Ultrahigh-energy cosmic rays (UHECR; E > 55 EeV) are usually assumed to originate outside our Galaxy, since at these energies (1) a Milky Way of arrival directions and (2) a dipole-anisotropy in the arrival directions are expected from Galactic sources, whereas the Pierre Auger Observatory has observed UHECR from all directions and has set strict upper bounds on the dipole-anisotropy. A quantitative response to these two arguments is given, which takes into account recent suggestions of a heavier composition at these energies. Proton and iron UHECR trajectories are simulated through (several versions of) two Galactic magnetic field (GMF) models by Sun et al. and one model by Jansson & Farrar. Two complementary methods are used: forwardtracking of cosmic rays from specific source distributions until the Earth is reached, and backtracking of the observed arrival directions until the backtracked trajectory intersects the Galactic plane. Both methods confirm that proton UHECR indeed form a Milky Way of arrival directions. However, iron UHECR can reach most regions of the sky if either a dipole field component is added to the models by Sun et al., or if their Halo field component is modified. The dipole-anisotropies obtained from forwardtracking iron UHECR from a spiral arm source distribution of 540 sources is several times the experimental upper bound, for all GMF models. Similar dipole amplitudes are obtained when the amount of sources or the energy is lowered, or when a fine-tuned source distribution is used. This rules out a Galactic origin of UHECR, even for an iron composition. It is furthermore argued that the lack of knowledge of the GMF forms the main bottleneck in the search for the extragalactic sources of UHECR, since the GMF can deflect extragalactic iron cosmic rays up to ~ 160 degrees before they reach the Earth.
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