Energy and flux measurements of ultra-high energy cosmic rays observed during the first ANITA flight

The first flight of the Antarctic Impulsive Transient Antenna (ANITA) experiment recorded 16 radio signals that were emitted by cosmic-ray induced air showers. The dominant contribution to the radiation comes from the deflection of positrons and electrons in the geomagnetic field, which is beamed in the direction of motion of the air shower. For 14 of these events, this radiation is reflected from the ice and subsequently detected by the ANITA experiment at a flight altitude of ∼36 km. In this paper, we estimate the energy of the 14 individual events and find that the mean energy of the cosmic-ray sample is 2.9 × 1018 eV, which is significantly lower than the previous estimate. By simulating the ANITA flight, we calculate its exposure for ultra-high energy cosmic rays. We estimate for the first time the cosmic-ray flux derived only from radio observations and find agreement with measurements performed at other observatories. In addition, we find that the ANITA data set is consistent with Monte Carlo simulations for the total number of observed events and with the properties of those events.