A Method of Searching for Origins of Cosmic Rays correcting for Galactic Magnetic Field Deflections and Charge Composition

We present a new method of searching for origins of ultra-high energy cosmic rays directly from observed data. We include corrections for deflections in the galactic magnetic field according to the individual cosmic ray charges. The analysis procedure is iterative and consists of the following steps. Initially, we assign to each cosmic ray a charge hypothesis and apply corresponding corrections for the galactic field to obtain directions outside our galaxy. We then search for directions indicating an enhanced cosmic ray arrival probability using a clustering algorithm. The cluster directions form a set of source candidates. Hereafter, the initial charge assignments of the cosmic rays are disregarded, and a stacked source analysis is performed to evaluate the validity of the set of source candidates. The consistency of the observed cosmic rays with the expected arrival probability distributions on Earth is used in a likelihood ratio method on one hand for the evaluation of the set of source candidates, and on the other hand for assigning charges to each cosmic ray. The procedure can be repeated optimizing for the most likely set of sources. We present the method and its performance using a simulated astrophysical scenario.