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

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

Station of Yakutsk EAS Array

The diagram of the trigger of the Yakutsk EAS array Red triangles - trigger-500 from cells, S II =6.8 km 2 up to cells S I =2.6 km 2 Blue ones - trigger-1000 from cells S II = 10.5 km 2 Green circle - 10 stations of the trigger-1000, working up to = 40 cells S I = 17.3 км 2 Each trigger station has 2 scintillator detectors (S det =2 m 2 ). The coincidences within a resolving time 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.

Estimation of shower energy E 0 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 = 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  10 4 / (  (X m /1000) in the interval of waves nm In view of mean atmospheric transmittance E el = 2.2  10 6  N s  N is the energy conveyed below the array level. It is estimated by the attenuation length N of the number of charged particles N s through the atmosphere depth E  =    N  is the energy of the muon component. It is estimated by the total number of muons N  and average energy on one muon   = 10.6  10 9 eV

E  i and E are the energy of muon losses on ionization and the neutrino E  i + E = 0.76  E  E h = 0.06  E i is the energy on nuclear reactions in the atmosphere. Red color allocates components are added on the basis of model calculation results. For E 0  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%

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

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 = ( ) ·(S 300 (0º)/10) –( ) for S 600 λ E = 250 g·cm -2, λ M = 2500 g·cm -2 β 600 = ( ) ·S 600 (0º) –( )

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

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

Dependence S 600 on temperature Molier unit S 600 (R 0 ) is recalculated on R 0 = 68 m. The formula is received from the assumption, that full number of particles equally for different R 0 R 0 = 68 corresponds T = -25°C - average temperature of the periods for Cerenkov light experiment.

Dependence K tmr on temperature

Cosθ > 0.95; T yan = -37, P yan =1008; T may = 8, P may =992

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 and δX) -Errors in parameters for calorimetric formula E 0 =(E 1 ± δE 1 )S 600 (0 o ) k ± δk Relative error δE 1 /E 1 = 25% is mainly connected with absolute calibration of Cherenkov light detectors and results in systematic shift of estimated energies of all events.

Area for events with E 0 > 4·10 19 eV

Errors of energy estimation in EAS with E 0 >4x10 19 eV

Differential Energy Spectrum at E 0 > eV

Integral Energy Spectrum of the Yakutsk Array

Largest events

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.

Comparison of the Yakutsk array Spectrum with accounts from AGN Berezinsky V.S., Gazizov A.Z., Grigorieva S.I. // preprint 2002, hep-ph/ The Spectrum obtained on the Yakutsk array will be agree with the assumption, that the particles with E 0 > eV are mainly formed in extragalactic sources

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 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 3·10 16 <E 0 <3·10 17 eV with respect to the right ascension and obtained a probably significant amplitude of the first harmonic r 1 = (1.35±0.36)% and the phase φ 1 = 123°±15°. On the Haverah Park: r 1 = (1.7±0.4)% but φ 1 = 218°±14° [R. N. Coy, et al., in Proc. 17th ICRC, Paris, 1981, Vol. 9, p. 183.].

Harmonic analysis. Interval about 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

The Influence of the inhomogeneity of the sky survey on parameters of a solar vector for events of the trigger 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

Parameters of anisotropy vectors for the trigger-500 at E 0 ~ eV

Harmonic analysis. Interval about 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 previous work (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)

Harmonic analysis. Interval about eV Parameters of anisotropy vectors for the trigger In a column R % confidence limit are given events

Harmonic analysis. Interval about eV RA 18.0<Log(E 0 )<18.5, Events: 27301, r 1 = (0.7 ± 0.9)% At ≈10 18 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.

Events with E 0 > eV Harmonic analysis RA: 19.0 <Log(E 0 )< 19.5, events 312, r 1 = (26.4 ± 8.0), α 1 = (2.3 ± 1.2) h, P = This result specifies existence anisotropic components of cosmic rays in the given interval of energy

Distribution of cosmic rays on galactic latitude R NSA = (n N -n S )/ (n N +n S ) - parameter of asymmetry where n N - number of particles from northern hemisphere, n S 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

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

Two-dimensional Marr wavelet: In an energy bin 19.0 < Log(E) < 19.5 eV the observed amplitude is significantly greater than isotropic one: W observed / W isotropic = 2.83 ± 0.51; α max = (2.3 ± 1.3) h; δ max = ± 7.50 Events with E 0 > eV

Direction of the increased intensity on a map

Map of distribution on arrival directions of cosmic rays with Е 0 > 8·10 18 eV in galactic coordinates on Yakutsk data and SUGAR. Intensity - in terms of a standard deviation of a difference of observable number and expected average for an isotropic flux. A bold line - a plane of the Supergalaxy

Events with E 0 > eV For showers with energy E 0 >10 19 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.