Cosmic Ray Anisotropy Analysis with a Full-Sky Observatory

A cosmic ray observatory with full-sky coverage can exploit standard anisotropy analysis methods that do not work if part of the celestial sphere is never seen. In particular, the distribution of arrival directions can be fully characterized by a list of spherical harmonic coefficients. The dipole vector and quadrupole tensor are of special interest, but the full set of harmonic coefficients constitutes the anisotropy fingerprint that may be needed to reveal the identity of the cosmic ray sources. The angular power spectrum is a coordinate-independent synopsis of that fingerprint. The true cosmic ray anisotropy can be measured despite non-uniformity in celestial exposure, provided the observatory is not blind to any region of the sky. This paper examines quantitatively how the accuracy of anisotropy measurement depends on the number of arrival directions in a data set.