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The chemical composition of the highest-energy cosmic rays, namely the atomicnumber $Z$ of rays with energies $E\gg1~\text{EeV}$, remains to date largelyunknown. Some information on the composition can be inferred from thedeflections that charged ultra-high-energy cosmic rays experience while theytraverse intervening magnetic fields. Indeed, such deflections distort andsuppress the original anisotropy in the cosmic rays arrival directions; thus, ameasure of the anisotropy is also a measurement of the deflections, which inturn informs us on the chemical composition. In this work, we show that, byquantifying ultra-high-energy cosmic ray anisotropies through the angular,harmonic cross-correlation between cosmic rays and galaxies, we are able toexclude iron fractions $f_{\rm Fe}\leq{\cal O}(10\%)$ on a fiducial hydrogenmap at $2\sigma$ level, and even smaller fractions in the reverse case ofhydrogen on an iron map, going below $f_{\rm H}\lesssim10\%$ when we mask theGalactic Centre up to latitudes of $40\,\text{deg}$. This is an improvement ofa factor of a few compared to our previous method, and is mostly ascribable toa new test statistics which is sensitive to each harmonic multipoleindividually. Our method can be applied to real data as an independent test ofthe recent claim that current cosmic-ray data can not be reproduced by anyexisting model of the Galactic magnetic field, as well as an additional handleto compare any realistic, competing, data-driven composition models.

Honing cross-correlation tools for inference on ultra-high-energy cosmic-ray composition