Reconstruction of inclined extensive air showers using radio signals: from arrival times and amplitudes to direction and energy

Radio detection is now an established technique for the study of ultra-high-energy (UHE) cosmic rays with energies above $\sim10^{17}$ eV. The next-generation of radio experiments aims to extend this technique to the observation of UHE earth-skimming neutrinos, which requires the detection of very inclined extensive air showers (EAS). In this article we present a new reconstruction method for the arrival direction and the energy of EAS. It combines a point-source-like description of the radio wavefront with a phenomenological model: the Angular Distribution Function (ADF). The ADF describes the angular distribution of the radio signal amplitude in the 50-200 MHz frequency range, with a particular focus on the Cherenkov angle, a crucial feature of the radio amplitude pattern. The method is applicable to showers with zenith angles larger than $60^\circ$, and in principle up to neutrino-induced showers with up-going trajectories. It is tested here on a simulated data set of EAS induced by cosmic rays. A resolution better than 4 arc-minutes ($0.07^\circ$) is achieved on arrival direction, as well as an intrinsic resolution of 5% on the electromagnetic energy, and around 15% on the primary energy.