Search for the Anomalous Events Detected by ANITA Using the Pierre Auger Observatory

A dedicated search for upward-going air showers at zenith angles exceeding 110 degrees and energies E > 0.1 EeV has been performed using the Fluorescence Detector of the Pierre Auger Observatory. The search is motivated by two "anomalous" radio pulses observed by the ANITA flights I and III that appear inconsistent with the standard model of particle physics. Using simulations of both regular cosmic-ray showers and upward-going events, a selection procedure has been defined to separate potential upward-going candidate events and the corresponding exposure has been calculated in the energy range [0.1-33] EeV. One event has been found in the search period between January 1, 2004, and December 31, 2018, consistent with an expected background of 0.27 +/- 0.12 events from misreconstructed cosmic-ray showers. This translates to an upper bound on the integral flux of (7.2 +/- 0.2) x 10$^{-21}$ cm$^{-2}$ sr$^{-1}$ y$^{-1}$ and (3.6 +/- 0.2) x 10$^{-20}$ cm$^{-2}$ sr$^{-1}$ y$^{-1}$ for an E$^{-1}$ and E$^{-2}$ spectrum, respectively. An upward-going flux of showers normalized to the ANITA observations is shown to predict over 34 events for an E$^{-3}$ spectrum and over 8.1 events for a conservative E$^{-5}$ spectrum, in strong disagreement with the interpretation of the anomalous events as upward-going showers.