COSI: From Calibrations and Observations to All-sky Images
Andreas Zoglauer, Thomas Siegert, Alexander Lowell, Brent Mochizuki, Carolyn Kierans, Clio Sleator, Dieter H. Hartmann, Hadar Lazar, Hannah Gulick, Jacqueline Beechert, Jarred M. Roberts, John A. Tomsick, Mark D. Leising, Nicholas Pellegrini, Steven E. Boggs, Terri J. Brandt
DDraft version March 1, 2021
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COSI: From Calibrations and Observations to All-sky Images
Andreas Zoglauer, Thomas Siegert, Alexander Lowell, Brent Mochizuki, Carolyn Kierans, Clio Sleator, Dieter H. Hartmann, Hadar Lazar, Hannah Gulick, Jacqueline Beechert, Jarred M. Roberts, John A. Tomsick, Mark D. Leising, Nicholas Pellegrini, Steven E. Boggs,
2, 1 andTerri J. Brandt Space Sciences Laboratory, UC Berkeley, 7 Gauss Way, Berkeley, CA 94720, USA Center for Astrophysics and Space Sciences, UC San Diego, 9500 Gilman Drive, La Jolla CA 92093, USA NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA U.S. Naval Research Laboratory, Washington, DC 20375, USA Department of Physics and Astronomy, Clemson University, Kinard Lab of Physics, Clemson, SC 29634, USA (Received February 25, 2021; Revised some time in the future; Accepted some time in the future)
Submitted to ApJABSTRACTThe soft MeV gamma-ray sky, from a few hundred keV up to several MeV, is one of the least exploredregions of the electromagnetic spectrum. The most promising technology to access this energy rangeis a telescope that uses Compton scattering to detect the gamma rays. Going from the measureddata to all-sky images ready for scientific interpretation, however, requires a well-understood detectorsetup and a multi-step data-analysis pipeline. We have developed these capabilities for the ComptonSpectrometer and Imager (COSI). Starting with a deep understanding of the many intricacies ofthe Compton measurement process and the Compton data space, we developed the tools to performsimulations that match well with instrument calibrations and to reconstruct the gamma-ray path inthe detector. Together with our work to create an adequate model of the measured background whilein flight, we are able to perform spectral and polarization analysis, and create images of the gamma-ray sky. This will enable future telescopes to achieve a deeper understanding of the astrophysicalprocesses that shape the gamma-ray sky from the sites of star formation ( Al map), to the history ofcore-collapse supernovae (e.g. Fe map) and the distributions of positron annihilation (511-keV map)in our Galaxy.
Keywords:
Compton telescope — gamma rays — reconstruction INTRODUCTIONThe gamma-ray sky from a few hundred keV to several MeV is host to a multitude of phenomena, including thelife cycle of matter in our Universe, the most energetic explosions (supernovae, mergers), and the most extremeenvironments such as pulsars and accreting black holes. Up to now, this energy range has not been very deeplyexplored, and a plethora of open questions remain, ranging from the origin of the 511-keV emission near the centerof our Galaxy (Prantzos et al. 2011; Churazov et al. 2020), to element creation during supernovae and mergers (Isernet al. 2021; Korobkin et al. 2020; Diehl et al. 2021), and more.The majority of these science goals require making images from the measured data showing point sources suchas pulsars, binaries, and AGN, as well as diffuse emission from, for example, nucleosynthesis (e.g. Al, Fe) andpositron annihilation (511-keV). There exist several approaches for all-sky imaging in this energy range, such ascoded-masks, rotating modulators, and Compton telescopes (see for example Sch¨onfelder 2001; Diehl et al. 2018, foroverviews). Their effectiveness to identify and suppress background, the capability to measure polarization, their
Corresponding author: Andreas [email protected] a r X i v : . [ a s t r o - ph . I M ] F e b Zoglauer et al.
Figure 1.
Schematic of the COSI telescope showing the 12 germanium detectors (GeD) in the center enclosed in a cryostatwhich is cooled by the cryocooler. The cryostat is on five sides surrounded cesium iodide (CsI) shields, which are read out byhigh-voltage photomultipliers (HV/PMTs). well-defined point-spread function, and their wide field-of-view give Compton telescopes a clear advantage over theother technologies in this energy regime to image point sources and diffuse emission. Therefore, Compton telescopesare at the center of this paper.The path from the raw detector data to all-sky images using Compton telescopes has the following main steps: • Perform calibrations with sufficient statistics to accurately capture all features of the detector such as the shapeof the energy response (photo peak as well as the Compton continuum), the shape and flux of the point spreadfunction (peak, wings, and any features from incomplete absorption), the absolute flux normalization, and thescatter angle modulations due to polarization and detector geometry to a required accuracy. • Implement well-benchmarked Monte-Carlo simulations tuned to accurately reproduce these calibration measure-ments with all their detector features. • Reconstruct the path of the gamma-ray scatters within the detector from just position and energy measurements. • Create a multi-dimensional imaging response using Monte-Carlo simulations which sufficiently describes thepoint-spread function of the instrument. • Develop a model of the the on-orbit background either from observations or simulations as a function of location,time, and other environmental parameters. • Determine the source distribution on the sky using either an imaging approach such as Richardson-Lucy ormaximum-entropy, or, alternatively, a model-fitting approach. All these methods need to take into account theall-sky scanning approach of modern Compton telescopes which means continuous slewing and maybe rockingof the instrument to achieve a close to flat exposure on the sky.This paper is intended as an overview of how to perform the analysis while meeting these challenges and the lessonslearned during the development of the data-analysis pipeline for COSI, the Compton Spectrometer and Imager (seeFigure 1 for a schematic). COSI is a compact Compton telescope operating in the energy range from 0.2 to 5 MeV,capable of observing 25% of the sky at any time. COSI is a flexible telescope design that works on a variety ofplatforms. Here we concentrate on COSI-2016 (Kierans et al. 2017), with some references towards a planned satelliteversion, COSI-SMEX (Tomsick et al. 2019). COSI-2016, in the following referred to simply as COSI, consists of 12
OSI: From Calibrations and Observations to All-sky Images × × . The individual strips have anenergy resolution of 2.5-4.0 keV FWHM and an average trigger threshold of 20 keV. The detectors are enclosed ina cryostat with a mechanical cryocooler keeping the germanium detectors at ∼
83 K. The cryostat is surrounded onfive sides by a 4-cm thick cesium iodide (CsI) shield which vetoes upward moving gamma rays and charged particlesoriginating from cosmic-ray interactions with Earth’s atmosphere.In 2016, COSI had a successful 46-day flight on a super-pressure balloon at an altitude of roughly 33.5 km launchingfrom Wanaka, New Zealand and landing in Peru (Kierans et al. 2017). During this flight COSI observed the Galactic511-keV emission (Kierans et al. 2020; Siegert et al. 2020), gamma-ray bursts (Lowell et al. 2017), the Crab pulsar(Sleator 2019), black holes (Cyg X-1 and Cen A), relativistic electron precipitation events, and more. Our work withthe COSI-2016 balloon data demonstrates the capability of this analysis pipeline for future flights on both balloon andsatellite platforms.Starting with a general introduction to Compton telescopes, the following sections will follow the data-analysis pathwith details on the steps outlined above, and ultimately demonstrate the pipeline by creating all-sky images from theCOSI-2016 flight with several independent approaches. HOW COMPTON TELESCOPES WORK2.1.
The principle of a Compton telescope
Compton telescopes are named after Arthur Holly Compton, who discovered the scattering of X- and gamma raysoff of electrons in 1923 and the relation between initial and final energy of the photon (Compton 1923), later calledthe Compton equation (see Equation 5). He received the Nobel prize in physics for this discovery in 1927.The operating principle of a non-electron tracking Compton telescope can be found in Figure 2: An incoming gammaray with energy E i and momentum (cid:126)p i scatters off of an electron in the active detector and transfers energy E e andmomentum (cid:126)p e to the electron. The scatter angle is called the Compton angle ϕ , and the corresponding electron iscalled the recoil electron. The gamma ray, which after the scatter has energy E g and momentum (cid:126)p g , continues on andundergoes either one or more Compton interactions or is absorbed in a final photo-effect interaction. The detectoritself sees a set of energy deposits E n at locations (cid:126)r n through ionization from the recoil or photo-electron. The truepath of the gamma ray has to be reconstructed from just the energy and position information since the time-of-flightbetween the interactions is too small to be measured in compact Compton telescopes.2.2. Compton equation and cross section
The scattering of a gamma ray off of an electron can be described in terms of conservation of energy and momentumof a photon and electron: E i + E i,e = E g + E e (1) (cid:126)p i + (cid:126)p i,e = (cid:126)p g + (cid:126)p e (2)The initial energy E i,e and momentum (cid:126)p i,e of a bound electron are not known beyond the boundaries set by atomicphysics. Therefore, it is commonly assumed that the electron is at rest, i.e. E i,e = 0 and (cid:126)p i,e = 0. The consequenceof not knowing the initial kinematics of the bound electron is a fundamental physical limit for the angular resolutionof a Compton telescope. This effect is called Doppler-broadening of the angular resolution (see also Section 2.4.2 andZoglauer & Kanbach (2003)).Assuming we can measure the energy and direction of the scattered gamma ray ( E g , (cid:126)e g ) and of the recoil electron( E e , (cid:126)e e ), we can use the relativistic energy-momentum relation E rele = (cid:112) E + p e c = E e + E (with E = m c )and the relation between energy and momentum of photons E g = p g c to derive the energy and direction of the initialphoton: E i = E e + E g (3) (cid:126)e i = (cid:112) E e + 2 E e E (cid:126)e e + E g (cid:126)e g E e + E g (4) Zoglauer et al.
Figure 2.
The operating principle of a non-electron-tracking, compact Compton telescope such as COSI. The primary gammaray undergoes one or more Compton interactions before it is ultimately stopped via a final photo absorption. The origin of thegamma ray can be restricted to a Compton event circle on the sky. The positions (cid:126)r and (cid:126)r determine the direction of the axisof the Compton event circle and the energies are used to determine the Compton scatter angle. In the same way, the scatter angle ϕ of the gamma ray can be determined. This is called the Compton equation :cos ϕ = 1 − E E g + E E g + E e (5)Compton telescopes consisting of large volume solid-state detectors, such as COSI, cannot determine the directionof the recoil electron (cid:126)e e . Due to this missing information, the origin probabilities of the gamma ray on the celestialsphere can only be restricted to a cone given by the above Compton-scatter angle and the direction of the scatteredgamma ray (see Figure 2, Compton event circle).Five years after Compton’s discovery, Klein & Nishina (1928) derived the differential Compton cross section (cid:0) dσd Ω (cid:1) for unpolarized photons scattering off unbound electrons and then Nishina (1928) derived the differential cross-sectionfor linearly polarized photons: (cid:18) dσd Ω (cid:19) Compton, unbound, polarized = r e (cid:18) E g E i (cid:19) (cid:18) E g E i + E i E g − ϕ cos ϑ (cid:19) (6)Here ϑ is the azimuthal or polar scatter angle. Linearly polarized incoming gamma rays result in a cosine-shapeddistribution in the azimuthal Compton scatter angle. This effect is most pronounced at lower energies and for Comptonscatter angles around 90 degrees. See Lei et al. (1997) for a more in depth description of Compton polarimetry.2.3. The Point-Spread Function and the Compton Data Space
Considering a normal camera (or even an X-ray focusing telescope), the direction of an incoming photon is translatedinto an x-y-position on the sensor. A point source will lead to a point-like peak on the sensor which is broadeneddue to imperfections in the optics. This is called the point-spread function (PSF). The space spanned by the x-y
OSI: From Calibrations and Observations to All-sky Images Figure 3.
Left: Schematic showing the connection between the Compton scattering process and the Compton data space: Agamma ray arrives at the detector from the direction ψ , ξ in Galactic coordinates. It undergoes Compton scattering with theCompton scatter angle ϕ , and the scattered gamma ray continues on in direction ψ g , ξ g in Galactic coordinates. Right: Thisinformation is then entered into the Compton data space spanned by the dimensions ψ , ξ , ϕ . In this data space, a point sourcecreates a cone with a 90-degrees opening angle which points at the origin of the gamma rays ( ψ , ξ ). measurement positions is called the data space, and the sky is the image space. In this simple setup, the image isreadily discernible in the x-y data space.A modern Compton telescope measures a set of positions with energies, i.e. the raw Compton data space consistsof the dimensions E , x , y , z , ..., E N , x N , y N , z N , where N is the number of interactions. The PSF is a complexhypersurface in this data space and an image is not easily discernible. However, this data space contains moreinformation than is strictly necessary for data analysis and especially image reconstruction. For example, the keyinformation that the interaction positions encode is contained in the first two interaction locations, representing thedirection of the scattered gamma ray. The key information that the energies encode is the Compton scatter angleof the first Compton scatter. The minimum data space for imaging therefore just contains these three dimensions:the direction of the scattered gamma ray in celestial coordinates such as Galactic longitude ψ and latitude ξ and theCompton scatter angle ϕ . To get images in celestial coordinates, all directions are converted from detector coordinatesto celestial coordinates considering the pointing of the instrument. In this data space, a point source creates a conewith opening angle 90 degrees pointing at the origin of the gamma rays in the sky ( ψ , ξ ). This is a more intuitivelydiscernible PSF of a Compton telescope. This data space is called the Compton data space (CDS) or sometimes, afterthe instrument it was first used for, the COMPTEL data space (e.g. Sch¨onfelder et al. 1993). Figure 3 illustrates theconnection between the Compton scattering process and the Compton data space.According to the Klein-Nishina equation, the orientation of the scatter plane defined by the directions of the initialand the scattered gamma ray is random in the absence of polarization and geometry effects, resulting in the cone shapeof the PSF. The cone points at the source of the gamma rays since — as the Compton scatter angle goes towards zero— the direction of the scattered gamma ray becomes identical with the direction of the incoming gamma ray, whichrepresents the source of the gamma rays (see Figure 3 left). The cone has a 90-degree opening angle since the deviationof the scattered gamma-ray direction from the known origin direction is the Compton scatter angle, the same as the ϕ -axis in the CDS. This means the Compton scatter angle is encoded twice in the PSF, once derived from geometryand once derived from the kinematics. While this might seem redundant, it encodes important information about theresponse of the instrument, i.e. how accurately we can determine the Compton scatter angle with the detector due tothe kinematics and position resolution. Zoglauer et al.
The occupancy of this Compton cone is not equal everywhere. Along the Compton scatter angle axis, the summedoccupancy is given by the probability that the gamma ray scatters by this Compton angle, which is determined bythe Klein-Nishina cross-section. In the ψ - ξ -plane, linear polarization of the incoming gamma ray would cause a cosineshaped amplitude modulation on the cone. Both distributions are modified again by the detector geometry, whichmight prefer or suppress certain scatter angles and directions.This data space is a simplification, because it does not include all of the information contained in the raw dataspace which comprises all interaction locations and deposited energies. For example, the distance between the firsttwo interactions influences the angular resolution. The uncertainties inherent to all measured locations influencethe determination of the axis of the Compton cone, and this influence is largest for small distances between theinteractions. As mentioned above, the occupancy of the cone along the Compton-scatter-angle axis is influenced bythe Klein-Nishina equation, and thus smaller Compton scatter angles dominate at higher energies. As a consequence,for the data analysis, in addition to the three dimensions in the default PSF, we ideally also want to include themeasured energy and the distance between the first two interactions.Concerning the relation of this data space with the image space, picking one ( ϕ , ψ , ξ ) element in data space, anddetermining which locations on the sky contribute to it, shows the classical Compton event circles in the sky (seeFigure 2), i.e. without knowing the direction of the recoil electron the gamma ray could have originated from anylocation on this Compton circle in the sky.The width of the cone wall determines the angular resolution of a Compton telescope. The most frequently usedproxy for the angular resolution is the ARM, the Angular Resolution Measure. An example can be found in Figure 6.The ARM is a one-dimensional projection of the Compton cone in the CDS; it is a histogram of the smallest distancebetween a measured ( ψ , ξ , ϕ )-value and the ideal Compton cone. Since the ARM is a one-dimensional projection of thethree-dimensional response, it has a few limitations. Especially at smaller Compton scatter angles, which dominate athigher energies, it overpronounces the wings of the response, since there the counts in the wings spread out over a muchlarger area in the three-dimensional CDS than in the one-dimensional ARM. In addition, any systematic deviationsfrom the ideal Compton cone lead to a broadening of the ARM. This, for example, happens for higher energy COSIevents (above a few MeV). At these energies, the recoil electron can travel a few strips. Since the start point cannotbe determined with COSI, the center of energy is used as the location of the interaction. This positional shift resultsin the direction of the scattered gamma ray to systematically being reconstructed a bit outside of the cone of the idealPSF. Since larger Compton scatter angles mean larger energy transfers to the recoil electron, this effect worsens withlarger scatter angles. Therefore, while in the CDS the width of the cone stays almost the same, the core of the ARMgets artificially broadened. However, despite these limitations, the FWHM of the ARM is the most frequently usedmeasure for the angular resolution of a Compton telescope.Overall, the CDS is the space where all of the actual data analysis happens, not the image space with its overlappingCompton circles. In the 3-dimensional CDS, a point source is represented by a 2D cone and thus very uniquelyconfined. It thus holds a strong discriminating power, and the most sensitive analysis can only happen in this dataspace.This is also the biggest advantage of Compton telescopes over their key competing telescope technology in thisenergy band, coded masks: while for a coded mask the PSF (the unique mask pattern for each direction) is distributedover the whole data space (in this case the detector plane), and therefore all measure background events contribute tothe source-to-background ratio, for a Compton telescope only the events below the core of the PSF contribute. Thisimproves the source-to-background ratio by typically a factor of 30–100 depending on the angular resolution.2.4. The broadening of the PSF
The PSF of a real-world Compton telescope is not a perfect cone. The cone wall is subject to broadening due to theuncertainties in the measurement process determining energies and positions, as well as due to physical limits. Beloware all effects listed which influence the COSI-2016 PSF, roughly sorted from largest to smallest contribution to theshape of the core of the PSF. However, as long as all of these effects are accurately accounted for in the simulations oradded in the post-processing of the simulation data (see Section 3.2, detector effect engine) and therefore are includedin the simulated PSF’s used for data analysis, no negative systematic effects are expected in the data analysis.2.4.1.
Position measurement uncertainty
COSI’s cross-strip detectors have a fixed position resolution for each voxel (2 × × ). This directly influencesthe accuracy with which the direction of the scattered gamma ray can be determined. This causes a certain jitter in OSI: From Calibrations and Observations to All-sky Images ψ , ξ )-dimension of the PSF. Due to the smaller average distance between interactions at lower energies, and thussmaller lever arms, this effect is more pronounced at lower energies.For COSI, another effect is the travel range of the electrons in the germanium. The recoil electrons resulting fromgamma rays with a several MeV can travel a few millimeters and thus can be measured across several strips. However,it is not possible to determine which strip has been initially hit. Therefore the average position is chosen as theinteraction position, increasing the position uncertainty.For COSI-2016, position uncertainties have the most influence on the width of the PSF and limit the angularresolution to a few degrees. 2.4.2. Doppler broadening
The standard Compton equation assumes that the gamma ray scatters off of an electron at rest. In reality the electronis bound to a germanium atom and has an unknown momentum at the moment of the scatter. This results in a slightlydifferent direction and energy of the scattered gamma ray compared to what is expected from the standard Comptonequation. For COSI, the additional broadening of the PSF is strongest at lowest energies and large scatter angles. Thiseffect is called Doppler broadening and is the fundamental limit to the angular resolution that a Compton telescopecan achieve (Zoglauer & Kanbach 2003). For germanium, this results in a roughly 1-degree (FWHM) resolution limitat 1 MeV (depending on the exact event selections), and roughly 3 degrees at 200 keV.2.4.3.
Energy measurement uncertainty
The precision with which the deposited energies can be measured depend on detector material and the read-outelectronics, and directly influence the calculated Compton scatter angle via Equation 5. Considering the 3D PSF,the energy resolution will cause a broadening of the PSF in the ϕ direction. However, this is not a trivial relation.For example, the nearly constant energy resolution as a function of energy of COSI has a more substantial impact atsmall and large scatter angles (see, e.g., Zoglauer 2005, chapter 2). Due to COSI-2016’s excellent energy resolution,on average, this effect has only a minor influence on the broadening of the PSF.2.4.4. Lost interactions
A realistic Compton detector contains passive material in addition to the active detectors and has a finite size. As aconsequence, some of the Compton interactions will be in passive material and the finite size means that photons canescape the detector volume. If just the first interaction is in passive material, then the Compton sequence will looksimilar to a “normal” one which is completely contained in the detector, but the event will be off its true location inthe Compton data space and will appear like background. This is also the case if one or more of the middle or thefinal interactions are missing. However, at least some of these events can be rejected in the reconstruction process,since none of the possible Compton sequences will be compatible with the kinematics of Compton scattering.2.4.5.
Charge sharing
While the recoil electron is slowed down and stopped in the germanium, it creates electron-hole pairs which moveto the opposing electrodes along the field lines. The distance travelled by the electron before it is stopped, alongwith charge diffusion and repulsion, cause a spread of the charge cloud. As a consequence, some interactions (more athigher energies) will be shared between multiple strips. This has the effect of worsening the energy resolution sincethe energy measurement uncertainty of each strip impacts the total energy uncertainty. In addition, in some cases theenergy shared on one of the strips might be below the read-out threshold leading to a energy loss up to the thresholdenergy. As consequence, the PSF will be broadened in the ϕ direction.2.4.6. Reconstruction
A critical step in the data analysis pipeline of Compton telescopes is determining the path of the gamma ray inthe detector (see Section 3.4). In a few cases it will not be possible to find the correct path, due to measurementuncertainties, Doppler broadening, and since it is not always possible to determine the direction using Comptonkinematics alone (see Zoglauer 2005). If events with two interactions are incorrectly reconstructed, the flight path willsimply be reversed. These events will create additional structures in the data space besides the Compton cone, andthus complicate the analysis. For three or more interactions, the number of possible paths scales with the factorial ofthe number of interactions and any additional structures quickly blend into the noise far off the Compton cone.
Zoglauer et al.
Excess interactions
It is possible to have excess interactions. These can originate from random coincidences of two or more gamma rays.Another possibility is a recoil electron leaving one germanium layer and hitting another one — some of these eventscan be rejected since the location of the two interactions is right at the top and bottom edge of adjacent detectors.Finally, at least at higher energies, bremsstrahlung photons emitted from higher energy recoil electrons can result instray hits. If these event types are not identified, they will again appear as background in the CDS.2.4.8.
Fluorescence
Both photoelectric effect and Compton scattering kick an electron out of the germanium atom and leave a hole. Theexcited atom then relaxes via Auger effect (electron emission) or fluorescence (photon emission). The highest energyfluorescence photons (the K-alpha’s and K-beta’s around 10 keV) can sometimes travel to the next strip, or, if theinteraction happened close to the top if the detector, escape the detector and either interact in the next detector or inpassive material. However, due to the low energy of these photons, any energy deposits are usually below the read-outthreshold. This results in a small energy loss, and thus an additional broadening of the PSF in the ϕ -direction.In summary, all these effects either influence the angular resolution or add background, and together ultimatelyreduce the sensitivity of the instrument. All of these effects are understood and accounted for the COSI data analysispipeline. THE DATA-ANALYSIS PIPELINEAn overview of the COSI data analysis pipeline that is typical for a modern Compton telescope can be seen inFigure 4. The COSI pipeline consists of two main software components and a few smaller ones based on the former:Nuclearizer (e.g. Lowell 2017) for all calibration tasks, and MEGAlib (Zoglauer et al. 2006) for simulations and dataanalysis. The pipeline starts with three different input data streams stemming either from real on-orbit observation(red), ground calibrations (blue), or Monte-Carlo simulations (green). The simulations have to pass through a detectoreffects engine (DEE) first, which applies resolutions, thresholds etc., which ensures that simulations and measurementshave identical characteristics. Subsequently, the three data streams pass through exactly the same pipeline, applyingthe calibration to measurements, reconstructing the events and identifying background, and finally high-level dataanalysis such as spectral and polarization analysis and all-sky imaging. Along this pipeline, the data are convertedfrom the initial hits in detector units such as detector IDs, strip IDs, and analog-digital-converter units before thecalibration, to event lists consisting of hits with positions and energies after the calibration, to photon lists containing,e.g., the parameters of the primary Compton interaction after the event reconstruction. The calibration measurementsare used for two main tasks, to (1) determine the calibration parameters, e.g., analog-digital-converter units of thedetector’s read-out electronics to energies, and to (2) benchmark the simulations, i.e., ensuring that the simulationsbehave exactly like measurements in all aspects. The benchmarked simulations can then be used to create responsefiles for imaging as well as other tasks such as to train neural networks for the event reconstruction. The followingsubsections describe the key elements of the pipeline in more details.3.1.
Calibration measurements
The first task of the calibration measurements is to create energy calibration files, dead strip lists, cross-talk correctionfiles, threshold files, etc. Then, these will be used to calibrate and qualify the individual event data in the eventcalibration step. The second task is to use the calibration measurements as a benchmark for simulations. This tasksets the most stringent requirements on the calibration data taken, since it requires the collection of enough photons toshow all effects causing the broadening of the response described in Section 2.4 as a function of energy and field-of-view.The following describes the key requirements to fulfill when developing a calibration plan for a Compton telescope. • The calibrations are best performed with (mono-energetic) lines from radioactive isotopes to disentangle fullabsorption (photo peak) from the Compton continuum. In addition, the calibrations need to cover the wholeenergy range of the instrument. This is especially important at the higher energy edge, as the response starts tobecome distorted. In the case of COSI, this is caused by escaping gamma rays, as well as a longer range of theelectrons in the germanium. This complicates the localization of the first interaction position and thus distortsthe PSF. Finally, the source activity needs to be well known. Since the calibrations directly inform the efficiencyof the instrument, any uncertainty here would limit the accuracy of the absolute response normalization.
OSI: From Calibrations and Observations to All-sky Images Figure 4.
The COSI data flow and data products from measurements, calibrations, and simulations to the final science results. Zoglauer et al. • Compton telescopes are inherently capable of observing gamma rays from all directions. Only geometry effects,shielding, and event selections can change that by blocking or rejecting some incoming directions, but even theseeffects need to be calibrated. As a consequence, the calibrations need to cover the complete field-of-view of theinstrument. The key modifier which needs to be calibrated here are geometry effects, such as the change of theefficiency of the instrument as a function of incidence angle. For example for COSI, the effective area as a functionof the incidence angle varies due to shield absorption and detector geometry. Finally, COSI’s anti-coincidenceshields do not block all of the gamma rays. Therefore, the transmission as function of incidence angle needs to becalibrated. Our experience with COSI-2016 showed that at least ∼
50 different incidence directions are requiredfor a good calibration of the instrument. However, these different directions can be done with different isotopes. • Simulations with at least a preliminary DEE are required to determine the minimum amount of photo-peakevents needed to identify all features of the PSF. Usually it is not the core of the PSF that determines thisamount but the wings of the response and any features in the wings in the Compton data space. See Figure 6for an illustration of the wings of the PSF in a one-dimensional projection. For COSI, the required number ofcalibration counts to fill the 4D data space of the response (PSF as a function of energy) is roughly 10 millionevents per line. However, not all calibration points need to have this number of triggers, since not all effectsinfluencing the PSF depend on incidence angle. Typically, one would perform large calibrations on-axis for eachsource and then typically two more for off-axis angles, and the remainder with roughly 1/10 of the statistics. • None of these calibrations need to be performed with sources positioned far away from the detector. About onemeter away (or just behind critical structures such as antennas) is enough. The main goal of these calibrations isto be a benchmark for the Monte-Carlo simulations. All the key far-field instrument parameters which describethe imaging performance such as effective area and angular resolution for a given incidence direction along withall response matrices can then be determined from the simulations. • The source positioning must be accurate enough to not affect the angular resolution uncertainty or localizationaccuracy beyond the overall acceptable ground calibration uncertainty. For example, for COSI, 0.2 degree sourceposition accuracy was acceptable given the instrument angular resolution of several degrees. The extent of thesource (i.e. the volume of the radioactive material) needs to be taken into account. • Knowing the environment around the detector is key to reproducing the calibration with simulations. Thisincludes the distance of the detector to the walls of the building, the material and density of the walls, any otherobjects close to the instrument of which gamma rays could scatter off (including the air with correct pressureand humidity), and any other radioactive sources close to the detector (e.g. Radon released into the air fromthe ground, K-40 included in concrete). In addition, good knowledge of the calibration source itself (material,amount, enclosure) is required, including the structure holding the source. All these need to be included in thesimulation model for benchmarking. It is not enough to just know the environment, but part of the calibrationplan should be regular background measurements, to understand the natural radioactivity around the source.While this consumes some calibration time, we emphasize the need to define the wings of the PSF of a Comptontelescopes accurately, especially because of the low number statistics there, and thus the relatively larger influenceof scattered gamma rays and the natural background. • Different objectives require different calibrations. For example, COSI’s polarization capabilities need to becalibrated with either a polarized source or a normal radioactive source Compton-scattered off a secondarydetector to create secondary polarization (Lowell 2017). All the above considerations (e.g. energy range, field-of-view) are still valid for polarization calibrations. In addition, for COSI’s low energy calibration, sources needto be placed close to the corners of the detectors, so that the low energy gamma rays can reach each detectorindividually. • Different instrument sub-systems require different calibrations. For example, COSI’s shields and the guard ringssurrounding COSI’s cross-strip detectors will need their own calibration plan and are as critical for getting thedata analysis correct as the main detector.
OSI: From Calibrations and Observations to All-sky Images
Simulations and Benchmarking
Monte-Carlo simulations are used to predict the performance of the instrument, to carry out trade-off studies forthe instrument design, for observation planning, to compare observations with simulations, to train machine learningtools for event reconstruction, and to create response files for imaging, spectral, and polarization analysis. In orderto accomplish these tasks, the simulations must be able to reproduce the measurements within a certain, acceptablemargin. The process of matching simulations with calibration measurements is called benchmarking. The part of thesoftware which makes the simulations resemble the actual measurements is the detector effects engine (DEE). COSI’ssimulations engine is cosima (Zoglauer et al. 2009). Cosima is part of MEGAlib and based upon Geant4 (Agostinelliet al. 2003; Allison et al. 2016) and Geant4 is very well benchmarked in COSI’s energy range. These are the steps thesimulations and DEE need to cover to achieve a good benchmarking: • A central element of the simulation and the DEE is the mass model of the telescope. This mass model shouldaccurately reproduce the actual setup regarding volumes, their material (elemental and isotopic composition,density), and their placement. The closer the volumes are to the detector, the more accurate the mass modelshould be. Inaccuracies here will show up in the efficiencies of the photo-peaks, the Compton continuum, andalso during simulations of instrumental activation which requires the correct isotopic composition. Concerningthe benchmarking of calibration sources, the mass model also should contain the details of the calibration sourceand the structures which hold the calibration source, since scatters in this material will be directly visible in themeasured spectra. In addition, the general environment such as air, walls, floors, and natural radioactivity needto be included. • In the case of simulations of actual on-orbit performance, the simulations have to include the full on-orbit back-ground including all components such as cosmic photons and primary cosmic-ray electrons, positrons, protons,and ions. If the instrument is close to Earth, it has to include the secondary radiation generated from cosmic-ray interactions with the atmosphere such as Albedo photons, protons, neutrons, electrons, and positrons. Ifthe satellite moves through the radiation belts (e.g. the South Atlantic Anomaly), the interactions with thoseprotons and electrons have to be included as well. Finally, besides the primary particles, the delayed radioactivedecays after a certain time in orbit (e.g. one year) resulting from proton, neutron, and ion activation have to beincluded. Cosima is set up to perform all these tasks. A detailed overview of the background model is presentedin Cumani et al. (2019). • The next step is to perform the actual Monte-Carlo simulation of the source with Cosima/Geant4. The simula-tions must include all the relevant physical processes the particles can undergo, ranging from photo effect to paircreation for gamma rays, from multiple scatters to bremsstrahlung for charged particles, from elastic to inelasticinteractions for hadrons, and nuclear decay for nuclei. Cosima/Geant4 are fully set up for these simulations. • The result of the simulation is an event list containing the locations of energy deposits in the detector withoutany simulated noise (energy resolutions, etc.) applied. These data need to be stored with enough accuracy sothat in a second simulation step the charge transport in the detectors can be simulated. • The next step is to apply the detector effects engine to the simulated data. For COSI, the DEE includesthe simulation of charge transport of electrons and holes to the electrodes, the discretization of the locationsinto strips, handling energy resolution and read-out thresholds, position resolutions, analog-to-digital converteroverflows, charge loss, coincidences, dead-time, and more. See Sleator et al. (2019) for an overview of the COSIDEE. • Benchmarking the DEE is a complex, iterative, and thus time-consuming task. It involves comparing manyaspects of the simulation data to the calibration data such as the individual spectra of individual strips, thecombined spectra, the interaction locations in x, y, z, trigger rates, number of triggered strips per event andas a function of energy, the distances between the interactions, Compton scatter angles, the angular resolution,and ultimately the whole PSF. When differences show up, either individual effects in the DEE or the mass-model need to be adjusted. For example, differences in the photo-peak count rates in individual strips can be Two limitations of the approach described in Sleator et al. (2019) have been identified, regarding the simulation of the charge sharingand the COSI depth resolution making the performance shown in Sleator et al. (2019) worse then it should be. Zoglauer et al. caused by differences in the coincidence and trigger system, issues with the mass model, wrong source intensity,incorrectly modeled charge sharing, etc. Differences in the width of the photo-peak usually just originate fromthe energy resolution. Tailing of the photo-peak, i.e. an asymmetry from the usually Gaussian shape extending tolower energies, originates from either charge loss between strips or charge sharing. Differences in the continuumcan again be attributed to, for example, charge sharing, scatters in the environment or the source holder, ordifferences in the instrument mass model (e.g. missing mass). Further details are presented in Sleator et al.(2019). 3.3.
Event calibration
Event calibration is the first step which is identical for all three data streams in Figure 4. In this step, the datain detector units (strip and detector number, ADC units for energy, timing) are converted to interaction locationsand measured energies in keV. For COSI, the event calibration is performed in the Nuclearizer tool (Lowell 2017) andconsists of these steps: • Coincidence: The time difference between hits is used to determine which hits belong to the same event. • Aspect determination and interpolation: The pointing information is determined more coarsely (once per second)compared to the number of triggered events. This step determines the pointing of the instrument in Galacticcoordinates at the time the event is measured. • Energy calibration: The measured energy is converted from ADC units to keV for each triggered strip. • Charge-loss correction: Interactions spanning two or more neighboring strips lose some energy in the gaps betweenthe strips. The energy loss follows a deterministic equation and thus can be corrected. • Cross-talk correction: Cross-talk is an artificial enhancement of the measured energy of one strip, when aneighboring strip also triggers. This effect can be calibrated and corrected in the COSI detectors. • Strip pairing: COSI’s detectors are cross-strip detectors, i.e. a location can be determined from the x and y striplocation. While this is trivial for one interaction, it is more complicated if there are two or more interactionsin the detector. However, using the energy information, either a Greedy (e.g. Jungnickel 1999) or χ -approach(Zoglauer 2005) can usually determine the interaction locations. • Depth calibration: When an interaction in the detector creates an electron-hole pair cloud, the electrons and holesdrift to different electrodes. The relative arrival time between the electrons and holes allows for the calculationof the depth (the z-axis value) of the interaction in the detector. • Position determination: The final step is to convert the interaction locations in the detector into the worldcoordinate system. 3.4.
Event Reconstruction
The next step in the data pipeline is the event reconstruction, which converts the unsorted hits consisting of locationand energy to the parameters of the initial Compton interaction (location, Compton scatter angle, etc.). This stepincludes the event pattern identification (is it a good Compton event?), Compton sequence determination (finding thepath of the gamma ray in the detector), and background probability determination (did the gamma ray originate fromthe atmosphere below or from internal decay; did it escape?). Within MEGAlib, the “Revan” tool is responsible forthe event reconstruction.The critical step here is the Compton sequence reconstruction. The COSI detector is too compact and the timeresolution in the germanium detectors is too coarse to determine the relative time of the individual interactionsaccurately enough to find the natural temporal sequence of the Compton interactions in the detector. Therefore COSIhas to rely on the kinematics along with the interaction probabilities to determine the sequence of interactions.The information which can be used includes: • The Klein-Nishina probability that a given Compton interaction happens with the detected Compton scatterangle given the measured energy of the event.
OSI: From Calibrations and Observations to All-sky Images Figure 5.
The goal of event reconstruction: From a set of positions r n and energies E n derive the known path of the gammaray within the detector with known Compton scatter angles ϕ n and flight directions d n . • The probability that the given distance between the interactions is observed given the material between theinteractions and the energy of the travelling gamma ray. If this is the last segment of the Compton track, thenthe photo-absorption probability is used. Otherwise, it uses the Compton scatter probability. • For middle interactions (see Figure 5), the Compton scatter angle ϕ l can be calculated via kinematics (Comptonequation using E l as energy of the recoil electron and E m as the energy of the scattered gamma ray) as wellas geometry (difference between the incoming d k and outgoing d l gamma-ray direction at interaction l ). Thedifference between those two angles should be zero within measurement uncertainties for the correct sequence.Any event reconstruction approach now needs to look at all possible paths and determine the above information foreach possible segment of the path. The number of possible paths is the factorial of the number of interactions, e.g.3!=6 for 3 interactions. The task of the reconstruction approach is then to find the path which is most in agreementwith the interaction physics, and therefore is most likely the correct path.To date, four unique approaches have been developed: the “classic” approach (e.g. Boggs et al. 2000; Zoglauer2005), a Bayesian approach (an older version is described in Zoglauer 2005; Zoglauer et al. 2007), and two machinelearning approaches where one is based on a random forest of decision trees and the other is based on a shallow neuralnetwork (an older version of this approach is described in Zoglauer & Boggs 2007). Figure 6 shows a comparisonof these approaches using an angular resolution measure (ARM) plot that includes data from an on-axis calibrationmeasurement of COSI with a Na source using the 511-keV line. The correctly reconstructed events show up around0 degrees, and wrongly reconstructed events accumulate to the right in the bump. Currently, the most accurateevent reconstruction approach is the neural-network method, since it produces the fewest number of incorrect eventreconstructions, and therefore has the smallest bump at large angles. Since the Na source has an additional line at1275 keV, the Compton continuum of this high-energy line contributes to the measured 511 keV photons used in thisanalysis. Therefore, the wings of the PSF are artificially broadened.3.5.
Response and machine learning data sets creation
Many of the approaches within the pipeline are driven by predefined data sets which describe how the instrumentworks. These include response files for spectral analysis and image reconstruction, as well as files containing the trainedrandom forest and neural networks for event reconstruction. In general, these data sets are created from simulationswhere all necessary information about the initial parameters of the gamma ray and its interactions in the detector arestored.For example, the training data sets for machine learning-based event reconstruction contain two data sets: one withthe parameters of all the correct paths, and another one with all the incorrect paths. The information is derived fromthe simulations file which contains the sequence of interactions. Then the two data sets are used to train the neuralnetwork or the random forest to classify a given path as correct or incorrect.Another example is the creation of response files for spectral analysis. This requires a large simulation of photonsimpinging isotropically on the detector with a flat spectrum covering the whole operating range of the detector. From4
Zoglauer et al.
Figure 6.
Comparison of the different COSI event reconstruction approaches using the ARM as the performance metric. Thecount rate on the y-axis is plotted in logarithmic scale to accentuate the “wings” of the PSF, i.e., the counts accumulated far offthe core of the PSF at 0 degrees. The correctly reconstructed events are in the peak around 0 degrees, wrongly reconstructedevents accumulated at the bump between 30 and 120 degrees. The lower the bump, the more accurate is the event reconstructionapproach. Therefore, the neural network approach is currently the best event reconstruction method. this information a 4D matrix is created connecting the initial direction and energy of the gamma ray with the measuredenergy of the event.An example of how to create the imaging response can be found in Section 4.2.3.6.
High-level data analysis
The final step is the high level data analysis. This includes spectral analysis (Sleator (2019) presents results for theCrab and GRB160530A), polarization analysis (Lowell (2017) shows results for GRB160530A), and image reconstruc-tion, to which the next chapter is dedicated. ALL-SKY IMAGINGThe measurement process of a Compton telescope can be described in the following way: D ( ψ, ξ, ϕ, E m ) = R ( ψ, ξ, ϕ, E m ; µ, ν, E i ) × I ( µ, ν, E i ) + B ( ψ, ξ, ϕ, E m ) (7)The sky distribution of gamma-ray emitting sources I , which is a function of the celestial sky coordinates (e.g. Galacticlongitude µ and latitude ν ) and the energy of the gamma ray E i , is convolved with the detector response R . Addingsome background B to the data space results in the measured data D . Here ψ and ξ are the direction of the scatteredgamma ray in celestial coordinates (e.g. Galactic longitude and latitude), ϕ is the Compton scatter angle, and E m is the measured energy. Inferring the sky distribution I from the measured data D is an inverse problem. Since thedetector measurement process includes a certain amount of randomness and due to the limited number of measuredgamma rays, the problem is not directly invertible. As a consequence, the source distribution can only be retrievedusing either model fitting approaches or iterative image reconstruction approaches.For imaging, six key elements are required: OSI: From Calibrations and Observations to All-sky Images • the infrastructure • the observed or simulated data • optimized event selections • an accurate detector response • a background model which ideally accounts for all individually varying background components • one or more image reconstruction methodsThe infrastructure is the MEGAlib toolkit and the observations and simulations are performed with COSI. Theother elements are described below. 4.1. Optimized event selections
Some parts of the data space are highly contaminated with background and do not contain a significant amount ofsource photons. Eliminating all these events can improve the sensitivity of the resulting images.For COSI, one of these selections is the so called Earth horizon cut. The Earth’s atmosphere at COSI’s flight altitudeis extremely bright in gamma rays, and can dominate any source. To avoid this, we apply the Earth horizon cut, whicheliminates all events whose Compton event circle dips below the 90-degrees zenith angle mark, which we consider beingEarth’s horizon.Another key selection for COSI is a distance cut between the interactions in the detector. Events with a very smalldistance between first and second interaction have a very bad angular resolution (e.g. ∼
55 degrees for 0 . ± .
05 cmdistance at 662 keV). These events do not contribute very much to the imaging performance and are frequentlyincorrectly reconstructed. Therefore, COSI uses a standard 0.5 cm minimum distance cut.4.2.
The Compton Imaging Response
The instrument imaging response connects the image space to the Compton data space described in Section 2.3.Assuming a binned image space spanning the celestial sphere in Galactic coordinates, the imaging response describesthe probability that an event emitted in the given image bin (with the given energy and possibly polarization) isdetected in a given data space bin. The simplest version suitable of nuclear-line imaging is a 5D matrix containingthe Galactic latitude µ and longitude ν and connecting these to the Compton data space with the three dimensionsCompton scatter angle ϕ and the direction of the scattered gamma ray in Galactic latitude ψ and longitude ξ . Pickingone image bin and looking at the 3D Compton data space, one would see the familiar Compton cone described inSection 2.3. On the other side, picking one data space bin and looking at the image space, one would see a Comptonevent circle centered on the direction of the scattered gamma ray with an opening angle corresponding to the Comptonscatter angle. This corresponds to the Compton event circle in Figure 2.Depending on the science objectives, different additional dimensions would be helpful for imaging. For continuumimaging, an energy dimension is required (ideally one for the image space and one for the data space) to do full spatial-spectral deconvolution. For polarization-resolved imaging, the polarization angle and amplitude could be added to theimage space. Furthermore, an additional dimension in the data space containing the distance between the first twointeractions can help improve the performance for COSI, since the angular resolution is strongly influenced by thisparameter — the smaller the distance the worse the angular resolution.Creating this response via simulations is the most computationally expensive task of the data analysis of a Comptontelescope. For COSI, we use a 5-degree/ ∼ ∼ π steradian of these are occupied due to the field-of-view of the instrument.As a remark, there is another approach to generate responses called “list mode” (e.g. Wilderman et al. 1998; Zoglauer2000; Zoglauer et al. 2011), where the response is calculated from the measured parameters directly. While this methodis well suited for terrestrial applications where the goal is to find single strong sources (e.g. environmental monitoringor even COSI calibrations), this method is not well suited for astrophysics, since it lacks the capability to modelanything outside the core of the response and does not allow the determination of the absolute flux.The initial response as simulated is in detector coordinates. However, in order to perform imaging in Galacticcoordinates, the response has to be converted into Galactic coordinates. COSI is a scanning instrument, i.e. it always6 Zoglauer et al. points upward and does not stare at a fixed location. As a consequence, its pointing in Galactic coordinates constantlychanges. Therefore, in order to get the response in Galactic coordinates, we have to follow the pointing in smalltime steps (see Siegert et al. 2020), and rotate the response into the new coordinates and scale with time. A specialconsideration for the COSI balloon flight is the atmospheric absorption of the gamma rays as a function of the zenithangle. This reduction of efficiency has to be considered when transforming the response into Galactic coordinates.This new response can then be directly used for imaging. It contains the probabilities that a gamma ray emitted froma certain position in the sky is detected in a certain data space bin within the total observation time.4.3.
The Background Model
The low-energy gamma-ray regime is dominated by background — a source to background ratio of 1 to 100 is notuncommon for sources at the detection limit, especially when the instrument is flown on a balloon platform. As aconsequence, the retrieval of the source parameters (flux, spectral parameters, etc.) requires a robust backgroundmodel. This can be developed in several different ways. For example, when looking at nuclear line emission fromthe Galactic disk, one can choose observations where the disk is not in the field-of-view. Alternatively, one canchoose adjacent energy bands, e.g. 1820-1850 keV when looking at the 1809 keV line. Another option, assuming thebackground is well enough understood and is reproducible with Monte-Carlo simulations, is to simulate the individualbackground components. This would then allow for the influence of different components to be disentangled, forexample, 511 keV from internal beta-decays versus 511 keV from atmospheric positron annihilation. Both componentsshould behave differently in the data space as a function of altitude, latitude, and longitude for a balloon flight, oras a function of time after the last SAA passage (resulting in increased short term detector activation) for a satellitemission.Similarly to the response, this initial background model will be in instrument coordinates and has to be rotated insmall time steps along the pointing changes of the instrument into Galactic coordinates and scaled with time. Theabsolute normalization of the model will be part of the next step. However, if the model (or some of its components)vary consistently with some external parameter (e.g. balloon altitude, geomagnetic cutoff), then this scaling can beapplied here. 4.4.
Creating images
Now everything is in place for the final all-sky image creation. An overview of all available approaches can befound in Frandes et al. (2016). For space-based Compton telescopes, the most commonly used approaches are theRichardson-Lucy (RL) approach which is also known as Maximum-Likelihood Expectation-Maximization (ML-EM)(Richardson 1972; Lucy 1974), the Maximum-Entropy (ME) approach (Strong 1995), the Multi-resolution RegularizedExpectation Maximization (MREM) approach (Kn¨odlseder et al. 1999), and model fitting (MF) methods (see e.g.Siegert et al. 2020, for a direct application to COSI).The different methods have their advantages and disadvantages. The model fitting approaches, as the name says,are an easy way to compare different source distribution models, but can only find features which are part of the modelor which can be composed of multiple copies of the model; MREM approaches can create a very smoothed solutionwith the risk of smoothing out weaker point sources or finer structures; RL approaches are better suited to find pointsources but tend to quickly amplify noise; ME approaches are a middle ground between RL and MREM. All iterativemethods (RL, MREM, ME) have the challenge that there is no well-defined way to determine when the iterationsshould stop. One approach is to look at the likelihood (RF, MREM) or the entropy (ME) at a given iteration, andstop the reconstruction when the changes fall below a preset level or start to oscillate. Another way is to look atstrong point sources (real ones or injected ones), and stop the reconstruction as soon as their resolution (e.g. FWHM)reaches the instrument resolution. 4.5.
Application to the COSI 2016 balloon flight
The most prominent all-sky source measured during the 2016 COSI balloon flight is the 511-keV annihilation line.As known from previous observations with SPI (e.g. Skinner et al. 2015), the emission is concentrated near theGalactic center region, with much weaker emission from the Galactic disk. With the limited balloon flight data,COSI achieved a 7-sigma spectral detection of this line itself (Kierans et al. 2020). However, spreading this 7-sigmasignal in image space to generate an all-sky image results in large uncertainties. Therefore, several approaches havebeen applied, including two image deconvolution approaches. The methods differ not only in the algorithm used, but
OSI: From Calibrations and Observations to All-sky Images Figure 7.
The 511-keV annihilation line image measured with COSI using 100 iteration of a Maximum-Entropy deconvolutionapproach.
Figure 8.
The 511-keV annihilation line image as measured with COSI using 26 iterations of an adapted Richardson-Lucyapproach (image adapted from Siegert et al. 2020). The black areas have no exposure and are excluded in the analysis. Zoglauer et al.
Figure 9.
Image of the Crab pulsar and nebula as seen with COSI in the 325-480 keV energy band using 98 iterations of anadapted Richardson-Lucy approach. The black areas have no exposure and are excluded in the analysis. also the event selections, observation time selection, background modeling, and ultimately implementation (MEGAlibbased on ROOT and C++ versus COSIpy, a Python3 tool, utilizing only parts of MEGAlib). Figure 7 shows the 511-keV emission after 100 iterations of a Maximum-Entropy approach (Strong 1995; Hollis et al. 1992), and Figure 8 showsthe 511-keV emission after 26 iterations of a modified Richardson-Lucy approach. Details on the latter method andthe event selections can be found in Siegert et al. (2020). The differences are mostly due to the limited statistics anddifferent data selections. The images have in common that the emission is concentrated near the Galactic Center regionand is extended, proving that COSI observed the Galactic 511 keV signal. For comparison, the angular resolutionof COSI at 511 keV is 6.6 degrees (Kierans 2018). The observed total flux is in agreement with SPI observations(see Siegert et al. 2020). However, none of the finer detailed features of these images are statistically significant.This example shows that having multiple imaging approaches is especially helpful for sources close to the detectionlimit: features appearing in images created by different approaches are likely real. A similar approach was taken forCOMPTEL’s analysis of the 1.8-MeV Al map (Kn¨odlseder et al. 1999) which used three different imaging methods.Figure 9 shows the same Richardson-Lucy approach applied to the observations of the Crab pulsar and nebula inthe 325–480 keV band — COSI’s efficiency peaks in this energy range. After 98 iterations, the Crab is clearly visibleas the brightest spot. The limited available simulation resources to create the seven dimensional continuum-imagingresponse — the five dimensions of the CDS plus two energy dimensions — limited the angular resolution in the imageto six degrees. For comparison, COSI’s angular resolution in this energy band in ∼ OSI: From Calibrations and Observations to All-sky Images Figure 10.
Measured Crab spectrum (black) which is in good agreement with the expected results: the measured power-lawindex is 2.5 ± paper. The only atmospheric effect included in the response is the reduction of the photo-peak flux due to atmosphericabsorption and scatters. This effect is not an issue for nuclear-line images, since the selection on the 511-keV lineautomatically excludes scattered 511-keV photons. In addition, it is also not a problem for space missions, since thereis no atmosphere. All other features are not statistically significant and appear near the edges of the field-of-view withlow statistics. The data used for the image include all times the Crab is less than 60 degrees away from the zenith. Asa side effect of this event selection, no other sources which have been detected with COSI are visible (Cen A, Cyg X-1),since they are too far away from the Crab. The flux value (3 . × − ph/cm /s, central plus eight surrounding pixelssince the angular resolution is larger than the pixel size) is within 5% of the expected value (4 . × − ph/cm /s,Jourdain & Roques 2020, table 2, 2012–2019 values) in this energy band. Determining the uncertainty on this fluxvalue would require detailed simulations of the scattering in the atmosphere and is beyond the scope of this paper.Figure 10 shows the observed spectrum of the Crab with a fitted power law. The error bars are determined duringthe fit of the power-law spectrum of a point source at the Crab position and the background model to the data in theCDS. The power-law index is 2.5 ± ± CONCLUSIONSThis paper has shown the measurement, calibration, and reconstruction steps necessary to turn Compton telescopein-flight data into all-sky images. We have been able to identify and quantify the many inherent systematic effectsinfluencing the COSI instrument and compact Compton telescopes in general. We have demonstrated a maturedata-analysis pipeline ready for analysis of observations from the next gamma-ray astrophysics missions, includingCOSI-SMEX and other future missions. ACKNOWLEDGMENTSWe would like to thank the NASA Columbia Scientific Balloon Facility team for enabling the successful COSI-2016balloon flight. The COSI-2016 balloon flight was funded by NASA APRA grant NNX14AC81G. Compton imagereconstruction developments were supported through NASA grant NNX17AC84G. Machine-learning developmentswere funded by NASA grant 80NSSC19K0349. Thomas Siegert is supported by the German Research Society (DFG-Forschungsstipendium SI 2502/1-1). The COSI response simulations were performed on the Cori supercomputer (partof the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of ScienceUser Facility operated under Contract No. DE-AC02-05CH11231).0
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Facilities:
COSI, CSBF, NERSC
Software:
MEGAlib (Zoglauer et al. 2006), Geant4 (Agostinelli et al. 2003; Allison et al. 2016)REFERENCES
OSI: From Calibrations and Observations to All-sky Images21