Radio detection of air showers at the Pierre Auger Observatory

High-energy cosmic rays impinging onto the atmosphere of the Earth induce cascades of secondary particles: extensive air showers. Many of the particles in a shower are electrons and positrons. The electrons and positrons interact with the geomagnetic field and emit radiation. We detect such radiation at frequencies of tens to hundreds of MHz with the Auger Engineering Radio Array (AERA) at the Pierre Auger Observatory in Argentina. The objective is to investigate the properties of cosmic rays at the expected transition from Galactic to an extragalactic origin at energies around 10¹⁷ to 10¹⁸ eV. We discuss the recent progress in radio detection of ultra-high-energy cosmic rays with AERA. To this end, we elaborate on our measurements of shower properties, such as the lateral distribution of the radio emission at ground level. In addition, we present methods to reconstruct the properties of the primary particle from the radio data. (paper)