1. QUARKS-2010, Kolomna1 Study of the Energy Spectrum and the Composition of the Primary Cosmic Radiation at Super-high Energies

2. QUARKS-2010, Kolomna2 By L.G. Dedenko 1, A.V. Glushkov 2, G.F. Fedorova 1, S.P. Knurenko 2, a.A. Makarov 2, M.I. Pravdin 2, T.M. Roganova 1, I.Ye. Sleptzov 2 1. M.V. Lomonosov Moscow State University, Faculty of Physics and D.V. Skobeltzin Institute of Nuclear Physics, Moscow, 119992, Leninskie Gory, Russian Federation 2. Insitute of cosmic rays and aeronomy. Yakutsk, Russian Federation

3. QUARKS-2010, Kolomna3 Yakutsk array The Yakutsk array includes the surface scintillation detectors (SD) and detectors of the Vavilov-Cherenkov radiation and underground detectors of muons (UD) with the threshold energy ~1 GeV.

4. QUARKS-2010, Kolomna4 Detectors readings induced by EAS particles The various particles of Extensive Air Showers (EAS) at the observation level hit detectors and induce some signals sampled as detector readings

5. QUARKS-2010, Kolomna5 Standard approach of energy estimation s(600) – signal at 600 m in the vertical EAS used to estimate energy E of EAS. DATA: 1. The CIC method to estimate s(600) from data for the inclined EAS. 2. T he signal s(600) is calibrated with help of the Vavilov-Cherenkov radiation E=4.6·10 17 · s(600), eV

6. QUARKS-2010, Kolomna6 Standard AGASA approach Like AGASA: 1. The CIC method to estimate s(600) from data for the inclined EAS. 2. Calculation s(600) for EAS with energy E: E=3·10 17 ·s(600), eV

7. QUARKS-2010, Kolomna7 Spectrum Energy spectra are different for these approaches

8. QUARKS-2010, Kolomna8 points ─ Yakutsk data circles ─ Yakutsk (calculation like AGASA) stars ─ PAO

9. QUARKS-2010, Kolomna9 The CIC method The constant intensity cut (CIC) method: systematic error! For Yakutsk array the absorption length 458 g/cm 2 (to be compared with 340 g/cm 2 )

10. QUARKS-2010, Kolomna10 Yakutsk array. New approach All detectors readings are suggested to be used to study the energy spectrum and the chemical composition of the primary cosmic radiation at ultra-high energies in terms of some model of hadron interactions.

11. QUARKS-2010, Kolomna11 The new method For the individual EAS the energy E and the type of the primary particle, (atomic number A), which induced EAS, parameters of model of hadron interactions, peculiar development of EAS in the atmosphere are not known

12. QUARKS-2010, Kolomna12 The new method The goal: to find estimates of the energy E and atomic number A, parameters of model of hadron interactions, peculiar development of EAS in the atmosphere for each individual shower

13. QUARKS-2010, Kolomna13 The new method It has been suggested for the one observed EAS to estimate all detector readings for many simulated individual showers, induced by various primary particles with different energies in terms of various models.

14. QUARKS-2010, Kolomna14 The new method All these detector readings for all simulated individual showers should be compared with detector readings of one observed EAS

15. QUARKS-2010, Kolomna15 The new method The best estimates of the energy E, the atomic number A and parameters of model and peculiar development of EAS in the atmosphere are searched by the χ 2 method.

16. QUARKS-2010, Kolomna16 The new method The best estimates of the arrival direction and core location are also searched by the χ 2 method.

17. QUARKS-2010, Kolomna17 Simulations Simulations of the individual shower development in the atmosphere have been carried out with the help of the code CORSIKA-6.616 [8] in terms of the models QGSJET2 [9] and Gheisha 2002 [10] with the weight parameter ε=10 -8 (thinning).

18. QUARKS-2010, Kolomna18 Simulations The program GEANT4 [11] has been used to estimate signals in the scintillation detectors from electrons, positrons, gammas and muons in each individual shower.

19. QUARKS-2010, Kolomna19 Detector model

20. QUARKS-2010, Kolomna20 Signals in scintillation detector Signals ∆E in MeV as functions of energy E and the cos( teta) (teta – the zenith angle) of incoming particles

21. QUARKS-2010, Kolomna21 Electrons

22. QUARKS-2010, Kolomna22 Positrons

23. QUARKS-2010, Kolomna23 Gammas

24. QUARKS-2010, Kolomna24 Отклики от мюонов Muons

25. QUARKS-2010, Kolomna25 Minimum of the function χ2 Readings of all scintillation detectors have been used to search for the minimum of the function χ2 in the square with the width of 400 m and a center determined by data with a step of 1 m. These readings have been compared with calculated responses for E 0 =10 20 eV multiplied by the coefficient C. This coefficient changed from 0.1 up to 4.5 with a step of 0.1.

26. QUARKS-2010, Kolomna26 Minimum of the function χ2 Thus, it was assumed, that the energy of a shower and signals in the scintillation detectors are proportional to each other in some small interval. New estimates of energy E =C·E 0 eV,

27. QUARKS-2010, Kolomna27 Results of energy estimations The 16 various values of energy estimates for 16 individual simulated showers induced by protons, He, O and Fe nuclei have been obtained for the same sample of the 31 experimental readings of the observed giant shower with different values of the function χ2.

28. QUARKS-2010, Kolomna28 Results for the most energetic shower observed at the Yakutsk array

29. QUARKS-2010, Kolomna29 Nucleus№s(600)E 0 /10 2 0 xyχ12χ12 P12341234 27.48 29.64 32.18 27.77 2.04 2.00 1.805 2.27 941 965 948 1011 -374 -406 -425 -421 0.88 0.945 1.019 1.03 He12341234 25.11 33.56 27.88 31.33 2.37 1.755 2.085 1.93 956 947 942 955 -408 -421 -389 -439 0.895 0.996 0.949 1. O12341234 30.73 31.03 29.90 31.66 1.78 1.86 1.94 1.75 909 943 940 912 -363 -387 -393 -428 0.97 0.942 0.904 0.997 Fe12341234 34.12 36.23 33.05 35.02 1.6 1.66 1.745 1.69 905 969 935 975 -353 -429 -437 -389 1.081 1.042 1.051 1.01 Experiment53.8811055-406

30. QUARKS-2010, Kolomna30 Simulations New estimates of energy of the giant air shower observed at YA have been calculated in terms of the QGSJET2 and Gheisha 2002 models: E≈2.·10 20 eV for the proton primaries and E≈1.7·10 20 eV for the primary iron nuclei.

31. QUARKS-2010, Kolomna31 Minimum of the function χ2 Coordinates of axis and values of the function χ2 have been obtained for each individual shower

32. QUARKS-2010, Kolomna32 Results of energy estimations The energy estimates are minimal for the iron nuclei primaries and change inside the interval (1.6−1.75)· 10 20 eV with the value of the χ2 ~ 1.1 per one degree of freedom.

33. QUARKS-2010, Kolomna33 Results of energy estimations For the proton and helium nuclei primaries energy estimates are maximal and change inside the interval (1.8−2.4)·10 20 eV with the value of the χ2 ~ 0.9 per one degree of freedom.

34. QUARKS-2010, Kolomna34 Results of energy estimations For the oxygen nuclei primaries the energy estimates are in the interval (1.8−2)·10 20 eV which is between intervals for proton and iron nuclei primaries with the value of the χ2 ~ 0.95 per one degree of freedom.

35. QUARKS-2010, Kolomna35 Results of energy estimations Dependence of the value χ2 per one degree of freedom on the coefficient C=E/(10 20 eV)

36. QUARKS-2010, Kolomna36

37. QUARKS-2010, Kolomna37

38. QUARKS-2010, Kolomna38

39. QUARKS-2010, Kolomna39

40. QUARKS-2010, Kolomna40 Reality of the Yakutsk DATA The sampling time of signal in the scintillation detetor τ=2000 ns

41. QUARKS-2010, Kolomna41 Fraction of signal: 1-100 m, 2- 600 m, 3- 1000 m, 4-1500 m

42. QUARKS-2010, Kolomna42 Energy spectrum The base spectrum J b (E)= A·(E) -3.25, and the reference spectrum J r (E) are introduced on the base of the HiRes data

43. QUARKS-2010, Kolomna43 Energy spectrum New variable y=lgE In four energy intervals y i (i=1, 2, 3 and 4) 17.<y 1 <18.65, 18.65<y 2 <19.75, 19.75<y 3 <20.01 and y 4 >20.01

44. QUARKS-2010, Kolomna44 Spectrum J r (E) has been approximated by the following exponent functions J 1 (E)=A·(E) -3.25, J 2 (E)=C·(E) -2.81, J 3 (E)=D·(E) -5.1, J 4 (E)=J 1 (E)=A·(E) -3.25 Constants C and D may be expressed through A and equations for J r (E) at the boundary points.

45. QUARKS-2010, Kolomna45 Spectrum we assume the reference spectrum as lgz i =lg(J i (E)/J 1 (E)), where i=1, 2, 3, 4.

46. QUARKS-2010, Kolomna46 Spectrum This reference spectrum is represented as follows lgz 1 =0, lgz 2 =0.44·(y -18.65), lgz 3 =0.484-1.85·(y -19.75) lgz 4 =0

47. QUARKS-2010, Kolomna47 Spectrum Results of the spectra J(E) observed at various arrays have been expressed as lg z=lg (J(E)/J b (E)) and are shown in comparison with the reference spectrum.

48. QUARKS-2010, Kolomna48 Spectrum Data lgz=lg(J(E)/J b (E)) observed at various arrays are shown in Fig. as follows: (a) − HiRes2 (open circles), HiRes1 (solid squares), (b) − PAO (solid circles), (c) − AGASA (solid triangles), (d) − Yakutsk (solid pentagons). The reference spectrum is also shown on all Figures (solid line).

49. QUARKS-2010, Kolomna49 HiRes

50. QUARKS-2010, Kolomna50 PAO

51. QUARKS-2010, Kolomna51 AGASA

52. QUARKS-2010, Kolomna52 Yakutsk

53. QUARKS-2010, Kolomna53 Tibet, Tunka-25, Cascade-Grande

54. QUARKS-2010, Kolomna54

55. QUARKS-2010, Kolomna55 Study of the chemical composition Muon density for the primary protons with the energy E: ρ μ (600)=a·E b b<1 Decay processes are decreasing for higher energies E.

56. QUARKS-2010, Kolomna56 Study of the chemical composition Muon density for the primary nuclei with atomic number A ρ μ (600)=a·A c ·E b c>0 (c=1-b) QGSJET2: b=0.895, c=0.105 For Fe: A 0.105 =1.53

57. QUARKS-2010, Kolomna57 Study of the chemical composition QGSJET2: Signal in SD s(600)=∆E·(E/3·10 17 eV) Signal in UD k·∆E·ρ μ (600) Coefficient k=1.15

58. QUARKS-2010, Kolomna58 Study of the chemical composition Muon fraction at 600 m: α=k·∆E·ρ μ (600)/s(600) Coefficient k=1.15 takes into account the difference in the threshold energies and signals in UD

59. Signal ∆ Е in underground muon detectors for deph h = 2.5 m: о – 0 о, stars– 45 о,solid – 10.5 МeV,dashed – 14.85 МeV.

60. QUARKS-2010, Kolomna60 Signal ∆ Е in underground muon detectors for deph h = 2.5 m: о– 0 о, stars– 45 о,solid – 10.5 МeV,dashed – 14.85 МeV.

61. QUARKS-2010, Kolomna61 Signal ∆ Е distributions in underground muon detectors for deph h = 3.2 m: a – Е μ = 1.05 GeV, b – Е μ = 1.5 GeV, c – Е μ = 10 GeV.

62. QUARKS-2010, Kolomna62 Gammas Possible signals in UD from gammas

63. QUARKS-2010, Kolomna63 Energy spectra of gammas in vertical EAS inside 100 m. 1 – Е = 10 17 eV, 2 – Е = 10 18 eV.

64. QUARKS-2010, Kolomna64 Mean signal ∆ Е in underground muon detectors from gammas with various energies for deph h : ● – h = 2.3 м, ○ – h = 3.2 м.

65. QUARKS-2010, Kolomna65 Signal ∆ Е distributions in underground muon detectors from gammas for deph h =2.3 m: a – Е γ = 5 GeV, b – Е γ = 10 GeV.

66. QUARKS-2010, Kolomna66 Muon fraction α at 600 m in vertical EAS. Points – [19], solid– protons, dashed – iron nuclei.

67. QUARKS-2010, Kolomna67 Results 1. Primary protons above 10 18 eV 2. Heavier primary nuclei below 10 18 eV

68. QUARKS-2010, Kolomna68 At energies E>10 20 eV No definite conclusion

69. QUARKS-2010, Kolomna69 χ2 1 vs E. Solid – protons, dashed – iron nuclei.

70. QUARKS-2010, Kolomna70 Conclusions are model dependent The most energetic EAS observed at the Yakutsk array may be induced by the primary particles with energy 2·10 20 eV. The primary protons may dominate at energies 10 18 – 3·10 19 eV. Heavy primary particles are possible at energies below 10 18 eV.

71. QUARKS-2010, Kolomna71 Conclusions are model dependent The Coulomb scattering of charged particle (electrons, positrons) and the p t distribution of hadrons (for muon scattering) should be taken into account precisely in calculations of lateral distributions of these particles.

72. QUARKS-2010, Kolomna72 Acknowledgements. Authors thank RFBR (grant 08-02- 00348), LSS (grant 959.2008.2) and Federal Agency on Science (State contracts 02.740.11.5092, 02.518.11.7173, 02.740.11.0248) for support.

73. QUARKS-2010, Kolomna73 Proton, SIBYLL (AIRES) Proton, QGSJET (AIRES) Proton, GEISHA, QGSJET (CORSIKA) Proton, FLUKA, QGSJET (CORSIKA) Proton, GEISHA, QGSJET2 (CORSIKA) Proton, FLUKA, QGSJET2 (CORSIKA) Iron, SIBYLL (AIRES) Iron, QGSJET (AIRES) 50 34 (VEM) SD+MC Average (    18%) FD Average (    30%) Fixed Beta Floating Beta Proton, SIBYLL (AIRES) Proton, QGSJET (AIRES) Proton, GEISHA, QGSJET (CORSIKA) Proton, FLUKA, QGSJET (CORSIKA) Proton, GEISHA, QGSJET2 (CORSIKA) Proton, FLUKA, QGSJET2 (CORSIKA) Iron, SIBYLL (AIRES) Iron, QGSJET (AIRES) Summary of S(1000) at 38 o and 10 EeV Proton Iron