  The Auger Engineering Radio Array (AERA) is part of the Pierre Auger
Observatory and is used to detect the radio emission of cosmic-ray air showers.
These observations are compared to the data of the surface detector stations of
the Observatory, which provide well-calibrated information on the cosmic-ray
energies and arrival directions. The response of the radio stations in the 30
to 80 MHz regime has been thoroughly calibrated to enable the reconstruction of
the incoming electric field. For the latter, the energy deposit per area is
determined from the radio pulses at each observer position and is interpolated
using a two-dimensional function that takes into account signal asymmetries due
to interference between the geomagnetic and charge-excess emission components.
The spatial integral over the signal distribution gives a direct measurement of
the energy transferred from the primary cosmic ray into radio emission in the
AERA frequency range. We measure 15.8 MeV of radiation energy for a 1 EeV air
shower arriving perpendicularly to the geomagnetic field. This radiation energy
-- corrected for geometrical effects -- is used as a cosmic-ray energy
estimator. Performing an absolute energy calibration against the
surface-detector information, we observe that this radio-energy estimator
scales quadratically with the cosmic-ray energy as expected for coherent
emission. We find an energy resolution of the radio reconstruction of 22% for
the data set and 17% for a high-quality subset containing only events with at
least five radio stations with signal.
