Full sky harmonic analysis hints at large UHECR deflections

The full-sky multipole coefficients of the ultra-high energy cosmic ray (UHECR) flux have been measured for the first time by the Pierre Auger and Telescope Array collaborations using a joint data set with E > 10 EeV. We calculate these harmonic coefficients in the model where UHECR are protons and sources trace the local matter distribution, and compare our results with observations. We find that the expected power for low multipoles (dipole and quadrupole, in particular) is sytematically higher than in the data: the observed flux is too isotropic. We then investigate to which degree our predictions are influenced by UHECR deflections in the regular Galactic magnetic field (GMF). It turns out that the UHECR power spectrum coefficients $C_\ell$ are quite insensitive to the effects of the GMF, so it is unlikely that the discordance can be reconciled by tuning the GMF model. On the contrary, a sizeable fraction of uniformly distributed flux (representing for instance an admixture of heavy nuclei with considerably larger deflections) can bring simulations and observations to an accord.