Timing analysis techniques at large core distances for multi-TeV gamma ray astronomy

We present an analysis technique that uses the timing information of Cherenkov images from extensive air showers (EAS). Our emphasis is on distant, or large core distance gamma-ray induced showers at multi-TeV energies. Specifically, combining pixel timing information with an improved direction reconstruction algorithm, leads to improvements in angular and core resolution as large as ~40% and ~30%, respectively, when compared with the same algorithm without the use of timing. Above 10 TeV, this results in an angular resolution approaching 0.05 degrees, together with a core resolution better than ~15 m. The off-axis post-cut gamma-ray acceptance is energy dependent and its full width at half maximum ranges from 4 degrees to 8 degrees. For shower directions that are up to ~6 degrees off-axis, the angular resolution achieved by using timing information is comparable, around 100 TeV, to the on-axis angular resolution. The telescope specifications and layout we describe here are geared towards energies above 10 TeV. However, the methods can in principle be applied to other energies, given suitable telescope parameters. The 5-telescope cell investigated in this study could initially pave the way for a larger array of sparsely spaced telescopes in an effort to push the collection area to >10 km2. These results highlight the potential of a `sparse array’ approach in effectively opening up the energy range above 10 TeV.

💡 Research Summary

The paper presents a novel analysis technique that exploits the timing information of Cherenkov images recorded by imaging atmospheric Cherenkov telescopes (IACTs) to improve the reconstruction of extensive air showers (EAS) at multi‑TeV energies, especially for events with large core distances (> 200 m). The authors focus on a “sparse array” concept: a cell of five telescopes arranged in a square of 500 m side length with a central telescope. Each telescope has a 6 m diameter f/1.5 mirror, an 8.2° field of view composed of 0.24° pixels, and a fast read‑out system sampling at 1 GHz with 12‑bit ADCs. Simulations are performed with CORSIKA and SYBYLL, generating gamma‑ray showers from 1 TeV to 500 TeV using a flat energy spectrum (dN/dE ∝ E⁰) to ensure good statistics at the highest energies. The observation altitude (220 m a.s.l.) and atmospheric model (MODTRAN tropical profile) are chosen to resemble typical Australian sites.

Standard image cleaning (8 pe picture threshold, 4 pe boundary) and Hillas parameterisation are applied. The conventional direction reconstruction (Algorithm 1) uses a weighted mean of the geometric intersections of image major axes, where the weight depends on the combined image size and the stereo angle between the axes. This method, while robust for dense arrays, suffers at large core distances because the image orientation becomes less precise and the stereo angle can be small.

The authors introduce an improved reconstruction (Algorithm 3) that incorporates per‑image error ellipses derived from lookup tables that map image size, width/length, and other Hillas parameters to expected uncertainties in the major‑axis direction and centre of gravity (cog). For each image, an expected angular distance dₚ between the cog and the true source position is predicted; this distance is used to shift the error ellipse along the major axis before combining the ellipses from all telescopes via a weighted mean. The process iterates two to three times until convergence, yielding a more accurate source position estimate.

The key innovation is the use of pixel‑wise timing information to extract a “time gradient” along the major axis. For each pixel, the arrival time t (relative to the amplitude‑weighted mean time of the image) is plotted against the projected distance dist along the major axis from the cog. The slope of this t‑vs‑dist relation correlates strongly with the core distance of the shower. By fitting a linear gradient, the authors obtain a more reliable estimate of dₚ, which in turn refines the placement of the error ellipses. This timing‑based correction is especially effective for large‑core events where the geometric information alone is ambiguous.

Simulation results demonstrate substantial performance gains. Above 10 TeV, the angular resolution improves from ~0.08° (standard method) to ~0.05°, a ~40 % enhancement. Core position resolution improves from ~20 m to < 15 m, a ~30 % gain. The off‑axis acceptance (FWHM) grows with energy, ranging from 4° at lower multi‑TeV energies to 8° at the highest simulated energies, and the system maintains near‑on‑axis angular resolution for off‑axis angles up to ~6°. The effective collection area of the five‑telescope cell reaches ~1 km² above 10 TeV and exceeds 1 km² already at 100 TeV, indicating that a modest number of sparsely spaced telescopes can achieve the large areas required for > 10 TeV astronomy.

The authors also discuss ancillary benefits of timing information: it enables adaptive signal integration windows (e.g., a 21 ns window centred on the peak) that improve signal‑to‑noise ratios, and it can be used for time‑based image cleaning to suppress night‑sky background. Although background rejection is not the focus of this study, the authors note that timing‑based parameters have been successfully employed in other experiments (MAGIC, VERITAS) for gamma/hadron discrimination, suggesting further gains when combined with the presented reconstruction.

In conclusion, the paper provides a compelling case that incorporating pixel timing into the reconstruction pipeline of a sparse IACT array yields markedly better angular and core resolution for multi‑TeV gamma‑ray showers, especially at large core distances. The demonstrated improvements, together with the modest hardware requirements (five telescopes, modest mirror size, fast digitisation), support the feasibility of building larger, sparsely spaced arrays with total areas > 10 km². Such arrays would open a new observational window above 10 TeV, enabling detailed studies of Galactic accelerators, probing the knee of the cosmic‑ray spectrum, and distinguishing hadronic from leptonic emission mechanisms in the most energetic astrophysical sources.