Erratum: ``Small-Scale Clustering in the Isotropic Arrival Distribution of Ultra-High-Energy Cosmic Rays and Implications for Their Source Candidates'' (Apj, 586, 1211 [2003])

Astronomy and Astrophysics – Astronomy

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Because of a numerical error in computing the arrival directions of ultra-high-energy cosmic rays (UHECRs), Figures 11-16 are altered. The figures are not altered dramatically, and the conclusions are unchanged, as explained below.
Figures 11 and 12 show the first and second harmonics as a function of the limiting magnitude of galaxies. In contrast to the uncorrected figures, the predicted large-scale isotropy is fully consistent with the AGASA data for almost all cases. The sudden increase of the amplitude for B=1 nG and Mlim=-21.5 is mainly due to a giant galaxy existing in the direction of (α~185deg,δ~15deg) in the vicinity of our Galaxy (at ~30 Mpc).
Figure 13 shows the two-point correlation function for various parameter sets (B,lc,Mlim). It is clear that the small-scale anisotropy cannot be seen, in contrast to the AGASA data. This is because it is difficult to obtain clusters that are likely to reflect pointlike sources in a case where there are a large number of UHECR sources. Accordingly, we investigate the dependence of the results on the source number density as follows.
Figures 14 and 15 show the first and second harmonics as a function of number fraction of UHECR sources relative to the Optical Redshift Survey (ORS) galaxies more luminous than Mlim=-20.5. Except for the case of B=100 nG, the large-scale isotropy is in good agreement with the AGASA data for almost any source number fraction. Figure 16 shows χ10 as a function of the source number fraction. It is apparent that the small-scale anisotropy is consistent with the AGASA data for (B,lc)=(1nG,1Mpc) and the source number fraction ~10-1. For a longer correlation length or stronger extragalactic magnetic field (EGMF), the correlation at small angles between UHECRs is reduced or eliminated by the effect of deflection when UHECRs propagate in the EGMF from sources to the Earth. Thus, the small-scale anisotropy is not well reproduced for such parameter sets. This fact can be seen from Figure 16, where the dependence of χ10 on number fraction has a trough at number fraction ~10-1 only for (B,lc)=(1nG,1Mpc).
In summary, the large-scale isotropy and small-scale anisotropy of UHECR arrival distribution observed by AGASA can be explained when EGMF is weak (B,lc)=(1nG,1Mpc) and the source number density ~10-6-10-5 Mpc-3. This conclusion remains unchanged.
Provided that the small-scale anisotropy cannot be well reproduced for strong EGMF, the local-enhancement model of UHECR sources in the Local Supercluster is disfavored by the observation because this model requires strong EGMF in order to explain the isotropic arrival distribution of UHECRs. Thus, we conclude that a large fraction of cosmic rays above 1020 eV observed by AGASA might originate in the top-down scenarios, or that the energy spectrum measured by the HiRes experiment might be better. This conclusion is also unchanged.
Finally, we comment on our papers scheduled for publication in the Astrophysical Journal after this paper (astro-ph/0302508 and astro-ph/0307038). In these papers, we perform numerical calculations for UHECR arrival distribution. However, these calculations were performed after having corrected the numerical error mentioned here.

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