Estimate of the correlation signal between cosmic rays and BL Lacs in future data

The existing correlation between BL Lacertae objects (BL Lacs) and cosmic-ray events observed by HiRes experiment provide sufficient information to formulate quantitatively the hypothesis about the flux of neutral cosmic-ray particles originated from BL Lacs. We determine the potential of future cosmic ray experiments to test this hypothesis by predicting the number of coincidences between arrival directions of cosmic rays and positions of BL Lacs on the celestial sphere, which should be observed in the future datasets. We find that the early Pierre Auger data will not have enough events to address this question. On the contrary, the final Pierre Auger data and the early Telescope Array data will be sufficient to fully test this hypothesis. If confirmed, it would imply the existence of highest-energy neutral particles coming from cosmological distances.