The leading candidates for the source of UHE cosmic rays are large, energetic structures where strong shocks are expected to be found. The most well known of these are supernova remnants, which have long been suspected to generate cosmic rays. In 1995, Japan's ASCA X-ray Satellite, reported positive observation non-thermal X-ray emissions from the Supernova Remnant SN1006. The observed emission spectrum is consistent with synchrotron emission by accelerated charged particles. This report is widely seen as confirmation of supernova remnants as a known source of cosmic rays.
The observed emission from SN1006, with some fine tuning of the emission models, can explain the existence of cosmic rays up to ~1015 eV. However, it is difficult to explain the existence of cosmic rays above 1018 eV, because supernovae are simply not large enough to maintain acceleration to the UHE regime. Furthermore, no positive correlation has been observed between the arrival directions of UHE cosmic rays and supernova remnants.
There are many larger objects in the sky where strong shocks are expected. For example, strong shocks are possible around colliding galaxies such as NGC 4038/9. However, there is no evidence to indicate these objects are sources of UHE cosmic rays.
Another class of objects which are candidate sources of UHE cosmic rays are active galactic nuclei (AGN). AGN is the generic name given to a class of galaxies which are suspected to have at their center a super massive black-holes. AGN's are typically accompanied by jets which can extend 50-100 thousand light-years. Roughly one of every ten known galaxy is an AGN. It is therefore always possible to find an AGN within error of the arrival direction of a UHE cosmic ray. Even so, there is still no evidence to indicate that AGN's actually produce UHE cosmic rays.