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

Abstract: Locating the sources of ultra-high energy cosmic rays (UHECRs) still remains a difficult puzzle for modern astrophysics. A major hurdle in the search for the sources is the fact that UHECRs are deflected by the Galactic magnetic field (GMF). Current knowledge of the GMF is limited, as most experimental measurements track line-of-sight--integrated quantities that are used to obtain best-fit parameters for global models including a large random component. The advent, however, of the Gaia era, with measurements of $\sim 10^9$ stellar parallaxes, in combination with upcoming large polarimetric surveys, make, for the first time, a 3D measurement of the GMF possible in principle. Such measurements can then be used to attempt a reconstruction of the trajectories of individual UHECRs through the Galaxy, in order to correct for their deflection. Motivated by these developments, in the present work, we study the limits of such a correction, by examining how its effectiveness depends on the uncertainty of any such future magnetic field measurements. To that end, we simulate attempts to reconstruct the trajectory of the cosmic ray by using hypothetical measurements of the GMF, based on values received from two recently updated GMF models. To simulate the uncertainty of a 3D measurement, random errors to these values are introduced separately for the plane-of-the-sky (POS) magnitude, the line-of-sight (LOS) magnitude and the POS direction. Our results highlight the conditions under which an effective correction is achievable. We find that the effectiveness is dependent on the particle rigidity and arrival direction, and can vary significantly depending on the GMF model used.