[Paper Review] Detector efficiency and exposure of Tunka-Rex for cosmic-ray air showers

Oleg Fedorov, P. A. Bezyazeekov+23 more|arXiv (Cornell University)|Dec 4, 2017

Astrophysics and Cosmic Phenomena5 references3 citations

TL;DR

This paper presents a comprehensive model for estimating the detection efficiency and exposure of the Tunka-Rex radio array for cosmic-ray air showers, using a Monte Carlo simulation of radio footprint size as a function of primary energy and arrival direction. The method accounts for irregular array geometry, time-dependent hardware status, and azimuthal dependence due to geomagnetic emission, enabling accurate exposure calculations essential for measuring cosmic-ray energy spectra.

ABSTRACT

Tunka-Rex (Tunka Radio Extension) is an antenna array for cosmic-ray detection located in Siberia. Previous studies of cosmic rays with Tunka-Rex have shown high precision in determining the energy of the primary particle and the possibility to reconstruct the depth of the shower maximum. The next step is the reconstruction of the mass composition and the energy spectrum of cosmic rays. One of the main problems appearing within this task is to estimate the detection efficiency of the instrument, and the exposure of the observations. The detection efficiency depends on properties of the primary cosmic rays, such as energy and arrival direction, as well as on many parameters of the instrument: density of the array, efficiency of the receiving antennas, signal-detection threshold, data-acquisition acceptance, and trigger properties. More than that, the configuration of detector changes with time. During the measurements some parts of the detector can provide corrupted data or sometimes do not operate. All these features should be taken into account for an estimation of the detection efficiency. For each energy and arrival direction we estimate the detection probability and effective area of the instrument. To estimate the detection probability of a shower we use a simple Monte Carlo model, which predicts the size of the footprint of the radio emission as function of the primary energy and arrival direction (taking into account the geometry of Earth's magnetic field). Combining these approaches we calculate the event statistics and exposure for each run. This is the first accurate study of the exposure for irregular large-scale radio arrays taking into account most important features of detection, which will be used for the measurement of primary cosmic-ray spectra with Tunka-Rex.

Motivation & Objective

• To develop a reliable method for estimating the detection efficiency and cumulative exposure of the Tunka-Rex radio array for cosmic-ray air showers.
• To account for the time-varying configuration of the detector, including hardware malfunctions, data corruption, and array upgrades.
• To incorporate the azimuthal dependence of radio emission due to Earth's magnetic field, which affects detection sensitivity.
• To enable precise measurement of the primary cosmic-ray energy spectrum using Tunka-Rex data.
• To validate the model against real data and CoREAS simulations for future high-precision spectral analysis.

Proposed method

• A toy Monte Carlo model simulates the size of the radio footprint of air showers as a function of primary energy, zenith angle, and arrival direction, including geomagnetic effects.
• Detection efficiency is calculated as the fraction of simulated showers that trigger at least three antenna stations: $ \varepsilon = N_{\text{detected}} / N_{\text{total}} $.
• The instantaneous aperture $ \mathcal{A}(E,t) $ is computed by integrating over time, solid angle, and core position, weighted by detection efficiency and $ \cos\theta $.
• Detector uptime and operational status are monitored via count rate distributions; non-Poissonian behavior indicates hardware issues and excludes data from exposure integration.
• The model accounts for hardware degradation by adjusting the effective area, with ~15% of the detector affected by malfunctions or noise.
• Exposure is calculated as $ \mathcal{E}(E) = \int_t \mathcal{A}(E,t) \, dt $, incorporating time-dependent array configuration and detection efficiency.

Experimental results

Research questions

• RQ1 How can detection efficiency be accurately estimated for an irregular, time-varying radio array like Tunka-Rex?
• RQ2 What is the impact of geomagnetic angle and array geometry on the azimuthal dependence of radio shower detection?
• RQ3 How do hardware malfunctions and data corruption affect the effective exposure and aperture of the detector?
• RQ4 To what extent does the model reproduce real data and CoREAS simulations for different array configurations?
• RQ5 What improvements are needed to reduce uncertainties in exposure estimation for precise cosmic-ray energy spectrum measurements?

Key findings

• The model shows good agreement with real Tunka-Rex data from 2012–2014, particularly for zenith angles between 30° and 50°, validating its core assumptions.
• The model overestimates detection efficiency for zenith angles below 30° and above 60°, indicating limitations in the current footprint model, especially regarding shower maximum distance and antenna response.
• Approximately 15% of the detector’s area is affected by hardware issues or data corruption, which reduces effective aperture and must be corrected in exposure calculations.
• The cumulative exposure of Tunka-Rex increases significantly after array upgrades, as shown in Fig. 6, reflecting improved sensitivity and duty cycle.
• The current uncertainty in exposure is too large for precise energy spectrum measurements, as it exceeds the 20% energy scale uncertainty of Tunka-Rex.
• Future improvements will include parameterization of distance to shower maximum and antenna response patterns to reduce systematic errors.