yr and assuming a steady state, the mean luminosity of UHECRs per unit volume must be about $10^{-37}$ W m$^{-3}$ or about $3\times 10^{44}$ erg Mpc$^{-3}$ yr$^{-1}$. That is comparable to the estimated mean volume luminosity of Gamma Ray Bursts, a fraction of one moderate Active Galactic Nucleus (AGN) inside 100 Mpc, or the power dissipated by the accretion shock of a cluster like Coma or Perseus, as examples of phenomena that have been called upon to explain UHECRs.

In summary, it seems likely that UHECRs are extragalactic in origin. If the GZK feature is not evident then the dominant sources should be within about 100 Mpc. If the feature is seen, and especially if there is a pile up around 100 EeV, then a more extended distribution of sources becomes more likely. There are a variety of phenomena that may be energetic enough to produce UHECRs. It is unclear yet if the distribution of events on the sky represents the distribution of sources or has been significantly modified by extragalactic magnetic fields. With these factors in mind let now look at some of the basic physics constraints that must be satisfied by successful accelerators of UHECRs.

How to Make 