Not saying you are wrong about the terminology, but if local photons are "produced at the source", the use of "local" seems to be redundant.

When would a photon not be created at the source? What is a non-local photon, only CMB photons?

I am probably being confusing because there are distinct photons involved here... the ones that protons interact with to make neutrinos, and the gamma rays (which are of course, just high-energy photons) detected by FERMI or MAGIC. '

The neutrinos are produced in the process:

proton + photon -> (usually) Delta_1232 (basically an excited proton, which is very unstable so that's why you may not have heard of it)-> neutron + pion -> proton + neutrinos, provided there is enough energy available to make pions. The same process also makes gammas (from a neutral pion instead of a charged pion), but there are also lots of other processes that produce gammas (which again, are just high-energy photons).

The protons are accelerated at the source. The photons that the protons interact with to make neutrinos may either be local to the source (i.e. in the same galaxy, such that the neutrino is produced within the galaxy) or the proton could propagate some distance, bending in the intergalactic magnetic field and, if it's energetic enough, interact with a CMB photon (which are very low energy but everywhere in the universe, courtesy of the big bang). The former are likely the astrophysical neutrinos, while the latter are by definition the GZK neutrinos. The astrophysical neutrinos are at lower energy because inside galaxies, photons with higher energy than the CMB photons are available, allowing pion production at lower energies.

Basically when talking about multiple particles, and using the term source, it would be clearer to say "source of x". Yet three times now you've just said "the source".

It seems needlessly confusing so I think there is some reason I'm not grasping that you keep saying "the source".

>"The protons are accelerated at the source."

So by "source" you mean "source of the protons"? And "local photons" means "produced near the source of the protons"?

If you're in a field in a windy day you cannot tell where the wind is originating from. If you're in a room with a fan turned on, you can tell where the wind is being sourced. The source of the wind has been localized in this latter scenario, whereas in the first you can detect the wind but you can't tell what the source of the wind is. That's the gist of the local versus non-local neutrinos being detected.

So if I know the source but you don't, its local to me but non-local to you?