  We interpret the correlation between local \sbg positions and
ultra-high-energy cosmic ray (UHECR) directions, recently reported by the
Pierre Auger Observatory, in terms of physical parameters: the local density of
sources and the magnetic fields governing the UHECR propagation. We include a
Galactic magnetic field model on top of a random extragalactic magnetic field
description to determine the level of UHECR deflections expected from an
ensemble of source positions. Besides deflections in magnetic fields, we also
take into account energy losses with background photon fields as well as
spectrum and composition measurements by Auger. We find consistency between the
Auger anisotropy measurement and the local \sbg density for large extragalactic
magnetic field strengths with $B > 0.6 \ \rm nG$ (for a coherence length of $1
\ \rm Mpc$) at the $5\sigma$ confidence level. Larger source densities lead to
more isotropic background and consequently allow for weaker extragalactic
magnetic fields. However, the acceleration of UHECR by such abundant sources is
more challenging to motivate. Too large source densities and extragalactic
magnetic field strengths, on the other hand, are also disfavored as that
decreases the expected level of anisotropy. This leads to upper limits of $B <
24 \ \rm nG$ and $\rho_0 < 9.0 \cdot 10^{-2} \ \rm Mpc^{-3}$ at the 90%
confidence level.
