GZK Horizons and the Recent Pierre Auger GZK Horizons and the Recent Pierre Auger Result on the Anisotropy of Highest-energy Result on the Anisotropy of Highest-energy

Cosmic Ray SourcesCosmic Ray Sources

Chia-Chun LuChia-Chun LuInstitute of Physics, National Chiao-Tung University, TaiwanInstitute of Physics, National Chiao-Tung University, Taiwan

Guey-Lin LinGuey-Lin LinInstitute of Physics, National Chiao-Tung UniversityInstitute of Physics, National Chiao-Tung University

Leung Center for Cosmology and Particle Astrophysics, TaiwanLeung Center for Cosmology and Particle Astrophysics, Taiwan

Candidate Sources of Ultra-Candidate Sources of Ultra-high Energy Cosmic Rayshigh Energy Cosmic Rays

Correlated Sources found in Correlated Sources found in Auger's New ResultAuger's New Result

November, 2007

Event Energy > 57 EeV, Dmax < 71Mpc,Ψ=3.2o (opening angle of the circle ) => protons dominatedFirst 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.

Correlation Search by YakutCorrelation Search by Yakutsksk

Using the parameters (E > 56 EeV,Using the parameters (E > 56 EeV, z < 0.018, and ψ = 3.10) recomme z < 0.018, and ψ = 3.10) recommended by Auger, it shows that 12 onded by Auger, it shows that 12 of 24 events correlate with the AGf 24 events correlate with the AGNs in V-C catalog (expected 5.6.) Ns in V-C catalog (expected 5.6.) The chance probability is 4*10The chance probability is 4*10-3-3..

A. A. Ivanov for Yakutsk group, arXiv:0803.0612 [astro-ph].

Another scanning of parameter sets (E > 40 EeV, 0.001 < z < 0.03, 10 < 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 ψ < 60) is performed to determine the maximum ratio of the difference in the observed number of coincidences and the number expected for tin the observed number of coincidences and the number expected for the isotropic case to the standard deviation. The maximum ratio appearhe isotropic case to the standard deviation. The maximum ratio appears to be reached for 22 events with energies above 60 EeV, 12 of which ars to be reached for 22 events with energies above 60 EeV, 12 of which arrive within ψ = 3rive within ψ = 300 of the AGNs (while an expected number is 4.1) at dista of the AGNs (while an expected number is 4.1) at distance from the Earth less than 63 Mpc. The chance probability is 2*10nce from the Earth less than 63 Mpc. The chance probability is 2*10-4-4..

Correlation Search by HiReCorrelation Search by HiRess

Using the parameters (E > Using the parameters (E > 56 EeV, z < 0.018, and ψ = 56 EeV, z < 0.018, and ψ = 3.10) recommended by Au3.10) recommended by Auger, it shows that 2 of 13 ger, it shows that 2 of 13 events correlate with the events correlate with the AGNs in V-C catalog. TheAGNs in V-C catalog. The chance probability is 0.82.chance probability is 0.82.

R. U. Abbasi et al., arXiv:0804.0382 [astro-ph].

The most significant correlation wThe most significant correlation was found to occur at (2.0◦, 15.8 Eeas found to occur at (2.0◦, 15.8 EeV, 0.016) with 36 correlated of 198 V, 0.016) with 36 correlated of 198 total events. This corresponds to a total events. This corresponds to a chance probability of 0.24.chance probability of 0.24.

A question concerning A question concerning consistency and consistency and

suggestions for the suggestions for the resolutionresolution The maximum valid distance of V-C catalog The maximum valid distance of V-C catalog

and Dand Dmaxmax found in the correlation analysis is found in the correlation analysis is 100 Mpc and 71 Mpc respectively, while the 100 Mpc and 71 Mpc respectively, while the GZK horizon for GZK horizon for protonsprotons with E with Ethth= 57 EeV is = 57 EeV is about 220 Mpc for uniform distribution of Uabout 220 Mpc for uniform distribution of UHECR sources.HECR sources.

Could we reduce the above deviatioCould we reduce the above deviation?n? Try local over-density of UHECR sourTry local over-density of UHECR sour

ces—n(l<30Mpc)/nces—n(l<30Mpc)/n00>1>1

GZK HorizonGZK 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.

D

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.

----uniform----n/n0=2----n/n0=4----n/n0=10

----uniform----n/n0=2----n/n0=4----n/n0=10

GZK Horizons for different degrees of over-density and EGZK Horizons for different degrees of over-density and Ethth

Lu & Lin, arXiv:0804.3122

Fittings with Source Fittings with Source Over-density to the Over-density to the

Auger SpectrumAuger Spectrum

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.Lu & Lin, arXiv:0804.3122FIG. 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 χ2 with 9 degrees of freedom

----uniform----n/n0=2----n/n0=4----n/n0=10dash lines: γ=2.5solid lines: γ=2.6

GZK Horizons for different degrees of over-density GZK Horizons for different degrees of over-density and Eand Ethth

Lu & Lin, arXiv:0804.3122

Energy CalibrationEnergy 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.

Alternative Energy Alternative Energy determination determination

R. Engel, ICRC 2007, arXiv:0706.1921 [astro-ph].

Constant-intensity-cut method: independent of fluorescence detector.

E=1.3EFD

Shift energies of Auger events by +30%

Fittings to the Shifted Fittings to the Shifted SpectrumSpectrum

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.

The energy calibration is very crucial !

Lu & Lin, arXiv:0804.3122

Total χ2 with 9 degrees of freedom

----uniform----n/n0=2----n/n0=4----n/n0=10dash lines: γ=2.5solid lines: γ=2.4

ConclusionConclusion Degrees of local over density constrained by the spectrum can Degrees of local over density constrained by the spectrum can

not resolve the deviation between the GZK horizon and the manot resolve the deviation between the GZK horizon and the maximum valid distance of V-C catalog or Dximum valid distance of V-C catalog or Dmax max found in correlatiofound in correlation analysis.n analysis.

Suitably adjusting the energies of UHECR events can resolve thSuitably adjusting the energies of UHECR events can resolve the above deviation, and fittings to the shifted spectrum imply n/e above deviation, and fittings to the shifted spectrum imply n/nn00 =(2~4). This can be examined by more events in the future. =(2~4). This can be examined by more events in the future.