The depth of the shower maximum of air showers measured with AERA

The Auger Engineering Radio Array (AERA) is currently the largest array of radio antennas for the detection of cosmic rays, spanning an area of $17$ km$^2$ with 153 radio antennas, measuring in the energy range from $10^{17.0}$ to $10^{19.0}$ eV. It detects the radio emission of extensive air showers produced by cosmic rays in the $30-80$ MHz band. The cosmic-ray mass composition is a crucial piece of information in determining the sources of cosmic rays and their acceleration mechanisms. The depth of the shower maximum, $X_{max}$, a probe for mass composition can be determined with a likelihood analysis that compares the measured radio-emission footprint on the ground to an ensemble of footprints from CORSIKA/CoREAS Monte-Carlo air shower simulations. These simulations are also used to determine the resolution of the method and to validate the reconstruction by identifying and correcting for systematic uncertainties. We will present the method for the reconstruction of the depth of the shower maximum, achieving a resolution of up to $15$ g/cm$^2$, show compatibility with the independent fluorescence detector reconstruction measured on an event-by-event basis, and show that the data taken over the past seven years with AERA shows a light cosmic-ray mass composition reconstruction in the energy range from $10^{17.5}$ to $10^{18.8}$ eV.