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
Candidate Sources of Ultra-high
Energy Cosmic Rays
Correlated Sources found in Auger's
New Result
November, 2007
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.
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].
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. The chance 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].
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
 Try
we reduce the above deviation?
local over-density of UHECR
sources—n(l<30Mpc)/n0>1
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.
D
----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.
GZK Horizons for different degrees of over-density and Eth
Lu & Lin, arXiv:0804.3122
Fittings with Source Over-density
to the Auger Spectrum
Total χ2 with 9 degrees of freedom
----uniform
----n/n0=2
----n/n0=4
----n/n0=10
dash lines: γ=2.5
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.
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.
GZK Horizons for different degrees of over-density and Eth
Lu & Lin, arXiv:0804.3122
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]
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%
Fittings to the Shifted Spectrum
Total χ2 with 9 degrees of freedom
----uniform
----n/n0=2
----n/n0=4
----n/n0=10
dash lines: γ=2.5
The energy
calibration is very
crucial !
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.
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.