Determination of the energy scale of cosmic ray measurements using the Auger Engineering Radio Array

The accurate determination of the absolute energy scale in cosmic ray measurements is both a challenging and fundamentally important task. We present how measurements of radio pulses from extensive air showers with the Auger Engineering Radio Array, combined with per-event simulations of radio emission using the CoREAS extension of CORSIKA, allow us to determine the energy scale of cosmic rays between $3\cdot 10^{17}$\,eV and several $10^{18}$\,eV. Our analysis accounts for many factors, each of which is controlled on the 5\% level or better. The absolute calibration of the antennas and the entire analog signal chain builds on a Galactic calibration in combination with a detailed understanding of the antenna-gain patterns. Additional key elements include compensation for temperature-dependent signal amplification, continuous detector health monitoring, an active veto for thunderstorm conditions, an unbiased event reconstruction, and per-event atmospheric modeling in the simulations. The analysis benefits from a high-statistics dataset of over 800 measured cosmic ray showers. We describe our analysis method, perform multiple cross-checks, and evaluate systematic uncertainties. We find that absolute energies determined with AERA are 12\% higher than those established with the Auger Fluorescence Detector, a result well in agreement within systematic uncertainties and thus a strong independent confirmation of the absolute energy scale of the Pierre Auger Observatory.