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9 0 The angular resolution of the Pierre Auger Observatory 0 2 C. Bonifazia∗ for the Pierre Auger Collaborationb n a aLPNHE, Université Paris VI-VII – CNRS/IN2P3. 4 place Jussieu, 75252 PARIS CEDEX 05, France J 0 bPierre Auger Observatory, av. San Mart´ın Norte 304, (5613) Malarguë, Argentina 2 ] Wediscusstheangularresolution obtainedforeventsregistered withthesurfacedetectoralone andforhybrid E events,i.e., those observed simultaneously by both the surface and fluorescence detectors. The angular accuracy H of the surface detector is directly extracted from the data itself and on an event by event basis, and is given as a function of the number of stations triggered by the event and of the zenith angle of the shower. We compare . h theangularresolutionofthesurfacedetectorobtainedfromhybrideventswiththeoneobtainedfromthesurface p detectoralone. - o r t s a 1. Introduction event basis, from the zenith (θ) and azimuth (φ) [ uncertainties obtained from the geometrical re- To fulfill the goal of the Pierre Auger Obser- 1 construction (section 3), using the relation [2,3]: v vatoryofdetermining the originofthe ultrahigh 2 8 energycosmicrays,theirarrivaldirectionmustbe F(η)=1/2 (V[θ]+sin (θ) V[φ]) 3 obtained with optimal accuracy. This includes a where η is the angle between the reconstructed 1 precise measure of the angular resolution (AR), shower direction and the true one, and V[θ] and 3 which we define as being the angular radius that V[φ] are the variances of θ and φ respectively. If . 1 contains68%ofthe showerscoming froma given θ and φ/sin(θ) have Gaussian distributions with 0 point source. varianceσ2,thenF(η)=σ2 andη hasadistribu- 9 0 The Pierre Auger Observatory consists of tionproportionaltoe−η2/2σ2 d(cos(η))dφ. Then, : two independent components: the surface de- accordingtoourdefinition,theangularresolution v i tector (SD), which is comprised of 1600 water is AR=1.5 F(η). X Cherenkov detectors distributed in a triangular The arrivapl direction of a SD event is deter- r grid with a separation of 1.5 km and cover- mined by fitting the arrival time of the first par- a ing an area of 3000 km2; and the fluorescence ticle in each station according to a shower front detector (FD), which is formed by 24 fluores- model. The accuracy achieved in the arrival di- cence telescopes located in 4 buildings overview- rection depends on the clock precision of the ing the surface detector [1]. Hybrid events, i.e., detector and on the fluctuations in the arrival events observed simultaneously by both compo- time of the first particle. The timing uncertainty nents, have smaller reconstruction uncertainties is directly modeled from the data in each sta- than the events observed with only the surface tion [4] (section 3.1). The model is adjusted us- component. On the other hand, the latter have ing pairs of adjacent stations located in the sur- much higher statistics than the former. face array. Then, it is validated by studying the The angular resolution for hybrid events is de- χ2 probabilitydistributionforthegeometricalre- terminedfromsimulations,bycomputingthe an- construction and by comparing two independent gle between the simulated event and its recon- reconstructions of the same event (section 3.2). structed direction (section 2). The angular reso- Theangularresolutioncanthereforebeestimated lution for the SD is determined, on an event by fortheSDreconstructiononaneventbyeventba- sis (section 3.3). Using the hybrid events, we are ∗[email protected] abletoextract,forasubsetofevents,theangular 1 2 resolution of the surface detector and compare it with the one obtained onan event by event basis (section 4). 2. Angular resolution of hybrid events The angular resolution for hybrid events is de- terminedfromsimulations,bycomputingthe angle (η) between the injected shower axis and the reconstructed one. We simulated 5678 proton showers with the Corsika 6.616 code [5] using QGSJetII-03 [6] and FLUKA [7] codes for high and low energy hadronic interaction models re- Figure 1. Angular resolutionofhybrideventsde- spectively. The showers were simulated up to a termined with simulations as a function of the ◦ zenith angle (θ) of 65 , with a distribution of energy. cos(θ)sin(θ), an uniform distribution in the azimuth angle, and for various energies from 0.1 process over a time interval T. The arrival time EeV to 10 EeV in steps of 0.25 in logarithmic of the first particle (T1) is used as the estimator scale. For each shower we generated uniformly a ◦ for the shower front arrival and its distribution corepositioninasliceof60 infrontofoneofthe function is given by: fluorescencetelescopes witha maximumdistance from the telescope increasingwith the energy ac- 1 −T1 cording to the triggerefficiency [8]. Once the hy- f(T1)= τ e τ , brid simulation was performed, we reconstructed 2 withτ =T/n,wherenisthenumberofparticles the simulated events with the same reconstruc- measured during the time T. Then, the variance tion chain used for data. In figure 1 we show the angular resolution, de- of T1 is τ2, but since we estimate the parameter T from the data itself, it is modified to [4]: terminedasthevaluewherethecumulativedistri- butionfunctionofη(θ)reaches0.68,asafunction 2 T n 1 of the energy. As can be observed, the angular V[T1]= − . (cid:18)n(cid:19) n+1 resolution improves for larger energy showers. It is worthwhile to remark that this behavior origi- The variance of T in the SD stations is given by s nates from the convolution of the dependence of the sum of the detector clock precision (b2) and the angular resolution with the different geomet- of the variance of T1. It then becomes: rical parameters. Also, it is important to check 2 these results using real data. For example, using 2 2 T50 n 1 2 V[T ]=a − +b , stereo events, which have fluorescence telescopes s (cid:18) n (cid:19) n+1 with triggered pixels in more than one building. where T50 is the time interval that contains the first 50% of the total signal as measured 3. Angular resolution of the surface detec- by the photomultiplier FADC (flash analog-to- tor digital converters) traces. The parameter a is a 3.1. Time variance model 2Tocalculatethenumberofparticlesn,weassumedthat The angular accuracy of the surface detector the muons are the particles that contribute the most to events is driven by the precision in the measure- the time measurement and in average cross the detector withthedirectiongivenbythezenithangleoftheshower. ment of the arrival time of the shower front (T ) s Thenumberofparticlesiscalculatedastheratiobetween at each station [4]. The particle arrival time in thetotalsignalinthestationsandthetracklengthofthe the shower front can be described as a Poisson particles. 3 scale factor, containing all the assumptions con- 1.4 gasthiindvedeernFtehAdbeDyiFnCAthtDhetrCeaGcmtPerosaS.dceecllTroeahcsnkeodlauptctahciroueanrmta(rce2eyt5ae/tr(m√abbe1no2stuhntodsu)o1,ln0dtehnbatsoet) ------------------------------------√(V[T]+V[T])1201..1640.2 0.3 0.4 0.5 0.6 0.7 0.8 0.c9os(θ)1 is b ≃ 12 ns. Both a and b are determined from T)/2 1 the data. T-d10.60 2.5 5 7.5 10 12.5 15 17.5 20 22.5 Aspecialsub-arrayofpairsofwaterCherenkov d detectors has been deployed as a part of the sur- S of ( 1.4 Signal [VEM] face array. These are adjacent detectors located RM 1 11mapart,andthereforearesamplingthesame 0.6 ∼region of the shower front. To determine the pa- 400 600 800 1000 1200 1400 Distance (m) rametersa andb we used allthe eventsthat pass our selection criteria [9] from April 2004 to the Figure 2. The RMS of the distribution of end of August 2008 with at least one pair in the ∆T/ V[∆T], as a function of the shower zenith event. There is total of 46416 events, which are anglep(top),theaveragesignalintheadjacentde- used to fit these two parameters yielding: tectors(middle),andtheirdistancetotheshower core (bottom). a = 0.60 0.01, ± b = (14.1 0.2)ns, ± withaχ2/ndof =0.9992. Moredetailsaboutthe near to the shower core. Wealsostudiedthedistributionoftheχ2prob- timevariancemodelandthefittingprocedurecan ability of the geometrical reconstruction. In fig- be found in reference [4]. ure 3 (top) we show the distribution for the 3.2. Validation of the time variance model 308234 events passing our quality cuts [9] with 4 In this section, we show that the model cor- or more stations. This distribution is almost flat rectly reproduces the uncertainties of the arrival asitshouldbeintheidealcase,despitethesmall time of the first particle in the stations. peakatlowvalues. Thissmallpeakcouldbedue, Wedefine the timedifference ∆T =dT1 dT2, for example, to some stations in the events that where dT1 (dT2) is the time residual of th−e first havelowsignal,causingalargeχ2. Butasisseen (second) twin station to the fitted shower front. infigure3(bottom),thepeakdisappearsforlarge If the time variance model describes correctly multiplicity events (for 5 or more stations). For the measurement uncertainties, the distribution both cases, we only plot χ2 probabilities larger of ∆T/ V[∆T], where V[∆T] = V[T1]+V[T2], than 1% to avoid the large peak at zero corre- shouldhpaveunitvariance. Infigure2weshowthe sponding to badly reconstructed events ( 5%). 2 ∼ RMS of the distribution of ∆T/ V[∆T] for the Also,westudytheχ probabilitydistributionfor adjacent detectors as a functionpof cos(θ) (top), twozenithangleranges,asshowninfigure4. The the average signal (middle), and the distance of χ2 probability distribution is flat for both large the paired detectors to the core position (bot- and small zenith angles, which means that the tom). In all the cases, the RMS is almost con- model worksfor all angles without compensating stant and close to unity, which shows that the one set from the other. This distribution shows time variance model adequately reproduces the that the variance model properly reproduces the experimentaldata. Itisworthwhiletonoticethat uncertainties of the arrival time of the particles the time variance model does not explicitly de- in the stations and allows us to determine the pend onthe distance ofthe stationto the shower angular resolution from the uncertainties in the core. Despitethis,theresultshowninthebottom reconstruction data. panel is satisfactory, with only a small tendency We areableto validateindependently the time to overestimate the variance for detectors very variance model by using the redundant informa- 4 8000 6000 For all the stations Entries 285 Entries 285 50 χ2 / ndf 10.29 / 15 50 χ2 / ndf 16.43 / 18 4000 µ -0.07 / 0.06 µ 0.10 / 0.07 40 σ 1.03 ± 0.05 40 σ 1.07 ± 0.07 2000 0 30 30 0 0.2 0.4 0.6 0.8 1 20 20 3000 For 5 or more stations 10 10 2000 0 0 -2.5 0 2.5 5 7.5 -2.5 0 2.5 5 7.5 1000 (θ1-θ2)/(V[θ1]+V[θ2])1/2 (φ1-φ2)/(V[φ1]+V[φ2])1/2 0 0 0.2 0.4 0.6 0.8 1 Probability Figure 5. Distribution ofthe difference of zenith (left) and azimuth (right) angles from each in- Figure 3. The χ2 probability distribution for all dependent reconstruction divided by the square events (top)andfor5ormorestations(bottom). root of the sum of its variances for the case of 6 See text for details. or more stations in the event. For 5 or more stations by the square root of the sum of its variances for 1500 Events with θ < 55o the case of 6 or more stations which corresponds 1000 to events withenergyhigher than10EeV.We fit 500 the distribution with a Gaussian and we obtain a sigma value compatible with 1. Despite of the 0 0 0.2 0.4 0.6 0.8 1 low statistics, this result shows that the uncertainties in the determination of the arrival time 1500 Events with θ > 55o of the first particle in the stations are well repre- 1000 sented. The same results are obtained for other 500 multiplicities, except for the 3-fold case, where 0 the sigma is about 0.75 which indicates that we 0 0.2 0.4 0.6 0.8 1 are slightly overestimating the uncertainties. PPrroobbaabbiilliittyy Figure 4. The χ2 probability distribution for 3.3. Angular resolution Considering the quality of the time variance events with 5 or more stations and with zenith ◦ model for the measurementuncertainties,we can anglesmaller(top)andhigher(bottom)than55 . calculate directly the angular resolution on an eventbyeventbasisoutofthe minimizationpro- cedure. In figure 6, we show the angular resolution given by the special sub-array of adjacent tion as a function of the zenith angle for various detectors. To perform this analysis, we select station multiplicities. ◦ thoseeventswithatleastthreepairsandwiththe The angular resolution is about 2.2 in the showercoreinsidetheregiondefinedbythesesta- worst case of vertical showers with only 3 stations, to guarantee a good reconstruction. Then tions hit. This value improves significantly for 4 the reconstruction is performed twice, each time and5stations. For6ormorestations,whichcor- using the information of one of the tanks in each responds to events with energies above 10 EeV, pair. This provides two quasi-independent esti- the angular resolution is in all cases better than ◦ ◦ matesofthearrivaldirectionofthesameshower. 1 . Above 60 , the event multiplicity increases In the left (right) panel of figure 5 we show the rapidly with zenith angle,and only a few low en- distribution of the difference of the zenith (az- ergy events trigger only 3 stations, thus the ac- imuth) angles from each reconstruction divided curacy decreases. Also, a hump appears around 5 grees)22.2.55 grees) 1.8 on (de 2 on (de 1.6 uti uti 1.4 ol1.75 ol Res Res 1.2 gular 1.5 gular 1 An1.25 An 1 0.8 0.75 0.6 3 stations 3 stations 0.5 4 stations 0.4 4 stations 0.25 56 sotra mtioonrse stations 0.2 56 sotra mtioonrse stations 0 0 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 θ (degrees) θ (degrees) Figure 6. Angular resolution as a function of Figure 7. Angular resolution as a function of the the zenith angle (θ) and for events with 3 sta- zenith angle (θ) for events with an energy above tions (circles), 4 stations (squares), 5 stations 3 EeV, and for various station multiplicities. (up-triangles), and 6 or more stations (down- triangles). thosetwoestimatesfordifferentmutiplicitiesand zenithangleranges. Then,theangularresolution ◦ of the surface detector can be obtained as: 40 , more visible in the 3-fold case. This is due to the contribution of the uncertainties on the AR = AR2 AR2 core position for events with lower energy (less SD q η− hyb than few EeV). In figure 7, we show the angu- whereAR isthevalueofηforwhichthecumula- η lar resolution as a function of the zenith angle tivedistributionfunctionofη(θ)reaches0.68and for events with an energy above 3 EeV, which is AR is the angular resolution of hybrid events hyb the energy corresponding to a trigger efficiency obtainedfromMonteCarlosimulations(shownin greater than 99% [10]. In spite of the degrada- figure 1). tion of the statistics for 3-fold events, the hump In figure 8 we show the angular resolution for disappearsandtheangularresolutiongetsbetter. the surfacedetector (AR ) usingthe hybridre- SD Forhighmultiplicityevents,asitisexpected,the construction as a reference, as a function of the angular resolution is not affected by the cut in zenith angle (θ) for different numbers of stations energy. We want to remark that all uncertainties in the event. This plot can be directly compared quoted in figures 6 and 7 are statistical only. We with the one in figure 6 despite the differences in did not, at this stage, investigate possible biases the statistics. The values obtainedinfigure8 are orsystematicsinthe determinationofthe arrival slightly higher than the ones obtained from the direction angles. direct determination of the angular resolutionon aneventbyeventbasis. Thiscouldbeduetosys- 4. Angular resolution of the surface detec- tematic uncertainties in the reconstructions. For tor using hybrid events the case of 3-fold events, this slight difference is notpresentandthiscouldbeduetothefactthat Hybrid events that trigger 3 or more stations the uncertainties seem to be overestimated (sec- can be reconstructed using both the hybrid and tion 3.2). the surface detector alone modes, giving two independent estimates of the geometry. The com- 5. Summary parison of these estimates is therefore an addi- tional independent check of the accuracy on the We have determined the angular resolution for determination of the arrival direction of the cos- the hybrid events using Monte Carlo simulations mic rays. Therefore,we compute the angle (η) of and we found that for energies above 3 EeV it 6 degrees)22.2.55 5. aDr.XiHv:e0c7k05.e1t856al[.a,str“oC-pOhR]SIKA: A Monte on ( 2 Carlo Code to Simulate Extensive Air uti Resol1.75 Showers”, Report FZKA 6019, (1998); ular 1.5 D. Heck, T. Pierog, J. Knapp, COR- g An1.25 SIKA: an air shower simulation program: 21 74 146 294 1 http://www-ik.fzk.de/corsika/ 525 706 0.75 6. S.Ostapchenko,Nucl.Phys.B(Proc.Suppl.) 3 stations 151, 143 (2006); [arXiv:hep-ph/0412332] 0.5 4 stations 5 stations 7. A. Fasso, A. Ferrari, J. Ranft, P.R. Sala, 0.25 6 or more stations FLUKA: a multi-particle transport code, 0 0 10 20 30 40 50 60 CERN-2005-10,2005. θ (degrees) 8. A. Ewers et al. [Pierre Auger Collaboration], Figure 8. Angular resolution for the surface de- in Proceedingsofthe 29th InternationalCos- tector events using the hybrid reconstruction as mic Ray Conference, Pune, India, vol. 7, pp. a reference, as a function of the zenith angle (θ) 115-118,(2005) andfordifferentnumbersofstationsintheevent. 9. D. Allard et al. [Pierre Auger Collaboration], See text for more details. in Proceedingsofthe 29th InternationalCos- mic Ray Conference, Pune, India, vol. 7, pp. is about 0.5◦. For the surface detector, we de- 287-290,(2005) termined the angular resolution from the data. 10. D. Allard et al. [Pierre Auger Collaboration], This could be done thanks to the time variance in Proceedingsofthe 29th InternationalCos- modeldevelopedtodescribethemeasurementun- mic Ray Conference, Pune, India, vol. 7, pp. certainties of the time arrival of the first parti- 71-74 , (2005); [arXiv:astro-ph/0511104] cle in the surface stations. Using this model we obtaines an optimal determination of the shower arrival direction and are able to extract the angular resolution of the surface detector on an event by event basis. We found the angular res- ◦ olution to be better than 2.2 for 3-fold events ◦ (E < 4 EeV), about 1.5 for 4-fold and 5-fold ◦ events (3 EeV< E < 10 EeV) and better than 1 for higher multiplicity events (E > 10 EeV). REFERENCES 1. J. Abraham et al. [Pierre Auger Collabora- tion], Nucl. Instr. & Meth. A 523, (2004) 2. C. Bonifazi [Pierre Auger Collaboration], in Proceedingsofthe 29thInternationalCosmic RayConference,Pune,India,vol.7,pp.1720, (2005) 3. M. Ave [Pierre Auger Collaboration], in Pro- ceedings of the 30th International Cosmic Ray Conference, Mérida, México, (2007); arXiv:0709.2125[astro-ph] 4. C. Bonifazi, A. Letessier-Selvon, E.M. San- tos, Astropart. Phys. 28, 523-528 (2008);