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Fluctuation in EAS development and estimates of energy and composition

Fluctuation in EAS development and estimates of energy and composition of the primary radiation by L. Dedenko, SINP, MSU. Yakutsk array. 1) surface scintillation detectors (SD) 2) detectors of the Vavilov-Cherenkov radiation (VCR) 3) underground detectors of muons (UD)

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Fluctuation in EAS development and estimates of energy and composition

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  1. Fluctuation in EAS development and estimates of energy and composition of the primary radiation by L. Dedenko, SINP, MSU

  2. Yakutsk array 1) surface scintillation detectors(SD) 2) detectors of the Vavilov-Cherenkov radiation (VCR) 3)underground detectors of muons(UD) (with the threshold energy ~1 GeV).

  3. Detectors readings • The various particles • of Extensive Air Showers (EAS) • at the observation level • hit detectors • and induce some signals sampled as • detector readings in (SD), (VCR) 18.05.2011. IWS. SINP. MOSCOW

  4. Detectors readings • Some particles (muons, gammas) • penetrate through some depth h of soil, hit underground detectors • and induce some signals sampled as • detector readings • in underground detectors of muons(UD) (with the threshold energy ~1 GeV). 18.05.2011. IWS. SINP. MOSCOW

  5. Standard approach of energy estimation • Signal s(600) in SD • at 600 m from the EAS core • in the vertical EAS • is used to estimate • energy E of EAS. 18.05.2011. IWS. SINP. MOSCOW

  6. Standard approach of energy estimation • DATA: • 1. The CIC method is used to estimate s(600) in vertical EAS from data for the inclined EAS. • 2. The signal s(600) for the vertical EAS is calibrated with the help of the • Vavilov-Cherenkov radiation • 3. E=4.6·1017· s(600), eV 18.05.2011. IWS. SINP. MOSCOW

  7. Standard AGASA approach:Like AGASA: • 1. The CIC method to estimate s(600) for the vertical EAS from data for the inclined EAS. • 2. Calculation s(600) for the vertical EAS with energy E: • 3. E=3·1017·s(600), eV • 1. L.G. Dedenko et al., Phys. of Atom. Nucl., 2007, vol. 70, No 1, pp. 170-174. 18.05.2011. IWS. SINP. MOSCOW

  8. Spectrum • Energy spectra are different for these approaches 18.05.2011. IWS. SINP. MOSCOW

  9. points ─ Yakutsk data, stars ─ PAO circles ─ Yakutsk like AGASA 18.05.2011. IWS. SINP. MOSCOW

  10. The CIC method • The constant intensity cut (CIC) method: • may be systematic error! • For Yakutsk array the absorption length • 458 g/cm2 • (to be compared with the simulated average value) • 340 g/cm2 18.05.2011. IWS. SINP. MOSCOW

  11. 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. 18.05.2011. IWS. SINP. MOSCOW

  12. The new approach • For the each one individual EAS • 1) the energy E and • 2) the type of the primary particle, (atomic number A), which induced EAS, • 3)parameters of model of hadron interactions, • 4) peculiar development of EAS in the atmosphere • are not known 18.05.2011. IWS. SINP. MOSCOW

  13. The new approach • The goal is to find estimates of • 1) energy E, • 2) atomic number A, • 3) parameters of model of hadron interactions, • 4) peculiar development of EAS in the atmosphere • for each individual shower 18.05.2011. IWS. SINP. MOSCOW

  14. The new approach It has been suggested for the every oneobserved EAS to use all detector readings which should be compared with the simulated ones • for manysimulated individual showers, • induced by 1) various primary particles • with 2) different energies • in terms of 3) various models. 18.05.2011. IWS. SINP. MOSCOW

  15. The new approach • 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 χ2 method. 18.05.2011. IWS. SINP. MOSCOW

  16. The new approach • The best estimates of the • 1) arrival direction • and • 2)core location • are also searched by the χ2 method. 18.05.2011. IWS. SINP. MOSCOW

  17. Simulations • Simulations of the individual shower developmentin the atmosphere • have been carried out with the help of • the codeCORSIKA-6.616 [8] • in terms of the models QGSJET2 [9] and Gheisha 2002 [10] • with the weightparameter ε=10-8(thinning). 18.05.2011. IWS. SINP. MOSCOW

  18. Simulations • The program GEANT4 has been used • to estimate signals in the scintillation detectors • from electrons, positrons, gammas and muons • in each individual shower. 18.05.2011. IWS. SINP. MOSCOW

  19. Detector model 18.05.2011. IWS. SINP. MOSCOW

  20. Signals in scintillation detector • Signals ∆E in MeV in detectors as functions of • 1) energy E • and • 2) the zenith angle θ(cos(θ)) • of various incoming particles: 18.05.2011. IWS. SINP. MOSCOW

  21. Electrons 18.05.2011. IWS. SINP. MOSCOW

  22. Positrons 18.05.2011. IWS. SINP. MOSCOW

  23. Gammas 18.05.2011. IWS. SINP. MOSCOW

  24. Muons 18.05.2011. IWS. SINP. MOSCOW

  25. 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. 18.05.2011. IWS. SINP. MOSCOW

  26. Minimum of the function χ2 These readings have been compared with calculated responses for E0=1020 eV (201*201 signals) multiplied by the coefficient C. • This coefficient C changed from 0.1 up to 4.5 with a step of 0.1. • (45 values) • L.G. Dedenko et al., JETP Letters, 2009, vol.90, No 11, pp. 691-696. 18.05.2011. IWS. SINP. MOSCOW

  27. 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·E0 , eV 18.05.2011. IWS. SINP. MOSCOW

  28. Results of energy estimations • 16*45=720 • of energy estimates for simulated showers induced by • protons, He, O and Fe nuclei • have been obtained • for the same sample of the 31 experimental readings of the • one observed giant shower. 18.05.2011. IWS. SINP. MOSCOW

  29. 10**20 eV Nuclei № s(600,Θ) C=E/10**20 eV x, m y, m minχ21 P 1 27.48 2.04 941 -374 0.88 2 29.64 2.00 965 -406 0.945 3 32.18 1.805 948 -425 1.019 4 27.77 2.27 1011 -421 1.03 He 1 25.11 2.37 956 -408 0.895 2 33.56 1.755 947 -421 0.996 3 27.88 2.085 942 -389 0.949 4 31.33 1.93 955 -439 1. O 1 30.73 1.78 909 -363 0.97 2 31.03 1.86 943 -387 0.942 3 29.90 1.94 940 -393 0.904 4 31.66 1.75 912 -428 0.997 Fe 1 34.12 1.6 905 -353 1.081 2 36.23 1.66 969 -429 1.042 3 33.05 1.745 935 -437 1.051 4 35.02 1.69 975 -389 1.01 DATA Yakutsk 53.88 1.1 1055 -406 Best estimates: 18.05.2011. IWS. SINP. MOSCOW

  30. Simulations • New estimates of energy E • of the giant air showerobserved at YA • have been calculated • in terms of the QGSJET2 and Gheisha 2002 models: • E≈2.·1020eV forthe proton primaries • and • E≈1.7·1020eV for the primary iron nuclei 18.05.2011. IWS. SINP. MOSCOW

  31. Minimum of the function χ2 • Coordinates of axis • and • values of the χ2 • have been obtained • for each individual shower 18.05.2011. IWS. SINP. MOSCOW

  32. Results of energy estimations • The energy estimates are minimal for theiron nuclei primaries • and change inside the interval • (1.6−1.75)· 1020 eV • with the value of the χ2 ~ 1.1 • per one degree of freedom. 18.05.2011. IWS. SINP. MOSCOW

  33. Results of energy estimations • For the proton and helium nuclei primaries • energy estimates are maximal and • change inside the interval • (1.8−2.4)·1020 eV • with the value of the χ2 ~ 0.9 • per one degree of freedom. 18.05.2011. IWS. SINP. MOSCOW

  34. Results of energy estimations • For the oxygen nuclei primaries the • energy estimates are in the interval • (1.8−2)·1020eV • which isbetween intervals for proton and iron nuclei primaries • with the value of the χ2 ~ 0.95 • per one degree of freedom. 18.05.2011. IWS. SINP. MOSCOW

  35. Results of energy estimations • Dependence of the χ12 • per one degree of freedom • on the coefficient • C=E/(1020 eV) 18.05.2011. IWS. SINP. MOSCOW

  36. protons 18.05.2011. IWS. SINP. MOSCOW

  37. helium nuclei 18.05.2011. IWS. SINP. MOSCOW

  38. oxygen nuclei 18.05.2011. IWS. SINP. MOSCOW

  39. iron nuclei 18.05.2011. IWS. SINP. MOSCOW

  40. Reality of the Yakutsk DATA • The time of sampling signal in the scintillation detectors • τ=2000 ns 18.05.2011. IWS. SINP. MOSCOW

  41. Fraction of sampled signal: 1-100 m, 2-600 m, 3-1000 m, 4-1500 m 18.05.2011. IWS. SINP. MOSCOW

  42. Energy spectrum • The HiRes data are used to construct • 1) the base spectrum • Jb(E)= A·(E)-3.25, • and • 2) the reference spectrum • Jr(E) 18.05.2011. IWS. SINP. MOSCOW

  43. Energy spectrum • Using new variable y=lgE • in four energy intervals of yi • (i=1, 2, 3 and 4) • 1)17.<y1<18.65, • 2) 18.65<y2<19.75, • 3) 19.75<y3<20.01 and • 4)y4>20.01 18.05.2011. IWS. SINP. MOSCOW

  44. Spectrum Jr(E)has been approximated by the following exponent functions • J1(E)=A·(E)-3.25, • J2(E)=C·(E)-2.81, • J3(E)=D·(E)-5.1, • J4(E)=J1(E)=A·(E)-3.25 • Constants C and D may be expressed through A and equations forJr(E) at the boundary points. 18.05.2011. IWS. SINP. MOSCOW

  45. Spectrum Jb(E)has been approximated by the following exponent function • Jb(E) = J1(E)=A·(E)-3.25, • L.G. Dedenko et al., Phys. of Atom. Nucl., 2010, vol. 73, No12, pp. 2182-2189. 18.05.2011. IWS. SINP. MOSCOW

  46. Spectrum • The reference spectrum • is assumed as • lgzi=lg(Ji(E)/J1(E)), • where i=1, 2, 3, 4. 18.05.2011. IWS. SINP. MOSCOW

  47. Spectrum • Results of the spectra J(E) • observed at various arrays • have been expressed as • lg z=lg (J(E)/Jb(E)) • and are shown • in comparison with • the reference spectrum. 18.05.2011. IWS. SINP. MOSCOW

  48. HiRes 18.05.2011. IWS. SINP. MOSCOW

  49. PAO 18.05.2011. IWS. SINP. MOSCOW

  50. AGASA 18.05.2011. IWS. SINP. MOSCOW

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