Measurement of the cosmic ray spectrum above $4\times {10}^{18}$ eV using inclined events detected with the Pierre Auger Observatory

A measurement of the cosmic-ray spectrum for energies exceeding $4\times {10}^{18}$ eV is presented, which is based on the analysis of showers with zenith angles greater than ${60}^{\circ }$ detected with the Pierre Auger Observatory between 1 January 2004 and 31 December 2013. The measured spectrum confirms a flux suppression at the highest energies. Above $5.3\times {10}^{18}$ eV, the “ankle”, the flux can be described by a power law $E^{-\gamma }$ with index $\gamma =2.70\pm 0.02\text{(stat)}\pm 0.1\text{(sys)}$ followed by a smooth suppression region. For the energy ($E_{\text{s}}$) at which the spectral flux has fallen to one-half of its extrapolated value in the absence of suppression, we find $E_{\text{s}}=(5.12\pm 0.25{\text{(stat)}}_{-1.2}^{+1.0}\text{(sys)})\times {10}^{19}$ eV.