Measurement of the UHECR energy spectrum using data from the Surface Detector of the Pierre Auger Observatory
aa r X i v : . [ a s t r o - ph ] J un TH I NTERNATIONAL C OSMIC R AY C ONFERENCE
Measurement of the UHECR energy spectrum using data from the Surface Detectorof the Pierre Auger Observatory M ARKUS R OTH , FOR THE A UGER C OLLABORATION Institut f¨ur Kernphysik, Forschungszentrum Karlsruhe, POB 3640, D-76021 Karlsruhe, Germany Observatorio Pierre Auger, Av. San Mart´ın Norte 304, (5613) Malarg¨ue, Mendoza, Argentina
Abstract:
At the southern site of the Pierre Auger Observatory, which is close to completion, an exposurethat significantly exceeds the largest forerunner experiments has already been accumulated. We reporta measurement of the cosmic ray energy spectrum based on the high statistics collected by the surfacedetector. The methods developed to determine the spectrum from reconstructed observables are described.The energy calibration of the observables, which exploits the correlation of surface detector data withfluorescence measurements in hybrid events, is presented in detail. The methods are simple and robust,exploiting the combination of fluorescence detector (FD) and surface detector (SD) and do not rely ondetailed numerical simulation or any assumption about the chemical composition. Besides presentingstatistical uncertainties, we address the impact of systematic uncertainties.
Introduction
The Pierre Auger Observatory [1] is designed tomeasure the extensive air showers produced by thehighest energy cosmic rays (
E > . eV) withthe goal of discovering their origins and composi-tion. Two different techniques are used to detect airshowers. Firstly, a collection of telescopes is usedto sense the fluorescence light produced by exci-tation of nitrogen induced by the cascade of parti-cles in the atmosphere. The FD provides a nearlycalorimetric, model-independent energy measure-ment, because the fluorescence light is producedin proportion to energy dissipation by a shower inthe atmosphere [2, 3]. This method can be usedonly when the sky is moonless and dark, and thushas roughly a 10% duty cycle [4]. The secondmethod uses an array of detectors on the ground tosample particle densities as the air shower arrivesat the Earth’s surface. The surface detector has a100% duty cycle [5]. A subsample of air show-ers detected by both instruments, dubbed hybridevents, are very precisely measured [6] and pro-vide an invaluable energy calibration tool. Hybridevents make it possible to relate the shower energy(FD) to the ground parameter S (1000) . Analysis procedure
The parameter S (1000) characterises the energy ofa cosmic ray shower detected by the SD array andis the signal in units of VEM that would be pro-duced in a tank at a distance of 1000 m from theshower axis. One VEM is the signal produced by asingle relativistic muon passing vertically throughthe centre of a water tank. A likelihood method isapplied to obtain the lateral distribution function,where the shower axis, S (1000) and the curvatureof the shower front are determined [7]. The se-lection criteria are such to ensure the rejection ofaccidental triggers (physics trigger) and the eventsare well contained in the SD array (quality trig-ger), i.e. we require that all six nearest neighboursof the station with the highest signal be active. Inthis way we guarantee that the core of the showeris contained inside the array and enough of theshower is sampled to make an S(1000) measure-ment. The present data set is taken from 1 January,2004 through 28 February, 2007 while the arrayhas been growing in size. To ensure an excellentdata quality we remove periods with problems dueto failures in data acquisition, due to lightning andhardware difficulties. We select events only if the EASUREMENT OF THE ENERGY SPECTRUM USING DATA FROM THE P IERRE A UGER O BSERVATORY
Figure 1: Integral number of events vs cos θ forthe indicated minimum value of S (1000) .zenith angle is less than ° and the reconstructedenergy is above 3 EeV. For this analysis, the arrayis fully efficient for detecting such showers, so theacceptance at any time is solely determined by thegeometric aperture of the array [8]. The integratedexposure mounts up to about 5165 km sr yr,which is a factor of more than 3 larger than theexposure obtained by the largest forerunner ex-periment AGASA [9]. Moreover the present ac-ceptance exceeds the one given in [10] by a fac-tor of about 3. For a given energy the value of S (1000) decreases with zenith angle, θ , due to at-tenuation of the shower particles and geometricaleffects. Assuming an isotropic flux for the wholeenergy range considered, i.e. the intensity distribu-tion is uniform when binned in cos θ , we extractthe shape of the attenuation curve from the data. InFigure 1 several intensities, I i = I ( > S i (1000)) ,above a given value of lg S i (1000) are shown asa function of cos θ . The choice of the threshold lg S (1000) is not critical since the shape is nearlythe same within the statistical limit. The fitted at-tenuation curve, CIC ( θ ) = 1 + a x + b x , is aquadratic function of x = cos θ − cos ◦ as dis-played in Figure 2 for a particular constant inten-sity cut, I = 128 events, with a = 0 . ± . and b = − . ± . . The cut correspondsto a shower size of about S ◦ =
47 VEM andequivalently to an energy of about 9 EeV. Sincethe average angle is h θ i ≃ ◦ we take this an-gle as reference and convert S (1000) into S ◦ by S ◦ ≡ S (1000) /CIC ( θ ) . It may be regardedas the signal S (1000) the shower would have pro- Figure 2: Derived attenuation curve, CIC ( θ ) , fit-ted with a quadratic function.duced had it arrived at θ = 38 ◦ . The reconstruc-tion accuracy of the parameter S (1000) , σ S (1000) ,comprises 3 contributions and these are taken intoaccount in inferring S ◦ and its uncertainty σ S ◦ :a statistical uncertainty due to the finite size of thedetector and the limited dynamic range of the sig-nal detection, a systematic uncertainty due to theassumptions of the shape of the lateral distribu-tion and finally due to the shower-to-shower fluc-tuations [11]. To infer the energy we have to es-tablish the relation between S ◦ and the calori-metric energy measurement, E F D . A set of hybridevents of high quality is selected based on the crite-ria reported in [6] without applying the cut on thefield of view, which appears to have a negligibleeffect for the topic addressed here. A small correc-tion to account for the energy carried away by highenergy muons and neutrinos, the so-called invisi-ble energy , depends slightly on mass and hadronicmodel. The applied correction is based on the av-erage for proton and iron showers simulated withthe QGSJet model and sums up to about andits systematic uncertainty contributes to the to-tal uncertainty in FD energy [3]. Moreover the SDquality cuts described above are applied. The cri-teria include a measurement of the vertical aerosoloptical depth profile (VAOD(h)) [12] using lasershots generated by the central laser facility (CLF)[13] and observed by the FD in the same hour ofeach selected hybrid event. The selected hybridevents were used to calibrate the SD energy. Thefollowing procedure was adopted. For each hy-brid event, with measured FD energy E F D , theSD energy estimator S ◦ was determined from the Final version October 27, 2018 TH I NTERNATIONAL C OSMIC R AY C ONFERENCE
Figure 3: Correlation between lg E F D and lg S ◦ for the 387 hybrid events used in the fit. The fullline is the best fit to the data. Events below thedashed line were not included in the fit.measured S (1000) by using the constant intensitymethod described above. For each event the uncer-tainty in S ◦ is estimated by summing in quadra-ture three contributions: the uncertainty in the con-stant intensity parametrization, σ S ◦ ( CIC ) , theangular accuracy of the event, σ cosθ , and the uncer-tainty in the measured S (1000) , σ S (1000) . The flu-orescence yield used to estimate the energy E F D istaken from [14]. An uncertainty in the FD energy, σ E FD , was also assigned to each event. Severalsources were considered. The uncertainty in thehybrid shower geometry, the statistical uncertaintyin the Gaisser-Hillas fit to the profile of the en-ergy deposits and the statistical uncertainty in theinvisible energy correction were fully propageted.The uncertainty in the VAOD measurement wasalso propagated to the FD energy on an event-by-event basis, by evaluating the FD energy shiftobtained when changing the VAOD profile by itsuncertainty. These individual contributions wereconsidered to be uncorrelated, and were thus com-bined in quadrature to obtain σ E FD . The dataappear to be well described by a linear relation lg E F D = A + B · lg S ◦ (see Figure 3). A lin-ear least square fit of the data was performed. Toavoid possible biases, low energy events, below thedashed line, which is orthogonal to the best fit lineand intersects it at lg( S ◦ =
15 VEM ) , were notincluded in the fit. Figure 4: Fractional difference between the FD andSD energy for the 387 selected hybrid events.An iterative procedure was used to determine thedashed line, and it was checked that the resultsof the fit were stable. The best fit yields A =17 . ± . and B = 1 . ± . with a reduced χ of 1.3 for lg E SD = A + B · lg S ◦ in [eV] . Therelative statistical uncertainty in the derived SD en-ergy, σ ESD / E SD , is rather small, e.g. of the orderof 5% at 10 eV. The energy spectrum J is dis-played in Figure 5 together with its statistical un-certainty. The individual systematic uncertaintiesin determining E SD coming from the FD sum upto 22%. For illustrative purposes we show in Fig-ure 6 the difference of the flux with respect to anassumed flux ∝ E − . . The largest uncertaintiesare given by the absolute fluorescence yield (14%),the absolute calibration of the FD (9.5%) and thereconstruction method (10%). The uncertainty dueto the dependence of the fluorescence spectrumon pressure (1%), humidity (5%) and temperature(5%) are take into account as well as the wave-length dependent response of the FD, the aerosolphase function, invisible energy and others, whichare well below 4% (see [4] for details). Discussion and outlook
When inferring the energy spectrum from SD datawe utilise the constant intensity method to cali-brate the SD data. The systematic uncertainties
Final version October 27, 2018
EASUREMENT OF THE ENERGY SPECTRUM USING DATA FROM THE P IERRE A UGER O BSERVATORY
Figure 5: Auger spectrum J as a function of energy. Ver-tical error bars represent thestatistical uncertainty only.The statistical and system-atic uncertainties in the en-ergy scale are of the order of ≈ and ≈ , respec-tively.have been scrutinised and the resulting spectrumis given. Several activities are on-going to reducethe systematic uncertainties of the energy estimate,e.g. the detector calibration uncertainty and the un-certainty of the fluorescence yield. Reducing theseFigure 6: Fractional difference between the de-rived spectrum and an assumed flux ∝ E − . asa function of energy.uncertainties will make it desirable to deconvolvethe energy spectrum using the estimate of the en-ergy resolution. The presented spectrum is com-pared with a spectrum derived on basis of hybriddata only in T. Yamamoto et al. [15]. Astrophysi-cal implications are also discussed there. References [1] J. Abraham [Pierre Auger Collaboration],NIM 523 (2004) 50.[2] M. Risse and D. Heck, Astropart. Phys. 20(2004) 661.[3] H. Barbosa et al., Astropart. Phys. 22 (2004)159.[4] B. Dawson [Pierre Auger Collaboration]these proceedings, (2007), th ICRC, Pune (2005), , 291.[8] D. Allard [Pierre Auger Collaboration], Proc. th ICRC, Pune (2005), , 71.[9] M. Takeda et al., Astropart. Phys. 19 (2003)447.[10] P. Sommers [Pierre Auger Collaboration],Proc. th ICRC, Pune (2005) , 387.[11] M. Ave [Pierre Auger Collaboration] theseproceedings, (2007), , 387.[11] M. Ave [Pierre Auger Collaboration] theseproceedings, (2007),