A global autocorrelation study after the first Auger data: impact on the number density of UHECR sources

We perform an autocorrelation study of the Auger data with the aim to constrain the number density n_s of ultrahigh energy cosmic ray (UHECR) sources, estimating at the same time the effect on $n_s$ of the systematic energy scale uncertainty and of the distribution of UHECR. The use of global analysis has the advantage that no biases are introduced, either in n_s or in the related error bar, by the a priori choice of a single angular scale. The case of continuous, uniformly distributed sources is nominally disfavored at 99% C.L. and the fit improves if the sources follow the large-scale structure of matter in the universe. The best fit values obtained for the number density of proton sources are within a factor ~2 around n_s ~ 10^{-4}/Mpc^3 and depend mainly on the Auger energy calibration scale, with lower densities being preferred if the current scale is correct. The data show no significant small-scale clustering on scales smaller than a few degrees. This might be interpreted as a signature of magnetic smearing of comparable size, comparable with the indication of a ~3 degrees magnetic deflection coming from cross-correlation results. The effects on the above results of some approximations done is also discussed.