Speaker
Description
The origin of ultra-high-energy cosmic rays (UHECRs), such as the recent $2.44×10^{20}$ eV "Amaterasu" event detected by the Telescope Array, remains one of the most intriguing mysteries in astrophysics. Identifying the sources of these particles is challenging because their trajectories are significantly deflected by cosmic magnetic fields. A promising approach to identifying UHECR sources is the observation of synchrotron γ-rays emitted by UHE protons in extremely strong magnetic fields ($B \gtrsim 10^{15}$ G), such as those associated with magnetars.
In this presentation, we propose a comprehensive theoretical framework for describing synchrotron emission from UHE protons in the intense magnetic field regime. Unlike conventional semiclassical approaches, our model is based on a fully relativistic quantum treatment using the Dirac equation, where the motion of particles is quantized into discrete Landau levels. In the UHE regime, the emission processes are not limited to electromagnetic γ-rays; strong-interaction particle production, including π and ρ mesons, becomes significant. Our formulation consistently incorporates these processes alongside proton recoil effects.
A significant computational challenge arises because the Landau quantum numbers for UHE protons can reach $N≳10^{15}$, rendering direct numerical calculations impractical. We overcome this difficulty by identifying and applying a generalized scaling rule for quantum transition probabilities. This rule allows us to reliably infer results for extremely large Landau numbers from calculations performed at lower, manageable values.
Our results reveal that proton recoil significantly modifies emission behavior. Specifically, we find that the decay width reaches a maximum and subsequently decreases with increasing magnetic field strength—a stark contrast to the monotonic increase predicted by classical theory. This work provides a rigorous theoretical foundation for interpreting high-energy radiation from UHECR acceleration sites and offers new insights into the nature of the most energetic particles in the universe.
References
[1] Telescope Array Collaboration, Science 382, 903 (2023).
[2] A. Tokuhisa and T. Kajino, ApJ. 525, L117 (1999).
[3] T. Maruyama et al., Phys. Rev. D113, 023023 (2026)..
| Category | Theory |
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