Energy determination of trans-EeV cosmic rays

This article gives a summary of the primary energy estimation by observing ultra-high energy cosmic ray induced extensive air showers (down to the EeV energies - the energy range of the Japanese AGASA experiment). The shower cascade in air initiated by cosmic rays is called Extensive Air Shower (EAS) which has been playing a key role in the detection of cosmic ray particles. There are two types of detection techniques available to measure the energy (as well as the arrival directions and mass composition) of the primary UHECR (ultra high energy cosmic rays) particles: the Ground Arrays and the Fluorescence Detectors. The two methods are highly complementary: the ground array method measures the lateral development of EAS cascades. The dynamics to determine the behavior of the lateral spread of particle distributions in EAS is well understood and rather reliable, regardless of the mass of the primary cosmic rays, but some uncertainties remain due to our incomplete knowledge concerning the hadronic interactions and the multiple scattering of secondary electrons. The fluorescence method observes the longitudinal development of cascades. It is similar to the concept of calorimetric detectors in high energy physics, since the fluorescence light generated by the charged particles in the shower is proportional to the energy deposited in the atmosphere. These two methods are complementary since they view different components of the EAS. The ground array observes the particles at ∼ 1 km away from the EAS axis while the fluorescence method is sensitive to particle energy distributions very close to the shower axis, typically less than 100 m. Therefore, both methods have their own advantage and disadvantage as far as the energy estimation is concerned. In the following sections, we discuss how to deduce the primary energy and the possible sources of the systematic uncertainties. The energy spectrum of UHECRs is a key clue for the understanding of the origin of UHE particle production. In order to reconstruct the spectrum, it is not only necessary to determine the energy of an individual event but also to calculate the detection efficiency, i.e., the aperture of the detector. This is a critical aspect of the fluorescence technique: the aperture increases with energy since the higher energy events produce enough light to be detected at large distances from the detector. It also strongly depends on the atmospheric extinction length and an accurate understanding of this parameter is also required. The aperture estimation is much simpler for a ground array. The total aperture depends mainly on the array geometry. For events with energies well above the triggering threshold, the aperture becomes independent of energy and is determined by the surface of the array and the solid angle which, for practical reasons, the incident directions are limited to by the detection technique. Under stable conditions, no Monte Carlo simulation is needed for this purpose. It should be remarked, however, that the reconstructed energy is NOT the true energy in all cases, because of the limited energy resolution