The primary energy spectrum measured by using the time structure of extensive air showers with compact EAS arrays (ID441) H. Matsumoto 1, A. Iyono 1, I. Yamamoto 1, K. Okei 2, S.Tsuji 2, T. Nakatsuka 3, N. Ochi 4, S. Ohara 5, T. Konishi 5, N. Takahashi 6 LAAS and the LAAS experiments 1 Okayama University of Science, Okayama , Japan 2 Kawasaki Medical School, Kurashiki , Japan 3 Okayama Shoka University, Okayama , Japan 4 Toyo University, Bunkyoku, Tokyo , Japan 5 Nara Sangyo University, Nara , Japan 6 Hirosaki University, Hirosaki , Japan ECRS2012, July 3-7, 2012, Moscow, Russia 1

Linsley’s method Extensive air shower (EAS) thickness depends on the core distance r, the zenith angle θ and the primary energy E 0. EAS thickness is defined by using the dispersion σ t of arrival time distribution of EAS particles. The dispersion of arrival time distribution of EAS particles as a function of EAS core distance r. 2

Aims of this applications The estimate of the primary energy spectrum by using Linsley’s EAS time structure method with compact EAS arrays. –Primary energy region : 10PeV – ~10EeV –Single observation (OUS1 array) –Coincidence observation (OUS1 array and OUS4 array) Observation for the primary cosmic ray by using multi EAS arrays spread over in Japan. (LAAS experiment) –Investigation the Gerasimova-Zatsepin events –Anisotropy 3

OUS1&4 array Detector Plastic scintillation counter (50cm×50cm×5cm, PMT:HAMAMATSU H7195) Data acquisition system ADC (Lecroy 2249W) TDC (Kaizuworks 3781) GPS module (Kaizuworks 3051A) Shift register (MPK NIM-ANY) Trigger condition More than 3 detectors (within 2.5μs time window) Array size ~200m 2 4

OUS4 detectors Detector Plastic scintillation counter Top&bottom: (40cm×50cm×1cm, PMT:HAMAMATSU H7195) Side: (50cm×50cm×5cm, PMT:HAMAMATSU H7195) Data acquisition system ADC (Lecroy 2249W) TDC (Kaizuworks 3781) GPS module Shift register Trigger condition Top&bottom (within 2.5μs time window) Restriction angle 25.6 [deg.] Linsley’ method can be applied in case of rather large core distance, but arrival direction can not be determined Zenith angle restriction are needed. This was pointed out at ISVHECR2006 in Weihai 5

Estimation procedure of primary energy 1.Arrival time distribution : t i (i=1,2,…,n) Gamma distribution 2.Estimation of the dispersion σ t estimator : median 3.σ t → r 4.Lateral distribution function (r, n)→E 0 data: (t i, n) OUS1 array 6

Detector simulation: FWHM: ( ) ( ) AIRES QGSJETII-3 / Hillas Splitting Algorithm Proton Single power-law spectrum Restriction of the zenith angle θ OUS1θ<60 [deg.] OUS1+4θ<25.6 [deg.] FWHM: ( ) ( ) 7

Systematics of energy OUS1:195% OUS1+4: OUS1:145% OUS1+4: 51% 8

Acceptance ~1/50 OUS1 OUS1+4 9

Conversion of spectral indices 10 Conversion table from observed spectral index |  ’| to primary spectral index | .

Data analysis Observation time [day] Total number of events Number of selected events OUS × ×10 5 OUS × ×10 3 Data period: (one more year data period added after ICRC2011) OUS1 2006/4 – 2011/12 OUS /8 – 2011/12 Restriction of the zenith angle θ OUS1θ<60 [deg.] OUS1+4θ<25.6 [deg.] Noise rate ~0.4% 11

Time difference between OUS1 and OUS4 GPS time accuracy : 1μsec. Coincident events (within 10μsec. ) 12

Observed flux at OUS1 array 13

Results: Primary energy spectrum (OUS1) eV eV eV α’-2.46± ± ±0.08 α-2.51( )-3.20 ( )-2.09 ( ) Single power-law spectrum 14

Observed flux at OUS1+4 array 15

Results: Primary energy spectrum (OUS1+4) Single power-law spectrum eV eV eV α’-3.01± ±0.22- α-3.13 ( )-3.60 ( )-

Derived by the application of Linsley’s EAS time structure method to LAAS-OUS1 single array observations.

Comparison of E ・ Flux [m -2 s -1 sr -1 ] 18 Compiled by Tsunesada-san at UHCR2012

Conclusions The primary energy spectrum is determined by compact EAS arrays according to the Linsley’s EAS structure method. The primary energy resolution of OUS1 have been improved by restricting the EAS zenith angle by using OUS4. But its acceptance decreased ~1/50. The obtained spectral index values: –OUS1: ( ) ( eV) ( ) ( eV) ( )( eV) –OUS1+4: ( )( eV) ( )( eV) The primary energy spectrum of the OUS1+4 is steeper than that of the OUS1 due to minimizing systematic errors. Observed EJ spectra is consistent with other experiments. 19

EJ, E 3 J 20

Observed flux at OUS1 and OUS1+4 21

UHCR2012 compiled by Tsunesada-san 22  1  2  3 Log10(EA) Log10(Es) AGASA 3.16(0.08) 2.78(0.3) Yakutsk 3.29(0.17) 2.74(0.20) (0.01) - HiRes 3.25(0.01) 2.81(0.03) 5.1(0.7) 18.65(0.05) 19.75(0.04) Auger 3.27(0.02) 2.68(0.01) 4.2(0.1) 18.61(0.01) 19.41(0.02) TA 3.33(0.04) 2.68(0.04) 4.2(0.7) 18.69(0.03) 19.68(0.09)