The energy spectrum of cosmic rays above $2.5\times {10}^{18}\mathrm{eV}$, derived from 20 000 events recorded at the Pierre Auger Observatory, is described. The spectral index $\gamma$ of the particle flux, $J\propto E^{-\gamma }$, at energies between $4\times {10}^{18}\mathrm{eV}$ and $4\times {10}^{19}\mathrm{eV}$ is $2.69\pm 0.02(\mathrm{stat})\pm 0.06(\mathrm{syst})$, steepening to $4.2\pm 0.4(\mathrm{stat})\pm 0.06(\mathrm{syst})$ at higher energies. The hypothesis of a single power law is rejected with a significance greater than 6 standard deviations. The data are consistent with the prediction by Greisen and by Zatsepin and Kuz’min.

53 pages. Submitted to Nuclear Instruments and Methods in Physics Research Section AInternational audienceThe Pierre Auger Observatory is a hybrid detector for ultra-high energy cosmic rays. It combines a surface array to measure secondary particles at ground level together with a fluorescence detector to measure the development of air showers in the atmosphere above the array. The fluorescence detector comprises 24 large telescopes specialized for measuring the nitrogen fluorescence caused by charged particles of cosmic ray air showers. In this paper we describe the components of the fluorescence detector including its optical system, the design of the camera, the electronics, and the systems for relative and absolute calibration. We also discuss the operation and the monitoring of the detector. Finally, we evaluate the detector performance and precision of shower reconstructions