Ter-Antonian, S V

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29th International Cosmic Ray Conference Pune (2005) 6, 101104Primary composition and energy spectra obtained with the GAMMAfacilityS.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, Universite 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-abs1-he12-oralOn the basis of the Extensive Air Shower (EAS) data observed by the GAMMA experiment, the energy spectraand elemental composition of the primary cosmic rays have been derived in the 	 TeV energy range.Reconstruction of the primary energy spectra are carried out in the framework of the SIBYLL and QGSJETinteraction models and the hypothesis of the power-law steepening primary energy spectra. All presentedresults are derived taking into account the detector response, reconstruction uncertainties of EAS parametersand fluctuation of EAS development.1. IntroductionThe investigation of the energy spectra and elemental composition of primary cosmic rays in the knee region( 		 TeV) remains one of the intriguing problems of modern high energy cosmic-ray physics. Despitethe fact that these investigations have been carried out for more than half a century, the data on the elementalprimary energy spectra at energies of  TeV need improvement.High statistical accuracies of recent EAS experiments already allowed us to infer that the rigidity-dependentsteepening energy spectra of primary nuclei can approximately describe the observed EAS size spectra in theknee region in the framework of conventional interaction models. However, the accuracies of the obtainedelemental primary energy spectra are still insufficient due to both the uncertainty of interaction model and theaccuracy of the solutions of the EAS inverse problem.2. GAMMA experimentThe GAMMA installation is a ground based array of 33 surface particle detection stations and 150 undergroundmuon detectors located on the south side of Mount Aragats, Armenia. Elevation of the GAMMA facility is3200 m above sea level, which corresponds to 700 g/cm  of atmospheric depth [1, 2]. The surface stationsof the EAS array are located on 5 concentric circles of radii: 20, 28, 50, 70, 100 m and each station contains3 square plastic scintillation detectors with the following dimensions: 1x1x0.05 m  . 150 underground muondetectors (muon carpet) are compactly arranged in the underground hall under 2.3 Kg/cm  of rock. Unbiased( ﬀﬂﬁﬃ ) estimations of ! #"%$'&$)(+*$),* shower parameters are obtained at - #"./ﬁ10'	 , 2-ﬀ/3 * , and 45ﬀ/6ﬁ mfrom the shower core to the center of the EAS array distances. Corresponding accuracies are derived from MCsimulations by the CORSIKA(EGS) [3] and are equal to: 78  #":9   #"-; %<= , 7-& ; >< ﬁ , 78(?$'78, ; >< ﬁ@m. The reconstruction accuracy of EAS muon truncated ( 4BACﬀﬁ m) size is equal to 7!8A 9 DA ; %<E6FG%< 3ﬁat DA ; 	Hﬂ respectively [2].102 S.V. Ter-Antonyan et al.106107EAS size, NchNch2.5 ´dF(θ)/dNch1.00-1.051.05-1.101.10-1.155sec(θ)- SIBYLL- QGSJET102x1357 (a)Nµ(R<50m)Nµ 3´dFµ(θ) /dN µ1.00-1.051.05-1.101.10-1.15sec(θ)- SIBYLL- QGSJET(b)EAS size, NchNch 2.5  ´dF(N)/dN ch   [ m2 ´sec´ster ] -11x1032x1034x1038x103Nµ > N- SIBYLL- QGSJET(c)Nµ(R < 50m)Nµ 1.5 ´dFµ(N) /dN µ   [1/EAS]5x1051x1062x106Nch > N- SIBYLL- QGSJET(d)EAS size, NchEAS age, s- SIBYLL- QGSJET- GAMMA data(e)Log(Nch)Log(Nµ(R < 50m)) SIBYLLmixedpFeQGSJETmixedpFe(f)10 510 6103104 11010 210610711010 4 10 50.70.80.9106 10733.544.556 6.5 7 7.5Figure 1. EAS data of the GAMMA experiment (symbols) and corresponding predictions in the framework of the SIBYLL(shaded areas and solid lines) and QGSJET (dashed lines) model.3. EAS dataThe EAS data of the GAMMA experiment are shown in Fig.1a-f (symbols). The EAS size spectra (1a) inunits of IKJ  0L&MONP0Q&	RSMTVUXWZY and normalized (1/EAS) EAS muon truncated size spectra (1b) at 3 zenith angularintervals are shown in Fig.1a,b. The EAS size spectra at different muon size thresholds (c) and normalized EASmuon truncated size spectra (d) at different EAS size thresholds are shown in Fig.1c,d. The average EAS ageparameter (s) versus EAS size is shown in Fig.1e. The ( - #">$[ A )-correlation plot is shown in Fig.1f. Theseresults were obtained at the \%<=	]!0%^ sec operation time (2002-2004). All the shaded areas and solid lines(dashed lines) in Fig.1a-f are the corresponding predictions obtained in the framework of the SIBYLL2.1 [4](QGSJET01 [5]) interaction model (next section).4. EAS inverse problemCombined 1,2-D approach: All observed quantities ( 7!_ 9 7a`bOc ) in the high energy EAS physics are ob-tained via convolutions of the energy spectra de	f9d of primary nuclei ( ghij$[ijM$Q<	<Q< ) with the differentialspectra klfmIK.$ b c U of the EAS parameters b c hn! #"$' A $'& at the observation level and EAS array responseo+pfqIKr$bc$[2U9o`bc [2]:7!_c7a`bcstfu:vdefdu:wxu:y?zklfmIK.$bcUo+pfo`bcdDd{rdbc$ (1)where the EAS parameter `b c is a reconstructed value of b c , d{|h}Q~2d(+d,d is an element of the multi-dimensional phase space ( { ) of the EAS detection taking into account the EAS selection criteria and triggerconditions, k f IK.$ bQc $)2U are the corresponding differential spectra of the EAS parameters ( bOc ) at the primaryenergy  , zenith angle of incidence 2 and a given kind of primary nucleus ( g ).The unambiguous way to interpret the experimental data above is to unfold the integral expression (1) usingPrimary composition and energy spectra ... 103Table 1. Parameters of primary energy spectra (2) at 1,2-D and 4-D analysis of EAS data. Scale factors H and particle’srigidity  have units of -ŁL  L' L X Q[ and (   ) respectively.Parameters (1,2D)SIBYLL (4D)SIBYLL (1,2D)QGSJET (4D)QGSJET%< >P%<  %< ]%< 3 ><\VF%< V ><	F>< V %<  6q%<  %< ﬁV3%< ﬁ >< ﬁm%<  >< 3VF>< V¡%< 6m%<  %< V]%<  >< ﬁm%< \ >< >	\>< 3¢ %< 6m%< 3 %< 6V]%< 3 >< >	%< 3 >< >ﬁm>< 6£ 6ﬁV\qG6V 3m3 3mﬁV 33m6¤3>< 6%P%< V 3%<=	\%<  3%<=	%< 3 3%<=	>< 3¥ 9 d><E¦< 6%< ﬁ <E6 6< \ <=parametrization of the unknown functions def 9 d at a given interaction model [6]. As a criterion of the valid-ity of the solutions, the ¥  test of the detected and expected data may be performed. Evidently, the accuraciesof the unfolding of expression (1) depend not only on number of measurement points (bins) and different mea-sured spectra but also on the wealth of information about the primary energy spectra and the interaction modelfolded in the given measured EAS spectra.The primary energy spectra in (1) were used based on the theoretically suggested power-law function [7] withthe ”knee” at the rigidity-dependent energies ¨§IKg©Us£0Vª and the same indices ( « ¤Y) and ( « ¤) beforeand after the knee respectively, for all kinds of primary nuclei ( g ):defdsfW¬	­§ ®§°¯W¬ (2)where ¤s¤Yh6< \ﬁ at ²±/F§%IKg@U , ¤s¤at ²³F§IKg©U and Z is a charge of A nucleus.The shower spectra dkafqIK.$ b c $)2U , ( b c h8 #"%$[ A $X&P<	<Q< ) on the observation level of the GAMMA facility wehave computed using the CORSIKA6031(NKG,EGS) EAS simulation code [3] with the QGSJET01 [5] andSIBYLL2.1 [4] interaction models for 4 groups ( ghﬂi´$'ijM$'µ!$'_¶M ) of primary nuclei at the power-law energyspectra ( ·5WZYX¸ ) in the ﬁB0q³ﬁ¶0:	 TeV energy range. The EGS mode of the CORSIKA was used forcomputations of the response functions of the GAMMA detectors taking into account the EAS gamma-quantacontributions and choice of the corresponding input parameters of the adequate NKG mode. All EAS muonswith energies of  A G GeV on the GAMMA observation level have passed through 2.3 Kg/cm  of rock to themuon scintillation carpet. Fluctuations of the muon ionization losses and electron (positron) accompanimentdue to the muon bremsstrahlung, direct pair production, knock on and photo-nuclear interactions are taken intoaccount [2].Using the aforementioned formalism and ( ¹s\ ) 2-dimensional examined functions from Fig.1a-d (symbols)and 1-dimensional functions from Fig.1e,f, the unknown spectral parametersIKg©UL$[B§%IKg©UL$¤were derivedby the minimization of ¥  at ¤Ys6%< \ﬁ and the degree of freedom º»Y°¼c;3ﬁ . The values of spectralparameters (2) obtained by the solution of the parameterized equation (1) are presented in Table 1 at corre-sponding interaction models. The derived primary energy spectra for ½?$[ijM$'µ!$'_¶M nuclei are shown in Fig.2(shaded areas) in comparison with the KASCADE data (symbols) from [8]. The expected spectra conformingthe examined data set according to the solutions above are shown in Fig.1a-f (lines and shaded area) for theQGSJET and SIBYLL interaction models.4-D approach: The combination of 1,2-dimensional approximations of EAS data above does not take intoaccount all the information about primary energy spectra folded in the detected EAS data. In general, theEAS inverse problem can be formulated in the multidimensional space of EAS parameters. In case of the104 S.V. Ter-Antonyan et al.10-210-11103 1040.010.11Primary energy E (TeV)E2.75 ´dF/dE  [m-2 sec-1 ster-1TeV1.75 ] KASCADE04SIBYLL- p- He- FeAll-particleO FeHepE (TeV)QGSJETAll-particleOFepHe10-210-11103 104 105Figure 2. Energy spectra and abundance of the primary nuclei (shaded areas) at the SIBYLL (left panel) and QGSJET(right panel) interaction models. The symbols are the KASCADE data from [8].4-parametric (   #" $[8A+$X&$)2 ) analysis, the expression (1) is written as [2]:7!_7`8 #"7`A7´`&7-stfu vdefdu y u w´¾fIK.$[2UpIK2USdBd{rd #"dDAd:&¶$ (3)where¾fqIK.$[2UjhoQklfmIKr$)2U9o8 #"oAo& , are the multidimensional differential EAS spectra at givengD$[.$[2 parameters of the primary nucleus,pI¿2U8ho	4-I¿2U9o`8 #"o`Ao`& are the error functions of the ex-periment. Evidently, the amount of information about primary energy spectra contained in the detected multi-dimensional spectrum 7!_ is always greater than the cumulative amount of information contained in the 1,2-dimensional spectra 7!_ c 9 7a`b	c of the expression (1). The difference is determined by the inter-correlations ofEAS parameters that are taken into account in the expression (3).On the basis of the EAS data set of the GAMMA experiment, the simulated EAS database and parameteriza-tion (2), the equations (3) were resolved by the ¥  -minimization method. The total number of the degree offreedom at 4-dimensional ¥  -minimization was equal to OﬁV\ . The values of spectral parameters (2) obtainedby the solution of the parameterized equation (3) are presented in Table 1 at the QGSJET and SIBYLL inter-action models.The obtained energy spectra of primary nuclei disagree (Fig.2) with the same KASCADE data [8] obtained byiterative method [9].References[1] R.M. Martirosov et al., 29 À " 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] D. Heck et al., FZKA 6019 (1998) 90 p.[4] R.S. Fletcher at al., Phys.Rev. D 50 (1994) 5710.[5] N.N. Kalmykov, S.S. Ostapchenko, Yad. Fiz. 56 (1993) 105.[6] S.V. Ter-Antonyan, P.L. Biermann, 27 À " ICRC, Hamburg (2001) 1051.[7] P.L. Biermann, Astron. & Astrph. 271 (1993).[8] K.-H. Kampert at al., astro-ph/0405608 v1 (2004).[9] R. Gold, ANL-6984 Report, Argonne (1964).

Primary composition and energy spectra obtained with the GAMMA facility

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