Reconstruction of cosmic ray energies using a single ARIANNA station

The ARIANNA (Antarctic Ross Ice-Shelf ANtenna Neutrino Array) detector is a pilot-stage antenna array for the detection of ultra-high energy neutrinos using radio signals. Since air showers caused by cosmic rays produce radio emissions similar to those from neutrino-induced showers inside the ice, they present a test case to demonstrate the ability to reconstruct particle shower properties from their radio signals. An important property of an air shower is its energy. It is usually measured by reconstructing the signal distribution as a function of distance to the shower axis. Since the ARIANNA geometry is optimized fo neutrinos and therefore very sparse, an air shower is only ever detected by a single ARIANNA station, which does not allow us to use methods based on the air shower footprint. We present a novel method that allows us to reconstruct the shower energy based on a single station's measurement. This is achieved by taking the signal's frequency spectrum into account, which is measured in a relatively broad band from 100-500 MHz in ARIANNA.