1. GZK Horizons and the Recent Pierre Auger Result on the Anisotropy of Highest-energy Cosmic Ray Sources Chia-Chun Lu Institute of Physics, National Chiao-Tung University, Taiwan Guey-Lin Lin Institute of Physics, National Chiao-Tung University Leung Center for Cosmology and Particle Astrophysics, Taiwan

2. Candidate Sources of Ultra-high Energy Cosmic Rays

3. Correlated Sources found in Auger's New Result November, 2007

4. Event Energy > 57 EeV, D max < 71Mpc, Ψ=3.2 o (opening angle of the circle ) => protons dominated First scanning (1 Jan. 2004 ~ 26 May 2006): 12 of 15 events correlated (3.2 expected with isotropic flux) Second scanning (27 May 2006 ~31 Aug. 2007): 8 of 13 events correlated (2.7 expected), the chance probability is 1.7*10 -3.

5. Correlation Search by Yakutsk Using the parameters (E > 56 EeV, z 56 EeV, z < 0.018, and ψ = 3.10) recommended by Auger, it shows that 12 of 24 events correlate with the AGNs in V-C catalog (expected 5.6.) The chance probability is 4*10 -3. A. A. Ivanov for Yakutsk group, arXiv:0803.0612 [astro-ph]. Another scanning of parameter sets (E > 40 EeV, 0.001 40 EeV, 0.001 < z < 0.03, 10 < ψ < 60) is performed to determine the maximum ratio of the di ff erence in the observed number of coincidences and the number expected for the isotropic case to the standard deviation. The maximum ratio appears to be reached for 22 events with energies above 60 EeV, 12 of which arrive within ψ = 3 0 of the AGNs (while an expected number is 4.1) at distance from the Earth less than 63 Mpc. The chance probability is 2*10 -4.

6. Correlation Search by HiRes Using the parameters (E > 56 EeV, z 56 EeV, z < 0.018, and ψ = 3.10) recommended by Auger, it shows that 2 of 13 events correlate with the AGNs in V-C catalog. The chance probability is 0.82. R. U. Abbasi et al., arXiv:0804.0382 [astro-ph]. The most significant correlation was found to occur at (2.0 ◦, 15.8 EeV, 0.016) with 36 correlated of 198 total events. This corresponds to a chance probability of 0.24. The most significant correlation was found to occur at (2.0 ◦, 15.8 EeV, 0.016) with 36 correlated of 198 total events. This corresponds to a chance probability of 0.24.

7. A question concerning consistency and suggestions for the resolution The maximum valid distance of V-C catalog and D max found in the correlation analysis is 100 Mpc and 71 Mpc respectively, while the GZK horizon for protons with E th = 57 EeV is about 220 Mpc for uniform distribution of UHECR sources. The maximum valid distance of V-C catalog and D max found in the correlation analysis is 100 Mpc and 71 Mpc respectively, while the GZK horizon for protons with E th = 57 EeV is about 220 Mpc for uniform distribution of UHECR sources. Could we reduce the above deviation? Could we reduce the above deviation? Try local over-density of UHECR sources — n(l 1 Try local over-density of UHECR sources — n(l 1

8. GZK Horizon Accumulative event probabilities of UHECR N(l, E th ) · dl is the number of cosmic ray events which are originated from sources at distances between l and l + dl from the Earth and arrive at the detector with energies above E th. D is the maximal distance of sources. P(D,E th )=0.9 ; D is the GZK horizon for corresponding E th. It means that 90% of the events with energies above E th come from the sources at distances smaller than D. D

9. The horizontal dash line in each panel denotes P (D, Eth) = 0.9. The intersection of this line with each color curve gives the GZK horizon corresponding to a specific local over-density characterized by the ratio n(l < 30Mpc)/n 0. The accumulative event probability with D=100Mpc is only 0.5 for E th =57EeV by assuming a uniform source distribution. ----uniform ----n/n 0 =2 ----n/n 0 =4 ----n/n 0 =10 ----uniform ----n/n 0 =2 ----n/n 0 =4 ----n/n 0 =10

10. GZK Horizons for different degrees of over-density and E th Lu & Lin, arXiv:0804.3122

11. Fittings with Source Over-density to the Auger Spectrum The model n(l<30Mpc)/n 0 =10 with χ 2 /d.o.f.~2 is not compatible to the spectrum at significance levelα=0.02.  The GZK horizon is larger than 155 Mpc. Lu & Lin, arXiv:0804.3122 FIG. 2: Fittings to the Auger measured UHECR spectrum where the red, green, blue and black curves denote the model with the local over-density n(l < 30Mpc)/n0 = 1, 2, 4, and 10 respectively. Solid curves correspond to γ = 2.6 while dash curves correspond to γ = 2.5. We take the source evolution parameter m = 3 throughout the calculations. Total χ 2 with 9 degrees of freedom ----uniform ----n/n 0 =2 ----n/n 0 =4 ----n/n 0 =10 dash lines: γ=2.5 solid lines: γ=2.6

12. GZK Horizons for different degrees of over-density and E th Lu & Lin, arXiv:0804.3122

13. Energy Calibration V. Berezinsky, arXiv:0801.3028 [astro-ph] Keeping the HiRes energy scale unchanged, the energy-adjustment factor λ is found to be 1.2, 0.75, 0.83 and 0.625 respectively for Auger, AGASA, Akeno and Yakutsk.

14. Alternative Energy determination R. Engel, ICRC 2007, arXiv:0706.1921 [astro-ph]. Constant-intensity-cut method: independent of fluorescence detector. E=1.3E FD  Shift energies of Auger events by +30%

15. Fittings to the Shifted Spectrum The χ 2 values here are smaller than the corresponding ones associated with unshifted spectrum and the best fit fall in the case of local over-density n/n 0 =2-4. In these cases, E th is 74 EeV due to the energy shift and the corresponding GZK horizons are 120(n/n 0 =2) and 105(n/n 0 =4)Mpc. They are now much closer to 100 Mpc. The energy calibration is very crucial ! Lu & Lin, arXiv:0804.3122 Total χ 2 with 9 degrees of freedom ----uniform ----n/n 0 =2 ----n/n 0 =4 ----n/n 0 =10 dash lines: γ=2.5 solid lines: γ=2.4

16. Conclusion Degrees of local over density constrained by the spectrum can not resolve the deviation between the GZK horizon and the maximum valid distance of V-C catalog or D max found in correlation analysis. Degrees of local over density constrained by the spectrum can not resolve the deviation between the GZK horizon and the maximum valid distance of V-C catalog or D max found in correlation analysis. Suitably adjusting the energies of UHECR events can resolve the above deviation, and fittings to the shifted spectrum imply n/n 0 =(2~4). This can be examined by more events in the future. Suitably adjusting the energies of UHECR events can resolve the above deviation, and fittings to the shifted spectrum imply n/n 0 =(2~4). This can be examined by more events in the future.