Monte Carlo Studies of medium-size telescope designs for the Cherenkov Telescope Array
MMonte Carlo Studies of medium-size telescope designs for the CherenkovTelescope Array
M. Wood a, ∗ , T. Jogler a , J. Dumm b , S. Funk a,c a SLAC National Accelerator Laboratory, 2575 Sand Hill Road M / S 29, Menlo Park, CA 94025, USA b Oskar Klein Centre and Dept. of Physics, Stockholm University, SE-10691 Stockholm, Sweden c Erlangen Center for Astroparticle Physics (ECAP) Friedrich-Alexander Universit¨at Erlangen-N¨urnberg Erwin-Rommel Strasse 1, 91058Erlangen, Germany
Abstract
We present studies for optimizing the next generation of ground-based imaging atmospheric Cherenkov telescopes(IACTs). Results focus on mid-sized telescopes (MSTs) for CTA, detecting very high energy gamma rays in the en-ergy range from a few hundred GeV to a few tens of TeV. We describe a novel, flexible detector Monte Carlo package,FAST (FAst Simulation for imaging air cherenkov Telescopes), that we use to simulate di ff erent array and telescopedesigns. The simulation is somewhat simplified to allow for e ffi cient exploration over a large telescope design pa-rameter space. We investigate a wide range of telescope performance parameters including optical resolution, camerapixel size, and light collection area. In order to ensure a comparison of the arrays at their maximum sensitivity, weanalyze the simulations with the most sensitive techniques used in the field, such as maximum likelihood templatereconstruction and boosted decision trees for background rejection. Choosing telescope design parameters representa-tive of the proposed Davies-Cotton (DC) and Schwarzchild-Couder (SC) MST designs, we compare the performanceof the arrays by examining the gamma-ray angular resolution and di ff erential point-source sensitivity. We furtherinvestigate the array performance under a wide range of conditions, determining the impact of the number of tele-scopes, telescope separation, night sky background, and geomagnetic field. We find a 30–40% improvement in thegamma-ray angular resolution at all energies when comparing arrays with an equal number of SC and DC telescopes,significantly enhancing point-source sensitivity in the MST energy range. We attribute the increase in point-sourcesensitivity to the improved optical point-spread function and smaller pixel size of the SC telescope design. Keywords:
Monte Carlo simulations, Cherenkov telescopes, IACT technique, gamma rays, cosmic rays
1. Introduction
The ground-based imaging atmospheric Cherenkovtelescope (IACT) technique has led to significantprogress in the field of very high energy (VHE; E >
100 GeV) gamma-ray astronomy over the last 25 years.To date, 145 sources have been detected at VHE with ∼
60 sources discovered only in the last five years .IACTs allow us to study a wide range of scientific top-ics, many uniquely accessible by VHE astronomy. Cur-rent and future generations of IACTs aim to probe the ∗ Corresponding author
Email addresses: [email protected] (M. Wood), [email protected] (T. Jogler), [email protected] (J. Dumm), [email protected] (S. Funk) http://tevcat.uchicago.edu/ origins and acceleration processes of cosmic rays [1, 2,3] and explore the nature of black holes and their rel-ativistic jets. Other key objectives include the searchfor dark matter, axion-like particles [4, 5], and Lorentzinvariance violation [6]. This will require extensive ob-servations on a number of source classes such as pulsarsand pulsar wind nebulae [7], galactic binaries [8], super-nova remnants [9], active galactic nuclei [10, 11], andgamma-ray bursts [12, 13]. The extragalactic sourcescan be used as “backlights” to study the attenuation onthe extragalactic background light, useful for constrain-ing star formation history and other cosmological pa-rameters such as the Hubble constant [14].VHE gamma rays entering the Earth’s atmosphereundergo e + e − pair production, initiating electromag-netic cascades. The relativistic charged particles in theshower emit Cherenkov ultraviolet and optical radia- Preprint submitted to Astroparticle Physics September 5, 2018 a r X i v : . [ a s t r o - ph . I M ] J un ion, which is detectable at ground level. The major-ity of the emitted Cherenkov light is narrowly beamedalong the trajectory of the gamma-ray primary in a conewith an opening angle of ∼ . ◦ . Due to the beaminge ff ect, the majority of the Cherenkov light falls withina Cherenkov light pool with a diameter of 200–300 mand a nearly constant light density. By imaging theCherenkov light emitted by the shower particles, IACTsare able to reconstruct the direction and energy of theoriginal gamma ray and to distinguish gamma rays fromthe much more prevalent cosmic-ray background. Highresolution imaging of the Cherenkov shower o ff ers sig-nificant benefits for IACTs by enabling a more accuratemeasurement of the shower axis which has an intrinsictransverse angular size of only a few arcminutes. How-ever the finite shower width and stochastic fluctuationsin the shower development fundamentally limit the per-formance of IACTs.The designs of IACTs are governed by a few key fac-tors. At low energy, the number of Cherenkov photonscompared to the night sky background necessitates alarge O (10–20 m) mirror diameter and high quantume ffi ciency camera. The camera must also be able tocapture the signal very quickly since the duration ofa Cherenkov pulse can be as short as a few nanosec-onds. The optical point-spread function (PSF) and cam-era pixel size should ideally be suitably smaller thanthe angular dimension of the gamma-ray shower. How-ever the high cost-per-pixel of camera designs used incurrent generation IACTs has generally dictated pixelsizes that are significantly larger (0 . ◦ –0 . ◦ ) than theangular size of shower structure. Multiple viewing an-gles of the same shower o ff ered by an array of tele-scopes drastically improves the reconstruction perfor-mance and background rejection. Finally, at high en-ergy, the sensitivity of IACTs is limited by gamma-raysignal statistics, requiring an array with a large e ff ectivegamma-ray collection area.The current generation of IACTs all have single-dishoptical systems. These have small spherical mirrorfacets attached to either a spherical dish (i.e. Davies-Cotton (DC) [15, 16]) or a parabolic dish. The parabolicdish reduces the time spread of the Cherenkov signalbut introduces a larger o ff -axis optical PSF. An interme-diate design with a spherical dish but a larger radius ofcurvature (intermediate-DC) can be used to achieve animproved time spread while maintaining o ff -axis perfor-mance [17, 18]. These single-dish designs are appealingbecause they are relatively inexpensive, mirror align-ment is straightforward, and the optical PSF at largefield angles is better than that of monolithic sphericalor parabolic reflectors [19]. The possibility of improving the PSF (especiallyo ff axis) and reducing the plate scale of IACTs hasdriven the study of Schwarzschild-Couder (SC) apla-natic telescopes with two aspheric mirror surfaces . Theimproved PSF across the field of view (FoV) allowsfor more accurate surveying and mapping of extendedsources. The reduced plate scale is highly compatiblewith new camera technologies such as Silicon photo-multipliers or multi-anode photomultiplier tubes. Thesetechnologies allow for a cost-e ff ective, finely-pixelatedimage over a large FoV. Studies have been performedproviding solutions for mirror surfaces optimized to cor-rect spherical and coma aberrations. These solutionsare also isochronous, allowing for a short trigger coinci-dence window [20]. The first SC prototype is still beingdeveloped [21] and has several challenges to overcome.In particular, the tolerances of the mechanical structurein the camera and mirror alignment system are relativelystringent, which translates to a higher cost. To providecomparisons at a fixed cost, our SC simulations use asmaller mirror area than that of the baseline DC design.The Cherenkov Telescope Array (CTA) is an exam-ple of a next-generation IACT observatory. CTA aims tosurpass the current IACT systems such as H.E.S.S. [22],MAGIC [23] and VERITAS [24] by an order of mag-nitude in sensitivity and enlarge the observable energyrange from a few tens of GeV to beyond one hundredTeV [25]. To achieve this broad energy range and highsensitivity, CTA will incorporate telescopes of three dif-ferent sizes spread out over an area of ∼ . Tele-scopes are denoted by their mirror diameter as large-size telescopes (LSTs, ∼
24 m), medium-size telescopes(MSTs, ∼
12 m), and small-size telescopes (SSTs, ∼ Though segmented, the mirror surfaces are often referred to as asingular mirror for brevity. ∼ four LSTs, ∼
30 MSTs, and ∼
50 SSTs. The sensitivity could beimproved by a factor of 2–3 in the core energy rangeby expanding the MST array with an additional 24–36SCTs. With these additional telescopes, the combinedMST and SCT array enters a new regime where the in-ternal e ff ective area is comparable to the e ff ective areaof events landing outside the array. These so-called con-tained events have much improved angular and energyresolution as well as background rejection. Extensivework is underway to optimize the design of CTA for thewide range of science goals [18]. The scope of previousstudies has been primarily on a straightforward expan-sion of existing telescope designs to larger arrays.In this paper, we describe a novel, flexible MonteCarlo simulation and analysis chain. We use them toevaluate the performance of CTA-like arrays over alarge range of telescope configurations and design pa-rameters. Section 2 describes this simulation and thesimplified detector model. In Section 3, we explain theanalysis chain, including a maximum likelihood showerreconstruction using simulated templates. This recon-struction was used for comparisons between the maxi-mum sensitivity for each array configuration. In Section4, we show comparisons between possible CTA designs,focusing primarily on the number of telescopes and theDC versus SC designs. We conclude in Section 5.
2. Simulation
We have studied the performance of a variety of arraygeometries and telescope configurations for a hypothet-ical CTA site at an altitude of 2000 m. Details of thesite model and array geometry are described in Sections2.1 and 2.2. Simulations of the telescope response wereperformed using a simplified detector model describedin Section 2.3.
Simulations of the gamma-ray and cosmic-ray airshower cascades were performed with the CORSIKAv6.99 Monte Carlo (MC) package [26] and the QGSJetII-03 hadronic interaction model [27]. We used a sitemodel with an elevation of 2000 m, a tropical atmo-spheric profile, and an equatorial geomagnetic field con-figuration with ( B x , B z ) = (27 . µ T , − . µ T). Thissite model is identical to the one used in [18] and hassimilar characteristics to the southern hemisphere sitesproposed for CTA.Gamma-ray showers were simulated as coming froma point on the sky at 20 ◦ zenith angle and 0 ◦ azimuth angle, as measured from the local magnetic north overthe energy range from 10 GeV to 30 TeV. Protons andelectrons were simulated with an isotropic distributionthat extends to 8 ◦ and 5 ◦ respectively from the directionof the gamma-ray primary. We use the spectral parame-terizations for proton and electron fluxes from [28]. Toaccount for the contribution of heavier cosmic-ray nu-clei we increase the proton flux by a factor 1.2. Proposed designs for CTA employ three telescopetypes (SST, MST, and LST) with variable inter-telescope spacing from 120 m to more than 200 m [18].The number of telescopes of each type and their separa-tions are chosen to optimize the di ff erential sensitivityover the full energy range of CTA. [18] found that twobalanced arrays (arrays E and I) that have 3–4 LSTs,18–23 MSTs, and 30–50 SSTs of 7 m diameter providethe best compromise in performance over the full en-ergy range of CTA while keeping the total cost of thearray within the projected CTA budget.For this study we simulated an array geometry whichis similar to the one used for MSTs and LSTs in ar-rays E and I. The array is composed of 61 telescopesarranged on a grid with constant inter-telescope spac-ing of 120 m (see Figure 1). A telescope spacing ofabout 120 m is well motivated by the characteristic sizeof the Cherenkov light pool for gamma-ray air show-ers and guarantees that multiple telescopes will sam-ple the shower within the shower light pool. Subsetsof telescopes from the baseline array were used to con-struct arrays with a reduced number of telescopes byremoving successive rings of telescopes along the arrayperimeter. These reduced arrays have between 5 and41 telescopes and encompass arrays that are similar intelescope number to both current IACT arrays (N tel =
5) and the array designs currently considered for CTA(N tel = Simulations of IACT arrays have traditionally beenperformed with highly detailed detector models that use3
00 600 400 200 0 200 400 600 800X Position [m]8006004002000200400600800 Y P o s i t i o n [ m ] N=5N=13N=25N=41N=61
Figure 1: Physical telescope positions for the five array geometriesused for this study. All geometries are composed of telescopes ar-ranged on a uniform grid with 120 m spacing. The smallest arrayis composed of five telescopes (black circles). The larger arrays areconstructed by the addition of successive rings of telescopes aroundthe array boundary up to a maximum of 61 telescopes in the baselinearray geometry. optical ray-tracing to track the trajectory and time of ar-rival of individual Cherenkov photons. Because thesemodels have a very large number of parameters, a bruteforce optimization of the telescope design presents asignificant computational challenge. In order to e ffi -ciently study the telescope design parameter space, wehave developed a simplified telescope simulation tool,FAST (FAst Simulation for imaging air cherenkov Tele-scopes), that is not tied to any particular mirror config-uration or camera technology. In the FAST model, thetelescope characteristics are fully described by the fol-lowing parameters: • E ff ective light collection area: A opt •
68% containment radius of the optical PSF: R psf • Camera pixel size: D pix • E ff ective camera trigger threshold: T th • Single photo-electron (PE) charge resolution: σ spe • Pixel read-noise: σ b • E ff ective integration window: ∆ T While this simplified model lacks the level of detail pro-vided by other simulation tools, the performance of arealistic telescope design can be approximated by anappropriate choice of these model parameters. In thissection we describe in detail the implementation of ourmodel and how each of these parameters influence thetelescope response.The geometrical model of the telescope consists ofa primary mirror of diameter D with physical mirrorarea A M = π ( D / . All Cherenkov photons that in-tersect with the primary mirror surface are propagatedthrough the telescope simulation. The photons collectedby the primary mirror are folded with a wavelength de-pendent photon detection e ffi ciency, (cid:15) ( λ ), that modelslosses from all elements in the optical system and cam-era (mirrors, lightguides, and photosensors). Applying adetection probability to each collected photon, we con-struct a list of detected photoelectrons (PEs) which areused as input to the simulation of the telescope trigger,camera, and optics.We quantify the total light-collecting power of a tele-scope by its e ff ective light collection area, A opt ( λ ) = A M (cid:15) ( λ ), the product of the physical mirror area with thetotal photon detection e ffi ciency at wavelength λ . Wecompute a wavelength-averaged e ff ective area by fold-ing A opt ( λ ) with a model for the wavelength distributionof Cherenkov light, A opt = (cid:90) λ λ P ( λ, z ) A opt ( λ ) d λ, (1)where P ( λ, z ) ∝ e − τ ( λ, z ) λ − (2)is the normalized wavelength distribution of Cherenkovlight at the ground for an emission altitude z and an op-tical depth for atmospheric extinction τ ( λ, z ). We usean atmospheric extinction model generated with MOD-TRAN [29] for the tropical atmosphere and an aerosollayer with a visibility of 50 km. For all further evalua-tions of A opt we use z =
10 km and an integration overwavelength from 250 nm to 700 nm.We define a benchmark telescope with a D =
12 mprimary diameter and a total photon detection e ffi ciencythat includes losses from mirror reflections and photo-sensor e ffi ciency. We use a photosensor model with aspectral response that is characteristic of photomulti-plier tubes and has a peak e ffi ciency of 24% at 350 nm.Losses from mirror reflections are evaluated for a singleoptical surface using a wavelength-dependent reflectiv-ity with a peak e ffi ciency of 89% at 320 nm. This reflec-tivity is similar to that of the aluminum and aluminized4
00 300 400 500 600 700Wavelength [nm]024681012141618 E ff e c t i v e A r e a [ m ] A opt ( λ )P( λ ,z) (arb. norm) Figure 2: E ff ective light collection area versus wavelength for thebenchmark telescope model with A opt = . The dashed blackline shows the spectral shape for Cherenkov light emitted at an eleva-tion of 10 km after absorption by the atmosphere. glass mirrors used in current generation IACTs. Figure2 shows the optical e ff ective area of the telescope modelas a function of wavelength. The e ff ective light collec-tion area of our benchmark telescope is 11.18 m whichis representative of medium-sized IACTs with ∼
10 maperture and 50–100 m mirror area. The response oftelescopes with larger or smaller light collection areasis modeled using the same spectral response and mirrorarea as the benchmark telescope model but scaling thephoton detection e ffi ciency by the ratio A opt / .
18 m .The imaging response of the telescope optical systemis simulated by applying a model for the optical point-spread-function (PSF) to the distribution of true pho-ton arrival directions in the camera image plane. Af-ter applying a survival probability for detection, eachCherenkov photon is assigned a random o ff set drawnfrom the optical PSF. We parameterize the optical PSFas a 2D Gaussian with a 68% containment radius, R psf ,that is constant across the FoV. We consider values of R psf between 0.02 ◦ and 0.08 ◦ which is comparable tothe range of PSF spot sizes for the CTA telescope de-signs at both small and large field angles. All telescopesare simulated with an 8 deg FoV with a light collectionarea that is constant with field angle.Telescopes are simulated with a camera geometrycomposed of square pixels of angular width D pix thatuniformly tile the camera FoV. Each pixel is assigneda time integrated signal that is the sum of the detectedCherenkov photons, night-sky background (NSB) pho-tons, and detector noise. The number of NSB photonsis drawn from a Poisson distribution where the average ( µ b ) is computed using an implicit time integration win-dow ( ∆ T ) of 16 ns. The mean number of NSB photonsper pixel for a telescope with e ff ective light collectionarea A opt and pixel solid angle ∆Ω is µ b = ∆ T ∆Ω (cid:15) (cid:90) F nsb ( λ ) A opt ( λ ) d λ, (3)where F nsb ( λ ) is the di ff erential NSB flux versus wave-length. We use the NSB spectral model from [30] whichis representative of the sky brightness of an extragalac-tic observation field. When folded with the optical e ffi -ciency of our benchmark telescope model, the integralflux of detected NSB photons is 365 MHz deg − m − .Our benchmark telescope model has an NSB surfacedensity in the image plane ( Σ nsb ) of 65.4 deg − for anintegration window of 16 ns. We model the photo-sensor single photoelectron response with a Gaussianwith σ spe = . σ b ) of 0.1 PE. For the rangeof pixel sizes and optical throughputs considered in thisstudy, the readout noise is a subdominant component ofthe pixel noise relative to NSB and is therefore not ex-pected to have a significant impact on the telescope per-formance. Fig. 3 shows simulated camera images fortelescope models with two di ff erent pixel sizes observ-ing the same 1 TeV gamma-ray shower.The trigger system of an IACT array rejects noise-induced events while maintaining high e ffi ciency forcosmic-ray signals. We simulate a two-stage trigger sys-tem composed of a camera-level trigger for each tele-scope and an array-level trigger that combines the cam-era triggers of multiple telescopes to form the final trig-ger decision. Camera trigger designs used by currentgeneration IACTs and envisioned for CTA are gener-ally based on a multi-level hierarchy whereby triggerinformation from individual pixels or camera subfieldsis combined to form the camera-level trigger decision[31, 32, 25]. The rate of accidental triggers is sup-pressed by requiring a time coincidence of triggers fromneighboring pixels or camera regions.A useful quantity for characterizing the performanceof di ff erent camera trigger designs is the e ff ective cam-era threshold, the true gamma-ray image amplitude inPEs at which the camera trigger is 50% e ffi cient. Tofirst order the e ffi ciency of the camera trigger dependsonly on the surface brightness of the Cherenkov showerimage. Because the angular size of the shower is onlya weak function of distance and energy, we can approx-imate the response of a camera trigger by applying afixed threshold on the true number of Cherenkov PEs inthe camera FoV.5 .5 2.0 1.5 1.0 0.5 0.0 0.5Azimuth Offset [deg]2.52.01.51.00.50.00.5 Z e n i t h O ff s e t [ d e g ] Z e n i t h O ff s e t [ d e g ] Figure 3: Camera images of the same 1 TeV gamma-ray shower with an impact distance of 120 m simulated with two di ff erent telescope pixelsizes: D pix = . ◦ ( left ) and D pix = . ◦ ( right ). Both telescope models have A opt = and R psf = . ◦ . The color scale denotes themeasured signal amplitude in PEs for each pixel. The white cross and solid line show the direction of the gamma-ray primary and the projection ofits trajectory to the telescope image plane, respectively. We simulate the camera trigger by applying a thresh-old T th on the true number of Cherenkov PEs detectedin the camera FoV. For showers that trigger one or moretelescopes, the array-level trigger is simulated requiringa multiplicity of at least two triggered telescopes. Thecamera threshold provides a single parameter model thatwe use to explore influence of the trigger threshold onthe array-level performance. By calibrating T th to thee ff ective camera threshold of a given trigger design, wecan also approximate the trigger response that would beobtained with a more detailed trigger simulation imple-mentation.Studies performed with the sim telarray detectorsimulation package [28] have shown that camera triggerdesigns currently considered for the MSTs can achievee ff ective trigger thresholds of 60–80 PE for a single tele-scope accidental trigger rate of 1–10 kHz. We adopteda trigger threshold of 60 PE for our baseline telescopemodel with A opt = which is comparable to thee ff ective threshold of the prod-2 MST model [33]. Tomodel the e ff ective trigger threshold for telescopes withdi ff erent light collection areas, we used a simple scal-ing formula that approximates the threshold needed tomaintain a constant rate of accidental triggers. If the to-tal pixel noise is dominated by NSB photons, the rate ofaccidental triggers should be proportional to the RMS fluctuations in the number of NSB photons collected ina trigger pixel which scales as A / if the angular pixelsize is held fixed. Telescopes with larger e ff ective lightcollection area achieve a lower trigger threshold throughthe suppression of these NSB fluctuations relative to thesignal amplitude which increases linearly with A opt . Weassign the e ff ective trigger threshold for a telescope withlight collection area A opt as, T th =
60 PE (cid:32) A opt .
18 m (cid:33) / . (4)For the studies presented in Section 4, we considera benchmark array (M61) with 61 identical telescopeswith A opt = , R psf = ◦ , D pix = ◦ , and T th =
60 PE. Our baseline telescope model is repre-sentative of a generic medium-sized telescope designwith SC-like imaging characteristics. In Section 4.2 weadditionally consider other telescope models that werespecifically chosen to match the characteristics of theproposed CTA telescope designs.
The FAST package uses a highly simplified modelof the telescope optics and camera. This allows us toperform a more general exploration of the IACT de-sign parameter space without focusing on the details of6ny specific optical design or camera technology. Thesesimplifications also make the FAST simulation muchless computationally intensive than traditional simula-tion tools such as sim telarray which further facili-tates the exploration of a large phase space of telescopeand array design concepts. When simulating compa-rable telescope designs with FAST and sim telarray we observe an order-of-magnitude reduction in compu-tation time. Here, we discuss the limitations of the ap-proach taken in the FAST simulation package and de-scribe the areas in which a more detailed simulation ofthe telescope camera and optics could potentially a ff ectour results.FAST does not use raytracing to account for shadow-ing of the camera by telescope structure and assumes asimple 2D Gaussian PSF that is constant over the FoV.Full raytracing simulations can be used to model e ff ectssuch as shadowing by the telescope structure and lightlosses from gaps in the mirror surfaces. Raytracing alsoallows a more realistic modeling of the telescope PSF.Optical aberrations intrinsic to the design of IACTs in-troduce a strong field-angle dependence to both the sizeand shape of the PSF. In the FAST telescope model, alle ff ects that influence the optical performance of the tele-scope are folded into the e ff ective optical area ( A opt ) andthe 68% containment radius of the PSF ( R psf ). Shadow-ing and other light losses in the optical system are thustaken into account by a reduction in the e ff ective opticalarea. The field-angle dependence of the PSF is stud-ied by comparing the performance of telescope designswith the best and worst PSF at any field angle. The per-formance of a real telescope should always fall betweenthat of telescopes with smallest and largest PSF in theFoV. We did not study the e ff ect of an asymmetric PSFbut it is plausible to assume that the array performancewith telescopes that have an asymmetric PSF can be es-timated by enlarging the symmetric PSF in FAST.FAST does not simulate the timing of signals and as-sumes an ideal data acquisition system that is only lim-ited by the irreducible noise from NSB photons. E ff ectsthat distort the measurement of the pixel charge suchas cross-talk, after-pulsing, timing jitter, non-linearity,and saturation might lead to a reduction in performance.However these e ff ects should a ff ect all telescope typesin a similar way in the sense that photon charges mightbe only partially reconstructed. Per the telescope perfor-mance requirements set forward by CTA, we expect theinfluence of these e ff ects to be sub-dominant to the irre-ducible limitations on the IACT technique set by showerphysics (NSB and shower fluctuations). Many of thesee ff ects can be partially mitigated with pixel-level cali-bration or pre-processing analysis procedures. For in- stance, suppression algorithms such as clipping of pixelsignal amplitudes or the removal of isolated high PEpixels have been demonstrated as e ffi cient techniquesto reduce the impact of after-pulsing. In principle thesee ff ects could also be approximated in the FAST detectormodel by increasing the pixel-level noise or worseningthe charge resolution. We note that our analysis doesnot use shower timing parameters or shower develop-ment timing in any explicit way and thus is robust withrespect to changes in timing requirements.Another simplification in FAST is the trigger thresh-old decision logic that assumes any shower image abovea certain threshold will trigger the telescope. Realis-tic trigger electronics might have several characteristicsthat have to be simulated in detail but in the early plan-ning state of an array our method is very valuable to givea solid estimate of the array performance as long as thetrigger threshold is not chosen aggressively and the re-quirements of the telescope array are met. Indeed weshow in Section 4.3 that our telescope threshold mightbe too conservative given that more realistic simulationsfind enhanced performance near the energy threshold ofsimulated arrays. For relative comparisons of arrays oursimplifications are unimportant. To estimate the influ-ence on the absolute performance impacts of our sim-plified simulations we compare our results to a muchmore sophisticated detector simulation in Section 4.3.
3. Analysis
The analysis of the telescope image data is performedusing well established techniques for the analysis ofIACT data. The analysis is performed in three stages:preparation of the telescope images, reconstruction ofthe event properties, and training and optimization ofcuts.
The image analysis is applied to the telescope pixelamplitudes to derive a set of telescope-level parameterswhich characterize the distribution of light in each tele-scope. Analysis of the telescope image data begins withthe application of an image cleaning analysis that se-lects pixels that have a signal amplitude that is largerthan noise. Traditionally image cleaning has been per-formed using variations of a nearest-neighbor algorithm[34]. A search is performed for groups of neighboringpixels which exceed a threshold defined in terms of theabsolute amplitude or the amplitude relative to the RMSnoise in the pixel. These algorithms work well as longas the dimension of the pixel is of the same order as the7herenkov image size. However in the limit of smallpixel sizes these algorithms will lose e ffi ciency for lowenergy showers where the signal is spread out over toomany pixels to be discernible above noise when onlyconsidering nearest neighbors.In order to circumvent the limitations of the nearest-neighbor pixel algorithms, we use an Aperture cleaningalgorithm that performs a smoothing over the camerawith an angular scale ( R = . ◦ ) that is of the sameorder as the width of a gamma-ray induced Cherenkovshower (0.1–0.2 ◦ ).In order to detect e ffi ciently images that lie on pixelboundaries we divide each pixel into N × N subpixels where N = (cid:100) D pix / . ◦ (cid:101) . We compute the image inten-sity in the neighborhood of subpixel i as¯ s ( R ) = (cid:88) j s j w i , j ( R ) , (5)where w i , j ( R ) is the fraction of the solid angle of pixel j contained within the circular aperture of radius R cen-tered on subpixel i (see Figure 4). The pixel imagethreshold is defined relative to the expected noise withinthe pixel aperture σ ( R ) = (cid:88) j ( σ b + µ b ) w i , j ( R ) / . (6)For the present analysis we adopt an image thresholdof ¯ s /σ = − and an inte-grated charge of 14.4 PE within the cleaning aperture.Any pixel for which one or more subpixels exceeds thecleaning threshold is flagged as an image pixel. Thesimulations do not include photodetector after-pulsing,which can cause noise isolated in single pixels. Thesemay need to be suppressed if the aperture cleaningmethod is applied in other scenarios. Telescope imagesare discarded at this point if fewer than three image pix-els are present.The image cleaning is only used by the geometric re-construction, itself a seed for the likelihood reconstruc-tion. As such, a relatively low threshold was chosen tomaximize the reconstruction e ffi ciency for low-energyevents.Following the image cleaning analysis, an imageanalysis is applied to the amplitudes of image pixels ( s j )to calculate a set of image parameters that characterizethe light distribution in the focal plane. The image pa-rameters include the total image size, S , the image cen-troid, the second central moments along the major andminor axes of the image denoted as length l and width Figure 4: Illustration of the aperture cleaning algorithm on small cam-era subsections with R = . ◦ . In the DC-like case ( left ), pixels aresubdivided since they are large compared to the aperture. Each sub-pixel is used as the center of an aperture for image intensity calcula-tion. This calculation is based on the number of PEs and the fractionof the pixel area within the aperture, normalized to the area of theaperture. For the SC-like case ( right ), smaller pixels do not requiresubdivision. w , and the orientation of the major axis in the imageplane. The shower reconstruction determines a trajectoryand energy for each event by fitting a shower model tothe telescope image data. The shower model parame-ters ( θ ) are the primary energy ( E ), the primary direc-tion ( e ), the primary impact position ( R ), and the atmo-spheric column depth of the first interaction point ( λ ).In an array of IACTs, each telescope views the showerfrom a di ff erent perspective and provides an indepen-dent constraint on the shower parameters. By usingimage data from multiple telescopes, one can performa stereoscopic reconstruction of the shower trajectory.For the analysis algorithms presented in this section, weassume on-axis observations of a gamma-ray source inparallel pointing mode whereby the optical axes of thetelescopes in the array are aligned with the shower di-rection. However the procedures described here can bealso applied to the case of non-aligned telescope point-ing.In presenting the implementation of the shower re-construction algorithms, we use a global coordinate sys-tem defined with the x -axis parallel to the directionof magnetic north and the z -axis perpendicular to theEarth’s surface. The positions of the array telescopesare denoted by r i . For the array layouts considered forthis study, the telescopes are arranged in a regular gridin the x - y plane with all telescopes located at the sameheight above sea level ( z = shower coordinate system8ith the z -axis aligned with the shower trajectory anddefined by the basis vectors:ˆ z (cid:48) = e ˆ y (cid:48) = ( e − (ˆ z · e ) ˆ z ) (cid:112) − (ˆ z · e ) × ˆ z ˆ x (cid:48) = ˆ z (cid:48) × ˆ y (cid:48) (7)We use r (cid:48) i and R (cid:48) to represent the projections of the tele-scope positions and the shower impact position to the x (cid:48) − y (cid:48) plane. An illustration of the geometry of a showeris shown in Figure 5. The shower impact vector, ρ i = R − r i − (ˆ z (cid:48) · ( R − r i ))ˆ z (cid:48) , (8)describes the location of the shower impact position rel-ative to telescope i in the x (cid:48) − y (cid:48) plane. The showerimpact distance ( ρ i = | ρ i | ) is the distance of closest ap-proach between the shower and the telescope.The geomagnetic field (GF) alters the developmentof the gamma-ray shower by deflecting the chargedparticles in the electromagnetic cascade. The GF de-flects particles in a plane perpendicular to their trajec-tories with a strength proportional to the perpendicularcomponent of the GF vector. For the shower particlesthat predominantly contribute to the emitted Cherenkovlight, the perpendicular component is comparable to theGF vector component perpendicular to the shower di-rection ( B ⊥ = B − ( B · ˆ z (cid:48) )ˆ z (cid:48) ). Deflection of the showerparticles by the GF breaks the azimuthal symmetry ofthe shower causing an elongation in the shower particledistribution in the plane orthogonal to B ⊥ .Due to the asymmetry in the shower development in-duced by the GF, the Cherenkov light distribution ob-served by a telescope depends on both the distance tothe shower impact position ( ρ ) and the orientation ofthe shower impact vector relative to the GF. We param-eterize the shower orientation with respect to telescope i by the shower position angle ( φ i ) defined bycos φ i = ˆ x (cid:48) · ρ i | ρ i | . (9)Telescopes with a shower position angle of 0 ◦ and 90 ◦ view the shower in the planes parallel and perpendicularto its elongated axis respectively (see Figure 5).The shower reconstruction is performed in two con-secutive stages. A geometric reconstruction algorithmis first used to obtain a robust estimation of the showerparameters. In this stage the shower energy and inter-action depth are initially assigned using look-up tables .In the second stage the shower parameters derived from R R r i r i ρ i e ˆ x ’ ˆ y ’ ˆ z ’ ˆ z ˆ x BB ⊥ B || φ i Figure 5: Illustration of the geometry of a gamma-ray shower asshown in the shower coordinate system. The gamma-ray trajectoryis defined by its impact position R (cid:48) in the x (cid:48) − y (cid:48) plane and arrivaldirection e . The GF induces an elongation in the shower in the planeorthogonal to B ⊥ (indicated by the grey shaded square). The showerimpact vector, ρ i , describes the position of the shower impact positionrelative to the telescope at r i (closed blue circle). The shower positionangle, φ i , is defined by the angle between the shower impact vectorand the x (cid:48) − axis. the geometric reconstruction are refined using a likeli-hood reconstruction algorithm that performs a joint fitto the image intensity in all telescopes. The geometric reconstruction algorithm is a 3-Dstereoscopic reconstruction technique based on the tra-ditional Hillas image parameterization of the showerimages [35]. The emitted Cherenkov light from agamma-ray shower produces an approximately ellipti-cal distribution in the telescope focal plane with the ma-jor axis of the ellipse aligned with the shower trajec-tory. The projected shower trajectory as observed by atelescope with impact vector ρ i can be described by theequation e s , i ( t ) = ρ i + e t | ρ i + e t | , (10)where t is the physical distance along the shower axisfrom its intersection with the shower plane. Each tele-scope that observes the shower constrains the trajectoryto lie in the plane formed by the vectors ˆ z (cid:48) and ρ i . Whenmultiple telescope images are present, the intersectionpoint of the projected shower axes provides a uniquesolution for both the shower direction ( e ) and its impactposition in the shower plane ( R (cid:48) ).The solution for the shower trajectory that bestmatches the projected shower axes of all telescopes is9ound by minimizing a pair of χ -like parameters thatindependently optimize the shower direction and coreposition. In the case of the shower direction we solvefor the vector e that minimizes χ e ( e ) = (cid:88) i κ ( S i , w i , l i ) ∆ e , i ( e ) , (11)where ∆ e , i ( e ) is the distance of closest approach betweenthe major axis of the image ellipse and the shower direc-tion projected to the image plane of telescope i , and κ isa weighting function that controls the contribution ofeach telescope to the total sum. Images that are brighterand more elongated provide a better constraint on theshower trajectory, and therefore we use as our weight-ing function the product of the image size with squareof the image ellipse eccentricity, κ ( S i , w i , l i ) = S i l i − w i l i . (12)The shower core position is reconstructed by mini-mizing χ R ( R ) = (cid:88) i κ ( S i , w i , l i ) ∆ R , i ( R ) , (13)where ∆ R , i ( R ) = (cid:12)(cid:12)(cid:12)(cid:12) ρ i ( R ) − (cid:16) ρ i ( R ) · e ρ, i (cid:17) e ρ, i (cid:12)(cid:12)(cid:12)(cid:12) (14)is the distance of closest of approach between the im-age axis of telescope i projected to the shower plane( e ρ, i ) and the core location. After reconstruction of theshower trajectory, the shower energy is reconstructedusing look-up tables for the shower energy as a func-tion of the image size and impact distance from the tele-scope. The shower energy estimate is calculated froma weighted average of telescope energy estimates givenby E = (cid:88) i σ E ( S i , ρ i ) − (cid:88) i E ( S i , ρ i ) σ E ( S i , ρ i ) , (15)where E ( S i , ρ i ) and σ E ( S i , ρ i ) are functions for the ex-pectation value and standard deviation of the shower en-ergy derived from simulations. The likelihood reconstruction performs a global fit tothe telescope image data using a model for the expectedpixel amplitude µ ( θ ) as a function of the shower param-eters θ . Pixel expectation values are evaluated from animage template model, I ( e ; ρ , θ ), a probability distribu-tion function for the image intensity in the direction e as measured by a telescope that observes a shower withparameters θ and impact vector ρ . More details on thegeneration of the image intensity model are presentedin Section 3.2.3. The agreement between the telescopeimage model and the data is evaluated by means of anarray likelihood function. Shower parameters are deter-mined by a maximization of an array likelihood func-tion. Maximization of the array likelihood as a functionof shower fit parameters is performed using a numeri-cal non-linear optimization technique. In order to en-sure stable fit convergence, the shower parameters areinitially seeded with a set of values derived by the geo-metric reconstruction ( θ geo ).We use a formulation of the array likelihood functionwhich is similar to the one presented in [36]. The ar-ray likelihood is computed from a pixel-by-pixel com-parison between the observed and predicted image in-tensities. The likelihood provides a statistical modelfor the measured pixel signal ( s ) as a function of in-put models for signal and background. The measuredpixel signal is modeled as the sum of three components:Cherenkov signal photons, NSB photons, and Gaussiannoise arising from detector fluctuations. The pixel like-lihood function is L pix ( s | µ ( θ ) , µ b , σ b , σ spe ) = (cid:88) n ( µ + µ b ) n e − ( µ + µ b ) n ! g ( s , n ) , (16)where µ is the model amplitude, µ b is the NSB ampli-tude, σ b is the standard deviation of the detector noise, σ spe is the width of the single PE response function, and g ( s , n ) = (cid:113) π (cid:16) σ b + n σ (cid:17) exp − ( s − n ) (cid:16) σ b + n σ (cid:17) . (17)The model amplitude for pixel j in telescope i is cal-culated by an integration of the image template modelover the pixel, µ i j ( θ ) = (cid:90) Ω ij I ( e ; ρ i , θ ) d Ω , (18)where Ω i j is the 2-D angular integration region.The array likelihood is calculated from the product ofthe pixel likelihoods in all telescopes, L ( s | µ ( θ ) , µ b , σ b , σ γ ) = (cid:89) i , j L pix ( s i j | µ i j ( θ ) , µ b , σ b , σ γ ) , (19)10here s i , j and µ i , j are the signal and model amplitude ofpixel i in telescope j . The set of pixels included in thecomputation of Equation 19 can encompass the entirecamera. Unlike for the geometric reconstruction tech-niques, each pixel is weighted by its expected contribu-tion to the total image intensity. Therefore the inclusionof pixels on the shower periphery does not significantlyimprove or degrade the reconstruction performance. Al-though the array likelihood can be calculated using allpixels in the camera, using a smaller number of pix-els significantly reduces the computation time neededfor the shower likelihood optimization. In order to se-lect pixels that will provide a useful constraint on theshower parameters, we choose a set of pixels P in eachtelescope that satisfies the relation (cid:88) j ∈P µ j ( θ geo ) ≥ f (cid:88) j µ j ( θ geo ) , (20)where µ j is the expected image intensity in pixel j and f is the fraction of the total image intensity. We build theset P by adding pixels in order of their expected inten-sity until the total amplitude fraction exceeds f . Havingfound that the reconstruction performance is relativelyinsensitive to f for values (cid:38) .
75, we use f = . The image model, I ( e ; ρ , θ ), is the probability distri-bution function for the measured telescope image inten-sity in photoelectrons (PEs) versus direction, e . Themodel is parameterized as a function of the showerproperties (energy and first interaction depth) and theimpact position of the shower relative to the telescope.The model is generated by averaging the intensity ofa large sample of simulated showers generated at a se-quence of fixed o ff sets, energies and interaction depths.The image templates for this study were generatedwith the CORSIKA shower simulation package and thedetector simulation described in Section 2.3. Whilethe image templates used for this study are MC-based A z i m u t h O ff s e t [ d e g ] R = 150.00 m λ = 1.00 X E = 100.00 GeV0 300 600 900 1200 1500 1800 2100 2400Image Intensity [PE deg − ]2.5 2.0 1.5 1.0 0.5 0.0 0.5Zenith Offset [deg]0.40.30.20.10.00.10.20.30.4 A z i m u t h O ff s e t [ d e g ] R = 150.00 m λ = 1.00 X E = 1000.00 GeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000Image Intensity [PE deg − ]2.5 2.0 1.5 1.0 0.5 0.0 0.5Zenith Offset [deg]0.40.30.20.10.00.10.20.30.4 A z i m u t h O ff s e t [ d e g ] R = 150.00 m λ = 1.00 X E = 10000.00 GeV0 15000 30000 45000 60000 75000 90000 105000Image Intensity [PE deg − ] Figure 6: Image intensity templates for three di ff erent three gamma-ray energies (100 GeV, 1 TeV, and 10 TeV) generated for a telescopemodel with R psf = . ◦ and A opt = .
18 m . The images showthe expectation for the measured intensity of Cherenkov light as afunction of angular o ff set from the primary gamma-ray direction. Theimage templates shown here are evaluated at an impact distance ( ρ ) of150 m and a first interaction depth ( λ ) of 1 X . we note that the likelihood reconstruction can also beapplied using templates generated with semi-analyticshower models [36].Because the templates are produced from a simula-tion of the shower, the image model incorporates all ef-fects that influence the measured image intensity includ-ing atmospheric attenuation, geomagnetic field, tele-scope optics, and telescope detector response. The im-age model is a continuous distribution for the showerphotons in the focal plane and the same template cantherefore be used to compute the image intensity forcameras with arbitrary pixel geometry and field-of-view. For this study, we use image templates computedfor the baseline telescope model with D =
12 m and A opt = .
18 m . The image intensity for other tele-scopes is calculated by rescaling the image intensityby the ratio of the telescope light collection area to the11aseline telescope model.The image intensity templates are stored on a six-dimensional grid: • log (Energy) and Interaction Depth (log E and λ ) • Core Impact Distance and Position Angle ( ρ and φ ) • Projected Zenith and Azimuth O ff set in ImageTemplate CoordinatesThe shower templates are defined in a coordinate systemrotated by φ i with respect to the shower axis such thatthe x -axis is aligned with the shower axis. In order tokeep the memory footprint of the full six-dimensionaltemplate at a manageable level, the image templates areonly defined over an angular region within one degreeof the shower axis.The expected image intensity is computed from theimage template sequence by a linear interpolation in thesix-dimensional template space. The templates are alsoused to derive first derivatives of the image intensity asa function of the shower parameters which are used forcalculation of the likelihood gradient.Figure 6 shows the image templates evaluated forgamma-ray showers of three di ff erent energies. Theprimary energy a ff ects both the total intensity of theshower image as well as its shape. Higher energy show-ers propagate further into the atmosphere and result inshower images that are more extended along the showeraxis. The core impact distance sets the geometricalperspective of the telescope and selects the Cherenkovlight emission from particles with a specific range ofangles with respect to the shower axis. Showers ob-served inside the Cherenkov light pool ( ρ (cid:46)
120 m)appear both brighter and narrower as the telescope ac-cepts Cherenkov light from higher energy particles thatare closely aligned with the shower primary. More dis-tant showers are dimmer and increasingly o ff set fromthe primary origin. The interaction depth sets the start-ing point of the shower and primarily influences the dis-placement of the shower image along the shower axis.In the absence of the GF, the shower template is sym-metric with respect to the shower position angle. TheGF breaks the axial symmetry as the Lorentz force pref-erentially perturbs the trajectory of the shower particlesinto the plane orthogonal to B ⊥ . The GF e ff ect is es-pecially pronounced for showers with small interactiondepth for which the average propagation distance be-tween the first and second interactions is large. Figure7 illustrates the impact of the GF on the image templatefor three values of the core position angle ( φ ): 0 ◦ (par-allel), 45 ◦ , and 90 ◦ (perpendicular). The shower width monotonically decreases as the shower position angle isincreased from 0 ◦ to 90 ◦ reflecting the asymmetry in theshower development. For intermediate viewing angles( φ = ◦ ), the GF also causes a rotation of the imagemajor axis relative to the shower axis. / Hadron Separation and Cut Optimization
The final stage of the event analysis determinesparameters that can be used for discrimination be-tween cosmic- and gamma-ray initiated air showers.The Cherenkov images produced by cosmic-ray show-ers can generally be distinguished from gamma-rayshowers by their wider and more irregular appearance.Hadronic subshowers may also produce isolated clus-ters of Cherenkov light in the telescope image plane. Awidely used set of parameters for background discrim-ination are the so-called mean scaled parameters de-fined already in the HEGRA collaboration [34] and ex-tensively used by current generation IACT experiments(see e.g., [37]). The mean scaled parameters providea measure of the deviation between the observed andexpected telescope image moments for a gamma-rayshower. Using a set of simulated gamma-ray showers,lookup tables for the mean and standard deviation of theimage moment parameters are produced as a function ofthe telescope image size and telescope impact distance(denoted here as p ( S , ρ ) and σ p ( S , ρ )). For a telescopeimage parameter p i we define the array-level parameteras p = (cid:88) i w i − (cid:88) i w i p i − p ( S i , ρ i ) σ p ( S i , ρ i ) , (21)where the sum is over all telescopes with reconstructedimage parameters and w i is a weighting factor. We use w i = S i /σ p ( S i , ρ i ) assigning a larger weight to tele-scopes with brighter images and a smaller expected dis-persion in the image parameter.A second class of discriminant variables can be ob-tained by computing a goodness-of-fit between the dataand the image template model evaluated at the best-fitshower parameters [36]. When considering Gaussian-distributed data the natural goodness-of-fit parameter isthe χ statistic. For the purposes of background dis-crimination, it is not critical to have an exact model forthe asymptotic distribution of the test statistic as long asit provides good separation power between signal andbackground. To quantify the agreement between themeasured and expected pixel signals we define a χ -likeparameter which we call the goodness-of-fit,12 .5 1.0 0.5 0.0Zenith Offset [deg]1.00.50.00.51.0 A z i m u t h O ff s e t [ d e g ] R = 150.00 m λ = 0.30 X E = 100.00 GeV φ = 0.00 ◦ I m a g e I n t e n s i t y [ P E d e g − ] A z i m u t h O ff s e t [ d e g ] R = 150.00 m λ = 0.30 X E = 100.00 GeV φ = 45.00 ◦ I m a g e I n t e n s i t y [ P E d e g − ] A z i m u t h O ff s e t [ d e g ] R = 150.00 m λ = 0.30 X E = 100.00 GeV φ = 90.00 ◦ I m a g e I n t e n s i t y [ P E d e g − ] Figure 7: Image intensity templates as a function of angular o ff set from the primary gamma-ray direction for three values of the shower positionangle: φ = ◦ , φ = ◦ , φ = ◦ . The templates shown are evaluated for a gamma-ray shower with an energy of 100 GeV, an impact distance of150 m, and an interaction depth of 0.3 X . The solid white line in each image shows the projection of the primary trajectory to the image plane. G = N (cid:88) i (cid:88) j ∈P i (cid:16) s i , j − µ i , j ( θ ) (cid:17) µ i , j ( θ ) + µ b , (22)where P i is a set of pixels in telescope i and N is thetotal number of pixels in the summation. We found thatthe best separating power was achieved by evaluatingEquation 22 using the set of telescope pixels that sur-vive image cleaning, which we refer to as the imagegoodness-of-fit .To maximally exploit the rejection power drawn fromthe ensemble of event parameters we further make useof boosted decision trees (BDTs) generated with theTMVA package [38]. The use of machine learning tech-niques have been shown to provide significant improve-ment in overall background rejection power when ap-plied to IACT data [39]. We specifically use BDTstrained with the GradBoost algorithm with 200 trees, amaximum depth of 8, and a shrinkage parameter of 0.1.We train the decision tree analysis using the followingsix parameters: mean scaled width, mean scaled length,mean scaled displacement, array core distance, first in-teraction depth, and image goodness-of-fit. In order toavoid overtraining we use a training data set that con-stitutes 20% of the total gamma-ray and proton MonteCarlo samples.
4. Results
Using the simulation and analysis frameworks de-scribed in Sections 2 and 3, we have explored the in-fluence of the telescope design on the sensitivity andgamma-ray reconstruction performance of various arraydesign concepts. Section 4.1 outlines the performancemetrics used for comparison of the arrays. Section 4.2defines a reference array alongside several benchmark configurations which are representative of realistic tele-scope and array configurations that will be chosen forCTA. In the subsequent sections we examine the influ-ence of each telescope parameter on the array perfor-mance. In Section 4.12 we study the performance of thebenchmark arrays.
Our primary metric for the comparison of di ff erent ar-ray and telescope designs is the di ff erential gamma-raypoint-source sensitivity evaluated following the stan-dard procedure for CTA-related studies [18]. The dif-ferential sensitivity is evaluated in a sequence of loga-rithmic bins of reconstructed energy with a width of 0.2dex (five bins per decade of energy). In each energy binwe calculate the expected number of signal and back-ground events within an energy-dependent aperture ofradius θ . The number of signal events is estimated as-suming a gamma-ray point-source in the center of theFoV. The residual background rate is estimated by scal-ing the number of background events reconstructed inthe inner 3 ◦ of the camera to the gamma-ray extrac-tion area. In each bin we require a 5 σ excess abovebackground and at least 10 signal events. The sourcesignificance is calculated using the method of [40] anda signal-free background region with a solid angle fivetimes larger than the signal aperture. We further requirea signal with a fractional amplitude above backgroundof 5% in order to account for systematic errors in back-ground estimation.Sensitivity to spatially extended gamma-ray sourcesis calculated following the same procedure but with thegamma-ray signal spread out uniformly over a disk withangular diameter D . For a source with a given flux, thedi ff use source sensitivity is always worse than the point-source sensitivity. In the case of a point-source, the13ensitivity depends on both background rejection e ffi -ciency and the PSF. The di ff use-source sensitivity, how-ever, depends primarily on the background rejection ef-ficiency and is nearly independent of the PSF when D islarger than the PSF.The quality of the gamma-ray reconstruction is esti-mated from the simulated gamma-ray PSF, shower coreresolution, and energy resolution. The most importantof these quantities is the gamma-ray PSF as it directlyimpacts the sensitivity to point-sources and the mor-phology of extended gamma-ray sources. We charac-terize the gamma-ray PSF by the radius that contains68% of the distribution of reconstruction errors (68%containment radius).When evaluating the performance of an array we ap-ply several selection criteria to reject both backgroundevents and gamma-ray events with poor reconstructionquality. Point-source cuts are composed of two energy-dependent selections on the gamma / hadron rejection pa-rameter and aperture radius, ξ ( E ) and θ ( E ), parame-terized as a cubic spline. The shape of these param-eterizations is independently optimized for each arrayand exposure time to maximize the di ff erential point-source sensitivity versus energy. At high energies wherethe sensitivity of IACT arrays transitions from beingbackground- to signal-limited, the optimal point-sourcesensitivity is obtained by increasing the gamma-ray e ffi -ciency and including events with poorer reconstructionquality and a higher background contamination level. Di ff use-source cuts are used when evaluating di ff usesource sensitivity and comprise the same selection onthe gamma / hadron parameter but with the aperture sizefixed to the radius of the source ( θ ( E ) = D / Reconstruction cuts are used to define a homoge-neous sample of well-reconstructed showers with corelocations within a predefined fiducial area of the array.Showers passing reconstruction cuts must have an im-pact distance from the array center that is less than 1.2times the distance from the center of the array to thenearest point along the array edge (as defined by theouter ring of telescopes). Showers with core locationsnear or within the array boundary ( contained events)are sampled by a large number of telescopes that viewthe shower from multiple perspectives and allow for amore precise stereoscopic reconstruction of the showertrajectory. In arrays with mean telescope separationson par with the Cherenkov light pool size, containedevents will also have one or more telescopes that samplethe shower within its Cherenkov light pool, where theCherenkov light from the highest energy shower parti-cles is visible. The light emitted from these particlesprovides a much better constraint on the shower trajec-
Table 1: Geometrical characteristics and optical performance of thecamera and optical systems of the DC-MST, SC-MST, and LST tele-scope designs chosen for the prod-2
MC design study [33]. The o ff -axis PSF performance is evaluated at a field angle equal to 3 / D pix is the width of a square pixel with the same solid angle as thehexagonal pixel used in that design. LST SC-MST DC-MST D pix [ ◦ ] 0.084 0.067 0.171 A M [m ] 412 50 100 A opt [m ] 52.5 7.29 13.65 R psf [ ◦ ] (on-axis) 0.03 0.04 0.04 R psf [ ◦ ] (o ff -axis) 0.12 0.04 0.08FoV [ ◦ ] 4.5 8 8tory than the light emitted by lower energy shower par-ticles. Events outside the array boundary ( uncontained events) are sampled by a smaller number of telescopesfor which the viewing angles are more closely aligned.This results in a less precise determination of the showertrajectory.Reconstruction cuts provide a measure of the gamma-ray reconstruction performance that can be evaluated in-dependently of the source strength and exposure time.Relative to point-source cuts, reconstruction cuts o ff erworse point-source sensitivity but a significantly bettergamma-ray PSF at high energies (above 1 TeV). Theimprovement in the gamma-ray PSF can be attributedto the removal of uncontained events which are brightenough to trigger the array at high energies. This se-lection is very useful when studying strong sources tocheck morphology and spectral features while not rely-ing on the best signal-to-noise ratio. The baseline CTA concept is an array of 50–100 tele-scopes distributed over an area of ∼ and com-posed of small-, medium-, and large-sized telescopes.Previous simulation studies have found that intermedi-ate layouts with a few (3-4) large-sized, on the order of20 medium-sized, and 50–60 small-sized telescopes of-fers the best tradeo ff in performance over the full energyrange of CTA [18]. Table 1 shows the primary char-acteristics of the currently considered designs for thelarge- and medium-sized telescopes. The LST designis optimized for sensitivity at gamma-ray energies be-low 100 GeV and features a large e ff ective mirror areawhich enables e ffi cient triggering and reconstruction oflow energy showers. The DC-MST and SC-MST aretwo alternative designs for the medium-sized telescopethat would provide sensitivity in the core energy range14f CTA (100 GeV–10 TeV). The DC-MST is a singledish telescope that is similar in overall design to currentgeneration IACTs with a camera composed of hexago-nal pixels with flat-to-flat spacing of 0.184 ◦ . The SC-MST employs the dual-mirror Schwarzschild-Couderoptical design and uses a smaller pixel size of 0.067 ◦ to achieve higher resolution imaging of the gamma-rayshower. Ray-tracing simulations of the SC-MST OSwith realistic alignment tolerances for the mirrors andcamera focal plane have demonstrated an optical PSFwith a 68% containment radius between 0.02 ◦ and 0.04 ◦ [21]. Although the array designs considered for previ-ous MC studies only incorporated DC-MSTs, the higherangular resolution SC-MST provides a potentially com-pelling option for the medium-sized CTA telescope.We consider several di ff erent benchmark array con-figurations shown in Table 2 to explore the performanceof di ff erent array and telescope designs for CTA. M61is a reference array configuration with an e ff ective lightcollection area that is intermediate between the DC- andSC-MST designs and an imaging performance similarto the SC-MST. M61SC is an array configuration withthe same imaging performance as M61 but with a re-duced light collection area that is more comparable tothe SC-MST design. M61DC and M25DC are chosen torepresent a 61 and 25 telescope array respectively com-posed of telescopes of the DC-MST design. The latterconfiguration corresponds to the number of MSTs in thebaseline CTA design [18]. Arrays L5 and L61 are com-posed of telescopes with an optical e ff ective area com-parable to the LST design and an imaging performancesimilar to the SC-MST.We show in Figure 8 the trigger e ff ective area for ar-rays M61, M61SC, M61DC, and L61. The camera trig-ger threshold of each array is set using the telescope ef-fective light collection area and Equation 4. The sharpdownturn in the e ff ective area of the MST arrays around100 GeV can be attributed to the onset of the triggerenergy threshold. Below the trigger threshold energy,the image amplitude of an average gamma-ray showeris insu ffi cient to trigger telescopes within the Cherenkovlight pool. At these energies only showers with largeinteraction depth can be e ff ectively recorded, and thetotal e ff ective area is primarily determined by the trig-ger e ffi ciency for contained showers that impact withinthe array perimeter. At higher energies all of the arraysbecome fully e ffi cient for triggering contained showersand di ff erences in the e ff ective area arise predominantlyfrom the e ffi ciency for detecting showers around the ar-ray perimeter. As the shower energy increases, the area Equivalent in solid angle to square pixels with D pix = . ◦ . Energy [GeV]10 E ff e c t i v e A r e a [ m ] M61SCM61M61DCL61
Figure 8: Trigger e ff ective area versus gamma-ray energy for arraysM61SC, M61, M61DC, and L61. The camera trigger thresholds ( T th )for these arrays are 45, 60, 80, and 123 PE respectively. over which the arrays are fully e ffi cient continues to in-crease and eventually extends well beyond the physicalfootprint of the array. Relative di ff erences in the e ff ec-tive area for telescopes with di ff erent A opt are signifi-cantly smaller at the highest energies as gains in the ef-fective area only come from showers around the arrayperimeter. The simplifications in the detector response of theFAST simulation yield a much faster simulation codeand enables the study of a broader parameter spacecompared to more detailed telescope simulations. Oursimplified telescope model also enables us to employa shower likelihood model which is nearly perfectlymatched to the response characteristics of the tele-scopes. These simplifications allow us to explore thetheoretical limit of the performance achievable by anIACT array when all characteristics of the telescope op-tics and camera are accounted for in the event recon-struction.We have assessed the impact of the simplificationsmade in the FAST tool on the derived point-sourcesensitivity and gamma-ray PSF by comparing FASTagainst the well-tested sim telarray package. Weuse both packages to simulate a 61 telescope arraywith the same geometry as our benchmark array lay-out with 120 m inter-telescope separation. For the sim telarray simulation we use the prod-2
SCTmodel [33] with a trigger pixel threshold of 3.1 PE. Forthe FAST simulations, we use a telescope model withthe same performance characteristics as the prod-2
SCT15 able 2: Number of telescopes and telescope model parameters of the benchmark array configurations used for this study. All arrays are composedof telescopes arranged on a uniform grid with constant inter-telescope spacing of 120 m as shown in Figure 1.
Name N tel A opt [m ] D pix [ ◦ ] R psf [ ◦ ] T th [PE] R nsb [MHz]M61 61 11.18 0.06 0.02 60 14.7M61SC 61 8.38 0.06 0.02 45 11.1M61DC 61 14.91 0.16 0.08 80 139.5M25DC 25 14.91 0.16 0.08 80 139.5L5 5 47.15 0.06 0.02 123 61.9L61 61 47.15 0.06 0.02 123 61.9 -14 -13 -12 -11 -10 E d F / d E [ e r g c m − s − ] FASTsim_telarrayArray I (Bernlöhr et al. 2013)10 Energy [GeV]0.40.60.81.01.21.41.61.82.0 R a t i o % C o n t a i n m e n t R a d i u s [ d e g ] FASTsim_telarray10 Energy [GeV]0.60.81.01.21.4 R a t i o Figure 9: Performance of a 61 telescope array simulated with FAST (black squares) and sim telarray (blue circles).
Left: Di ff erential point-source sensitivity for a 50 h observation time. Shown as the solid gray line is the di ff erential sensitivity of Array I from [18] evaluated with themost sensitive analysis at each energy from the four alternative analyses presented in that work (MPIK, IFAE, SAM, and Paris-MVA). Right: point-source cuts . model shown in Table 1 and a camera trigger thresholdof 42 PE. Relative to the telescope model used for theM61SC benchmark array, the prod-2 SCT model has alarger pixel size and optical point-spread function anda slightly smaller light collection area. For gamma-rayshowers near the trigger threshold (E ∼
100 GeV), the sim telarray telescope model has a slightly lower ef-fective camera threshold as compared to the telescopein our simplified simulations. The choice of a higherthreshold for our simulations was made to be conser-vative and limit possible overestimations in sensitivityclose to the threshold.Fig. 9 shows the comparison of the array perfor-mance obtained when simulating the same array with sim telarray and FAST. We include in the same fig-ure the point-source sensitivity of Array I from [18]which was simulated using sim telarray but with adi ff erent array and telescope setup. At energies above75 GeV the point-source sensitivity obtained with theFAST simulations is 20% better than the sim telarray simulations. The gamma-ray PSF and gamma-ray re- construction e ffi ciency is similar over the same energyrange indicating that the improvement in point-sourcesensitivity can be attributed to an enhanced gamma-hadron separation in the FAST simulations. Below50 GeV the sim telarray simulations yield a 40%better sensitivity due to the slightly lower telescopetrigger threshold. Although we observe measurabledi ff erences in the array performance when comparingour simulations with sim telarray , the di ff erences inpoint-source sensitivity are much smaller than the dif-ferences between individual analysis packages that usethe same sim telarray simulations as input (see e.g.the comparison of alternative analyses in [18]). Further-more the conclusions drawn in this work about the rel-ative performance of di ff erent array and telescope de-signs is most likely not a ff ected by these di ff erences.It is thus easy to scale our results and readily comparethem to other sim telarray results.16 -14 -13 -12 -11 -10 E d F / d E [ e r g c m − s − ] LikelihoodLikelihood (No GoF)Moment10 Energy [GeV]0.51.01.52.02.5 R a t i o % C o n t a i n m e n t R a d i u s [ d e g ] LikelihoodLikelihood (No GoF)Moment10 Energy [GeV]0.60.81.01.21.41.6 R a t i o Figure 10: Reconstruction performance and gamma-ray point-source sensitivity of array M61 obtained with di ff erent event reconstruction andanalysis algorithms: likelihood (black, solid), likelihood without goodness-of-fit (blue, dashed), and moment (red, dot-dashed). Left: Di ff erentialpoint-source sensitivity for a 50 h observation time. Right:
68% containment radius of the gamma-ray PSF after point-source cuts . Relative to moment-based reconstruction techniques,likelihood-based reconstruction algorithms have beenshown to provide better gamma-ray angular resolutionas well as improved separation between gamma-rayand cosmic-ray induced showers [41, 36, 18]. We as-sess the relative improvement from the likelihood ap-proach by comparing its performance with an analysisthat uses only the geometric trajectory reconstructionand moment-based image parameterization described inSection 3.2 which we refer to here as the moment re-construction. Because the moment reconstruction ismore sensitive to the presence of noise fluctuations inthe image, we use a slightly higher cleaning thresh-old ( ¯ s /σ =
9) than the threshold used for the likeli-hood analysis. We use a BDT background discriminanttrained with the same settings described in Section 3.3but excluding parameters derived from the likelihoodanalysis.Figure 10 shows the comparison of the point-sourcesensitivity obtained with the moment analysis, the like-lihood analysis, and a likelihood analysis in which thegoodness-of-fit (GOF) parameter is excluded from thetraining of the decision tree. With the likelihood-basedanalysis, we find a factor of two improvement in point-source sensitivity and a 30-40% improvement in thegamma-ray PSF over the full energy range. As seenfrom the comparison between the likelihood analysesperformed with and without the GOF parameter, the im-provement in the point-source sensitivity is attributableto gains in both the gamma-ray angular resolution andthe background rejection power. The addition of the GOF parameter provides an additional 30% improve-ment in sensitivity.We also observe that the energy threshold for the like-lihood analysis is considerably lower ( E th (cid:39)
50 GeV)relative to the moment reconstruction ( E th (cid:39)
100 GeV).The improved performance of the likelihood analysis atlow energies can be attributed to both the higher im-age reconstruction e ffi ciency and the smaller bias of thelikelihood energy estimator. Because the likelihood re-construction is insensitive to the inclusion of pixels withsmall signals, the cleaning threshold can be optimized tomaximize the reconstruction e ffi ciency for low-energyshowers without impacting the performance at higherenergies. The deflection of charged particles in the EM showerby the geomagnetic field (GF) can significantly distortthe shapes of gamma-ray images recorded by IACTs[42, 43, 44]. The strength and orientation of the GF isthus an important consideration for the selection of can-didate sites for an IACT observatory. Its influence canbe as large or larger than the site elevation [45]. Themagnitude of the induced deflection is proportional tothe perpendicular component of the GF ( B ⊥ ) and there-fore the strength of the GF e ff ect depends on both themagnitude of the GF vector as well as its orientationrelative to the shower trajectory. Due to the asymmetryin the shower shape induced by the GF, the distortionvisible to a telescope also depends on the orientation ofthe shower impact point relative to the telescope posi-tion. Telescopes with shower position angles close to 0 ◦ -14 -13 -12 -11 -10 E d F / d E [ e r g c m − s − ] µ T10.35 µ T20.7 µ T10 Energy [GeV]0.70.80.91.01.11.21.31.41.51.6 R a t i o -2 -1 % C o n t a i n m e n t R a d i u s [ d e g ] µ T10.35 µ T 20.7 µ T 0 µ T ( λ> . X )10.35 µ T ( λ> . X )20.7 µ T ( λ> . X )10 Energy [GeV]0.70.80.91.01.11.21.31.41.51.6 R a t i o Figure 11: Performance of array M61 simulated with the equatorial GF ( B ⊥ = . µ T; red diamonds and solid line), a GF configuration witha reduced perpendicular component ( B ⊥ = . µ T; blue circles and solid line), and no GF (black squares and solid line).
Left: Di ff erentialpoint-source sensitivity for a 50 h observation time. Right:
Gamma-ray angular resolution (68% containment radius) after reconstruction cuts.Dashed curves show the same comparison for gamma-ray showers with an interaction depth ( λ ) greater than 1.0 X . or 180 ◦ see a larger GF e ff ect as the GF-induced elon-gation in the shower occurs primarily in the plane per-pendicular to the telescope pointing.To obtain a realistic assessment of the GF e ff ect forany given observatory site would require simulationswith many telescope orientations as they occur for re-alistic observation profiles of gamma-ray sources. Wedid not carry out such simulations and instead focusedon the e ff ect of the GF for a few representative valuesof B ⊥ . Our baseline site configuration has ( B x , B z ) = (27 . µ T , − . µ T) with B ⊥ = . µ T when observ-ing a shower with Zn = ◦ and Az = ◦ . To test theinfluence of the GF strength we performed simulationsof array M61 for two additional site models: a site with( B x , B z ) = (19 . µ T , − . µ T) that has a perpendicu-lar GF component that is half as large as for our baselinesite ( B ⊥ = . µ T) and a site with no geomagneticfield. By limiting ourselves to these few cases we canonly give a general guidance for e ff ects of the magneticfield on any observable gamma-ray source. Dependingon the specific source observation profile, the e ff ect ofthe GF for an individual source might be di ff erent.The configurations we tested have a range offield strengths that are comparable to the southernHemisphere sites considered for CTA. The Namib-ian H.E.S.S. site and the Argentinian Leoncito siteshave ( B x , B z ) = (12 . µ T , − . µ T) and ( B x , B z ) = (20 . µ T , − . µ T), respectively [45]. Because thestrength and orientation of the GF is generally a slowlyvarying function of the site latitude and longitude thesetwo sites provide a good representation of the expected GF e ff ect for sites in Africa and South America. Whenobserving a shower at Zn = ◦ and Az = ◦ the Namib-ian and Argentinian sites have perpendicular compo-nents of 2 . µ T and 14 . µ T. However a more realisticmeasure of the expected GF e ff ect is the average perpen-dicular component over the range of azimuth angles thata gamma-ray source is observed. The Namibian and Ar-gentinian sites have an average GF strength at Zn = ◦ of 13 . µ T and 19 . µ T, respectively.The comparison of the array performance for thethree GF configurations is presented in Figure 11. Wefind that the e ff ect of the GF strength is strongest at100 GeV where the point-source sensitivity is reducedby 50% when increasing B ⊥ from 0 µ T to 20 . µ T. Wealso observe that the e ff ect of the GF scales linearly with B ⊥ such that the site configuration with B ⊥ = . µ Tsu ff ers approximately half of the reduction in sensitiv-ity relative to our baseline site configuration. Belowenergies of 100 GeV, the e ff ect of the GF is lessenedbecause only gamma rays that convert deep in the at-mosphere can be e ffi ciently reconstructed. The lowerthe particle interacts in the atmosphere the less it is af-fected by the GF. At higher gamma-ray energies the im-pact of the GF is lessened due to both the higher energyof the secondary particles and the larger path length inthe atmosphere. As shown in the right panel of Fig-ure 11 the GF worsens the point-source sensitivity pri-marily by degrading the gamma-ray PSF. For showerswith interaction depths larger than 1 X , di ff erences inthe gamma-ray PSF between the di ff erent GF configu-rations are found to be less than 20% illustrating that18he influence of the GF increases with decreasing inter-action depth. The telescope design has a large impact on the result-ing gamma-ray PSF obtained with the complete array.The optical design of the individual telescopes definestheir achievable optical PSF and the camera design de-termines how e ffi ciently the optical PSF can be trans-lated into an improved gamma-ray PSF. For a given op-tical PSF, the gamma-ray PSF can be improved by re-ducing the camera pixel size. In the limit that the pixelsize is much smaller than the PSF, the improvement ofthe gamma-ray PSF saturates and a further reduction inpixel size does not provide any measurable advantagebut increases the cost of the camera. Thus the optimaltradeo ff between performance and cost is one in whichthe pixel size is appropriately matched to the quality ofthe optical PSF. Current generation IACTs have camerasusing pixel sizes from 0.1 ◦ to 0.16 ◦ and an optical PSFat the center of the FoV which is considerably smallerthan the pixel size. Here we explore a new parameterspace for the IACT imaging resolution by examining theperformance of camera designs with pixel sizes between0.04 ◦ and 0.1 ◦ . Such designs begin to resolve the coreof the Cherenkov shower which has an intrinsic angularsize of ∼ ◦ .The left panel of Fig. 12 shows the gamma-ray PSFversus pixel size for arrays with di ff erent optical PSFs.For an optical PSF of 0 . ◦ the gamma-ray PSF showsonly a modest improvement of ∼
10% when reducingthe pixel size from 0 . ◦ to 0 . ◦ . An optical PSF be-tween 0 . ◦ and 0 . ◦ is found to be critical to real-ize the full improvement in gamma-ray PSF that can beachieved by reducing the camera pixel size below 0 . ◦ .The improvement of the gamma-ray PSF at di ff erent en-ergies when reducing the pixel size is shown in Fig. 12.The gamma-ray PSF is significantly better at all ener-gies when reducing the pixel size. There is a slight mod-ulation seen in the improvement versus energy morepronounced for larger pixel sizes. The smaller pixel sizeperforms best at low and high energies ( E <
100 GeVand E > . . ◦ to 0 . ◦ demonstrates a realistic di ff erence between cur-rently considered optical telescope designs for CTA.The e ff ect of the pixel size on the di ff erential point-source sensitivity is shown in Fig.13. The pixel size hasthe strongest impact at low energies ( <
100 GeV) wherea factor of two relative improvement is observed when the pixel size is reduced from 0 . ◦ to 0 . ◦ . At higherenergies the smaller pixel size results in a smaller butstill measurable improvement in point-source sensitiv-ity of 30-40%. Above 3 TeV di ff erences between ad-jacent pixel sizes become indistinguishable due to thelimited background statistics that make evaluation ofsmall sensitivity di ff erences very di ffi cult. The gamma-ray PSF is clearly improved over the complete energyrange by about 50% as the pixel size is reduced from0 . ◦ to 0 . ◦ . The observed improvement in sensitiv-ity demonstrates that the intrinsic shower features thatcan be used for background suppression and directionreconstruction are still smaller than the pixel sizes ofcurrently operating Cherenkov telescopes. The telescope light collection area determines thesignal-to-noise ratio (SNR) of the shower images andthe e ffi ciency with which these images can be recordedby the telescope trigger. Therefore we expect that alarger A opt increases the trigger e ffi ciency and providesbetter defined images and hence improves performanceof the array. The role of the A opt parameter is partic-ularly relevant for the performance of the array at lowenergies where the smaller light yield per image makesreconstruction and analysis of the gamma-ray showersmore challenging.The assumed design, size, and cost of the proposedtelescopes yields distinct A opt values. We studied the ef-fect of the A opt on the gamma-ray PSF and point-sourcesensitivity of the array by examining the performanceof telescope models with A opt between 2 m and 50 m .These models span the range of light collection areasbetween SST-like and LST-like telescope designs. TheSST, MST, and LST telescope designs have A opt of ap-proximately 1–2 m , 5–10 m , and ∼
50 m respectively[46, 33].Figure 14 shows the comparison of the gamma-rayPSF and point-source sensitivity for telescopes with A opt between 1.98 m (SST-like) and 47.15 m (LST-like). A opt has only a minor e ff ect on the gamma-ray PSF inmost of the energy range investigated here. In the mid-dle energy range between 100 GeV and 1 TeV we findan improvement of 5–10 % when increasing the tele-scope light collection area from 11.18 m to 47.15 m .The almost insignificant improvement around 100 GeVis caused by a selection e ff ect of the reconstructedgamma-ray events. At these low energies, telescopeswith smaller A opt can only trigger on the brightest show-ers that convert deep in the atmosphere. As discussed inSection 4.5 the larger interaction depth of these showers19 .05 0.10 0.15 0.20Pixel Size [deg]0.0300.0350.0400.0450.0500.055 % C o n t a i n m e n t R a d i u s [ d e g ] R psf = 0.02 ◦ R psf = 0.04 ◦ R psf = 0.08 ◦ -2 -1 % C o n t a i n m e n t R a d i u s [ d e g ] R pix = 0.06 ◦ R pix = 0.12 ◦ R pix = 0.20 ◦ Energy [GeV]0.91.01.11.21.31.41.51.61.7 R a t i o Figure 12:
Left:
68% containment angle of the gamma-ray PSF at 317 GeV versus camera pixel size for telescope models with di ff erent opticalPSFs ( R psf ): 0 . ◦ (black squares), 0 . ◦ (blue circles), 0 . ◦ (red diamonds). The gamma-ray PSF is evaluated after applying reconstruction cuts .The baseline configuration for all simulations is array M61. Right:
68% containment angle of the gamma-ray PSF versus gamma-ray energy forarray M61 with R psf = . ◦ simulated with di ff erent telescope pixel sizes: 0 . ◦ (black squares), 0 . ◦ (blue circles), 0 . ◦ (red diamonds). lessens the impact of the GF and results in a more ac-curate reconstruction of the direction. Larger telescopescan e ffi ciently trigger on showers with both large andsmall interaction depths which results in a larger e ff ec-tive area but a worsening of the overall gamma-ray PSF.This e ff ect reverses at the very lowest energies (30–50 GeV) where the reduced SNR images recorded bytelescopes with small A opt dominates the reconstructionquality.The light collection area has a measurable impacton the point-source sensitivity only at energies below300 GeV with telescopes with larger light collectionarea yielding better sensitivity. The increase in sensi-tivity is most significant below 100 GeV and is a re-sult of the reduction in the telescope trigger thresholdand resulting increase in the gamma-ray e ff ective area.The larger light collection area also yields better SNR inthe shower images improving the reconstruction of lowenergy events. At higher energies the impact of lightcollection area is significantly reduced as the array be-comes fully e ffi cient for triggering and reconstructingevents that impact within the array boundary. Improvingthe image SNR provides little improvement at these en-ergies because the reconstruction is predominantly lim-ited by intrinsic shower fluctuations. Remarkably theimprovement in point-source sensitivity is almost neg-ligible between telescopes with 26 .
51 m and 47 .
15 m over the whole energy range.The observed improvements in array performanceabove the trigger threshold are small when consider-ing that light collection area is the dominant parameter influencing the telescope cost. Given the small di ff er-ences in reconstruction performance, the primary moti-vation for choosing a telescope design with larger lightcollection area is to reduce the array energy threshold.However for an array of fixed cost increasing the lightcollection area also entails a reduction in the number oftelescopes. For gamma-ray energies between 100 GeVand 1 TeV, a telescope with A opt of 5–10 m (MST-like)clearly provides the best performance to cost ratio. Ar-ray designs that include a small number of telescopeswith larger light collection area can lower the energythreshold while keeping the cost of the total array withinreasonable limits. Performance of arrays with di ff er-ent numbers of telescopes are studied further in Section4.11. The inter-telescope separation determines both thephysical area of the array footprint as well as the averagenumber of telescopes that will participate in the recon-struction of individual showers. Smaller telescope sep-arations improve reconstruction quality for containedshowers at the cost of lowering the total e ff ective areaof the array. Larger telescope separations are generallypreferred when optimizing for sensitivity at higher en-ergies since the point-source sensitivity of IACT arraysat moderate exposures (10–50 hours) is signal limitedabove 1–3 TeV. Another important consideration whenoptimizing the telescope separation is the number oftelescopes within the Cherenkov light pool. Telescopeswithin the Cherenkov light pool sample light emitted by20 -14 -13 -12 -11 -10 E d F / d E [ e r g c m − s − ] ◦ ◦ ◦ ◦ ◦ Energy [GeV]0.40.60.81.01.21.41.61.8 R a t i o % C o n t a i n m e n t R a d i u s [ d e g ] ◦ ◦ ◦ ◦ ◦ Energy [GeV]0.60.81.01.21.41.61.8 R a t i o Figure 13: Performance of array M61 simulated with pixel sizes from 0 . ◦ to 0 . ◦ . Left: Di ff erential point-source sensitivity for a 50 hobservation time. Right:
68% containment angle of the gamma-ray PSF evaluated after point-source cuts. -14 -13 -12 -11 -10 E d F / d E [ e r g c m − s − ] Energy [GeV]0.00.51.01.52.02.53.0 R a t i o -2 -1 % C o n t a i n m e n t R a d i u s [ d e g ] Energy [GeV]0.80.91.01.11.21.31.41.5 R a t i o Figure 14: Performance of array M61 simulated with di ff erent values of A opt : 1.98 m (black squares), 4.71 m (blue circles), 11.18 m (reddiamonds), 26.51 m (magenta triangles), and 47.15 m (cyan triangles). Left: Di ff erential point-source sensitivity for a 50 h observation time. Right:
68% containment angle of the gamma-ray PSF after reconstruction cuts. higher energy particles in the shower core and providea more accurate determination of the shower trajectory.Telescope separations that are comparable to the size ofthe Cherenkov light pool (100–150 m) ensure that mul-tiple telescopes will sample each shower within its lightpool. Finally smaller separations may potentially im-prove background rejection by increasing the e ffi ciencyfor detecting Cherenkov light from hadronic subshow-ers produced in cosmic-ray background events.The impact of the telescope separation on the gamma-ray PSF is illustrated in the top panel of Fig. 15 whichshows a comparison of arrays with separations between60 m and 200 m. In this comparison we consider onlyshowers passing reconstruction cuts with core positions near or within the array boundary. These cuts selectevents with the best PSF and reduce the di ff erences inperformance caused by the finite array size. The re-duction of the telescope grid spacing from 120 m to60 m results in a 20% improvement of the gamma-rayPSF between 30 GeV and 10 TeV. However this rathersmall improvement would require a quadrupling in thenumber of telescopes to cover a similar area. Thus theimprovement of the gamma-ray PSF from reducing thetelescope spacing has to be compared to the reduction ofe ff ective detector area when fixing the number of avail-able telescopes.The lower left and right panels of Fig. 15 show thegamma-ray PSF and point-source sensitivity for the set21 -2 -1 % C o n t a i n m e n t R a d i u s [ d e g ]
60 m80 m120 m160 m200 m10 Energy [GeV]0.70.80.91.01.11.21.31.41.51.6 R a t i o Energy [GeV]10 E ff e c t i v e A r e a [ m ]
60 m80 m120 m160 m200 m10 -14 -13 -12 -11 -10 E d F / d E [ e r g c m − s − ]
60 m80 m120 m160 m200 m10 Energy [GeV]0.00.51.01.52.02.5 R a t i o % C o n t a i n m e n t R a d i u s [ d e g ]
60 m80 m120 m160 m200 m10 Energy [GeV]0.60.81.01.21.41.61.82.0 R a t i o Figure 15: Performance of array M61 simulated with di ff erent inter-telescope separations: 60 m (black squares), 80 m (blue circles), 120 m (reddiamonds), 160 m (magenta triangles) and 200 m (cyan triangles). Top Left:
68% containment angle of the gamma-ray PSF after reconstruction cuts.
Top Right:
Gamma-ray e ff ective area after point-source cuts. Bottom Left: Di ff erential point-source sensitivity for a 50 h observation time. Bottom Right:
68% containment angle of the gamma-ray PSF after point-source cuts . of telescope separations evaluated with a selection op-timized for point-source sensitivity. The increase ofe ff ective area with larger telescope spacing generallyoutweighs the reduction of sensitivity due to a worsen-ing of the gamma-ray PSF. The point-source sensitivityimproves with increasing telescope spacing at energiesabove 100 GeV with the best sensitivity achieved witha telescope spacing of 160–200 m. When increasing thetelescope spacing to 200 m a noticeable worsening ofthe sensitivity below 300 GeV is seen because the num-ber of individual telescopes triggering on each event isreduced and hence the information available for direc-tion and particle type reconstruction.When evaluated with point-source cuts as shown inthe bottom right panel of Fig. 15, the gamma-ray PSFabove 300 GeV becomes worse as the telescope separa-tion is decreased. Although a smaller separation gives a better reconstruction for contained events, the smallerarray footprint results in a larger fraction of uncontainedevents which tend to dominate the PSF at high energies.This emphasizes that for most applications where themaximum sensitivity of the array is required the PSFhas a quite di ff erent behavior compared to the theoret-ically possible behavior. A wider spacing of the MSTswill provide a much better performance for most sci-ence cases compared to a narrow spacing that would beonly beneficial for the very few cases where the gamma-ray PSF is much more important than sensitivity. Thusthe best spacing for the MSTs for all purposes is about160 m. The telescope trigger threshold is an important quan-tity to determine the accessible energy range by any22 -14 -13 -12 -11 -10 E d F / d E [ e r g c m − s − ]
34 PE45 PE60 PE80 PE10 Energy [GeV]0.00.51.01.52.02.53.0 R a t i o Energy [GeV]10 E ff e c t i v e A r e a [ m ]
34 PE45 PE60 PE80 PE
Figure 16: Performance of array M61 simulated with di ff erent camera trigger thresholds: 34 PE (black squares), 45 PE (blue circles), 60 PE (reddiamonds), 80 PE (magenta triangles). Left: Di ff erential point-source sensitivity for a 50 h observation time. Right:
Gamma-ray e ff ective areaafter point-source cuts. telescope array. The impact of the individual tele-scope trigger threshold is studied on the di ff erentialpoint-source sensitivity of the M61 baseline array (seeFig. 16). As expected for an MST-like array with A opt (cid:39)
10 m the trigger threshold has little e ff ect on the sen-sitivity at energies above 100 GeV. At higher energiesthe telescope trigger becomes fully e ffi cient for show-ers impacting within the array and reducing the triggerthreshold only increases the e ffi ciency for showers onthe array periphery. Because these distant showers aregenerally not well reconstructed they do not contributeto the array sensitivity.Reducing the telescope trigger threshold of Ar-ray M61 is found to significantly improve the point-source sensitivity below 100 GeV. A reduction of thetrigger threshold from 80 PE to 34 PE results in a sig-nificant improvement at energies below 100 GeV andreaches up to an order of magnitude at 30 GeV. How-ever, in a realistic telescope design the accidental triggerrate can not be arbitrarily high due to the limitations onthe readout rate that can be sustained by the telescopedata acquisition. The 60 PE e ff ective trigger thresholdchosen for Array M61 is a realistic target for a trig-ger implementation that follows the same design usedby current generation IACTs. Lower trigger thresholdsmay be achievable by employing more sophisticated de-signs for the camera- and array-level triggers such as re-quiring additional trigger topologies for individual tele-scopes or higher multiplicities for the array trigger. Iffurther improvements in the performance of the triggercan be realized then the presented sensitivities at low en-ergies could be further improved. Furthermore, it is evi- dent that the likelihood reconstruction is very e ffi cient atlow energies and that any reduction in trigger thresholdis directly translated into an improvement in sensitivity.The same statement is not necessarily true for the mo-ment reconstruction that usually has a higher analysisthreshold compared to the likelihood reconstruction asshown in Fig. 10. Night-sky background (NSB) is caused by the pres-ence of light sources such as stars, the Moon, and arti-ficial light pollution and represents an irreducible back-ground for the reconstruction and analysis of gamma-ray air showers. Because the Cherenkov photons de-tected in a single pixel have an intrinsic arrival time dis-persion of 3–6 ns, IACTs can significantly reduce theNSB by integrating the Cherenkov signal in a narrowtime window (typically with ∆ T ∼
10 ns). The inte-grated NSB level thus depends on both the NSB rate aswell as the size of the window used for signal integra-tion. The need for a small integration window motivatescamera designs with high bandwidth readout electronicswhich would allow the integration window to be madeas small as possible. The impact of the NSB rate on thesensitivity of the array is also important when consid-ering possible observatory sites and performing obser-vations during moonlight. Moonlight observations canconsiderably increase the duty cycle of the observatoryalthough the exact amount of observation time gaineddepends on the NSB rate that the individual telescopecan handle.We studied the impact of NSB on the performance23 -14 -13 -12 -11 -10 E d F / d E [ e r g c m − s − ] M61DCM61DC (NSB x3)M61DC (NSB x6)M61SCM61SC (NSB x3)M61SC (NSB x6)10 Energy [GeV]0.00.51.01.52.02.53.03.54.0 R a t i o Energy [GeV]10 E ff e c t i v e A r e a [ m ] M61DCM61DC (NSB x3)M61DC (NSB x6)M61SCM61SC (NSB x3)M61SC (NSB x6)
Figure 17: Performance of arrays M61DC (red) and M61SC (blue) simulated with a baseline NSB flux of 365 MHz deg − m − (circles and solidlines) and an NSB flux that is 3 (dashed) and 6 (dash-dotted) times higher than the baseline value. Left: Di ff erential point-source sensitivity for a50 h observation time. Right:
Gamma-ray e ff ective area after point-source cuts. of the array by performing simulations with three NSBflux levels: a baseline flux level with an integral fluxof 365 MHz deg − m − and NSB fluxes that are 3 and6 times higher than the baseline flux. As described inSection 2.3, the baseline flux level corresponds to theexpected night-sky intensity for a dark, extragalacticfield. The higher NSB fluxes are representative of eithera higher NSB rate due to operation under high night-skybrightness (moonlight) or a longer e ff ective integrationwindow. A higher NSB rate also increases the rate ofaccidental triggers and would require a higher triggerthreshold in order to maintain the accidental trigger rateat a constant level. For this study we kept the triggerthreshold fixed at its nominal value and only examinethe impact of the NSB on the pixel SNR.Figure 17 shows the comparison of the point-sourcesensitivity and gamma-ray e ff ective area of arraysM61SC and M61DC simulated at the three NSB levels.The NSB level only appreciably a ff ects the sensitivitybelow 300 GeV where the SNR of the shower imageis lowest. Most of the reduction in sensitivity is a re-sult of the lower reconstruction e ffi ciency as low SNRimages are removed at the cleaning stage of the anal-ysis. Remarkably the reduction in sensitivity is muchmore pronounced in the case of larger pixels (DC-liketelescope). In case of the SC telescope design, opera-tion at a six times higher NSB rate would only degradethe sensitivity below about 100 GeV and only up to afactor of two. The DC-like design would also su ff er sig-nificant sensitivity loss only below about 100 GeV butto a much greater degree. Here it should be noted thatthe sensitivity advantage of the DC telescopes below 50 GeV under low NSB is lost in case of three times in-creased NSB and that the SC design is better for sixtimes higher NSB at all energies. One of the most important parameters concerning thesensitivity of an IACT array is the number of telescopes.A larger number of telescopes increases both the totale ff ective area for triggering and reconstructing gamma-ray showers but also increases the average number oftelescopes that participate in the reconstruction of eachshower. Increasing the number of telescopes leads tobetter point-source sensitivity and an improved gamma-ray PSF.Figure 18 compares the performance of arrays withbetween 5 and 61 telescopes. We investigate the scal-ing relation of the improvement in sensitivity with in-creasing number of telescope. In the limit of an infi-nite array the point-source sensitivity should scale withthe number of telescopes as N / . However we observean increase of sensitivity that is slightly better than theN / at all energies. This emphasizes that in the caseof small telescope arrays increasing the number of tele-scopes yields larger improvements as compared to thecase of extending large arrays. Adding 36 telescopes toa 25 telescope array improves the sensitivity by a factorof ∼ E <
300 GeV the im-provement is only clearly visible between 5 and 13 tele-24 -14 -13 -12 -11 -10 E d F / d E [ e r g c m − s − ] N = 5N = 13N = 25N = 41N = 6110 Energy [GeV]0.00.51.01.52.02.53.03.5 R a t i o % C o n t a i n m e n t R a d i u s [ d e g ] N = 5N = 13N = 25N = 41N = 6110 Energy [GeV]0.00.51.01.52.02.53.03.5 R a t i o Figure 18: Performance of array layouts with telescope number (N tel ) from 5 to 61. All arrays are simulated with a 120 m inter-telescope separationand the same telescope model as Array M61.
Left: Di ff erential point-source sensitivity for a 50 h observation time. Right:
68% containment angleof the gamma-ray PSF after applying point-source cuts. scopes. At high energies the curves in Fig. 18 showa clearer separation demonstrating that more telescopeshelp to better localize the showers above 1 TeV. Theenergy dependency has its origin in the fact that onlyhigh energy showers produce enough light to trigger dis-tant telescopes. Thus larger arrays with more telescopesbenefit at high energies because the average number oftelescopes participating in the shower reconstruction isincreased. In the case of lower energy showers, thenumber of telescopes contributing to the shower anal-ysis is limited by the telescope spacing and not the ab-solute number of telescopes in the array. Increasing thefootprint of the array also increases the parallax betweentelescopes observing an uncontained shower. The largerparallax yields a better shower direction reconstructionand further improves the reconstruction performance athigh energies.
After studying the e ff ect of individual telescope pa-rameters on the point-source sensitivity and gamma-ray PSF, we now compare realistic telescope designsagainst each other to find a suitable array design forCTA. To achieve a comprehensive comparison we in-vestigate all the benchmark arrays defined in Table 2and give a quantitative comparison between the di ff er-ent telescope layouts. Among the benchmark arrays arealso two more theoretically interesting cases. Array L61is representative of the theoretical limit for an IACT ar-ray if the budget is not limited and only the number oftelescopes is fixed. In a similar fashion, Array L5 isincluded to study the contribution of an LST subarray with 3–5 telescopes such as currently considered for thebaseline configuration of CTA.Fig. 19 shows that Array M61SC is more sensi-tive than Array M61DC at all energies above 50 GeV,where the increase in sensitivity is about 30%. In ad-dition to the improvement in point-source sensitivity,the M61SC array also has a better gamma-ray PSF atall energies. The smaller gamma-ray PSF would helpto determine the morphology of extended sources andhelp to separate point sources. These additional impor-tant e ff ects are di ffi cult to assess quantitatively becausethey heavily rely on the source population and proper-ties in the sky. The di ff use source is simulated as anuniformly extended disk with a radius of 0 . ◦ . Thedi ff use-source sensitivity does not show any improve-ment of the M61SC array over the M61DC array be-cause the gamma-ray PSF does not help to reduce thebackground but still the M61SC would enable for a non-uniform source to asses the morphology better than Ar-ray M61DC. The di ff use source sensitivity emphasizesthat the sensitivity gain of the SC array compared to theDC array comes almost entirely from the PSF improve-ment while the improvement in the background rejec-tion power is marginal.Array M25DC is representative of the MST subsetof the CTA array design as it was planned without aUS contribution. Comparing the Array M61SC andArray M61DC to the M25DC baseline configuration,it is obvious that adding MST telescopes will improvethe sensitivity of CTA in the key energy range between100 GeV and about 1 TeV by about a factor two regard-less of their design. This is expected from the fact that25 Energy [GeV]0.020.040.060.080.100.120.140.160.18 % C o n t a i n m e n t R a d i u s [ d e g ] M61SCM61DCM25DCL5L61 10 Energy [GeV]10 E ff e c t i v e A r e a [ m ] M61SCM61DCM25DCL5L6110 Energy [GeV]10 E d R / d E [ G e V s − d e g − ] M61SCM61DCM25DCL5L61 10 Energy [GeV]10 E d R / d E [ G e V s − d e g − ] M61SCM61DCM25DCL5L6110 Energy [GeV]10 -14 -13 -12 -11 -10 E d F / d E [ e r g c m − s − ] M61SCM61DCM25DCL5L61Array I (Bernlöhr et al. 2013) 10 Energy [GeV]10 -14 -13 -12 -11 -10 E d F / d E [ e r g c m − s − ] M61SCM61DCM25DCL5L61
Figure 19: Performance of benchmark arrays: M61SC, M61DC, M25DC, L5, and L61.
Top Left:
68% containment angle of the gamma-rayPSF after applying point-source cuts.
Top Right:
Gamma-ray e ff ective area after point-source cuts. Middle Left: Di ff erential rate of the totalcosmic-ray background (protons and electrons) after point-source cuts. Middle Right: Di ff erential rate of protons after point-source cuts. BottomLeft: Di ff erential point-source sensitivity for a 50 h observation time. Shown as the solid gray line is the di ff erential sensitivity of Array I from[18] evaluated with the most sensitive analysis at each energy from the four alternative analyses presented in that work (MPIK, IFAE, SAM, andParis-MVA). Bottom Right: Di ff erential di ff use-source sensitivity ( D = . ◦ ) for a 50 h observation time. ff erential sensitivity curve that is constructedby taking the best sensitivity in each energy bin from thefour alternative analyses presented in that work (MPIK,IFAE, SAM, and Paris-MVA). Although the simulationsin this paper were performed with di ff erent telescopemodels and a di ff erent detector simulation package, thisarray is representative of the expected performance ofthe baseline CTA concept. In the central energy rangefrom 100 GeV to 3 TeV, Arrays M61DC and M61SCprovide a factor of 3–4 improvement in point-sourcesensitivity relative to Array I. This improvement canbe primarily attributed to the increase in the number ofMSTs from 18 to 61. Array I performs better at ener-gies below 50 GeV and above 3 TeV as compared toArray M25DC and even Arrays M61DC and M61SC.This improvement can be attributed to the inclusion of56 SSTs and 3 LSTs in Array I. Array L5 was simu-lated with five LSTs very similar to the ones includedin Array I, and the sensitivity curve obtained for L5matches very well the sensitivity of Array I at low ener-gies, demonstrating that the advantage of Array I at lowenergies does in fact come from the LSTs.Finally Array L61 yielded only an improvement be-low 100 GeV, making such an array impractical basedon the large cost di ff erential between a single MST andLST. However the performance of this array shows whatis theoretically achievable in the case of no budget con-straints. Array M61SC provides comparable sensitivityto Array L61 at all energies above 100 GeV and thus isvery close to the performance of an ideal array in thisenergy range.In case of the di ff use source sensitivity the numberof telescopes is the found to be the most important fac-tor. Again the addition of MSTs of either type (SC orDC) would result in a considerable improvement com-pared to M25DC (similar to Array I) in the whole en-ergy range. However the improvement is slightly lesssignificant when compared to the relative improvementin the point-source sensitivity.
5. Conclusions
This paper describes a new simulation and analy-sis chain that is used to study and compare array andtelescope design concepts for CTA. We specifically fo-cus on the role of MST arrays which are optimized forperformance in the core energy range of CTA between100 GeV and 1 TeV. The simplified detector model used for this study allows for investigation of a wide rangeof telescope parameters: e ff ective light collection area,optical PSF, camera pixel size, e ff ective camera trig-ger threshold, and e ff ective integration window in time.The simplified telescope description allows us to isolatethe most important telescope design characteristics andfully explore their influence on the performance of thefull array. Realistic telescope designs can be mapped toour simplified detector model by choosing telescope pa-rameters that are matched to the physical characteristicsof each design (mirror area, focal length, photosensore ffi ciency, etc.). This paper also investigates several as-pects of the array geometry optimization including theimpact of the number of telescopes and their separationon array performance.A benchmark telescope array was used to assess theinfluence of each of the telescope and array parame-ters. Performance is evaluated for nominal observingconditions corresponding to a zenith angle of 20 ◦ andan NSB rate computed for a dark extragalatic field. Wealso examined the influence of the GF and higher NSBrates. Under all conditions, an optimized analysis is per-formed using a likelihood reconstruction based on sim-ulated image templates and BDTs for signal extraction.The likelihood reconstruction based on simulatedtemplates o ff ers a factor of two improvement in pointsource sensitivity (30–40% improvement in gamma-rayPSF), as well as a reduced energy threshold relative toimage moment-based analysis. The likelihood recon-struction takes advantage of the possibility of fully re-solving showers with a finely pixelated camera. Thistechnique, coupled with BDTs for event selection, al-lowed us to compare arrays very close to their maximumachievable sensitivity.We find that the substantial improvements in both thegamma-ray point-source sensitivity and angular reso-lution of an IACT array can be realized by telescopeswith imaging resolution better than current-generationIACT designs. We find a 30–40% improvement in thegamma-ray point-source sensitivity between 100 GeVand 3 TeV when the telescope pixel size is reducedfrom 0.16 ◦ to 0.06 ◦ . The gain in point-source sensitivitycomes primarily from the improvement in the gamma-ray angular reconstruction enabled by the higher reso-lution imaging of the shower axis. Over the same en-ergy range, the performance of an MST array is muchless sensitive to the telescope light collection area andtrigger threshold. We find that these parameters are im-portant in determining the array energy threshold buthave little influence on the array performance above thethreshold energy.With higher resolution shower images, the GF be-27omes more relevant than ever for the sensitivity of anIACT array. To determine the impact of the GF, wecompared the same array simulated with values of B ⊥ between 0 µ T and 20 . µ T. For an MST array, the im-pact of the GF is largest around 100 GeV where thepoint-source sensitivity is reduced by 50%. The GFshould be an important factor in selecting a site forfuture arrays and possibly for designing an observingstrategy.Increasing the number of telescopes in the array ex-pands the e ff ective area, improves reconstruction, andincreases background rejection capabilities. The sensi-tivity can be improved faster at very low and very highenergies by adding LSTs and SSTs. However, in the en-ergy range between a few hundred GeV and tens of TeV,expanding the MST array e ffi ciently improves the sensi-tivity, regardless of the telescope design. In the limit ofa finite array for which uncontained showers constitute asignificant fraction of the total reconstructed event sam-ple, the improvement in point-source sensitivity scalesfaster than the square root of the number of telescopesbetween 300 GeV and 3 TeV. If the baseline CTA designis expanded to include 36 more MSTs, the point-sourcesensitivity in the core energy is improved by a factor oftwo.When considering arrays with the same number oftelescopes, we find that the SC telescope design yieldsa 30-40% improvement in point-source sensitivity overthe DC telescope design because of its superior imag-ing resolution. The DC telescope on the other handhas a slightly lower energy threshold resulting in betterpoint source sensitivity below 75 GeV. The improvedperformance in a wide energy range from the SC designwarrants further investigation. The improved sensitiv-ity reduces the total exposure time required for everyscience topic, while the smaller gamma-ray PSF addi-tionally helps with source confusion and morphologystudies. The higher resolution shower images of the SC-like telescopes are also much less a ff ected by noise fromNSB. This translates to a much lower energy thresh-old during brighter sky conditions, e.g. in the galacticplane. This may lead to a much higher e ff ective dutycycle since observations can be continued into brightermoon phases without sacrificing the low energy regime.While the SC-like array is more sensitive in compari-son to the DC-like design, no SC MST telescope has yetbeen built. Construction of an SC prototype at the site ofVERITAS is under way. This prototype o ff ers a chanceto study the performance of the SC optics in realisticcircumstances. This experience should also provide amore realistic cost model for the two-mirror systems.At this point in the design of CTA, it is unlikely that all MST telescopes would be of the SC design. If the SCprototype can be built successfully and cost-e ffi ciently,the baseline CTA array could be expanded to include anadditional number of SC MSTs. The study of mixed ar-rays is ongoing. No matter which optical design is cho-sen, expanding the MST arrays o ff ers significant ben-efits for the performance of CTA in the central energyrange between 100 GeV and 1 TeV. Acknowledgements
We thank Brian Humensky, Emiliano Carmona, andthe anonymous referees for their valuable comments.This work was supported in part by the Department ofEnergy contract DE-AC02-76SF00515.
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