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