The Fortuitous Latitude of the Pierre Auger Observatory and Telescope Array for Reconstructing the Quadrupole Moment

Abstract

Determining anisotropies in the arrival directions of cosmic rays at the highest energy is an important task in astrophysics. It is common and useful to partition the sky into spherical harmonics as a measure of anisotropy. The two lowest nontrivial spherical harmonics, the dipole and the quadrupole, are of particular interest, since these distributions encapsulate a dominant single source and a plane of sources, as well as offering relatively high statistics. The best experiments for the detection of ultra high energy cosmic rays currently are all ground-based, with highly nonuniform exposures on the sky resulting from the fixed experimental locations on the earth. This nonuniform exposure increases the complexity and error in inferring anisotropies. It turns out that there is an optimal latitude for an experiment at which nonuniform exposure does not diminish the inference of the quadrupole moment. We derive the optimal latitude, and find that (presumably by a fortuitous coincidence) this optimal latitude runs through the largest cosmic ray experiment, Pierre Auger Observatory (PAO) in the Southern Hemisphere, and close to the largest cosmic ray experiment in the Northern Hemisphere, Telescope Array (TA). Consequently, assuming a quadrupole distribution, PAO and TA can reconstruct the cosmic ray quadrupole distribution to a high precision, without concern for their partial sky exposure.