Comm 124 290Nakar E 2007 Phys Rep 442 166Paciesas W S Meegan C A Pendleton G N et al 1999 ApJS 122

465Paciesas W S Meegan C A von Kienlin A et al 2012 ApJS 199 18Rees M J amp Meacuteszaacuteros P 1992 MNRAS 258 41Sakamoto T Barthelmy S D Baumgartner W H et al 2011 ApJS 195 2Tanvir N R Wiersema K Levan A J Greiss S amp Gaensicke B 2011

GCN Circ 12365 1Vieregg A G Palladino K Allison P et al 2011 ApJ 736 50Waxman E 1995a Phys Rev Lett 75 386Waxman E 1995b ApJ 452 L1Waxman E 2000 ApJS 127 519Waxman E amp Bahcall J 1997 Phys Rev Lett 78 2292Woosley S E amp Bloom J S 2006 ARAampA 44 507

1 Institut drsquoInvestigacioacute per a la Gestioacute Integrada de les ZonesCostaneres (IGIC) ndash Universitat Politegravecnica de ValegravenciaCParanimf 1 46730 Gandia Spain

2 GRPHE ndash Institut universitaire de technologie de Colmar 34 rue duGrillenbreit BP 50568 68008 Colmar France

3 CPPM Aix-Marseille Universiteacute CNRSIN2P3 Marseille France4 Technical University of Catalonia Laboratory of Applied

Bioacoustics Rambla Exposicioacute08800 Vilanova i la GeltruacuteBarcelona Spain

5 INFN ndash Sezione di Genova Via Dodecaneso 33 16146 GenovaItaly

6 Friedrich-Alexander-Universitaumlt Erlangen-Nuumlrnberg ErlangenCentre for Astroparticle Physics Erwin-Rommel-Str 1 91058Erlangen Germany

7 Direction des Sciences de la Matiegravere ndash Institut de recherche surles lois fondamentales de lrsquoUnivers ndash Service drsquoEacutelectronique desDeacutetecteurs et drsquoInformatique CEA Saclay 91191 Gif-sur-YvetteCedex France

8 Nikhef Science Park 105 1098XG Amsterdam The Netherlands9 APC Universiteacute Paris Diderot CNRSIN2P3 CEAIRFU

Observatoire de Paris Sorbonne Paris Citeacute 75205 Paris France10 IFIC ndash Instituto de Fiacutesica Corpuscular Edificios Investigacioacuten de

Paterna CSIC ndash Universitat de Valegravencia Apdo de Correos 2208546071 Valencia Spain

11 LAM ndash Laboratoire drsquoAstrophysique de Marseille Pocircle de lrsquoEacutetoileSite de Chacircteau-Gombert 38 rue Freacutedeacuteric Joliot-Curie 13388Marseille Cedex 13 France

12 INFN ndash Sezione di Bologna Viale Berti-Pichat 62 40127 BolognaItaly

13 Dipartimento di Fisica dellrsquoUniversitagrave Viale Berti Pichat 62 40127Bologna Italy

14 INFN ndash Sezione di Roma Ple Aldo Moro 2 00185 Roma Italy15 Dipartimento di Fisica dellrsquoUniversitagrave La Sapienza Ple Aldo

Moro 2 00185 Roma Italy16 Institute for Space Sciences 77125 Bucharest Magurele Romania17 Clermont Universiteacute Universiteacute Blaise Pascal CNRSIN2P3

Laboratoire de Physique Corpusculaire BP 10448 63000Clermont-Ferrand France

A9 page 8 of 11

The ANTARES Collaboration Search for muon neutrinos from GRBs with ANTARES

18 Geacuteoazur Universiteacute Nice Sophia-Antipolis CNRSINSU IRDObservatoire de la Cocircte drsquoAzur Sophia Antipolis France

19 INFN ndash Sezione di Bari via E Orabona 4 70126 Bari Italy20 INFN ndash Laboratori Nazionali del Sud (LNS) Via S Sofia 62 95123

Catania Italy21 Mediterranean Institute of Oceanography (MIO) Aix-Marseille

University 13288 Marseille Cedex 9 France22 Universiteacute Paris-Sud 91405 Orsay Cedex France23 Kernfysisch Versneller Instituut (KVI) University of Groningen

Zernikelaan 25 9747 AA Groningen The Netherlands24 INFN ndash Sezione di Pisa Largo B Pontecorvo 3 56127 Pisa

Italy25 Dipartimento di Fisica dellrsquoUniversitagrave Largo B Pontecorvo 3

56127 Pisa Italy26 Royal Netherlands Institute for Sea Research (NIOZ) Landsdiep 4

1797 SZ rsquot Horntje (Texel) The Netherlands27 Institut fuumlr Theoretische Physik und Astrophysik Universitaumlt

Wuumlrzburg Am Hubland 97074 Wuumlrzburg Germany28 Universiteit Utrecht Faculteit Betawetenschappen Princetonplein

5 3584 CC Utrecht The Netherlands29 Universiteit van Amsterdam Instituut voor Hoge-Energie Fysica

Science Park 105 1098 XG Amsterdam The Netherlands30 Dr Remeis-Sternwarte and ECAP Universitaumlt Erlangen-Nuumlrnberg

Sternwartstr 7 96049 Bamberg Germany

31 Moscow State University Skobeltsyn Institute of Nuclear PhysicsLeninskie gory 119991 Moscow Russia

32 INFN ndash Sezione di Catania Viale Andrea Doria 6 95125 CataniaItaly

33 Dipartimento di Fisica ed Astronomia dellrsquoUniversitagrave Viale AndreaDoria 6 95125 Catania Italy

34 Direction des Sciences de la Matiegravere ndash Institut de recherche surles lois fondamentales de lrsquoUnivers ndash Service de Physique desParticules CEA Saclay 91191 Gif-sur-Yvette Cedex France

35 Deacutepartement de Physique Nucleacuteaire et Corpusculaire Universiteacute deGenegraveve 1211 Geneva Switzerland

36 IPHC ndash Institut Pluridisciplinaire Hubert Curien ndash Universiteacute deStrasbourg et CNRSIN2P3 23 rue du Loess BP 28 67037Strasbourg Cedex 2 France

37 ITEP ndash Institute for Theoretical and Experimental Physics BCheremushkinskaya 25 117218 Moscow Russia

38 Universiteit Leiden Leids Instituut voor Onderzoek inNatuurkunde 2333 CA Leiden The Netherlands

39 Dipartimento di Fisica dellrsquoUniversitagrave Via Dodecaneso 33 16146Genova Italy

40 University Mohammed I Laboratory of Physics of Matter andRadiations BP 717 6000 Oujda Morocco

41 Universiteacute du Sud Toulon-Var CNRS-INSUIRD UM 110Marseille 83957 La Garde Cedex France

Pages 10 to 11 are available in the electronic edition of the journal at httpwwwaandaorg

A9 page 9 of 11

The ANTARES Collaboration Search for muon neutrinos from GRBs with ANTARES

18 Geacuteoazur Universiteacute Nice Sophia-Antipolis CNRSINSU IRDObservatoire de la Cocircte drsquoAzur Sophia Antipolis France

19 INFN ndash Sezione di Bari via E Orabona 4 70126 Bari Italy20 INFN ndash Laboratori Nazionali del Sud (LNS) Via S Sofia 62 95123

Catania Italy21 Mediterranean Institute of Oceanography (MIO) Aix-Marseille

University 13288 Marseille Cedex 9 France22 Universiteacute Paris-Sud 91405 Orsay Cedex France23 Kernfysisch Versneller Instituut (KVI) University of Groningen

Zernikelaan 25 9747 AA Groningen The Netherlands24 INFN ndash Sezione di Pisa Largo B Pontecorvo 3 56127 Pisa

Italy25 Dipartimento di Fisica dellrsquoUniversitagrave Largo B Pontecorvo 3

56127 Pisa Italy26 Royal Netherlands Institute for Sea Research (NIOZ) Landsdiep 4

1797 SZ rsquot Horntje (Texel) The Netherlands27 Institut fuumlr Theoretische Physik und Astrophysik Universitaumlt

Wuumlrzburg Am Hubland 97074 Wuumlrzburg Germany28 Universiteit Utrecht Faculteit Betawetenschappen Princetonplein

5 3584 CC Utrecht The Netherlands29 Universiteit van Amsterdam Instituut voor Hoge-Energie Fysica

Science Park 105 1098 XG Amsterdam The Netherlands30 Dr Remeis-Sternwarte and ECAP Universitaumlt Erlangen-Nuumlrnberg

Sternwartstr 7 96049 Bamberg Germany

31 Moscow State University Skobeltsyn Institute of Nuclear PhysicsLeninskie gory 119991 Moscow Russia

32 INFN ndash Sezione di Catania Viale Andrea Doria 6 95125 CataniaItaly

33 Dipartimento di Fisica ed Astronomia dellrsquoUniversitagrave Viale AndreaDoria 6 95125 Catania Italy

34 Direction des Sciences de la Matiegravere ndash Institut de recherche surles lois fondamentales de lrsquoUnivers ndash Service de Physique desParticules CEA Saclay 91191 Gif-sur-Yvette Cedex France

35 Deacutepartement de Physique Nucleacuteaire et Corpusculaire Universiteacute deGenegraveve 1211 Geneva Switzerland

36 IPHC ndash Institut Pluridisciplinaire Hubert Curien ndash Universiteacute deStrasbourg et CNRSIN2P3 23 rue du Loess BP 28 67037Strasbourg Cedex 2 France

37 ITEP ndash Institute for Theoretical and Experimental Physics BCheremushkinskaya 25 117218 Moscow Russia

38 Universiteit Leiden Leids Instituut voor Onderzoek inNatuurkunde 2333 CA Leiden The Netherlands

39 Dipartimento di Fisica dellrsquoUniversitagrave Via Dodecaneso 33 16146Genova Italy

40 University Mohammed I Laboratory of Physics of Matter andRadiations BP 717 6000 Oujda Morocco

41 Universiteacute du Sud Toulon-Var CNRS-INSUIRD UM 110Marseille 83957 La Garde Cedex France

Pages 10 to 11 are available in the electronic edition of the journal at httpwwwaandaorg

A9 page 9 of 11

AampA 559 A9 (2013)

Table A1 Usage of the GRB parameter catalogues

Source Position Time Fluence Spectrum Duration Redshift Start amp StopSwiftBAT 37 [3] 112 [3] 105 [3] 142 [3] 88 [3] 44 [2] ndashSwiftXRT 172 [2]SwiftUVOT 112 [1]Swift BAT2 112 [2] 101 [2] 98 [2] 112 [2] 44 [1] 101 [2]Fermi 679 [4] 777 [1] 777 [1] 362 [1] 774 [1] ndash 777 [1]IceCube 17 [4] 44 [4] 24 [4] 03 [3] 112 [3]

Notes The numbers in square brackets give the assigned priority of this source of information with respect to the parameter(s)

Table A2 Standard gamma-ray-burst parameters as described in thetext

α = 1 β = α + 1 εpeak = 200 keVz = 215 Liso = 1052 erg sminus1

Γ = 316 εe = 01 εB = 01fe = 01 〈xprarrπ〉 = 02 tvar = 001 s

Appendix A GRB selection

The table of the Swift satellite7 contains data from the three on-board instruments BAT (gamma rays) XRT (X-rays) and UVOT(ultraviolet) ordered with increasing position-measurement ac-curacy from arcminutes to sub-arcseconds The information pro-vides BAT spectral measurements in the energy range from 15to 150 keV The Swift BAT2 Catalogue (Sakamoto et al 2011)8

provides re-analysed Swift data so the spectral informationtherein is considered to be more accurate The Fermi GBM BurstCatalogue9 (Goldstein et al 2012 Paciesas et al 2012) suppliesthe best spectral information in the energy range from 10 keVto 1 MeV the peak flux spectrum and the spectrum averagedover the burst duration (which is eventually used for the neu-trino spectrum calculation) is fitted with four different spectralfunctions The angular resolution is of the order of degrees TheIceCube Collaboration also provides a table with GRB parame-ters10 (Aguilar 2011) which is created by parsing the Gamma-ray Coordinates Network (GCN) notices11 This table is used tofill up missing parameter values for GRBs that have been foundin at least one of the other tables

When merging the information on the GRB parameters weassigned priorities to the measured values according to theirconsidered accuracy The priorities of parameters are shown inTable A1 in square brackets as well as the percentage of howoften information was obtained from each source

When a parameter could not be measured standard values asgiven in Table A2 were used to calculate the spectra The formof the photon spectrum is determined by the spectral indices αand β with the break energy εpeak giving their transition Theisotropic luminosity Liso can be calculated from the redshift z andthe total measured fluence in gamma rays F (given in the energyrange from Emin to Emax) via Liso = 4πd2

LF

T90with the luminos-

ity distance dL In case of unknown redshift z we took the de-fault value of Liso T90 is the time in which 90 of the fluence is

7 Swift httpswiftgsfcnasagovdocsswiftarchivegrb_tablehtml8 BAT2 httpvizieru-strasbgfrviz-binVizieR-source=JApJS19529 Fermi httpheasarcgsfcnasagovW3Browsefermifermigbrsthtml10 IceCube httpgrbwebicecubewiscedu11 GCN httpgcngsfcnasagovgcn3_archivehtml

Table A3 Gamma-ray-burst parameters of GRB 110918 as describedin the text

α = 12 β = 20 εpeak = 150 keVF = 75 times 10minus4 erg cmminus2 Emin = 002 MeV Emax = 10 MeVUT = 21 26 57 dec = 325a RA = minus271a

∆err = 05primeprime T100 = 694 sb z = 0982 c

Notes All values are read from the IceCube table Values mea-sured by Konus-Wind (Golenetskii et al 2011) if not marked oth-erwise (a) Measured by the Isaac Newton Telescope (Tanvir et al2011) (b) Integration time of Konus-Wind (Golenetskii et al 2011)(c) Determined from Gemini-N (Levan et al 2011) and the GTC tele-scope (de Ugarte Postigo et al 2011)

emitted The other parameters such as the jet Lorentz boost fac-tor Γ the fraction of jet energy in electrons εe and in the magneticfield εB the ratio of energy in electrons and protons fe the av-erage fraction of proton energy transferred to a pion 〈xprarrπ〉 andthe variability of the gamma-ray light curve tvar are not present inthe tables and hence were taken as default The standard valuesare the same as given in Aguilar (2011) with some differences tothe IC 22 (Abbasi et al 2010) default values z = 20 Γ = 300Liso = 1051 erg sminus1 Baerwald et al (2012) give a very elaborateoverview about the NeuCosmA spectra changing with the inputparameters

The parameters of the extraordinarily strong GRB 110918are presented in Table A3

The time window of the search Tsearch for emission fromeach burst is delineated by the start and stop times as measuredby the satellites or when these are not provided in the cata-logues as T90 plusmn 30 Additionally we accounted for the detec-torrsquos data acquisition uncertainty (04 s) the satellite time givenin integer seconds (1 s) and the light propagation from a satel-lite through Earth to the detector (05 s) by adding another plusmn2 sto the search-time window

Appendix B Background estimation

We estimated the background event rate for each GRB sepa-rately First the time-averaged reconstructed event rate in thedata from late 2007 to 2011 from the direction of the GRB wasestimated Either the rate averaged over all data-taking runs atthe GRBrsquos position (θ φ)GRB was used or ndash if resulting in ahigher rate ndash the mean of the corresponding time-averaged rateswithin a 10 cone around this position This establishes a con-servative background estimate accounting for non-uniformity ofthe background in the vicinity of the GRBrsquos position

To take into account the varying efficiency of the detectorwith time this average rate was then scaled by a correctionfactor ci for each data-taking run i of sim25 h Each ci was

A9 page 10 of 11

The ANTARES Collaboration Search for muon neutrinos from GRBs with ANTARES

calculated by the ratio of the total number of events (in alldirections) in the corresponding run ni to the average to-tal number of events for the respective run duration ti (seeEq (B1)) As ni may be very small for short runs the 90CL upper limit was used instead Additionally factors forspecific run periods cperiod were applied taking into accountdifferences between longer phases of similar run conditionsThese values were obtained by fitting the background ratein certain periods separately This approach assumes that thetotal number of events ndash dominated mostly by downgoingatmospheric muons ndash is proportional to the number of upgoing

events To test this assumption we determined the measured andestimated rates of upgoing events in longer time periods of a fewdays excluding data-taking runs in which GRBs occurred Themeasured rate was always found to be micromeas lt 15 microest thus weconservatively increased the estimate by 50 Consequently theexpected number of background events in coincidence with eachGRB search-time window Tsearch was calculated via

microb(θ φ)GRB = Tsearch times 〈n(θ φ)GRB〉all runscicperiod15 (B1)

with ci = [ni]90

tisum

n jsum

t j where j includes all data-taking runs

A9 page 11 of 11

• Introduction
• ANTARES detector and data taking
• GRB selection and parameters
• Calculation of neutrino spectra
• • Analytic approaches
  • NeuCosmA model
  • • Simulation and signal probability density function
    • Background estimation
    • Pseudo-experiments and extended maximum-likelihood ratio
    • Search optimisation
    • Results and discussion
    • Conclusion
    • References
    • GRB selection
    • Background estimation