Chia-Chun Lu Institute of Physics, National Chiao-Tung University, Taiwan Guey-Lin Lin

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, Dmax < 71Mpc, Ψ=3.2o (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 < 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. • Another scanning of parameter sets (E > 40 EeV, 0.001 < z < 0.03, 10 < ψ < 60) is performed to determine the maximum ratio of the difference 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 = 30 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. A. A. Ivanov for Yakutsk group, arXiv:0803.0612 [astro-ph].

6. Correlation Search by HiRes • Using the parameters (E > 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. Thechance probability is 0.82. • 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. R. U. Abbasi et al., arXiv:0804.0382 [astro-ph].

7. A question concerning consistency and suggestions for the resolution • The maximum valid distance of V-C catalog and Dmax found in the correlation analysis is 100 Mpc and 71 Mpc respectively, while the GZK horizon for protons with Eth= 57 EeV is about 220 Mpc for uniform distribution of UHECR sources. • Could we reduce the above deviation? • Try local over-density of UHECR sources—n(l<30Mpc)/n0>1

8. D GZK Horizon Accumulative event probabilities of UHECR N(l, Eth) · 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 Eth. D is the maximal distance of sources. P(D,Eth)=0.9 ; D is the GZK horizon for corresponding Eth. It means that 90% of the events with energies above Eth come from the sources at distances smaller than D.

9. ----uniform ----n/n0=2 ----n/n0=4 ----n/n0=10 ----uniform ----n/n0=2 ----n/n0=4 ----n/n0=10 • 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)/n0. • The accumulative event probability with D=100Mpc is only 0.5 for Eth=57EeV by assuming a uniform source distribution.

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

11. Fittings with Source Over-density to the Auger Spectrum Total χ2 with 9 degrees of freedom The model n(l<30Mpc)/n0=10 with χ2/d.o.f.~2 is not compatible to the spectrum at significance levelα=0.02. The GZK horizon is larger than 155 Mpc. ----uniform ----n/n0=2 ----n/n0=4 ----n/n0=10 dash lines: γ=2.5 solid lines: γ=2.6 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.

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

13. Energy Calibration 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. V. Berezinsky, arXiv:0801.3028 [astro-ph]

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

15. Fittings to the Shifted Spectrum Total χ2 with 9 degrees of freedom The energy calibration is very crucial ! ----uniform ----n/n0=2 ----n/n0=4 ----n/n0=10 dash lines: γ=2.5 solid lines: γ=2.4 Lu & Lin, arXiv:0804.3122 The χ2 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/n0=2-4. In these cases, Eth is 74 EeV due to the energy shift and the corresponding GZK horizons are 120(n/n0=2) and 105(n/n0=4)Mpc. They are now much closer to 100 Mpc.

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 Dmax found in correlation analysis. • Suitably adjusting the energies of UHECR events can resolve the above deviation, and fittings to the shifted spectrum imply n/n0 =(2~4). This can be examined by more events in the future.