Lifetime of a cosmic-ray spot

We investigate the existence, angular sizes, and durations of ultrahigh-energy cosmic-ray (UHECR) hotspots as observed at Earth after the UHECRs propagate through the Galactic magnetic field. We show that, during a period of observation of typically 5 years, cosmic-ray hotspots with rigidities $\sim {10}^{19}$ V from sources whose propagation distances are smaller than 10 kpc are steady, while those much further may change position in the observer's sky due to motion of the Earth. (Note that the propagation distance—the total length of the trajectory connecting source to Earth—is always greater than the distance to the source.) However, this effect can be observed only if the spread in rigidity of the UHECRs is small enough; we show that for an energy bin width of 10%, typical of CR observatories, the effect of Earth motion over 5 years would be undetectable.