Reconstructing Galactic magnetic fields from local measurements for backtracking ultra-high-energy cosmic rays

Abstract

Context. Ultra-high-energy cosmic rays (UHECRs) are highly energetic charged particles with energies exceeding 1018 eV. These energies are far greater than those achieved in Earth-bound accelerators, and identifying their sources and production mechanism can shed light on many open questions in both astrophysics and high-energy physics. However, due to the presence of the Galactic magnetic field (GMF) they are deflected, and hence the location of their true source on the plane of the sky (PoS) is concealed. The identification of UHECR sources is an open question, excacerbated by the large uncertainties in our current understanding of the three-dimensional structure of the GMF. This difficulty arises from the fact that currently all GMF observations are integrated along the line of sight (LoS). However, thanks to upcoming stellar optopolarimetric surveys as well as Gaia data on stellar parallaxes, we expect that local measurements of the GMF in the near future will become available. Aims. Given such a set of (sparse) local GMF measurements, the question is how to optimally use them in backtracking UHECRs through the Galaxy. In this paper, we evaluate the reconstruction of the GMF, in a limited region of the Galaxy, through Bayesian inference, using principles of information field theory. Methods. We employed methods of Bayesian statistical inference in order to estimate the posterior distribution of the GMF configuration within a certain region of the Galaxy from a set of sparse simulated local measurements. Given the energy, charge, and arrival direction of a UHECR, we could backtrack it through GMF configurations drawn from the posterior, and hence calculate the probability distribution of the true arrival directions on the PoS, by solving the equations of motion in each case. Results. We show that, for a weakly turbulent GMF, it is possible to correct for its effect on the observed arrival direction of UHECRs to within ~3°. For completely turbulent fields, we show that our procedure can still be used to significantly improve our knowledge on the true arrival direction of UHECRs.