Cosmic Rays have been widely observed since then and are found just about everywhere in our Galaxy. One characteristic which provides a clue as to how cosmic rays are accelerated is the spectrum of particles we catch here on Earth. The slope is flatter at high energies than the thermal spectrum, for example, so that there are more cosmic rays at high energies. Any theory of cosmic ray origins must account for this shape. The standard belief is that some cosmic rays are accelerated in the Galaxy and some are accelerated outside the Galaxy.
Nobody knows exactly where they are produced and a source has yet to be precisely detected.
They are hard to pin down, since at such high energies there are so few of them that it is hard to tell exactly where they come from. It is difficult enough to observe these particles, never mind determine directly where their origin is. For a number of reasons, it is suspected that these cosmic rays above the ankle are extragalactic in origin, perhaps generated in the cores of Active Galactic Nuclei , in powerful radio galaxies , or by cosmic strings. These sources are known to have the tremendous amounts of energy needed to accelerate particles to such high energies, though a direct correlation has yet to be found. This is an area of active research, and as more and more sensitive detectors come on line and more evidence is gathered, scientists will have a better picture of where these extraordinarily high energy particles are generated.