Signal model and event reconstruction for the radio detection of inclined air showers

The detection of inclined air showers (zenith angles θ ≳ 65°) with kilometer-spaced radio-antenna arrays allows measuring cosmic rays at ultra-high energies (E ≲ 10$^{20}$ eV). Radio and particle detector arrays provide independent measurements of the electromagnetic and muonic shower components of inclined air showers, respectively. Combined, these measurements have a large sensitivity to discriminate between air showers initiated by lighter and heavier cosmic rays. We have developed a precise model of the two-dimensional, highly complex and asymmetric lateral radio-signal distributions of inclined air shower at ground — the "radio-emission footprints". Our model explicitly describes the dominant geomagnetic emission with a rotationally symmetric lateral distribution function, on top of which additional effects disturb the symmetry. The asymmetries are associated with the interference between the geomagnetic and sub-dominant charge-excess emission as well as with geometrical projection effects, so-called "early-late" effects. Our fully analytic model describes the entire footprint with only two observables: the geometrical distance between the shower impact point at the ground and the shower maximum d$_{max}$, and the geomagnetic radiation energy E$_{geo}$. ... mehrWe demonstrate that with this model, the electromagnetic shower energy can be reconstructed by kilometer-spaced antenna arrays with an intrinsic resolution of 5% and a negligible bias.