[Paper Review] Correlations in energy in cosmic ray air showers radio-detected by CODALEMA

Ahmed Rebai, Pascal Lautridou+2 more|arXiv (Cornell University)|Oct 5, 2012

Astrophysics and Cosmic Phenomena4 references4 citations

TL;DR

This study demonstrates a strong correlation between the primary energy of ultra-high-energy cosmic rays and the peak electric field amplitude measured by the CODALEMA radio array, achieving an estimated energy resolution below 20%. The method uses the radio lateral distribution function to extract the core electric field, with corrections for geomagnetic effects and a scalar contribution from coherent charge emission, suggesting radio detection as a viable, high-precision alternative to particle detectors.

ABSTRACT

A study of the response in energy of the radio-detection method of air showers initiated by ultra-high-energy cosmic rays is presented. Data analysis of the CODALEMA experiment shows that a strong correlation can be demonstrated between the primary energy of the cosmic ray and the electric field amplitude estimated at the heart of the radio signal. Its sensitivity to the characteristics of shower suggests that energy resolution of less than 20% can be achieved. It suggests also that, not only the Lorentz force, but also another contribution proportional to all charged particles generated in the development of the shower, could play a significant role in the amplitude of the electric field peak measured by the antennas (as coherence or the charge excess).

Motivation & Objective

• To establish a robust radio-based energy estimator for ultra-high-energy cosmic rays using electric field measurements.
• To assess the energy resolution and calibration accuracy of radio-detection relative to conventional particle detectors.
• To investigate whether additional emission mechanisms beyond the geomagnetic effect (e.g., coherent charge excess) contribute to the radio signal amplitude.
• To evaluate the potential of radio detection as a cost-effective, high-duty-cycle alternative to fluorescence and particle detectors.
• To determine if the radio signal's core electric field amplitude can serve as a reliable proxy for primary cosmic ray energy.

Proposed method

• The CODALEMA experiment uses a 24-element dipole antenna array (600×500 m) to measure transient radio electric field waveforms in the 24–82 MHz band.
• The electric field amplitude at the shower core is reconstructed via an exponential Radio Lateral Distribution Function (RLDF), using measured field values and arrival time consistency across antennas.
• Particle detector data from 17 scintillator stations (80 m spacing) provide reference energy estimates via the CIC method and lateral distribution function fitting.
• The energy resolution is evaluated by simulating distributions of (E₀ - Eₚ)/Eₚ, with E₀ from radio and Eₚ from particle detectors, varying σ(E₀)/E₀ and σ(Eₚ)/Eₚ.
• Corrections for the geomagnetic effect are applied to the electric field amplitude, and a scalar contribution (e.g., from charge excess or coherence) is considered to improve correlation.
• The analysis compares simulated energy resolution to experimental data, assuming no bias from shower depth uncertainty due to full atmospheric integration in radio signals.

Experimental results

Research questions

• RQ1 Can the peak electric field amplitude measured at the core of a cosmic ray air shower be used as a reliable estimator of the primary cosmic ray energy?
• RQ2 What is the achievable energy resolution of the radio-detection method when calibrated against particle detector measurements?
• RQ3 To what extent do non-geomagnetic effects, such as coherent charge emission or charge excess, contribute to the observed electric field amplitude?
• RQ4 How does the radio-detection method's energy resolution compare to that of conventional particle detectors in the same energy range?
• RQ5 Is the radio signal's correlation with primary energy robust against uncertainties in shower development depth or core location?

Key findings

• A strong linear correlation is observed between the primary cosmic ray energy and the peak electric field amplitude measured at the shower core by the CODALEMA radio array.
• The energy resolution of the radio-detection method is estimated to be below 20% when the particle detector resolution is 30%, indicating high potential precision.
• The inclusion of a scalar contribution—potentially from coherent charge emission or charge excess—improves the correlation between radio and particle-based energy estimates.
• The radio signal integrates the entire shower development, reducing bias from depth-of-interaction uncertainty, which enhances the robustness of the energy estimator.
• The method remains viable even with limited data, and the current energy resolution is likely a pessimistic estimate, as more data and improved RLDF models are expected to enhance performance.
• The absolute calibration of the radio energy estimator is consistent with particle detector measurements, supporting its use as a reliable alternative.