Comparing Two-Level and Time Next Neighbor Cleaning Protocols for Optimizing CTA Image Cleaning

Transcription

1 Comparing Two-Level and Time Next Neighbor Cleaning Protocols for Optimizing CTA Image Cleaning Samantha Gilbert University of Chicago Chicago, Illinois Columbia University, Nevis Laboratories REU August 5, 2016 Contents 1 Theory and Introduction Cherenkov Telescope Array Schwarzschild-Couder Telescopes Gamma-Ray Showers Imaging Atmospheric Cherenkov Technique Method Calibration Trace Integration Image Cleaning Two-Level Cleaning Time Next Neighbor Cleaning Motivation 5 4 Data Analysis and Results Monte Carlo Simulations and Software Packages Analysis Chain Comparing Events and Efficiency Plots for Different Cleaning Protocols and Parameters Conclusion and Outlook 16 6 Acknowledgments 17 Abstract CTA is the next generation of ground-based gamma-ray telescopes. Its mission is to improve upon the telescope sensitivity of its predecessors by a factor of 10. One of the factors that impacts telescope sensitivity is the image cleaning performed during the data analysis process. In order to accomplish this task, we compare the efficiency in keeping events for two different cleaning protocols, two-level and time next neighbor cleaning, along with a variety of parameters. The air shower generator CORSIKA is used in order to simulate gamma ray-induced Cherenkov light as well as the cosmic ray background, and the sim telarray package is used to simulate the telescope response to the simulated air showers. The simulated data is then analyzed with the software package eventdisplay. We find that the time next neighbor cleaning produces similar efficiency ratios to the most relaxed cleaning methods, indicating that we are not losing as many events as we would with the most restrictive cleanings. Using eventdisplay to compare images of events for these cleaning methods, we find that time next neighbor cleaning demonstrates the highest efficiency ratio for keeping events without allowing too many noisy pixels to pass the cleaning. The next step in this analysis is to produce the IRFs in order to determine how time next neighbor cleaning compares with the other methods in terms of energy resolution, angular resolution, and telescope sensitivity. 1

2 1 Theory and Introduction 1.1 Cherenkov Telescope Array The study of very high energy (VHE) gamma rays in the energy range >100 GeV has the potential to yield many interesting scientific results, especially regarding the search for dark matter, pulsars, active galactic nuclei, and supernova remnants both inside and outside our galaxy [7]. Perhaps the most exciting application of gamma-ray studies on the horizon is the potential to follow up on LIGO gravitational wave (GW) detections; if we can detect the electromagnetic counterparts to GW transients, we may be able to help locate the source of these GWs in the universe [3]. Since the vast majority of gamma rays that reach Earth are absorbed by our atmosphere, this leaves us only two viable options for studying VHE gamma rays. The first option is to send detectors directly into space, thereby bypassing this issue of atmospheric absorption. Unfortunately, the number of gamma-ray events decreases sharply with energy, so very few photons are observed over relatively long timescales [7]. For example, even the Crab Nebula, the standard candle for high-energy astrophysical studies and one of the brightest sources in our sky, only has a photon flux of about 6 photons m year 1 above 1 TeV [7]. As a result, from a practical standpoint, sending detectors into space via satellite is not viable because the detectors would have to have massive collection areas in order to ever have any hope of studying the universe in these higher energy regimes [7]. However, there are smaller gamma-ray satellites that may be used to study lower energy gamma rays below 100 GeV, such as Fermi-LAT. Thus, we are left with a second and final option: ground-based gamma-ray telescopes, which indirectly study extragalactic VHE gamma-ray sources through the collection of Cherenkov light. The Cherenkov Telescope Array (CTA) is the next generation in ground-based gamma-ray telescopes. The array is planned to have one location in the southern hemisphere in Paranal, Chile, and one in the northern hemisphere in La Palma, Spain in order to provide a full view of the sky. CTA aims to achieve a factor of 10 greater sensitivity than any of the existing ground-based gamma-ray telescopes, covering a range of energy from tens GeV to hundreds TeV [8]. CTA notably improves upon its predecessors with a proposed array of telescopes; VERITAS and HESS both consist of only 4 telescopes, for comparison. Additionally, each CTA camera is slated to have pixels, whereas VERITAS cameras have only 499 pixels. 1.2 Schwarzschild-Couder Telescopes In order to probe this broader energy range, CTA plans to incorporate three different-sized telescopes into the array: 4 large-size telescopes (LSTs) with a diameter of 24 m, 30 medium-sized telescopes (MSTs) with a diameter of 12 m, and 50 small-size telescopes (SSTs) with a diameter of 4 m [12]. SSTs are optimized for studying the higher energy range of gamma rays (>10 TeV), while MSTs are optimized for studying the core energy rage ( TeV) and LSTs are optimized for studying the lower energy range (<100 GeV) [1]. The current generation of IACTs have small spherical mirror facets attached to a spherical dish (Davies- Cotton optical design) or a parabolic dish [12]. The desire to improve the optical point-spread function and reduce the plate scale of the current IACTs has motivated the development of Schwarzschild-Couder telescopes (SCTs) [12]. CTA plans to use a two-mirror SCT with aspheric optics that allows for a large field-of-view, and a reduced plate scale focal surface that will be equipped with a highly pixelated (11328) Silicon photomultiplier camera. The SC design will be implemented for the MSTs, with a compact camera close to the secondary mirror [1]. An artist s rendering of the SC-MST is shown below. The analysis described in this paper uses the medium-sized prototype SC telescope (psct) to study simulated data. Figure 2: An artist s depiction of the Schwarzschild-Couder MST [1]. Figure 1: An artist s depiction of the planned CTA array [1]. 1.3 Gamma-Ray Showers When a VHE gamma ray reaches Earth, it interacts with particles in Earth s atmosphere to produce an electronpositron pair, and these particle collisions occur many times over to produce a cascade of electromagnetic particles [7]. More specifically, the gamma ray pair produces electrons and positrons in the presence of an at- 2

3 mospheric nucleus. These electrons and positrons then radiate bremsstrahlung photons when their trajectories are bent by the magnetic fields of particles in the upper atmosphere. These bremsstrahlung photon will pair produce again until their energy is less than the sum of the masses of the electron and positron. These charged particles move at relativistic speeds that exceed the speed of light in air, and consequently produce Cherenkov radiation [7]. This radiation reaches the ground in the form of a bluish pool of light that we can then detect with ground-based telescopes. Similarly, cosmic rays, which consist of charged, relativistic protons and nuclei, also produce particle showers in the upper atmosphere [7]. In the energy range 100 GeV, there are 10 4 more cosmic ray than gamma-ray showers; in this way, cosmic rays constitute a large background from which we want to separate the gamma-ray showers. In contrast to the gamma rays, cosmic ray-induced showers ultimately produce muons, neutrinos, and hadrons as one of their products. These muons from the cosmic ray-incident showers often reach the ground, creating an explicit difference in the morphology between gamma rayinduced showers and cosmic ray-induced showers, shown in the figure below [9]. mirror to collect Cherenkov photons, and a photon detector with an oscilloscope to record them [7]. Next, large convex reflectors focus the Cherenkov light onto a camera consisting of photo-detecting pixels. The camera then records an image of the shower. The shape, intensity, and orientation of this image are later used to study the properties of the shower [7]. Ground-based gamma-ray telescopes like VERITAS and CTA exploit an array consisting of multiple telescopes, as this stereoscopy offers multiple views of the same shower. A depiction of the stereoscopic imaging technique is shown in fig. 4 [7]. Figure 4: VHE gamma rays collide with particles in Earth s atmosphere to produce a pool of Cherenkov light. Multiple telescopes within the light pool image the shower from multiple perspectives, exploiting stereoscopy to reconstruct the arrival direction of the gamma ray [7]. Figure 3: A comparison of the morphologies of gamma rayinduced (photon) showers and cosmic ray-induced (proton) showers from Monte Carlo simulations of the particle tracks [9]. Red particle tracks, which dominate both images, indicate electrons, positrons, and gamma rays, green tracks represent muons, and blue tracks represent hadrons [8]. The cosmic ray showers are clearly poorly formed in comparison to the well-formed gamma-ray showers. In this manner, while cosmic ray showers are much more prevalent than gamma-ray showers, their morphologies can be used to distinguish gamma rays from this large cosmic ray background [7]. 1.4 Imaging Atmospheric Cherenkov Technique We detect the Cherenkov light emanating from gamma ray-induced showers in the upper atmosphere with a large 2 Method 2.1 Calibration Calibration of the simulated data is essential for determining the average pedestal and its RMS (pedvar). The pedvar quantifies the night-sky background (NSB), while the pedestal is a constant offset in the channel. Simulating the pedvar values determines whether or not a pixel s pulse charge sufficiently stands out against the background to be classified as an image or border pixel. We can quantify the NSB in this way by measuring the output from the PMTs when the telescopes are not detecting Cherenkov light [6]. 2.2 Trace Integration A crucial step that precedes image cleaning is the integration of the FADC trace over a time window set by the user. This step is performed with a double-pass method, in which the first pass determines the start of the pulse T zero and the second pass integrates the FADC trace over 3

4 the aforementioned time window. This integration yields the total charge in each pixel, which is then compared against two set pulse charge threshold values in the case of two-level cleaning, or pulse charge threshold values and time coincidence windows for different next neighbor clusters in the case of next neighbor cleaning [6]. These cleaning methods are elaborated in greater detail in the next section of this paper. the signal from the shower. There are a variety of image cleaning methods available for analysis, including two-level cleaning, time next neighbor cleaning (both of which are detailed, analyzed, and compared in this paper), cluster cleaning, time cluster cleaning, and time two-level cleaning. Additionally, the cleaning may be based on either set thresholds (fixed cleaning) or a couple of multiplicative factors used to multiply the pedvars (variable cleaning) [8]. In the analysis represented in this paper, we have left all cleanings fixed. We observed a peak average pedestal value of 25 d.c. for all the runs, as shown in the figure below. This average value was used in order to determine different combinations of cleaning thresholds to test for the twolevel cleaning protocol. While this value does not actually represent the NSB, we can reasonably use it as a point of reference for determining these cleaning thresholds ped htemp Entries Mean 23.6 RMS Figure 5: An example of a typical trace integration window, with the number of samples along the x-axis and the charge in d.c. units on the y-axis [2] Accordingly, the optimization of trace integration has a direct impact on the optimization of image cleaning. For example, if an excessively large time window is set by the user, the trace integration may misrepresent the total charge in each pixel to be larger than it really is. Ultimately, such a generous integration time window may allow more pixels to pass the cleaning and thus produce a noisier shower image. Similarly, a too-small time window may have the impact of making the image cleaning more restrictive, resulting in a greater loss of true image or border pixels and thus a loss of information about the shower. Since a detailed analysis of different trace integration methods is outside the scope of this paper, the standard trace integration setting with a window size of 6 samples has been applied throughout the image cleaning analysis presented here. 2.3 Image Cleaning While the telescopes are surveying the sky, they are triggered by the gamma-ray sources that interest us, cosmic rays, and the night-sky background (NSB). The NSB is a constant source of noise over which gamma-ray and cosmic ray showers occur. We designate the pixels triggered by the NSB to be noisy pixels. The purpose of image cleaning is to remove as many of these noisy pixels from the actual shower image as possible, while preserving those pixels that make up the image and the border of Figure 6: An example of a histogram plot of the pedestal values for a simulated gamma run, rendering a peak average pedestal value of 25 d.c Two-Level Cleaning The two-level cleaning protocol uses a double-pass system to classify pixels as either image, border, or noise pixels based on a set of threshold values. The upper threshold designates the value of integrated charge that the pixel in question must have in order to be classified as an image pixel. If the pixel does not overcome this threshold, it may pass the lower threshold value. This lower threshold designates the value of integrated charge that a pixel must have in order to be classified as a border pixel, given that at least one of the pixels immediately near it ( neighboring pixels) passes this threshold as well [11]. If the pixel again does not overcome this lower threshold, or if it does not have any neighboring pixels, it will be classified as a noise pixel and it will be cleaned from the shower image. The issue of neighboring pixels is a complicating factor in the image cleaning process. Unlike the hexagonal pixels in the existing VERITAS array, the CTA will have thousands of square pixels. Accordingly, it is ambiguous ped 4

5 as to whether or not corner pixels, or the pixels that diagonally neighbor the pixel in question, should count as neighboring pixels. This is determined by the neighbor distance factor in the parameter file. If the factor is 1, then only the pixels that make lateral contact with the given pixel count as neighboring pixels. If the factor is 1.4, then the pixels that make diagonal contact are also included. Throughout this analysis process, we have used a neighbor distance factor of 1. 2NN, 3NN, and 4NN, where each next neighbor group has different pulse charge and time coincidence thresholds associated with it. An example of what these clusters might look like on the camera are shown in fig. 8. This multiplicity of next neighbor groups with different pulse charge thresholds and time windows creates a wider range of conditions that may trigger the software to accept the image, thereby ensuring that the software will retain as many true events as possible through the cleaning process [10]. The software uses these three compact NN groups to form the shower image [11]. The cleaning protocol checks that the pixels in each group demonstrate a pulse charge above the threshold value associated with its NN group, along with pulse time coincidences below the threshold value associated with its NN group [11]. Figure 7: Moving clockwise: a simulated view of square camera pixels in eventdisplay, a view of VERITAS s hexagonal camera pixels from the McGill DQM viewer, and a simplified representation of the ambiguity in determining what constitutes a next-neighbor pixel when the pixel in question is square. The VERITAS camera field-of-view is 3.5 deg, while the SC-MST camera field-of-view will be 8 deg. In this regime, the parameter we vary are the upper and lower charge thresholds. The default setting is an image pixel threshold of 300 d.c. and a border pixel threshold of 150 d.c., constituting factors of 12 and 6 times the average pedestal value of 25 d.c., respectively. Accordingly, this combination of parameters is denoted throughout the analysis process in this paper according to these factors, i.e., 2LC 12.6 denotes two-level cleaning with factors 12 and 6 times the pedestal. We processed events with this default setting along with pedestal factors 8.4, 10.4, 10.6, 12.4, 12.6, 12.8, 14.6, 14.8, 16.6, and Time Next Neighbor Cleaning Time next neighbor cleaning theoretically improves upon the traditional two-level cleaning method by considering the arrival time differences when examining neighboring pixels [11]. Accordingly, this cleaning protocol works to form the shower image by searching for next neighbor, or NN, groups in a time coincidence window [10]. There are three compact next neighbor groups, referred to as Figure 8: A zoomed-in view of a grid of pixels on the CTA camera. The parameter we vary in this regime is the fake probability, or the likelihood that a purely background event survives the cleaning. The higher the fake probability, the less restrictive the cleaning becomes because more pixel clusters are incorporated into the shower image. The default value is 0.05%, and we processed events with this default setting along with fake probability values of 0.03%, 0.04%, 0.06%, and 0.07%. This fake probability is assigned globally to all NN groups [11]. In this manner, the main difference between the time next neighbor cleaning regimen and the two-level cleaning regimen is that the inclusion of time information allows lower signals to pass the cleaning to ultimately preserve parts of the true image that may normally be lost during two-level cleaning due to the higher threshold demands it makes on the pixels in question [10]. 3 Motivation The goal of optimizing image cleaning for CTA is to produce clean shower images that do not inadvertently remove the true pixels that provide crucial information about the shower primary. The efficiency for keeping events is used to generate the instrument response functions (IRFs), which determine the energy resolution, reconstruction of the arrival direction, and the telescope sensitivity of the array. 5

6 Optimizing the sensitivity of the instrument is essential for CTA to accomplish its mission of achieving an order of magnitude greater sensitivity than its predecessors. In this manner, optimizing the efficiency of the image cleaning is similarly essential for accomplishing CTA s aims. 4 Data Analysis and Results 4.1 Monte Carlo Simulations and Software Packages It is important to note that all the numerical results used to analyze image cleaning in this paper are the products of simulations, since the CTA is not projected to be completed until A prototype Schwarzschild-Couder telescope (p-sct) is currently under construction. In the analysis elaborated in this paper, the Monte Carlo simulation method was essential for studying the optimization of image cleaning. In general, the Monte Carlo method employs repetitious random sampling in order to extract quantitative results. The purpose of applying this simulation method to CTA is to optimize the configuration of the array, which poses a major challenge given the large parameter space for a variety of steps in the analysis chain, including trace integration and image cleaning [4]. The air shower generator CORSIKA 1 is used in order to simulate gamma ray-induced Cherenkov light as well as the cosmic ray background, and the sim telarray package [4] is used to simulate the telescope response to the simulated air showers. The simulated data is then analyzed with the software package eventdisplay 2. Originally designed to analyze VERITAS prototype data, this software developed by Gernot Maier (DESY) and Jamie Holder (University of Delaware) has since become a full analysis package, and is regularly used for analyzing both VERITAS data and CTA simulations [8]. Finally, for all simulations, we use a single telescope located in the direct center of the projected array, with the air shower s arrival direction similarly located in the direct center of the camera. 4.2 Analysis Chain In order to understand the analysis chain that would be necessary for analyzing CTA simulations, we first analyze the Crab Nebula, one of the brightest (and moststudied) sources. For learning purposes, we analyzed a single Crab run, or a defined period of observation of a source typically lasting 30 minutes. The analysis tools used in the eventdisplay package include evndisp, mscw energy, anasum, and shared library tools and macros [5]. The evndisp step in the analysis calibrates and parametrizes the images and reconstructs events. The mscw energy tool uses look-up tables to produce mean-scaled width, mean-scaled length and energies, and the anasum tool produces maps and calculates the results of the analysis. Finally, shared library tools and macros produce the energy spectrum, integral fluxes, plot maps, and other results. Once all these analysis steps are complete, we print the results in the form of sky maps, sigma plots, and significance plots, examples of which are shown in fig. 9 and fig. 10. [deg] declination J HIP26451 BMag:2.8 Crab Crab Pulsar right ascension [deg] J2000 HIP25539 BMag: significance [σ] Figure 9: Crab sky map indicating the significance of each region of the sky. The Crab pulsar is clearly visible as the spot towards the center of the map with 25σ significance. Figure 10: Crab spectrum indicating the energy changes for each event observed at different energy ranges with significances. The analysis chain for optimizing image cleaning involves converting sim telarray files using a python script, and processing 86 GB of gamma data and 147 GB of proton data through eventdisplay with different 6

7 cleaning protocols and different combinations of parameters therein. The total number of simulated events used in this analysis is 200, Comparing Events and Efficiency Plots for Different Cleaning Protocols and Parameters In order to compare the efficiency plots for two-level and time next neighbor cleaning, along with the different parameters of interest, we produce and overlay histograms of the number of events that survive each cleaning method compared to the number of events that triggered the telescopes over a range of energies. The primary region of interest in these plots are the lower energies TeV, given this is the region with the greatest risk of losing shower information if the cleaning method is too restrictive. This is because lower energy showers result in less light deposited on the camera, thereby generating fainter and smaller images. Such images have a greater chance of not surviving the image cleaning. The error in these histograms is calculated using the usual relation for Poisson statistics: δn= n, (1) where n is the number of events. In order to compare the efficiencies, we produce plots of the ratios of the number of events that survive cleaning divided by the number of events that triggered the telescopes. The error in these efficiency ratios may be propagated using the relation for correlated variables δr= ( δn c ) n 2 +( n c δn t ) t n n 2 c δn c n t, (2) t n 3 t where n c is the number of events that pass the cleaning, n t is the number of events that triggered the telescopes, and δn c n t = nc n t represents the covariance between these two variables. All histograms are displayed on pages 8-13 of this report. For an initial comparison of the cleaning protocols, fig. 11 and fig. 12 are two histograms (one for the gamma data and one for the proton data), comparing the default two-level cleaning (2LC) with thresholds 300/150 d.c. (12.6) and the default time next neighbor (TNN) cleaning with fake probability It is immediately obvious that at higher energies ( >1 TeV), both cleaning protocols allow approximately the same number of events to pass the cleaning. In our region of interest, however, time next neighbor cleaning seems to salvage a greater number of events. For a more thorough analysis, we generate the histograms shown in fig. 13 and fig. 14 to compare all the different combinations of parameters for the two different cleaning methods. At first glance, there are clearly a number of cleanings that, within uncertainties, allow the same number of events to pass the cleaning. However, it is possible that the surviving events may have a different number of image pixels, which would in turn either improve or degrade the telescope sensitivity. Further studies may be necessary to assess the differences between the cleanings, but for the purposes of this analysis we are only focusing on the cleaning efficiency. In order to simplify the analysis, we can generally consider these parameter combinations to be redundant and remove them from the histograms in order to produce the histograms shown in fig. 15 and fig. 16. For these histograms, we remove 2LC 10.4, 2LC 10.6, 2LC 16.6, TNN , TNN , TNN , and TNN These methods were chosen for removal by zooming in on the histograms at the lower energies and observing by eye those that overlapped within uncertainties. With the number of cleaning protocols reduced, we can now observe that it will also be useful to zoom in on a smaller range of energies, specifically those in the on the logarithmic TeV scale. This range of energies is our primary region of interest, given that the cleaning efficiencies begin to converge at the higher energies and that we are most interested in preserving the events we typically lose at the lower energies. Furthermore, it is interesting to note that the least restrictive cleaning, 2LC 8.4, generates an efficiency ratio of 1, meaning all the events that triggered the telescopes have also passed the cleaning. While this might seem optimal, such a relaxed cleaning will most likely generate a rather noisy shower image. We can now calculate the uncertainties in the ratios using equation (2), and quantitatively determine which cleaning method is most efficient. The ratios, the uncertainties, and the associated bin energies for both the gamma and proton simulations are shown in table 1 and table 2, respectively. 7

8 Comparing Energies for Default 2LC and TNN Cleaning Number of Events 10 4 Triggered Events LC 12.6 TNN 0.05% Ratio of Events Figure 11: A histogram comparing the default 2LC with the default TNN cleaning for simulated gamma showers. The default levels for 2LC are 300/150, or a factor of 12.6 times the pedestal. The default fake probability for TNN cleaning is 0.05%. 8

9 Comparing Energies for Default 2LC and TNN Cleaning Number of Events 10 4 Triggered Events LC 12.6 TNN 0.05% Ratio of Events Figure 12: A histogram comparing the default 2LC with the default TNN cleaning for simulated protons. 9

10 Comparing All 2LC Thresholds Combinations and TNN Fake Probabilities Number of Events Triggered Events 2LC 8.4 2LC LC LC LC LC LC LC LC LC 16.8 TNN 0.03% TNN 0.04% TNN 0.05% TNN 0.06% TNN 0.07% Ratio of Events Figure 13: A histogram comparing all the different combinations of cleaning thresholds for 2LC with the different fake probabilities for TNN cleaning for the simulated gamma showers. 10

11 Comparing All 2LC Thresholds Combinations and TNN Fake Probabilities Number of Events Triggered Events 2LC 8.4 2LC LC LC LC LC LC LC LC LC 16.8 TNN 0.03% TNN 0.04% TNN 0.05% TNN 0.06% TNN 0.07% Ratio of Events Figure 14: A histogram comparing all the different combinations of cleaning thresholds for 2LC with the different fake probabilities for TNN cleaning for the simulated protons. 11

12 Comparing Reduced 2LC Thresholds Combinations and Default TNN Fake Probability Number of Events Triggered Events 2LC 8.4 2LC LC LC LC LC LC 16.8 TNN 0.05% Ratio of Events Figure 15: A histogram comparing a reduced number of combinations of cleaning thresholds for 2LC with the default fake probability 0.05% for TNN cleaning for the simulated gamma showers. Redundant cleanings have been removed based on those that overlapped within uncertainties. 12

13 Comparing Reduced 2LC Thresholds Combinations and Default TNN Fake Probability Number of Events Triggered Events 2LC 8.4 2LC LC LC LC LC LC 16.8 TNN 0.05% Ratio of Events Figure 16: A histogram comparing a reduced number of combinations of cleaning thresholds for 2LC with the default fake probability 0.05% for TNN cleaning for the simulated protons. Redundant cleanings were removed using the same method previously described. 13

14 Table 1: A table of the efficiency ratios for the gamma shower data. log10(e (TeV)) Cleaning Efficiency ( nc n t ) LC ± LC ± LC ± LC ± LC ± LC ± LC ± TNN ± LC ± LC ± LC ± LC ± LC ± LC ± LC ± TNN ± LC ± LC ± LC ± LC ± LC ± LC ± LC ± TNN ± LC ± LC ± LC ± LC ± LC ± LC ± LC ± TNN ± LC ± LC ± LC ± LC ± LC ± LC ± LC ± TNN ± log10(e (TeV)) Cleaning Efficiency ( nc n t ) LC ± LC ± LC ± LC ± LC ± LC ± LC ± TNN ± LC ± LC ± LC ± LC ± LC ± LC ± LC ± TNN ± LC ± LC ± LC ± LC ± LC ± LC ± LC ± TNN ± LC ± LC ± LC ± LC ± LC ± LC ± LC ± TNN ± LC ± LC ± LC ± LC ± LC ± LC ± LC ± TNN ±

15 Table 2: A table of the efficiency ratios for the proton data. log10(e (TeV)) Cleaning Efficiency ( nc n t ) LC ± LC ± LC ± LC ± LC ± LC ± LC ± TNN ± LC ± LC ± LC ± LC ± LC ± LC ± LC ± TNN ± LC ± LC ± LC ± LC ± LC ± LC ± LC ± TNN ± LC ± LC ± LC ± LC ± LC ± LC ± LC ± TNN ± LC ± LC ± LC ± LC ± LC ± LC ± LC ± TNN ± log10(e (TeV)) Cleaning Efficiency ( nc n t ) LC ± LC ± LC ± LC ± LC ± LC ± LC ± TNN ± LC ± LC ± LC ± LC ± LC ± LC ± LC ± TNN ± LC ± LC ± LC ± LC ± LC ± LC ± LC ± TNN ± LC ± LC ± LC ± LC ± LC ± LC ± LC ± TNN ± LC ± LC ± LC ± LC ± LC ± LC ± LC ± TNN ±

16 Comparing the table values within uncertainties, we find that for the gamma simulations, the time next neighbor default cleaning largely produces either equal or greater efficiency ratios within uncertainties than the default two-level cleaning with pedestal factor For the higher energy bins, the ratios begin to converge. In contrast, for the lowest energy bins, the time next neighbor default cleaning clearly saves more events than the default two-level cleaning, and any two-level cleaning that is more restrictive. For the proton simulations, the time next neighbor default cleaning saves more events than the twolevel cleaning with pedestal factor 12.4, as well as more events than any of the more restrictive two-level cleanings. Although the least restrictive two-level cleanings, such as those with pedestal factors 8.4 and 12.4, appear to save more events than time next neighbor cleaning for both gamma and proton simulations, it is likely that these looser cleanings are allowing noisy pixels to form the shower image. In this manner, we cannot make a stronger statement about the efficiency of the time next neighbor method without comparing actual event images. We can compare representative examples of the same events for the same runs with different cleaning levels in order to determine whether or not the time next neighbor method is similarly allowing noisy pixels to form the final shower image. These examples are shown in fig. 17 and fig. 18. Figure 17: A noisy shower image produced by cleaning method 2LC 8.4 for run 2222, event Image generated by the eventdisplay package. Figure 18: A shower image produced for the same run 2222, event as that shown in fig. 17. In comparison, the image produced by the time next neighbor method is much cleaner, promising a successful reconstruction of the arrival direction of the shower primary. The shower image generated with the time next neighbor cleaning is clearly much cleaner than that produced by the two-level cleaning with pedestal factor 8.4. While it is not possible to display the reconstructed arrival direction of the shower primary since we are running the simulations with only one telescope, the centroid of the ellipse is clearly skewed away from the center of the shower by all the noisy pixels. As a result, while both cleaning methods demonstrate the more similar efficiency ratios than any of the other cleaning methods, the time next neighbor cleaning is superior at generating a clean shower image. 5 Conclusion and Outlook We find that for the gamma simulations, the time next neighbor default cleaning largely produces either equal or greater efficiency ratios within uncertainties than the default two-level cleaning with pedestal factor For the proton simulations, the time next neighbor default cleaning saves more events than the two-level cleaning with pedestal factor 12.4, as well as more events than any of the more restrictive two-level cleanings. For the lowest energy bins, the time next neighbor default cleaning clearly saves more events than the default two-level cleaning, and any twolevel cleaning that is more restrictive. Since we had more statistics for the proton simulations, these results suggest that, perhaps with more gamma statistics we would achieve a similar result for those simulated showers. By comparing representative event images, we find that time next neighbor cleaning saves the most true events, meaning that its images are both cleaner and contain more information 16

17 than those produced by looser two-level cleaning methods. A potential issue in the lower energy regime is that keeping more and more low energy showers with images that are difficult to reconstruct may make the process of classifying events as gamma or proton less efficient in this energy range. Finally, the next steps in this analysis would be to generate the instrument response functions (IRFs), or the look-up tables, effective areas, and the radial acceptances for the telescopes. In this case, generating the IRFs would help us to assess how image cleaning is impacting the energy resolution, arrival direction reconstruction, and telescope sensitivity, a result that is of primary interest in the development of CTA. References [1] Acharya, B.S., et. al. Introducing the CTA concept Seeing the High-Energy Universe with the Cherenkov Telescope Array - The Science Explored with the CTA. Astroparticle Physics. Vol. 43. March [2] Agarwal, Abhineet. Image produced using the eventdisplay package. [3] Bartos, I., et. al. Cherenkov Telescope Array is well suited to follow up gravitational-wave transients. Monthly Notices of the Royal Astronomical Society. Oxford Univ. Press. 16 Jun [4] Bernlöhr, K., et. al. Monte Carlo design studies for the Cherenkov Telescope Array. Seeing the High-Energy Universe with the Cherenkov Telescope Array - The Science Explored with the CTA. Astroparticle Physics. Vol. 43. March [5] GammaWiki. Eventdisplay Manual. [6] Guenette, Roxanne. Chapter 4: VERITAS analysis. Thesis. [7] Holder, Jamie. Atmospheric Cherenkov Gamma-ray Telescopes. World Scientific Review Volume. University of Delaware, Newark DE Oct [8] Prokoph, Heike. Observations and modeling of the active galactic nucleus B together with performance studies of the ground-based gamma-ray observatories VERITAS and CTA. Dissertation. Humboldt-Universität zu Berlin, Germany. 16 Aug [9] Schmidt. F. Images produced using the CORSIKA package. fs/showerimages.html. [10] Shayduk, M., Th. Hengstebeck, O. Kalekin, N.A. Pavel, Th. Schweizer. A New Image Cleaning Method for the MAGIC Telescope. Proc. of the 29th International Cosmic Ray Conference. Pune, India Aug pp.223, vol.5. [11] Shayduk, M. Optimized next-neighbor image cleaning method for Cherenkov Telescopes. 33rd Annual International Cosmic Ray Conference. Rio de Janeiro, Brazil [12] Wood, M., Jogler, T., Dumm, J., Funk, S. Monte Carlo Studies of medium-size telescope designs for the Cherenkov Telescope Array. 24 Jun Acknowledgments This work was funded by the National Science Foundation. Thank you to the Nevis REU program for offering me this great opportunity, to Amy Garwood and John Parsons for all the administrative work associated with keeping this program afloat, and to Bill Seligman for his enlightening ROOT tutorial. I also owe my gratitude to my fellow REU students for their assistance, encouragement, and companionship throughout the program. Finally, I would like to offer special thanks to Abhineet Agarwal for being my research partner in the first stages of this project, and Brian Humensky, Reshmi Mukherjee, Marcos Santander, and Daniel Nieto for their mentorship and support, as well as their supervision of this work. 17