  The longitudinal profile of the most energetic cosmic-ray air shower measured
so far, the event recorded by the Fly's Eye detector with a reconstructed
primary energy of about 320 EeV, is compared to simulated shower profiles. The
calculations are performed with the CORSIKA code and include primary photons
and different hadron primaries. For primary photons, preshower formation in the
geomagnetic field is additionally treated in detail. For primary hadrons, the
hadronic interaction models QGSJET01 and SIBYLL2.1 have been employed. The
predicted longitudinal profiles are compared to the observation. A method for
testing the hypothesis of a specific primary particle type against the measured
profile is described which naturally takes shower fluctuations into account.
The Fly's Eye event is compatible with any assumption of a hadron primary
between proton and iron nuclei in both interaction models, although differences
between QGSJET01 and SIBYLL2.1 in the predicted profiles of lighter nuclei
exist. The primary photon profiles differ from the data on a level of ~1.5
sigma. Although not favoured by the observation, the primary photon hypothesis
can not be rejected for this particular event.
