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 density 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.
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