Erratum: ``Propagation of Ultra-High-Energy Cosmic Rays above 1019 eV in a Structured Extragalactic Magnetic Field and Galactic Magnetic Field'' (ApJ, 639, 803 [2006])

Details Erratum: ``Propagation of Ultra-High-Energy Cosmic Rays above 1019 eV in a Structured Extragalactic Magnetic Field and Galactic Magnetic Field'' (ApJ, 639, 803 [2006]) Erratum: ``Propagation of Ultra-High-Energy Cosmic Rays above 1019 eV in a Structured Extragalactic Magnetic Field and Galactic Magnetic Field'' (ApJ, 639, 803 [2006])

Dec 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006apj...653.1584t&link_type=abstract

The Astrophysical Journal, Volume 653, Issue 2, pp. 1584-1585.

Astronomy and Astrophysics

Astrophysics

2

Scientific paper

Because of a numerical error in computing the arrival distribution of ultra-high-energy cosmic rays (UHECRs), Figures 9 and 14 are incorrect. We considered number densities of UHECR sources with 10-5-10-6 Mpc-3 however, the number density of UHECR sources that best reproduces the AGASA results is outside this range, at 10-4 Mpc-3.
The large-scale isotropy was estimated using harmonic analysis (see our original Figs. 7 and 8). When we recalculate the first and second harmonics, for all number densities from 10-3 to 10-6 Mpc-3, these amplitudes are consistent with the isotropy obtained by AGASA within 1 σ total statistical errors.
The corrected Figure 9 given here shows χ10, defined in equation (18), as a function of the number density of UHECR sources. The χ10 plot shows the goodness of fit of the calculated two-point correlation functions and the function obtained by AGASA. The revised figure shows that the number density of the sources that best reproduces the AGASA results is 10-4 Mpc-3, since this has the smallest χ10.
The corrected Figure 14 shows the two-point correlation functions calculated from source distributions that reproduce the large-scale isotropy observed by AGASA. The number of such source distributions is 20 in the uncorrected calculation. Here, however, 21 source distributions with number densities of 10-4 Mpc-3 reproduce the large-scale isotropy. Most of the source distributions that do not reproduce the large-scale isotropy have very near and bright sources. The contributions to arriving cosmic-ray flux from such sources result in strong anisotropies. In the left panel of the revised Figure 14, it can be seen that the two-point correlation function is in fact consistent with the AGASA result, although it is not consistent in our original paper. This difference results from increasing the source number density.
In summary, the large-scale isotropy and small-scale anisotropy observed by AGASA are reproduced with a source number density of 10-4 Mpc-3 with a locally structured extragalactic magnetic field and a Galactic magnetic field. Note that we have adopted a luminosity-weighted source model, as in equation (12). The number density of UHECR sources increases more than in the source model independent of source luminosity, since luminous sources are the main contributors of cosmic-rays.

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