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° 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)×10^{-21}  cm^{-2} sr^{-1} y^{-1} and (3.6±0.2)×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.