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Locating the sources of ultra-high energy cosmic rays (UHECRs) still remainsa difficult puzzle for modern astrophysics. A major hurdle in the search forthe sources is the fact that UHECRs are deflected by the Galactic magneticfield (GMF). Current knowledge of the GMF is limited, as most experimentalmeasurements track line-of-sight--integrated quantities that are used to obtainbest-fit parameters for global models including a large random component. Theadvent, however, of the Gaia era, with measurements of $\sim 10^9$ stellarparallaxes, in combination with upcoming large polarimetric surveys, make, forthe first time, a 3D measurement of the GMF possible in principle. Suchmeasurements can then be used to attempt a reconstruction of the trajectoriesof individual UHECRs through the Galaxy, in order to correct for theirdeflection.  Motivated by these developments, in the present work, we study the limits ofsuch a correction, by examining how its effectiveness depends on theuncertainty of any such future magnetic field measurements. To that end, wesimulate attempts to reconstruct the trajectory of the cosmic ray by usinghypothetical measurements of the GMF, based on values received from tworecently updated GMF models. To simulate the uncertainty of a 3D measurement,random errors to these values are introduced separately for theplane-of-the-sky (POS) magnitude, the line-of-sight (LOS) magnitude and the POSdirection.  Our results highlight the conditions under which an effective correction isachievable. We find that the effectiveness is dependent on the particlerigidity and arrival direction, and can vary significantly depending on the GMFmodel used.

Deflections of ultra-high energy cosmic rays by the Milky Way magnetic field: how well can they be corrected?