A probabilistic model for the efficiency of cosmic-ray radio arrays

Digital radio detection of cosmic-ray air showers has emerged as an alternative technique in high-energy astroparticle physics. Estimation of the detection efficiency of cosmic-ray radio arrays is one of the few remaining challenges regarding this technique. To address this problem, we developed a new approach to model the efficiency based on the explicit probabilistic treatment of key elements of the radio technique for air showers: the footprint of the radio signal on ground, the detection of the signal in an individual antenna, and the detection criterion on the level of the entire array. The model allows for estimation of sky regions of full efficiency and can be used to compute the aperture of the array, which is essential to measure the absolute flux of cosmic rays. We also present a semi-analytical method that we apply to the generic model, to calculate the efficiency and aperture with high accuracy and reasonable calculation time. The model in this paper is applied to the Tunka-Rex array as example instrument and validated against Monte Carlo simulations. The validation shows that the model performs well, in particular, in the prediction of regions with full efficiency. It can thus be applied to other antenna arrays to facilitate the measurement of absolute cosmic-ray fluxes and to minimize a selection bias in cosmic-ray studies.