The Telescope Array (TA) shows a 20$^{\circ}$ hotspot as well as an excess of UHECRs above 50~EeV when compared with the Auger spectrum. We consider the possibility that both the TA excess and hotspot are due to a dominant source in the Northern sky. We carry out detailed simulations of UHECR propagation in both the intergalactic medium and the Galaxy, using different values for the intergalactic magnetic field.
We consider two general classes of sources: transients and steady, adopting a mixed UHECR composition that is consistent with the one found by Auger. The spatial location of the sources is draw randomly. We generate Auger-like and TA-like data sets from which we determine the spectrum, the sky maps and the level of anisotropy. We find that, while steady sources are favored over transients, it is unlikely to account for all the currently available observational data. Most of the simulated data sets with a flux excess compatible with TA (at most a few percent depending on density model) show a much stronger anisotropy than the one observed. We find that the rare cases in which both the spectrum and the anisotropy are consistent require a steady source within $\sim 10$ Mpc, to account for the flux excess, and a strong extragalactic magnetic field $\sim 10$ nG, to reduce the excessive anisotropy.