Data collected at the Pierre Auger Observatory are used to establish an upper limit on the diffuse flux of tau neutrinos in the cosmic radiation. Earth-skimming ${\nu }_{\tau }$ may interact in the Earth’s crust and produce a $\tau$ lepton by means of charged-current interactions. The $\tau$ lepton may emerge from the Earth and decay in the atmosphere to produce a nearly horizontal shower with a typical signature, a persistent electromagnetic component even at very large atmospheric depths. The search procedure to select events induced by $\tau$ decays against the background of normal showers induced by cosmic rays is described. The method used to compute the exposure for a detector continuously growing with time is detailed. Systematic uncertainties in the exposure from the detector, the analysis, and the involved physics are discussed. No $\tau$ neutrino candidates have been found. For neutrinos in the energy range $2\times {10}^{17}\mathrm{eV}<E_{\nu }<2\times {10}^{19}\mathrm{eV}$, assuming a diffuse spectrum of the form $E_{\nu }^{-2}$, data collected between 1 January 2004 and 30 April 2008 yield a 90% confidence-level upper limit of $E_{\nu }^{2}d{N}_{{\nu }_{\tau }}/d{E}_{\nu }<9\times {10}^{-8}\mathrm{GeV}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{sr}}^{-1}$.

• Received 2 March 2009

DOI:https://doi.org/10.1103/PhysRevD.79.102001