being within the Virgo cluster. (See the lecture in this volume by Biermann for more details.) On the other hand, the existence of this field structure is not established by other means, so it remains hypothetical. We may hope that greatly improved UHECR statistics in the next several years will either define unique event patterns or exclude them from consideration.

Incidentally, strong deflections of particle trajectories also add to the path lengths, so increase the influence of the photopion production losses above the GZK feature unless the sources are particularly close by. (Virgo is only about 18 Mpc away, so this is not much of an issue in that case.) Since the path lengths become energy dependent, it would also spread out the arrival times of simultaneously emitted particles with the highest energy particles arriving first.

There is at least one other basic constraint we can establish for the UHECR sources from the limited information already established. The measured flux combined with the energy loss rates establishes an estimate for the energetics of the associated phenomenology. The flux at 100 EeV translates into a local energy density of about $3\times 10^{-22}$ J m$^{-3}$. Taking the loss time as $3\times 10^8$ 