Ultra-high-energy cosmic rays (UHECRs) are deflected by extragalactic magnetic fields (EGMFs) as they propagate from their sources to Earth. The angular spread of UHECRs around their source positions provides a means to constrain the strength of turbulent EGMFs along their paths. Recent results from the Pierre Auger Observatory (PAO) indicate correlations between the arrival directions of UHECRs with energies above 32~EeV and catalogs of starburst galaxies (SBGs) and jetted active galactic nuclei (AGNs).
In this work, re-interpret these observations using the same methodology as Auger but taking EGMF deflections into account. Including EGMF deflections allows us to obtain upper limits on the strength of turbulent EGMFs between nearby UHECR sources and the Milky Way under the conservative assumption of negligible deflections in the Galactic magnetic field.
We show that, the expected anisotropies in arrival directions of jetted AGNs are dominated by Centaurus A only, contrary to the PAO analysis where Mrk 421 and NGC 1275 contribute significantly as well. For SBGs, the same sources as in the PAO analysis dominate the correlations.
Using our framework, we derive 90\% confidence level upper limits for the turbulent EGMF strength (including its coherence length) between the dominant UHECR sources and the Milky Way of 4.4~nG~Mpc$^{1/2}$ for SBGs and 6.7~nG~Mpc$^{1/2}$ for jetted AGNs.