Searches for statistically significant correlations between arrival directions of ultra-high energy cosmic rays and classes of astrophysical objects are common in astroparticle physics. We present a method to test potential correlation signals of a p
riori unknown strength and evaluate their statistical significance sequentially, i.e., after each incoming new event in a running experiment. The method can be applied to data taken after the test has concluded, allowing for further monitoring of the signal significance. It adheres to the likelihood principle and rigorously accounts for our ignorance of the signal strength.
Air fluorescence detectors measure the energy of ultra-high energy cosmic rays by collecting fluorescence light emitted from nitrogen molecules along the extensive air shower cascade. To ensure a reliable energy determination, the light signal needs
to be corrected for atmospheric effects, which not only attenuate the signal, but also produce a non-negligible background component due to scattered Cherenkov light and multiple-scattered light. The correction requires regular measurements of the aerosol attenuation length and the aerosol phase function, defined as the probability of light scattered in a given direction. At the Pierre Auger Observatory in Malargue, Argentina, the phase function is measured on an hourly basis using two Aerosol Phase Function (APF) light sources. These sources direct a UV light beam across the field of view of the fluorescence detectors; the phase function can be extracted from the image of the shots in the fluorescence detector cameras. This paper describes the design, current status, standard operation procedure, and performance of the APF system at the Pierre Auger Observatory.
