1. Properties of giant air showers and the problem of energy estimation of initial particles M.I. Pravdin for Yukutsk Collaboration Yu.G. Shafer Institute of Cosmophysical Research and Aeronomy, 31 Lenin Ave., 677980 Yakutsk, Russia

2. THE GZK PROBLEM AGASA - Super GZK-particles exist 11events above 10 20 eV. No GZK cutoff HiRes – Steeping of the spectrum above 10 19.8 eV. GZK cutoff is observed Yakutsk – 4 events above 10 19.99 eV. Statistics is insufficient Auger SD – No events above 10 20 eV. But no steeping of the spectrum Research of the GZK problem is started for a long time, but the exact answer is not received yet. Results of different experiments in the GZK cutoff region of the energy spectrum will not be coordinated:

3. Differential Energy Spectrum at E 0 > 10 17 eV

4. THE GZK PROBLEM Energy spectra obtained in different experiments correspond quite well in shape but differ in intensity. The data from the Yakutsk array near 10 19 eV are higher by a factor of 2.5 than HiRes data and 30% than AGASA’s. Problem of a agreement of energy estimation in different experiments

5. Estimation of shower energy E 0 in Yakutsk The calorimetric method The relation between parameters S 300 or S 600 and primary particle energy E 0 for showers close to the vertical has been determined by the calorimetric method. For the average showers with different S 300 or S 600 E 0 is estimated as the sum separate a components: E 0 = E i + E el + E μ + E μi + E ν + E h E i is the energy lost by a shower over the observation level. E el is the energy conveyed below the array level. E  is the energy of the muon component. E  i and E are the energy of muon losses on ionization and the neutrino E h is the energy on nuclear reactions in the atmosphere. Red color allocates components are added on the basis of model calculation results

6. . Ei = k  is estimated by measurements of total Cerenkov light flux , and k = 2.16  104 / (0.37 + 1.1  (Xm /1000) in the interval of waves 300-800nm. In view of mean atmospheric transmittance For E 0  10 19 eV : E i / E 0  74%; E el / E 0  15%; E μ / E 0  3.6%; (E μi + E ν + E h ) / E 0  7.4%

7. Ratio between shower energy E 0 and S 600 (0º) determined by the calorimetric method E O = (4.6  1.2)  10 17  S 600 (0  ) 0.98  0.03

8. Zenith-Angular Dependence of S 300 and S 600 We assume that S 300 (S 600 ) dependence on the atmospheric depth must be described as S(θ) = S(0º)·{(1-β)·exp((X 0 -X)/λ E ) + β·exp((X 0 -X)/λ M )} X 0 = 1020 g·cm -2, X=X 0 /cos(θ) β is a portion of the «muon» component in the total response of S(0 º ) at the depth of X 0 = 1020 g·cm -2 for S 300 λ E = 200 g·cm -2, λ M = 1000 g·cm -2 β 300 = (0.368 + 0.021) ·(S 300 (0º)/10) –(0.185 + 0.02) for S 600 λ E = 250 g·cm -2, λ M = 2500 g·cm -2 β 600 = (0.39 + 0.04) ·S 600 (0º) –(0.12 + 0.03)

9. β 600 versus the shower parameter S 600 (0º)

10. S 600 versus the atmospheric depth X for different energies. The red lines are the change of S 600 depending on X by using formula with 2 exponents

11. Errors of energy estimation in giant air showers The relative error in energy estimation for individual event δE/E depends on several factors: -Errors in determination of S 600 (θ) (δS/S(θ)) and zenith angle (δθ) -Errors in parameters for zenith angular dependence (δβ) -Errors in parameters for calorimetric formula E 0 =(E 1 ± δE 1 )S 600 (0 o ) k ± δk

12. Errors of energy estimation in EAS with E 0 >4x10 19 eV (only δS/S(θ), δθ, δβ)

13. Errors of energy estimation in giant air showers Errors in parameters for calorimetric formula - systematic errors of energy spectrum E 0 =(E 1 ± δE 1 )S 600 (0 o ) k ± δk Relative error δE1/E1 = 25% is mainly connected with absolute calibration of Cherenkov light detectors and results in systematic shift of estimated energies of all events. δk = 0.03 increases errors of an estimation with energy rise. For 10 20 uncertainty makes 30 %

14. Comparison of the Yakutsk array Spectrum with accounts from AGN Berezinsky V.S., Gazizov A.Z., Grigorieva S.I. // preprint 2002, hep-ph/0204357

15. Comparison of the Yakutsk spectrum at reduction E 0 by the factor 1.6 with the HiRes data

16. Muon Component of EAS In Yakutsk array experimental data about increase of muon fraction in giant air showers are received We have - 5 muon detectors: Area = 20 m2; Threshold energy of muons – 1/cosθ GeV - Big Muon Detector: Area = 180 m2 Threshold – 0.5/cosθ GeV

17. A plan of the location of detector stations of the Yakutsk EAS Array

18. Lateral Distribution For the description of lateral distribution muons and all particles function is used as ρ(R)  (R/R 0 )  a (1 + R/R 0 ) a-b (1 + R/2000) -g for all particles: R 0 - Molier unit (70 m), a=1.3, g=1 for muons: R 0 =280 m, a=0.75, g=6.5

19. Lateral Distribution of muons and all particles in EAS with θ=12  Open circles – muons, close one – all particles

20. Lateral Distribution of muons and all particles in EAS with θ=55  Open circles – muons, close one – all particles

22. Energy dependence of the parameter b  in different zenith angle intervals

23. Energy dependence of the parameters b  and b s in vertical showers (cosθ>0.9)

24. The muon fraction at R=300m and R=600m (cosθ>0.9) Open circles – R=600m; close one – R=300m

25. The muon fraction in full number of particles at distances from 100m up to 1000m (cosθ>0.9)

26. Conclusions The muon contribution in the response scintillation detectors at Е 0 near 10 19 eV starts to grow. Models predict reduction. Probably it reflects existence of unknown processes in nuclear interactions. The energy fraction of EAS transmitted in muons becomes essentially more and increases with growth of energy. Fluorescent detectors do not see the contribution muon component and can underestimate energy of a gain showers. For a correct energy estimation of showers and the decision of GZK problem it is necessary to carry out complex researches of EAS properties including muon component.