Introduction

An imaging atmospheric Cherenkov telescope sees a few degrees of sky. Point every telescope in an array the same way and their fields of view land on top of one another, so the array sees what its widest camera sees and no more: CTAO-North’s widest camera has an angular radius of 3.8°, giving the array 46 deg²; CTAO-South’s is 4.4°, giving 61 deg². Fifty-one telescopes do not watch fifty-one times more sky than one of them — pointed conventionally, adding telescopes buys sensitivity, not sky.

Several observing programmes CTAO plans need more sky than that at one instant. The Extragalactic Survey proposes to cover a quarter of the sky in a fixed time budget set by how much sky one pointing covers. A gravitational-wave alert arrives with a 90% credible region anywhere from ten to a thousand square degrees, and these regions are rarely compact: the first sky map circulated for GW170817 covered 187 deg², but its containment radius, the angular radius of the smallest cone enclosing it, was 62.1° — against a camera radius of about 4°, the shortfall is in reach, not in collecting area.

There are three ways to close that gap. Tiling keeps the telescopes together and visits the region in pieces, spending time instead of sky. Divergent pointing tilts the telescopes apart so their fields of view overlap only partially, widening the instantaneous footprint at the cost of the number of telescopes seeing any given direction. Splitting the array points independent groups at different parts of the region at once. All three are geometric decisions, and all three are constrained by the same fact: a shower must be recorded by at least two telescopes to be reconstructed stereoscopically, so sky seen once is not sky observed.

A large part of that trade-off does not need a shower simulation to evaluate. Given a layout and a set of pointings, whether a sky direction falls inside a camera is a geometric fact. The number of telescopes containing a given direction — the multiplicity — is therefore exact, and so is everything built from it: the combined field of view, the part of it that is stereoscopic, and the divergence at which stereoscopic coverage stops improving. What geometry cannot supply is the map from multiplicity to sensitivity, which is a separate measurement, not an assumption this package makes.

In this studies section, you will find:

  • Definitions sets out the quantities divtel computes — the hyper field of view, the multiplicity, and the mean multiplicity — since everything that follows is written in them, and shows what an array and its coverage look like.

  • Tracking a source points at a real source and tracks it across a night, interactively.

  • The divergence spread and ceiling answers the question the rest of this section builds towards: how far an array can usefully be spread, and what that is worth for CTAO-North and CTAO-South.