  We use the reconstructed properties of the Amaterasu particle, the
second-highest energy cosmic ray ever detected, to map out three-dimensional
constraints on the location of its unknown source. We highlight possible
astrophysical sources that are compatible with these regions and requirements.
Among these, M82, a powerful starburst galaxy, stands out as a strong candidate
due to its position and proximity. To derive our constraints, we use CRPropa 3
to model all relevant propagation effects, including deflections in the
Galactic and extra-Galactic magnetic fields. We consider key input quantities
such as source distance, position, energy, and the strength and coherence
length of the extra-Galactic magnetic field as free parameters. We then infer
constraints on these parameters by applying approximate Bayesian computation.
We present our results, demonstrating the impact of different assumptions for
the arrival mass of the Amaterasu particle and the systematic uncertainties on
the energy scale.
