Composition-dependent acceleration of UHE Cosmic Rays in AGN electric fields

Abstract

The origin of ultra-high-energy cosmic rays (UHECRs) remains elusive, as proposed acceleration mechanisms are rarely connected directly to composition-sensitive air-shower observables. We establish such a connection for voltage-drop acceleration in near-horizon current sheets of magnetically arrested disks around supermassive black holes. Fragmentation is represented by a log-normal distribution of effective potential-sampling factors $η$, with $μ_η=\langle\lnη\rangle$, $σ_η=[\mathrm{Var}(\lnη)]^{1/2}$, and median $\widetildeη=e^{μ_η}$, while the energy gain scales with nuclear charge $Z$ and maximum potential $\mathcal{V}_{\max}$. We propagate the accelerated particles through Bethe--Heitler and adiabatic losses, proton photopion attenuation, and a mass-evolving photodisintegration cascade, and predict $\langle X_{\max}\rangle$ and $σ(X_{\max})$. We perform Bayesian fits to the Pierre Auger Observatory 2025 DNN measurements for two fixed injection templates and propagation distances of 10, 30, and 100 Mpc. An Auger-inspired, proton-poor injection reproduces both shower moments at 10 and 30 Mpc, with $χ^2/ν=0.33$ and $0.47$. At 30 Mpc, $σ_η=0.59^{+0.13}_{-0.10}$, corresponding to a multiplicative dispersion of approximately 1.8. The median sampling factor and maximum potential remain strongly degenerate, with $\widetildeη\mathcal{V}_{\max}$ more directly constrained. A metal-enriched injection containing $\sim53\%$ hydrogen gives $χ^2$ larger by 17.9 and 25.9 at 10 and 30 Mpc. Both templates remain viable at 10 and 30 Mpc but fit poorly at 100 Mpc. Within the scenarios tested, the results favour a relatively proton-poor accelerated population and show that the shower-width evolution can constrain the stochastic structure of electric-field acceleration in nearby AGN.