Influence of the Galactic Halo on the UHECR Multipoles

We examine the effects of a giant magnetized halo around the Galaxy on the angular distribution of the arriving ultra-high energy cosmic rays (UHECR) observed at Earth. We investigate three injection scenarios for UHECRs, and track them through isotropic turbulent magnetic fields of varying strengths in the Galactic halo. We calculate the resultant dipole and quadrupole amplitudes for the arriving UHECRs detected by an observer in the Galactic plane region. We find that, regardless of the injection scenario considered, when the scattering length of the particles is comparable to the size of the halo, the UHECRs skymap resembles a dipole. However, as the scattering length is increased, the dipolar moment always increases, and the quadrupolar moment increases rapidly for two of the three cases considered. Additionally, the quadrupole amplitude is highlighted to be a key discriminator in discerning the origin of the observed dipole. We conclude that, to understand the origin of the UHECR dipole, one has to measure the strength of the quadrupole amplitude as well.