Refractive displacement of the radio-emission footprint of inclined air showers simulated with CoREAS

The footprint of radio emission from extensive air showers is known to exhibit asymmetries due to the superposition of geomagnetic and charge-excess radiation. For inclined air showers a geometric early-late effect disturbs the signal distribution further. Correcting CoREAS simulations for these asymmetries reveals an additional disturbance in the signal distribution of highly inclined showers in atmospheres with a realistic refractive index profile. This additional apparent asymmetry in fact arises from a systematic displacement of the radio-emission footprint with respect to the Monte-Carlo shower impact point on the ground. We find a displacement of $\sim 1500\,\text{m}$ in the ground plane for showers with a zenith angle of $85^\circ$, illustrating that the effect is relevant in practical applications. A model describing this displacement by refraction in the atmosphere based on Snell's law yields good agreement with our observations from CoREAS simulations. We thus conclude that the displacement is caused by refraction in the atmosphere.