[Paper Review] Photon Reconstruction for H.E.S.S. Using a Semi-Analytical Shower Model

M. Holler, A. Balzer+3 more|arXiv (Cornell University)|Sep 9, 2015

Astrophysics and Cosmic Phenomena3 references19 citations

TL;DR

This paper presents the adaptation of a semi-analytical shower model for photon reconstruction in the H.E.S.S. II five-telescope array, enabling monoscopic and stereoscopic analysis with improved energy threshold and sensitivity. The Combined analysis mode achieves the broadest energy coverage by merging monoscopic and stereoscopic reconstructions, outperforming individual modes in effective area and sensitivity across energy ranges.

ABSTRACT

The High Energy Stereoscopic System (H.E.S.S.) is an array of five Imaging Atmospheric Cherenkov Telescopes (IACTs) designed to detect cosmogenic gamma-rays with very high energies. Originally consisting of just four identical IACTs (CT1-4) with an effective mirror diameter of 12$\,$m each, it was expanded with a fifth IACT (CT5) with a mirror diameter of 28$\,$m in 2012. Being the largest IACT worldwide, CT5 allows to lower the energy threshold of H.E.S.S., making the array sensitive at energies where space-based detectors run out of statistics. Events can be analysed either monoscopically (i.e. using only information of CT5) or stereoscopically (requiring at least two triggered telescopes per event). To achieve a good performance, a sophisticated event reconstruction and analysis framework is indispensable. This is particularly important for H.E.S.S. since it is now the first IACT array that consists of different telescope types. An advanced reconstruction method is based on a semi-analytical model of electromagnetic particle showers in the atmosphere (model analysis). The properties of the primary particle are reconstructed by comparing the image recorded by each triggered telescope with the Cherenkov emission from the shower model using a log-likelihood maximisation. Due to its performance, this method has become one of the standard analysis techniques applied to CT1-4 data. Now it has been modified for use with the five-telescope array. We present the adapted model analysis and its performance in both monoscopic and stereoscopic analysis mode.

Motivation & Objective

• To extend the semi-analytical model analysis—previously used for four 12 m telescopes (H.E.S.S. I)—to the new five-telescope H.E.S.S. II array, including the 28 m CT5 telescope.
• To address the challenge of reconstructing gamma-ray showers in a heterogeneous array with different telescope types and sizes, requiring a unified reconstruction framework.
• To develop and validate a new Combined analysis mode that leverages both monoscopic (CT5-only) and stereoscopic (multi-telescope) reconstruction to maximize sensitivity and energy coverage.
• To evaluate the performance of monoscopic, stereoscopic, and combined analysis modes using simulations and Crab Nebula data, focusing on effective area and differential sensitivity.

Proposed method

• A semi-analytical electromagnetic shower model computes Cherenkov light distribution in the atmosphere as a function of primary energy (E), shower depth (T), and impact distance (R), with templates precomputed for various parameters.
• For each telescope's camera image, the log-likelihood function is computed by comparing measured pixel intensities (s) to model-predicted expectations (μ), accounting for pedestal noise (σp), photoelectron peak width (σγ), and calibration uncertainty (σc), using the likelihood formula: P(s|μ,σp,σγ,σc) = ∑n [μ^n * e^(-μ) / (n! * √(2π(σp² + nσγ² + n²σc²))) * exp( - (s - n)² / (2(σp² + nσγ² + n²σc²)) )].
• The log-likelihood is maximized using the Levenberg–Marquardt algorithm to reconstruct primary particle parameters: direction (Dir), energy (E), shower depth (T), and impact distance (R).
• Event-wise uncertainties are estimated from the second derivatives of the log-likelihood, e.g., ΔDir = 1 / √(∂²lnL/∂Dir²).
• Three analysis modes are implemented: Mono (CT5-only), Stereo (CT1–CT5), and Combined (selects best result from Mono or Stereo per event based on directional uncertainty).
• Performance is evaluated using Monte Carlo simulations with a point source at 18° zenith angle and 0.5° wobble offset, and background events from real data to ensure realistic conditions.

Experimental results

Research questions

• RQ1 How can the semi-analytical model analysis be adapted to handle the heterogeneous telescope configuration of H.E.S.S. II, including the large 28 m CT5 telescope?
• RQ2 What are the relative performances of monoscopic, stereoscopic, and combined analysis modes in terms of effective area and differential sensitivity?
• RQ3 Can a Combined analysis mode that fuses monoscopic and stereoscopic reconstructions achieve better overall energy coverage than either mode alone?
• RQ4 How does the energy threshold and sensitivity of the new model analysis compare to the original H.E.S.S. I (CT1–CT4) stereoscopic mode?
• RQ5 What impact do selection cuts, particularly the θ² cut, have on background rejection and sensitivity in the Combined mode?

Key findings

• The Combined analysis mode achieves the broadest energy coverage by merging the low-energy threshold of monoscopic reconstruction (CT5-only) with the high detection efficiency of stereoscopic reconstruction at higher energies.
• The effective area of the Combined mode exceeds that of both Mono and Stereo modes at low energies (E < 300 GeV), while maintaining high performance at high energies, as shown in Fig. 4.
• For a 50-hour observation, the Combined mode achieves a differential sensitivity that is at least as good as the Mono mode and outperforms it at medium and high energies, though it currently lags behind the Stereo mode due to suboptimal cuts.
• The Stereo mode achieves the best signal-to-background (S/B) ratio, while the Combined mode yields the highest excess rate and significance, indicating superior overall sensitivity.
• The model analysis maintains good agreement with simulations at large θ² values, confirming its reliability for source detection and background suppression.
• The method successfully enables high-sensitivity reconstruction in the H.E.S.S. II array, which is the first IACT system with telescopes of different sizes, demonstrating its robustness and adaptability to complex instrument configurations.