Design of an Imaging Air Cherenkov Telescope array layout with differential programming

TL;DR

The paper tackles the high computational cost of optimizing Imaging Air Cherenkov Telescope (IACT) arrays by proposing a differentiable framework based on surrogate instrument response functions to estimate stereoscopic performance. By deriving monoscopic performance from a parametric survival probability and propagating it to the array level, the authors implement a gradient-based layout optimization tested on a simplified two-SST-1M configuration at the Hanle site. A loss function that balances energy-weighted effective area and angular resolution identifies a geometry that optimizes gamma-ray detectability for a source with spectral index Γ = -2. The approach paves the way for scalable optimization of larger, heterogeneous IACT arrays and can incorporate additional metrics and quality cuts to reduce systematics in future ground-based gamma-ray observatories.

Abstract

Current optimization of ground-based Cherenkov telescopes arrays, also called Imaging Air Cherenkov Telescope (IACT) arrays, relies on brute-force human-driven approaches based on large simulations requiring both high amount of storage and long computation time. To explore the full phase space of telescope positioning of a given array even more simulations would be required. To optimize any array layout, we explore the possibility of developing a differential program with surrogate models of IACT arrays based on high-level instrument response functions (IRFs). The simulation time of a single telescope to a cosmic-ray event can be significantly reduced with its instrument response function or with generative models. However, it is not straight forward to model the array of telescopes from a set of single telescope surrogate models as the array is a stereoscopic imaging system. The complexity increases as well if the telescopes in the array are of different types. Additionally, the optimum of the array layout depends on the scientific use case. Current array layout optimization are obtained by minimizing the sensitivity of the array, a metric that depends on several high-level parameters such as the trigger efficiency, the energy and angular resolution, as well as the background rejection capability. The variety of telescopes types in IACT arrays, such as in the Cherenkov Telescope Array Observatory (CTAO), not only extends the sensitive energy range but also allows for cross-calibration of the instruments. Therefore, the optimal array layout is not only which minimizes sensitivity but also which reduces the systematic uncertainties. We focus on the optimization of a telescope array based on the SST-1M IACTs in Hanle, Ladakh India aiming at building a generic optimization pipeline for future ground-based cosmic-ray observatories

Figures (6)

• Figure 1: Schematic of the array layout optimization workflow.
• Figure 2: Left: Survival probability vs. impact distance for all energy bins. Center: Parametrized survival probability curves (Eq. \ref{['eq:mono_trigger_probability']}). Right: Effective area computed from Eq. \ref{['eq:mono_effective_area']}.
• Figure 3: Survival probability parameters vs. energy: $p_{\rm max}(E)$ (left), $r_{1/2}(E)$ (center), and $k(E)$ (right).
• Figure 4: Left: Effective area of a two-SST-1M array ($m=2$) vs. energy for various separations. Center: Angular resolution vs. energy and separation. Right: Cost function vs. separation $\Delta x$. A quality selection criteria of the stereo angle $\Delta \psi \geq 1^\circ$ was used in all figures.
• Figure 5: Left: Illustration of the "miss" distance $d$ between the source direction and the major axis of the image. Right: Standard deviation $\sigma_{\theta}$ of the monoscopic angular separation as a function of impact distance for different energy bins.