2005 1 3 5.0 10 15 7.5 10 15 ev 300 12 40 Mrk421 Mrk421 1 3.7 4 20 [1] Grassberger-Procaccia [2] Wolf [3] 11 11 11 11 300 289 11 11 1
1.7 D D 2 100m 10 9 ev f(x) xf(x) = c(s)x (s 1) (x + 1) (s 4.5) (1) s age parameter x f(x) 1 2005 1 3000 ev 10 9 ev 2
1 The size distribution of the air showers observed at Kinki University 300 12 30 2 11 3
2 The example of the diagram of the fractal dimension analysis for the 300 chaotic time series of air showers D m C m D C m r D (2) 300 1.0 10 4 < size < 7.5 10 6 95% 5% 1.0 10 4 3 2005 7 12 10 4
3 The size range of analyzed air showers vs. emergence frequency of the chaotic 300 events air showers 7.5 10 6 1% 5.0 10 6 7.5 10 6 2005 1 3 1 1 1 2.5 0.30 1 5 2.9 0.35 1 24 1.8 0.30 2 7 2.6 0.30 2 25 1.8 0.30 3 2 2.5 0.32 3 3 2.7 0.31 3 7 2.4 0.34 3 17 2.3 0.32 3 27 2.1 0.30 1 The chaotic air shower size groups detected between Jan. and Mar. in 2005 2.4 2.4 11 300 0.30 0.35 0.1 1 4 5
4 The convergence of the maximum Lyapnov exponent for the chaotic 300 time series data of air showers 2005 1 3 300 10 5.0 10 6 7.5 10 6 5 6 12 40 5 5 The distribution of the right ascension for the chaotic events 6 The distribution of the declination for the chaotic events 6
3 2005 1 3 12 40 1 1 D m 0 7 1 7 The change of the slope of D m curve analyzed using 180 events (6 hours) during 6 days 8 The spectrum for the change of the slope of D m curve shown in Fig.7. The spectrum was calculated by FFT 8 1 5 6 2005 1 3 12 40 5.0 10 15 ev 7
100µG 12 40 Mrk421 11 38 1ES1218 12 30 TeV 100TeV 9 TeV [4] 9 The active galaxies where TeV gamma rays are observed 10 15 ev Mrk421 30% 2005 3 17 300 30% 1.0 10 4 < size < 1.0 10 6 10 E 2.7 8
10 The chaotic feature is conserved with the mixture of 30 percent noise 10 15 ev 4 1.0 10 13 7.5 10 15 ev 2.4 10 15 ev Mrk421 100TeV 100TeV 4 20 20 12 200 11 9
LAAS Large Area Air Shower [5] [6] 11 The new air shower arrays on the roof of the 1st building in Nara Sangyo University [1] Ohara, S., Konishi, T., Tsuji, K., Chikawa, M., Kato, Y., Wada, T., Ochi, N., Yamamoto, I., Takahashi, N., Unno, W., Kitamura, T., & LAAS Group 2003, Journal of Physics G:Nucl. Part. Phys., 29, 2065 [2] Grassberger, P. & Procaccia, I. 1983, Phys. Rev. Lett., 50, 346 [3] Wolf, R. C. L. 1992, J. Roy. Statist. Soc. Ser.B, 54, 353 [4] Fegan, S. J. et al. 2007, Proceeding of 30th International Cosmic Ray Conference [5] Konishi, T., Chikawa, M., Kato, Y., Ochi, N., Ohara, S., Takahashi, N., Tsuji, K., Wada, T., Yamamotoand, I., & LAAS Group 2001, Nuovo Cimento C, 24, 859 [6] Iyono, A., Konishi, T., Morita, T., Nakatsuka, T., Noda, C., Ochi, N., Ohara, S., Okita, M., Ryou, J., Tada, J., Takahashi, N., Tokiwa, M., Tsuji, S., Wada, T., Yamamoto, I., & Yamashita, Y. 2005, Proceeding of 29th International Cosmic Ray Conference 10
Chaos and its Anisotropy in the Energy Time Series Data of the Primary Cosmic-Rays Soji Ohara, Takeharu Konishi, and Atsushi Mukai Faculty of Informatics, Nara Sangyo University Abstract The primary cosmic-ray energies were simulated by the Nishimura-Kamata equation with the particle density distribution for the observed air showers. More than 50 thousands events were analyzed to find 10 groups of 300 events which have the chaotic feature and the fractal dimension for the data embedded in the phase space. The average fractal dimension is 2.4. The frequency of the chaotic feature confirms that the cosmic rays which have the energy between 5.0 10 15 ev and 7.5 10 15 ev contribute most effectively to the chaotic feature. The right ascensions of the cosmic rays which have the primary energy between 5.0 10 15 ev and 7.5 10 15 ev belonging to the chaotic 10 groups have the anisotropy oriented around 11h. The active galaxy Mrk421 is in this direction. The high energy gamma rays around 10 15 ev which have the nonlinear correlation are expected to arrive at the earth quite frequently. 3-12-1 Tatsuno-kita, Sango-cho, Nara 636-8503, Japan 11