A likelihood method to cross-calibrate air-shower detectors

Abstract

We present a detailed statistical treatment of the energy calibration of hybrid air-shower detectors, which combine a surface detector array and a fluorescence detector, to obtain an unbiased estimate of the calibration curve. The special features of calibration data from air showers prevent unbiased results, if a standard least-squares fit is applied to the problem. We develop a general maximum-likelihood approach, based on the detailed statistical model, to solve the problem. Our approach was developed for the Pierre Auger Observatory, but the applied principles are general and can be transferred to other air-shower experiments, even to the cross-calibration of other observables. Since our general likelihood function is expensive to compute, we derive two approximations with significantly smaller computational cost. In the recent years both have been used to calibrate data of the Pierre Auger Observatory. We demonstrate that these approximations introduce negligible bias when they are applied to simulated toy experiments, which mimic realistic experimental conditions.

10 pages, 7 figures

References in corpus (3)

• The Cosmic Ray Energy Spectrum Observed with the Surface Detector of the Telescope Array Experiment
• Hadronic Multiparticle Production at Ultra-High Energies and Extensive Air Showers
• A comprehensive study of shower to shower fluctuations

Cited by in corpus (10)

• Measurement of the cosmic-ray energy spectrum above $2.5\times 10^{18}$ eV using the Pierre Auger Observatory
• Energy Estimation of Cosmic Rays with the Engineering Radio Array of the Pierre Auger Observatory
• Report on Tests and Measurements of Hadronic Interaction Properties with Air Showers
• Measurement of the Radiation Energy in the Radio Signal of Extensive Air Showers as a Universal Estimator of Cosmic-Ray Energy
• The energy spectrum of cosmic rays beyond the turn-down around $10^{17}$ eV as measured with the surface detector of the Pierre Auger Observatory
• Measurement of the fluctuations in the number of muons in extensive air showers with the Pierre Auger Observatory
• Measurement of the cosmic ray spectrum above $4\times 10^{18}$ eV using inclined events detected with the Pierre Auger Observatory
• Computing mean logarithmic mass from muon counts in air shower experiments
• Search for a diffuse flux of photons with energies above tens of PeV at the Pierre Auger Observatory
• An Improved Method of Estimating the Uncertainty of Air-Shower Size at Ultra-High Energies