de Naurois, M.

Djannati-Atai, A.

Guy, J.

Tavernet, J-P.

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Application of an analysis method based on asemi-analytical shower model to the first H.E.S.S.telescopeM. De Naurois, J. Guy, A. Djannati-Atai, J-P. TavernetTo cite this version:M. De Naurois, J. Guy, A. Djannati-Atai, J-P. Tavernet. Application of an analysis methodbased on a semi-analytical shower model to the first H.E.S.S. telescope. Kajita T. Asaoka Y.Kawachi A Matsubara Y. Sasaki M. International Cosmic Ray Conference 28 ICRC 2003, Jul2003, Tsukuba, Japan. Universal Academy Press, pp.2907-2910, 2003. <in2p3-00013847>HAL Id: in2p3-00013847http://hal.in2p3.fr/in2p3-00013847Submitted on 1 Oct 2003HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.28th International Cosmic Ray Conference 2907Application of an analysis method based on a semi-analytical shower model to the first H·E·S·S· telescopeM. de Naurois1, J. Guy1, A. Djannati-Ata¨ı2 , J.-P. Tavernet1 for the H·E·S·S·collaboration3.(1) LPNHE-IN2P3/CNRS Universite´s Paris VI & VII, Paris, France(2) PCC-IN2P3/CNRS Colle`ge de France Universite´ Paris VII, France(3) http://www.mpi-hd.mpg.de/HESS/collaborationAbstractThe ﬁrst H·E·S·S· telescope has been in operation on-site in Namibia sinceJune, 2002. With its ﬁne-grain camera (0.16◦ pixelization) and large mirror light-collection area (107m2), it is able to see more detailed structures in the Cherenkovshower images than are characterized by the standard moment-based (Hillas) im-age analysis. Here we report on the application of the analysis method developedfor the CAT detector (Cherenkov Array at Themis) which has been adapted forthe H·E·S·S· site and telescopes. The performance of the method as comparedto the standard image analysis, in particular regarding background rejection andenergy resolution, is presented. Preliminary comparisons between the predictedperformance of the method based on Monte Carlo simulation and the results ofthe application of the method to data from the Crab Nebula are shown.1. IntroductionIn order to take advantage of the ﬁne pixelization of the CAT camera, a newanalysis method for Imaging Atmospheric Cherenkov Telescopes was developed[3]. The comparison of the shower images with a semi-analytical model was usedto successfully discriminate between γ-ray and hadron-induced showers and toprovide an energy measurement with a precision of the order of 20%, without theneed for stereoscopy. The H·E·S·S· experiment, in operation in Namibia since June2002, combines the advantages of the diﬀerent previous-generation telescopes:large mirror, ﬁne-pixel camera and stereoscopy. In this paper, we present theimprovements made to the CAT analysis in the framework of H·E·S·S· (operatingin single telescope mode).2. Model generationHillas [2], studied the mean development of electromagnetic showers. Weused his parametrization to construct a model of shower development, which wefeed into a detector simulation to take into account instrumental eﬀects. Afterpp. 2907–2910 c©2003 by Universal Academy Press, Inc.2908this procedure, we obtain for each zenith angle θ, primary energy E and impactparameter ρ the predicted intensity in each pixel of the camera. Model imageshave been generated for 30 values between 50GeV and 10TeV, zenith anglesup to 60◦, and impact parameters up to 300m from the telescope. A multi-linear interpolation method is used to compute the pixel intensity for intermediateparameters. The model generation has been extensively tested against simulationand agrees within 10% up to 10TeV.3. Event reconstructionThe event reconstruction is based on a maximum likelihood method whichuses all available pixels in the camera. The probability density function of ob-serving a signal S, given an expected amplitude µ, a ﬂuctuation of the pedestalσp (due to night sky background and electronics) and a ﬂuctuation of the singlephotoelectron signal (p.e.) σs ≈ 0.4 (PMT resolution) is given byP (S|µ, σp, σs) =∞∑n=0e−µµnn!√2π(σ2p + nσ2s)exp(− (S − n)22(σ2p + nσ2s))(1)The likelihoodL = 2 ∑pixellog [Pi(Si|µ, σp, σs)] (2)is then maximized to obtain the primaryenergy, the target direction T and theimpact point I. This ﬁve parameter ﬁtcan be reduced to four parameters E, ρ,φ (azimuthal angle in the camera) and d(angular distance of the shower barycen-ter to the primary direction, see ﬁg. 1),using the alignement of the image centreof gravity with TI.Fig. 1. Deﬁnition of geometrical pa-rameters used for the shower re-construction. O is the center ofthe camera, G the image barycen-ter and T the reconstructed targetdirection.4. Signal extractionThe following cuts are used in signal extraction• A cut on the ratio of the shower length L to its amplitude S, designed toreject small muon images : L/S ≤ 1.6× 10−2mrad p.e.−1• A geometrical cut of the distance mismatch |δD| ≤ 5 mrad, where δD =|TG| − |OG|. This cut selects γ-rays originating from the center of the ﬁeldof view and is orthogonal to the commonly used α orientation angle.• A goodness of ﬁt G < 0.07 deﬁned from the likelihood distribution as func-tion of the number of operating pixels Ndof as G = (〈L〉−L)/Ndof , where the2909µ0 2 4 6 8 10 12 140123456 = 0.5pσ = 1.5pσ <-L>2LσConstant  798.2Mean      0.00245Sigma     0.06165G-0.5 0 0.5 1 1.5 2nb events0100200300400500600700800Real OFF source datao, 800 GeV, 37γSimulated Fig. 2. Left: Likelihood curves for diﬀerent night sky backgrounds. Solid curves arenumerical integrations, dashed curves are simple analytical approximations (eq. 3).Right: Goodness of ﬁt (G) distribution after L/S and D cuts, for simulated γ andreal OFF source events.average likelihood and its RMS are obtained by integration of an analyticalapproximation of eq. 1:〈L〉 = −∑pixel(1 + log 2π + log(µ(1 + σ2s) + σ2p)), σ2L = 2 (3)The distribution of G for simulated γ-rays and real hadrons is shown in ﬁg.2 together with the likelihood’s average and RMS. The distribution for γ-rays iscompatible with an expected mean of 0.0 and has a slightly larger RMS than theexpected value√2/Ndof ≈ 5× 10−2. A cut G ≤ 0.07 keeps 77% of the γ-rays andrejects 82% of the hadrons.5. ResultsWe have analysed 20 pairs on the Crab Nebula, corresponding to 4.65hours (live-time corrected) of data. Fig. 3 shows the comparison between thestandard H·E·S·S· analysis [4] and this work. The model analysis alone producesan α plot extending up to 180◦. The signiﬁcance in the α < 9◦ is better in thehillas analysis (21 σ against 16.9 σ), mainly because the hadron rejection is not yetfully optimized for the model analysis, but the α resolution is much better in theModel analysis (2.7◦ against 4.2◦), thus providing a better signal to backgroundratio in the ﬁrst bins.More interesting is the background rejection capability of a combined anal-ysis. The lower plot of ﬁg. 3 shows the α distribution of the events passing boththe Hillas and Model analysis cuts. The signal over background ratio is increasedby a factor of more than 3, reaching the value of 4.8 for α < 9◦ wheras less than15% of the γ-rays are lost. This also results in a net increase in signiﬁcance up to25.2 σ. The complementarity of the hadron rejection capabilities of both analyses2910)° (α0 10 20 30 40 50 60 70 80 90050100150200250300350400450500Hillas analysis)° (α0 20 40 60 80 100 120 140 160 180050100150200250300350400450500Model analysis)° (α0 20 40 60 80 100 120 140 160 180050100150200250Combined analysisFig. 3. Results of the model analysis. Solid lines: ON source. Dashed lines: OFFsource. top left: α plot with standard H·E·S·S· analysis based on hillas parameters.top right: Corresponding α plot for the model analysis. bottom: Eﬀect of thecombination of the cuts on the background.is a very powerful instrument for ﬁnding faint sources, and was successfully usedto detect the blazar PKS 2155-304 in October 2002 at the level of 7.4 σ [1].This analysis also provides energy and shower impact measurements withrespective resolutions of about 20% and 20 m at 800GeV.6. ConclusionWe have developed a powerful analysis for H·E·S·S· based on the compari-son of shower images with a semi-analytical model. This analysis provides a betterα angle measurement than the standard analysis (base on Hillas parameters), aswell as good energy and shower impact resolution. Moreover, the combination ofboth analysis provides an additional background rejection factor of about 3, whichleads to an important increase in signiﬁcance. This combination method has beensuccessfully used to detect the blazar PKS 2155-304 at the level of respectively13 σ and 7.4 σ in July and October 2002. Further results will be presented at theconference.7. References1. Djannati-Ata¨ıA, These proceedings2. Hillas A.M.. 1982, J. Phys. G 8, 14613. Le Bohec S et al., NIM A416 (1998) 4254. Masterson C, These proceedings

Application of an analysis method based on a semi-analytical shower model to the first H.E.S.S. telescope

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