Yakutsk results: spectrum and anisotropy

1. Yakutsk results: spectrum and anisotropy M.I. Pravdin for Yukutsk Collaboration Yu.G. Shafer Institute of Cosmophysical Research and Aeronomy, 31 Lenin Ave., 677980 Yakutsk, Russia

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

3. Station of Yakutsk EAS Array

4. The diagram of the trigger of the Yakutsk EAS array Each trigger station has 2 scintillator detectors (Sdet=2 m2). The coincidences within a resolving time 2.0 - 2.2 μs is required. EAS is selected when an event is registered simultaneously by three neighboring stations forming a triangle. Resolving time in this case equals 40 μs. Red triangles - trigger-500 from 1992 - 63 cells, SII=6.8 km2 up to 1992 - 19 cells SI =2.6 km2 Blue ones - trigger-1000 from 1990 - 24 cells SII = 10.5 km2 Green circle - 10 stations of the trigger-1000, working up to 1990 24+16 = 40 cells SI = 17.3 км2

5. Estimation of shower energy E0The calorimetric method • The relation between parameters S300 or S600 and primary particle energy E0 for showers close to the vertical has been determined by the calorimetric method. For the average showers with different S300 or S600 E0 is estimated as the sum separate a components: • E0 = Ei + Eel + Eμ+ Eμi + Eν + Eh • Ei = kis the energy lost by a shower over the observation level. It 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 • Eel = 2.2106NsNis the energy conveyed below the array level. It is estimated by the attenuation lengthNof the number of charged particlesNsthrough the atmosphere depth • E = Nis the energy of the muon component. It is estimated by the total number of muonsNand average energyon one muon = 10.6109 eV

6. Eiand E are the energy of muon losses on ionization and the neutrino Ei + E = 0.76E Eh = 0.06Eiis the energy on nuclear reactions in the atmosphere. Red color allocates components are added on the basis of model calculation results. For E0 1019 eV : Ei / E0 74%; Eel / E0 15%; Eμ / E0 3.6%; (Eμi + Eν + Eh) / E0 7.4%

7. Ratio between shower energy E0 and S600(0º) determined by the calorimetric method EO = (4.6  1.2)1017S600(0)0.98  0.03

8. Zenith-Angular Dependence of S300 and S600 We assume that S300 (S600) dependence on the atmospheric depth must be described as S(θ) = S(0º)·{(1-β)·exp((X0-X)/λE) + β·exp((X0-X)/λM)} X0 = 1020 g·cm-2, X=X0/cos(θ) β is a portion of the «muon» component in the total response of S(0º) at the depth of X0 = 1020 g·cm-2 for S300 λE = 200 g·cm-2, λM = 1000 g·cm-2 β300 = (0.368 + 0.021) ·(S300(0º)/10)–(0.185 + 0.02) for S600λE = 250 g·cm-2, λM = 2500 g·cm-2 β600 = (0.39 + 0.04) ·S600(0º)–(0.12 + 0.03)

9. β600 versus the shower parameter S600(0º)

10. S600 versus the atmospheric depth X for different energies. The red lines are the change of S600 depending on X by using formula with 2 exponents

11. Dependence S600 on temperature • Molier unit • S600(R0) is recalculated on R0 = 68 m. The formula is received from the assumption, that full number of particles equally for different R0 • R0 = 68 corresponds T = -25°C - average temperature of the periods for Cerenkov light experiment.

12. Dependence Ktmr on temperature

13. Cosθ > 0.95; Tyan= -37, Pyan=1008; Tmay= 8, Pmay=992

14. Errors of energy estimation in giant air showers • The relative error in energy estimation for individual event δE/Edepends on several factors: • Errors in determination of S600(θ) (δS/S(θ)) and zenith angle (δθ) • Errors in parameters for zenith angular dependence (δβ and δX) • Errors in parameters for calorimetric formula E0=(E1 ± δE1)S600(0o) 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.

15. Area for events with E0 > 4·1019 eV

16. Errors of energy estimation in EAS with E0>4x1019 eV

17. Differential Energy Spectrum at E0 > 1017 eV

18. Integral Energy Spectrum of the Yakutsk Array

19. Largest events

20. On the Yakut EAS array four events with energy greater GZK-cutoff are registered. It specifies absence of such cutoff in cosmic rays spectrum. But because of small statistics and errors of energy estimation in individual events reliability of such conclusion while is insufficient.

21. Comparison of the Yakutsk array Spectrum with accounts from AGN Berezinsky V.S., Gazizov A.Z., Grigorieva S.I.// preprint 2002, hep-ph/0204357 The Spectrum obtained on the Yakutsk array will be agree with the assumption, that the particles with E0 > 1019 eV are mainly formed in extragalactic sources

22. Anisotropy. Harmonic analysis. For an estimation of cosmic ray anisotropy it is possible to use the harmonious analysis of showers distribution on a sidereal time or on right ascension. We carried out such analysis for different intervals on energy Interval about 1017 eV is near to the threshold of the trigger – 500 of Yakutsk array. In [MikhaÏlov and Pravdin, JETP Lett. 66, 305 (1997)] we studied the data in the energy range of 3·1016 <E0 <3·1017 eV with respect to the right ascension and obtained a probably significant amplitude of the first harmonic r1 = (1.35±0.36)% and the phase φ1 = 123°±15° . On the Haverah Park: r1 = (1.7±0.4)% but φ1 = 218°±14° [R. N. Coy, et al., in Proc. 17th ICRC, Paris, 1981, Vol. 9, p. 183.].

23. Harmonic analysis.Interval about 1017 eV • The further analysis shown, that on results near to a threshold essential are influenced inhomogeneous sky survey and seasonal variations of shower frequency. • The reasons resulting in the inhomogeneous sky survey by array: • Short-term switching-off of operation (most often in the daytime) • Temporary failure of certain trigger station (varies the collection area) • To estimate inhomogeneity of the sky survey we calculate relative distribution of the effective area of array on minutes of day (for each time - solar, sidereal and antisidereal) • Near threshold the effective area is proportional to the number of triangles in the trigger that actually register the events

24. The Influence of the inhomogeneity of the sky survey on parameters of a solar vector for events of the trigger - 500. The contribution of seasonal variations to sidereal vector (VAR) is determined from an antisidereal vector. Analogical contribution on right ascension is determined from an antisidereal vector and zenith- angular distribution of events

25. Parameters of anisotropy vectors for the trigger-500 at E0 ~ 1017 eV

26. Harmonic analysis.Interval about 1017 eV The inhomogeneity of the sky survey is essential to the Yakutsk EAS array. Its account considerably decreases amplitudes of anisotropy vectors Taking account distorting factor, the statistical significant anisotropy of the first and second harmonics is not observed: By sidereal time amplitude of the first harmonic is smaller than 0.6% with the probability 0.95 and for second harmonic it is 0.65%; In the analysis samples of previouswork (1997) the amplitude of the first harmonic with respect to the RA with regard to the perturbing factors is (0.45 ± 0.55)%.(Instead of 1.35)

27. Harmonic analysis.Interval about 1018 eV Parameters of anisotropy vectors for the trigger-1000. In a column R0.95 95 % confidence limit are given. 34596 events

28. Harmonic analysis.Interval about 1018 eV RA 18.0<Log(E0)<18.5, Events: 27301, r1 = (0.7 ± 0.9)% At ≈1018 eV the statistically significant anisotropy is not observed. Our results do not confirm given AGASA. The Yakutsk array cannot observe the center of the Galaxy.

29. Events with E0 > 1019 eV Harmonic analysisRA: 19.0 <Log(E0)< 19.5, events 312, r1 = (26.4± 8.0),α1 = (2.3 ± 1.2) h, P = 0.004 This result specifies existence anisotropic components of cosmic rays in the given interval of energy

30. Distribution of cosmic rays on galactic latitude RNSA = (nN-nS)/ (nN+nS) - parameter of asymmetry where nN -number of particles from northern hemisphere, nS from southern. Points - experimental data of the Yakutsk array. Curves - results of model calculations for a mix of isotropical extragalactic protons with nucleus (Nu) and protons (P) from a disk of the Galaxy

31. Two-dimensional Marr wavelet on the equatorial sphere (’Mexican Hat’) Two-dimensional wavelet amplitude asa function of energy and declination.

32. Events with E0 > 1019 eV Two-dimensional Marr wavelet: In an energy bin 19.0< Log(E) < 19.5 eV the observedamplitude is significantly greater than isotropic one: Wobserved/Wisotropic = 2.83±0.51; αmax= (2.3 ± 1.3)h; δmax= 52.50 ± 7.50

33. Events with E0 > 1019 eV Direction of the increased intensity on a map

34. Map of distribution on arrival directions of cosmic rays with Е0 > 8·1018 eVin galactic coordinates on Yakutsk data and SUGAR. Intensity - in terms of a standard deviation of a difference of observable number and expected averagefor an isotropic flux. A bold line - a plane of the Supergalaxy

35. Events with E0 > 1019 eV For showers with energy E0 >1019 eV the deviation of experimental distribution on arrival directions from isotropic one is observed. Probably it is caused by some excess of events from a Supergalaxy plane.