Ter-Antonian, S V

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29th International Cosmic Ray Conference Pune (2005) 6, 105108All-particle primary energy spectrum in the knee regionS.V. Ter-Antonyan , Y.A. Gallant, A.P. Garyaka , L.W. Jones, R.M. Martirosov ,N.M. Nikolskayaand J. Procureur(a) Yerevan Physics Institute, Yerevan, Armenia(b) Laboratoire de Physique Th  orique et Astroparticules, Universit  Montpellier II, France(c) Department of Physics, University of Michigan, USA(d) Moscow Lebedev Physics Institute, Russia(e) Centre d Etudes Nucleaires de Bordeaux-Gradignan,Gradignan,FrancePresenter: S.V. Ter-Antonyan (samvel@yerphi.am), arm-ter-antonian-S-abs2-he12-posterWe present the all-particle primary energy spectrum obtained by new 7-parametric event-by-event method ofdetermination of the primary energy on the basis of EAS size ( 	 ), truncated muon size  (  GeV, m), shower age (  ) and zenith angle (  ) parameters measured by the GAMMA facility at mountainlevel (700 g/cm ﬀ ). 7-parametric energy estimator was developed using the CORSIKA EAS simulation codewith the QGSJET and SIBYLL interaction models, taking into account the response of GAMMA detectors andthe reconstruction uncertainties of EAS parameters. We attained practically unbiased (ﬂﬁ ) primary energyestimations with accuracy about ﬃ !ﬃ"#ﬁ in the ﬃ$ %ﬃ& PeV energy range respectively.1. IntroductionThe mountain location of the GAMMA experiment and the agreement of observed and simulated data inthe measurement range (')ﬃ"ﬂ*!+,-ﬃ&ﬂ. [1, 2, 3] allowed to obtained with high reliability the all-particle energy spectrum. The method is based on an event-by-event evaluation of the primary energy usingreconstructed parameters /10/20/ﬂ03 of detected EAS. Such possibilities have been studying for a long timein the different works [4, 5, 6] and a main difficulty is to obtain an unbiased energy estimation at an existent(but unknown) abundance of the primary nuclei taking into account the fluctuations of shower developmentand detector response.2. GAMMA experimentThe main characteristic features of the GAMMA experiment [1, 4] are the mountain location (3200 m a.s.l.),symmetric disposition of the surface EAS detectors and underground muon scintillation carpet to detect EASmuon component at   ! GeV energies.The ground based array consists of 33 surface particle detection stations disposed on 5 concentric circlesof radii: 20, 28, 50, 70, 100 m. Each station contains 3 square plastic scintillation detectors with dimensions1x1x0.05 m 4 .The photomultiplier tube is positioned on the top of the aluminum casing covering the scintillator.One of the three station’s detectors is examined by two photomultipliers, one of which is designed for fast-timing measurements [1].150 underground muon detectors (muon carpet) are compactly arranged in the underground hall under 2.3Kg/cm ﬀ of rock. The dimensions, casing and applied photomultipliers are the same as in the EAS surfacedetectors. The trigger condition provides EAS detection with the EAS size threshold 5-76819: !ﬃ;<'=ﬃ&ﬂ* atthe location of the EAS core within the>!? m circle.Unbiased (ﬂﬁ ) estimations of   0@ﬂ03ACB#03DB shower parameters are obtained at   E'Cﬃ&* , GFB ,andHI? m from the shower core to the center of the EAS array distances. Corresponding accuracies arederived from MC simulations by the CORSIKA(EGS) [7] and are equal to: J- ﬂK  ML C9Nﬃ , JO L C9 # ,106 S.V. Ter-Antonyan et alJAP0QJD L C9 R Sﬃ m [2]. The reconstruction accuracy of EAS muon truncated ( m) size is equal toJ- CK  OL C9? T19F at  -L ﬃ&ﬂ*U !ﬃ"4 respectively [1, 2].The EAS zenith angle (  ) is estimated on the basis of the measured shower front arrival times by 33 fast-timingsurface detectors, applying the maximum likelihood method and the flat-front approach. The correspondinguncertainty are tested by MC simulations and is equal to: VW6Xﬂ; L ﬃ9: B .3. Event-by-event analysis and all-particle spectrumUsing the simulated database [2, 3], Y[Z\ﬃ9:-'1ﬃ&ﬂ] EAS events were taken for each of ^Zﬃﬂ0_9&9_9`0ba kinds( cd0QcMe#0Qf-0bghe ) of primary nuclei and each interaction model (SIBYLL2.1 [8], QGSJET01 [9]). The details ofEAS simulation by CORSIKA code taking into account detector response and electron (positron) accompani-ment of muons in the underground muon hall are presented in [2, 3].The reconstructed /  0/  0/ shower parameters, known zenith angle  and primary energy iB were used atminimization [2]jﬀ6lk1mn0_9_9&9_0Qk=o;pZﬃa1Y(qsr	qtﬃ]uvxwmyuz wm6l{N|Rm@}v}zq~{N| B }v}z;3ﬀVﬀ(1)where  m Z6lk m 0&9_9_9&0bk oC /  0/  0/ﬂ03ﬂ; is the investigated parametric function with k m 0_9_9&9`0bk o parameters,VZ!C9Nﬃ is expected accuracy of the  m evaluated energy. The best estimations were achieved at 7-parametric0.050.10.150.20.256 6.5 7 7.5 8Log(E0[GeV])<((E1-E 0)/E0)2>1/2- 3- 4- 7- p- He- O- Fe p Fe All Gaussδ = ∆EA/EAdW/dδ0123-0.5 -0.25 0 0.25 0.5Figure 1. Accuracy (RMSD) of the primary energy evaluations at different number of approximation parameters (leftpanel) and distribution of errors of the primary energy estimation by event-by-event 7-parametric t at different primarynuclei.(r(Z ) fit:{N|RmZ!k1m`A-kﬀTk4k]Tk*enWkŁ6lAq~k.D;0 (2)where AIZ{|I/  , D!Z{|7/  6=d; ,  Z`# and energy  m has units of GeV. The values of thekm0_9_9&9_0Qk.parameters for both interaction models and the corresponding j ﬀ obtained from (1) at V  Z19ﬃ"All-particle primary energy spectrum ... 107Table 1. Approximation parameters 1@@@x@# of primary energy evaluation (2) and corresponding   , obtained from (1)at the SIBYLL and QGSJET interaction models.Model k1m kﬀk4k]k*k#Ł k.jﬀSIBYLL 1.03 3.96 -4.24 1.99 -1.14 11.7 0.94 0.85QGSJET 1.04 4.55 -4.97 2.51 -1.38 13.1 0.93 0.92are displayed in Table 1. The root mean square deviations of the energy estimation by 7-parametric fit (2) inthe framework of SIBYLL model is shown in Fig. 1 (left panel). The corresponding results at three (only A¡0/variables) and 4-parametric ( A¡0/ﬂ0b`# ) fits are shown in Fig. 1, as well.The obtained error distributions estimating primary energy by 7-parametric approximation (2) are shown in0.10.20.30.40.50.60.70.80.9104105Primary energy E (TeV)E2.75 ´dF/dE   [m-2 sec-1 ster-1TeV1.75 ]KASCADE01KASCADE02KASCADE05 (QGSJET)KASCADE05 (SIBYLL)GAMMA02 (α-parameter)MulticomponentGAMMA dataSIBILL    : 7-fit,QGSJET: 7-fit,unfoldedunfoldedFigure 2. All particle primary energy spectra obtained by event-by-event 7-parametric analysis (lled red and blue symbols)and EAS inverse problem solutions (solid and dashed color lines) [2, 3] on the basis of GAMMA 2002-2004 database andparametrization of the primary energy spectra. The red (blue) symbols and lines correspond to the SIBYLL (QGSJET)interaction model. KASCADE data were taken from [12, 13] and obtained by unfolding of EAS inverse problem usingiterative method [14].Fig. 1 (right panel) for cd0bcMe#0@f-0bghe nuclei. The red line corresponds to the Gaussian distribution at the sameparameters as the cumulative distribution (solid line).The all-particle energy spectrum derived on the basis of the GAMMA 2002-2004 EAS data set [2, 3] and fit(2), at the QGSJET (red filled square symbols) and SIBYLL (blue filled circle symbols) interaction models areshown in Fig. 2.Notice, that the energy spectrum obtained by event-by-event method claims additional corrections, because theerrors V  ZVW6¢J K E; and power-law energy spectra ( £¤¥2¦ ) lead to an overestimation of the spectrum§Z[¨_©ª«6b636X¬(qtﬃ";­V;­ﬀK?; times. Moreover, the inevitable biases of energy estimations ®6l¯R;°Zm"K±B	108 S.V. Ter-Antonyan et aldepend on primary nuclei and shift the corresponding energy spectra ²U6l¯R;hZ³®`¦#¥ m times. The spectral shiftdue to ²U68¯i;h´Z[ﬃ impossible to take into account without information about abundance of primary nuclei.The observed biases of 7-parametric fit (2) are distributed from ®6µr¶; L ﬃﬂ9 ?ﬁ up to ®6lghen; L C9 ·ﬂ¸#ﬁ (Fig. 1)and here are neglected. In the results shown in Fig. 2, the corrections of § 68E; are taken into account using theexpected accuracies from Fig. 1.The solid (red) and dashed (blue) lines in Fig.2 represent the all-particle primary energy spectra obtained onthe basis of GAMMA data set by the solution of parametrized EAS inverse problem in the framework of theSIBYLL and QGSJET models respectively [2, 3]. The event-by-event analysis of the GAMMA data at theQGSJET interaction model using ¹ -parametric method [4] also shown in Fig. 2 (asterisk symbols). The dottedline in Fig. 2 represents the parametrized solutions of the EAS inverse problem for the KASCADE EAS data atrigidity-dependent steepening primary energy spectra [10]. The results of KASCADE02 in Fig. 2 obtained bythe non-parametric event-by-event analysis was taken from review [11]. The KASCADE01,05 data (iterativemethod [14]) were taken from [12, 13] respectively .AcknowledgmentsWe are grateful to all of our colleagues of the Moscow Lebedev Institute and the Yerevan Physics Institute whotook part in the development and exploitation of the GAMMA facility.This work has been partly supported by research grant No 1465 from the Armenian government, NFSAT bilat-eral U.S.-Armenian grant AS084-02/CRDF 12036, by the CRDF grant AR-P2-2580-YE-04 and the ”Hayastan”All-Armenian Fund in France.References[1] R.M. Martirosov et al., 29 º  ICRC, Pune, HE.1.5 (2005) arm-martirosov-R-abs1-he15-oral.[2] S.V. Ter-Antonyan et al., astro-ph/0506588 v.1 (2005).[3] S.V. Ter-Antonyan et al., 29 º  ICRC, Pune, HE.1.2 (2005) arm-ter-antonian-S-abs1-he12[4] A.P. Garyaka, R.M. Martirosov, J. Procureur et al., J. Phys G:Nucl. Part. Phys. 28 (2002) 2317.[5] J.-N. Capdevielle et al., Proc. 27 º  Inter. Cosmic Ray Conf., Hamburg (2001) 306.[6] A. Chilingaryan, S. Ter-Antonyan et al, Nucl. Phys.B 60B (1998) 117.[7] D. Heck, J. Knapp, J.N. Capdevielle, G. Schatz, T. Thouw, Forschungszentrum Karlsruhe Report, FZKA6019 (1998) 90 p.[8] R.S. Fletcher, T.K. Gaisser, P. Lipari, T. Stanev, Phys.Rev. D 50 (1994) 5710.[9] N.N. Kalmykov, S.S. Ostapchenko, Yad. Fiz. 56 (1993) 105 (in Russion).[10] Samvel Ter-Antonyan and Peter Biermann, 28 º  Intern. Cosmic Ray Conf. Tsukuba HE1 (2003) 235.[11] S.P. Swordy, L.F. Fortson et al., Astropart. Phys. 18 (2002) 129.[12] H. Ulrich et al., Proc. 27 º  Intern. Cosmic Ray Conf., Hamburg 1 (2001) 97.[13] T. Antoni et al., astro-ph/0505413 v1 (2005) (accepted in Astropart. Phys.)[14] R. Gold, ANL-6984 Report, Argonne (1964).

All-particle primary energy spectrum in the knee region

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