1. Convergence to GZK prediction in UHE measurements of the primary energy spectrum of cosmic rays J. N. Capdevielle, APC, University Paris Diderot capdev@apc.univ-paris7.fr

2. Outline General properties of giant EAS General properties of giant EAS The extrapolation at UHE The extrapolation at UHE The treatment of inclined GAS in AGASA The treatment of inclined GAS in AGASA The treatment of the vertical energy estimator The treatment of the vertical energy estimator Amendments of experimental data and general convergence to GZK prediction Amendments of experimental data and general convergence to GZK prediction Mass composition at UHE Mass composition at UHE

4. Propagation : coupure GZK Greisen, Zatsepin, Kuzmin Interaction des hadrons avec le fond de photons à 3K (CMB) E seuil = 70 EeV protons Les sources doivent être proches !

5. Individual showers Individual showers

7. Differential Primary Energy Spectrum of Cosmic Rays Isotropic distribution of sources

9. 1 = 500 g/cm 2 2 = 594 g/cm 2 AGASA conversion 600 600 Treatment of inclined EAS data from surface arrays and GZK prediction Jean Noël CAPDEVIELLE, F.COHEN, B.SZABELSKA, J.SZABELSKI Measured: lateral distribution + direction (θ, φ) Density (600m, θ) Density(600m, 0) Energy That conversion is energy/size independent See J.phys. G 36 (2009) 075203 by J.N.Capdevielle., F. Cohen, B. Szabelska and J. Szabelski for detailed treatment of inclined EAS

10. Treatment of inclined EAS data from surface arrays and GZK prediction Jean Noël CAPDEVIELLE, F.COHEN, B.SZABELSKA, J.SZABELSKI Results of CORSIKA simulations show complicated and energy dependent form example: Conversion to ''vertical density''

11. Treatment of inclined EAS data from surface arrays and GZK prediction Jean Noël CAPDEVIELLE, F.COHEN, B.SZABELSKA, J.SZABELSKI Cascade theory and CORSIKA simulations results for the highest energies depend on interaction model, but suggest overestimation of energy at AGASA

13. Treatment of inclined EAS data from surface arrays and GZK prediction Jean Noël CAPDEVIELLE, F.COHEN, B.SZABELSKA, J.SZABELSKI From Bergman spectrum to AGASA spectrum using AGASA conversion Grey area: D.R.Bergman et al. (HiRes Collaboration) 29th ICRC, Pune, India, 2005 Red points: AGASA energy spectrum histograms: MC generated spectrum following Bergman approximately recalculated spectrum using AGASA conversion

14. Treatment of inclined EAS data from surface arrays and GZK prediction Jean Noël CAPDEVIELLE, F.COHEN, B.SZABELSKA, J.SZABELSKI How does the conversion to ''vertical density'' work ?

19. Treatment of inclined EAS data from surface arrays and GZK prediction The spectrum from surface array has to be corrected from the overestimation of the primary energy between 10°-35° in the last decade the amended spectrum of AGASA (ISVHECRI aug. 06) is progressing in this direction The overestimation in AGASA data was coming up to 50% (in reason of the maximum depth given by AUGER) of the special properties of 3D Electromagnetic cascade near maximum It could be more for a pure proton component and less in case of a heavy composition

22. Fluctuations at constant primary energy 100 EeV 80 EAS Left wing dominated by the effect of cross section

23. Same EAS taking into account axis localization ( +/- 30m) and density measurement (10% error)

25. Knee turns from 3 to 5, ankle 3to 2

26. Statistical knee effect, decreases the population of high energy EAS in the right wing-- Lower Energy Overestimation

27. Statistical ankle effect, larger population of EAS in right wing- larger Energy Underestimation

28. Distribution of Energies contributing to S600= 300

33. Conversion S600 Eo dashed curve both spectra error on axis of 30m, lower curve 50m, 10% on density

34. Corrections for 11 of the most energetic cascades in AGASA

35. AGASA (squares), AUGER(discs), HIRES(stars)

36. EUSO ~ 1000 x AGASA ~ 30 x Auger EUSO (Instantaneous) ~ 5000 x AGASA ~ 150 x Auger AGASA JEM-EUSO tilt-mode JEM-EUSO FoV

37. Principle of EUSO - first remote-sensing from space, opening a new window for the highest energy regime From College de France: better data now TPC-like natural chamber Cf: Ground-based arrays < 100 EUSO (1)Scintillator array,(2)Fluorescence telescope array 10 20 eV

38. Conclusions The primary energy measured in giant surface arrays may be overestimated in two steps.: 1/ conversion of inclined density S600 to vertical density of reference without taking into account the behavahiour of the estimator versus zenith angle when the maximum depth is close of the level of the array 2/ conversion of the vertical density to the primary energy without taking into account the statistical disturbances generated by a knee in the differential primary spectrum When corrected for both procedures, AGASA data reflects a GZK behaviour of the primary energy spectrum of cosmic rays in agreement with HIRES and AUGER.

39. Perspectives New chances for Proton &Gamma ray Astronomy at UHE from ISS with JEM-EUSO New results of LHC updating the simulation. Xmax behaviour and change in p-Air interaction above 3 EeV? Ratio of light at 500g/cm2 to 1100g/cm2 depends on mass (in favour of p composition at UHE for HIRES)

40. G.COCCONI, 1961 Ne t e r

41. Cascade électromagnétique (NKG) Cascade électromagnétique (NKG)

42. Trans GZK AREA New scales Adequate Advanced Technologies Milesbornes to Quantum Gravity earliest approaches, EUSO and JEM-EUSO

43. Astronomie proton 1000 evts à répartir sur un certain nombre de sources éventuelles avec leur spectre respectif

45. Fonction Gaussienne hypergéométrique f(x) = N e x s-a (1+x) s-b (1+d.x) -c À angle fixe, il va falloir ajuster les paramètres : a, b, c, r 0, r 1,,,, r 0 et r 1 N e, N et s sont donnés par la simulation Avec x = r / r 0 et d = r 0 / r 1 Électrons Muons f(x) = N x - (1+x) -( - ) (1+.x) - Avec x = r / r 0 et = r 0 / r 1

46. Treatment of inclined EAS data from surface arrays and GZK prediction Jean Noël CAPDEVIELLE, F.COHEN, B.SZABELSKA, J.SZABELSKI Georgi Timofeevich Zatsepin (2006) Vadim Alekseyevich Kuzmin (2006)

47. Résultats des ajustements

53. Xmax (g/cm2) and Nmax for p, Fe initiated showers