A new method to search for a cosmic ray dipole anisotropy

We propose a new method to determine the dipole (and quadrupole) component of a distribution of cosmic ray arrival directions, which can be applied when there is partial sky coverage and/or inhomogeneous exposure. In its simplest version it requires that the exposure only depends on the declination, but it can be easily extended to the case of a small amplitude modulation in right ascension. The method essentially combines a $\chi^2$ minimization of the distribution in declination to obtain the multipolar components along the North-South axis and a harmonic Rayleigh analysis for the components involving the right ascension direction.