A Study of background for IXPE
Fei Xie, Riccardo Ferrazzoli, Paolo Soffitta, Sergio Fabiani, Enrico Costa, Fabio Muleri, Alessandro Di Marco
AA Study of background for IXPE
F. Xie a, ∗ , R. Ferrazzoli a , P. So ffi tta a , S. Fabiani a , E. Costa a , F. Muleri a , A. Di Marco a a INAF-IAPS, via del Fosso del Cavaliere 100, I-00133 Roma, Italy
Abstract
Focal plane X-ray polarimetry is intended for relatively bright sources with a negligible impact of background. However this mightnot be always possible for IXPE (Imaging X-ray Polarimetry Explorer) when observing faint extended sources like supernovaremnants. We present for the first time the expected background of IXPE by Monte Carlo simulation and its impact on realobservations of point and extended X-ray sources. The simulation of background has been performed by Monte Carlo based onGEANT4 framework. The spacecraft and the detector units have been modeled, and the expected background components in IXPEorbital environment have been evaluated. We studied di ff erent background rejection techniques based on the analysis of the trackscollected by the Gas Pixel Detectors on board IXPE. The estimated background is about 2.9 times larger than the requirement, yetit is still negligible when observing point like sources. Albeit small, the impact on supernova remnants indicates the need for abackground subtraction for the observation of the extended sources. Keywords:
X-Ray, polarimeter, background
1. Introduction
The Imaging X-ray Polarimetry Explorer (IXPE) is a NASAAstrophysics Small Explorer (SMEX) mission, selected in Jan-uary 2017. The launch is scheduled for 2021, by means of aFalcon 9 rocket that will deliver IXPE into an equatorial or-bit with an altitude of 600 km. IXPE is dedicated to X-raypolarimetry between 2 and 8 keV with photoelectric polarime-ters based on the Gas Pixel Detector (GPD) ([1], [2]). Themain scientific goals will be reached through the observationsof known bright X-ray sources of di ff erent classes, includingneutron stars, black holes, supernovae remnants (SNR), activegalactic nuclei (AGN). X-ray polarimetry promises to evolu-tionize the knowledge of the X-ray sources.Since X-rays from Scorpius X-1 have been detected in 1962([3]), many space missions have been approved for X-ray spec-troscopy, imaging, and timing, unfortunately only very fewmeasurements have been conducted on X-ray polarization. In1971, an Aerobee-350 sounding rocket was launched with twotypes of X-ray polarimeters onboard, a Thomson scattering po-larimeter made of metallic lithium and a Bragg di ff raction po-larimeter made of graphite crystals. Both instruments used pro-portional counters as detectors. Limited by the observationtime and unexpected high background level, only polarizationof 15.4% ± ±
10° from theCrab nebula was measured with a statistical confidence levelof 99.7% ([4]). Later in 1975, the Orbiting Solar Observatory(OSO-8) satellite with two graphite polarimeters onboard waslaunched. A more precise polarization measurement of the X-ray flux from the Crab nebula has been reported in [5], to be ∗ Corresponding author
Email address: [email protected] (F. Xie) ± . ± . ± . ± . ff ect in the gas. The emission directions ofthe photoelectrons are related to the polarization of the inci-dent X-ray photons. The GPD gas cell is filled with DimethylEther (DME) gas at 0.8 atm, which is closed on the top by theTitanium frame and the Beryllium window. An electric fieldparallel to the optical axis drifts the primary electrons producedby the photoelectron in the gas to the Gas Electron Multiplier(GEM), which is also the bottom of the active volume. Sec-ondary electrons, generated by the GEM, are collected by apixellated plane at the top of an Application Specific IntegratedCircuit (ASIC). The side of the gas cell are Macor spacers. The Preprint submitted to Elsevier February 15, 2021 a r X i v : . [ a s t r o - ph . I M ] F e b as cell has dimension of 60 × ×
10 mm , but the active vol-ume, defined as the region where charge generated by an energydeposit can be read out by the ASIC pixels, is only the central15 × ×
10 mm volume. The ASIC has 352 ×
300 pixels ar-ranged in a hexagonal pattern with 50 µ m pitch, and it providesthe fine spatial resolution required to resolve the photoelectrontrack.The standard parameter to express the sensitivity to polariza-tion is the Minimum Detectable Polarization (MDP) at a confi-dence level of 99%. It is defined as ([12]): MDP = . µ S (cid:114) S + BT (1)Where S and B are the count rates of the source and back-ground, T is the total exposure time and µ is the modulationfactor representing the amplitude of the response to 100% po-larized beam. Reducing the background is vital for achieving ahigh sensitivity. For bright point sources ( S (cid:29) B ), backgroundis negligible in practical cases as we will demonstrate below.But for extended sources, even the brightest ones, like pulsarwind nebulae, SNRs, and AGN large scale jets, for which IXPEwill perform X-ray polarimetric imaging for the first time, thebackground modeling must be treated with care.In this paper, we evaluate the background based on MonteCarlo simulation, to estimate the in-flight background level in adetailed way. By understanding the characteristics of the back-ground and their impact on the statistics of the measurement,methods for background rejection are proposed. This paper isorganized as it follows: Section 2 presents the details of thesimulations, and Section 3 presents results from the simula-tion as well as the developing of the rejection methods. Sec-tion 4 discusses the impact of background for point and ex-tended sources, and Section 5 presents the conclusion of thework.
2. Background simulation
Background simulation are developed based on the Geant4framework ([13]), a toolkit for Monte Carlo simulations. Bytracking the particles interacting with the detector, the originand the phenomenology of the background are understood. Toperform the simulation, the geometric model of the spacecraft,the input background spectra of the orbit environment and thephysics model of the interaction are needed. Then, mimick-ing the data processing and analysis of real data, selections areapplied in order to determine the background rates. Geant4 ver-sion 10.03.p01 has been used in this work. The geometric model is an important ingredient for MonteCarlo simulation. In IXPE simulator, the construction of thegeometric model is based on the latest design ([10]) and imple-mented in two steps. The first step is the construction of the http://geant4.web.cern.ch/support/download_archive?page=1 core payload GPD, which is implemented in the ixpesim soft-ware developed by the IXPE Italian Team. From the top to thebottom there are 50 µ m Beryllium window with 53 nm Alu-minum coating layer, 10 mm DME gas and 50 µ m GEM with5 µ m Copper coating on both sides. Gas is enclosed at theirsides by the MACOR (a glass ceramic mainly composed of sil-ica SiO and various oxides, including MgO, Al O K O andB O etc.) spacer. This is the basic setup in the laboratory.Both simulations and measurements show that when a photonis absorbed near the surface separating the DME gas cell andthe passive materials that seal it, in many cases the charges pro-duced by ionization processes are partially generated in the gas,where they are detected, and partially in the Be window or inthe GEM where they are lost. Further events could be generatedin the gas though the initial photons are already lost in the pas-sive materials. These kind of events usually result in a left tailin addition to the Gaussian profile for a monochromatic beamand have relatively smaller track size. But this also requiresthat the materials contiguous to the gas cell are described verycarefully in the mass model. Figure 1: A sketch of the Geant4 mass model of one detector unit, collimator(white), calibration wheel and calibration sources (grey), GPD (magenta) andPCBs (green) are presented. Structural details are hidden for a clear illustration.
To evaluate the background in a realistic configuration, webuilt on top of the first step a model of the whole satellite. Ma-terials around the detector are essential for background simula-tion. Background particles mainly come from the region out-side the field of view (FoV). They come across the materialaround the detector producing secondary particles. Some inter-act with the detector leaving a stream of charge in the gas whichare eventually detected by the GPD. For each DU, the calibra-tion wheels, the collimator, the detector shielding box and the2ack-end electronic box are implemented, as shown in Fig. 1.Three identical DUs are located on the top deck of the platformwith 120 ◦ clocking of one DU with respect to the others. Themirror modules, the deployable boom and the spacecraft areconstructed as well, though with less details. In order to speedup the simulation, the mirrors and boom are eventually removedfrom the mass model, therefore an e ffi cient spatial sampling ofthe primary source particles has been applied. The test sampleshows that the lack of mirrors and boom have no influence onthe background rate as they are far away from the sensitive de-tector, except for the cosmic X-ray background (CXB). The ma-terials around the detectors stop the low energy CXB photonswell. Without the mirrors, the background rate induced by theCXB increases significantly because the active volume of thedetector is now directly exposed to the sky through the apertureof the stray-light collimator. A cut on the incidence angle hasbeen applied on the CXB background data, by assuming thatmirrors stop the CXB background totally. The CXB reflectedby the mirrors is not part of the present work, as it gives a minorcontribution to the background in the IXPE energy band. IXPE will be launched into an equatorial orbit with an al-titude of 600 km, which minimizes the detector backgroundand optimizes the observing e ffi ciency by minimizing the pas-sage in the South Atlantic Anomaly (SAA), achieving a min-imum duty cycle of 60% from the 94.6-minute orbital period.In the radiation environment outside the SAA, the backgroundsources which need to be considered are primary (protons, elec-trons, positrons and alpha particles) and secondary (protons,electrons, positrons) cosmic rays. Primary cosmic rays are ac-celerated by celestial sources and travel through the galaxy be-fore reaching the Earth. The dominant component ( ∼ ◦ , then adapted forthe XIPE (X-ray Imaging Polarimetry Explorer) mission phaseA study with 0 ◦ inclination baseline design at similar altitude,and eventually used for IXPE in this work. The input spectra ofthese sources are detailed in Fig. 2. In order to fully describe the interactions in the spaceenvironment, electromagnetic, hadronic, and decay pro-cesses are included. For the electromagnetic inter-action, a reference physics list provided by Geant4,“G4EmLivermorePolarizedPhysics” , has been chosen as https://geant4.web.cern.ch/node/1619 Figure 2: The spectra of the background components expected in the IXPEorbital space environment. the starting point. It is a physics list recommended forlow energy electromagnetic processes, describing the inter-actions of electrons and photons with matter down to about250 eV, with the polarized gamma models included. Afterthe cross check with laboratory data, physics processes andparameters are fine tuned to fit the specific case of IXPE.For example, when considering the photoelectric e ff ect, thebuild-in “G4LivermorePolarizedPhotoElectricModel” has beenreplaced by “G4LivermorePolarizedPhotoElectricGDModel”.Because this model is optimized for measuring linearly polar-ized X-rays in the energy range of few keV, and it properlytakes the directions of the photoelectrons into account ([16]).The other physics processes are covered by Shielding physicslist, which is another reference list for space missions. Di ff er-ent production thresholds for secondary are applied for di ff er-ent regions. A default value of 0.7 mm has been kept for theworld, while 0.05 mm is applied for gas cell. This means thesecondary particles are only generated when the kinetic energyis large enough for them to travel 0.05 mm in the gas. When a particle arrives at the telescope, all the interactionsare tracked, including the secondaries generated by this parti-cle that we name primary. For clarity, the terms primary andsecondary used here are not the same as the definitions in 2.2.Referred to the technique of simulation, each individual inci-dent particle is a primary, it could be any kind of particle weare interested in. One primary particle, especially an energeticone, may generate a bunch of secondary particles through inter-actions with the mass model built inside the simulator. Thesesecondaries have possibilities to be detected and become back-ground events. Considering the storage space, only the energydeposited inside the gas is recorded. If the particle is a photon,it either passes through the gas without any interaction, or scat-ters on the electrons, or excites the inner-shell electrons to freewith kinetic energy of the di ff erence between the photon energyand the binding energy. If it is a charged particle, it ionizes the3as along the path or scatters with the nuclei, untill running outof the kinetic energy or exiting the sensitive area. Along thepath inside the gas cell, starting from the point of entry up toeither the zero-kinetic-energy or the point of exit, hundreds ofelectrons are generated and their positions are recorded. Elec-trons are drifted to the corresponding holes of the GEM, mean-while the transverse di ff usion, the Fano factor and the absorp-tion attachment ([17]) of the gas are considered. An analyticmultiplication is applied on the number of electrons for eachhole of the GEM, to represent the avalanche multiplication ofcharges. By taking into account the front-end gain, the full-scale voltage range and the resolution of the analog to digitalconverter (ADC), the Monte Carlo digitize the charge (numberof electrons) into the ADC value and projects them to the cor-responding hexagonally patterned ASIC pixels. The projectedcharge distribution on the pixelated ASIC plane is defined asthe track.As for the real detector, an event is read out only when it ful-fills two conditions: (1) At least one mini-cluster (2 ×
3. Results
We simulated CXB, albedo gamma, albedo neutron, primaryand secondary cosmic rays as mentioned above, with exposurelong enough to achieve a su ffi cient statistic. The backgroundrates of all the components are listed in Table 1. The column‘Rate in total’ are the read out events fulfilled conditions in-troduced in Section 2.4, showing that the recorded events aremainly from the primary proton, primary alpha and the sec-ondary cosmic rays. Photon-origin background including CXBand albedo gamma are not significant, while contribution fromalbedo neutron, primary electron and positron are negligible.An energy selection for the range between 2 and 8 keV cutsthe total background rate down to 1 . × − counts s − , witha rejection e ffi ciency of 70.5%, as shown in Table 1. Photon-origin background have the lowest rejection e ffi ciencies withthis method.The scientific requirement of the background level is 4 × − counts s − cm − for one DU in 2 to 8 keV, which is es-timated considering the most extended and faintest sources in the IXPE target list (X-rays reflected from the Sgr B2 molecu-lar clouds in the vicinity of the Galactic Center). Consideringthe geometric area of one DU of 2.25 cm , a background levelof (1 . × − ) / (2.25) = . × − counts s − cm − is theresult with only energy selection. This is about 12 times higherthan the requirement. An e ffi cient background rejection methodis needed. Background rejection methods are based on the fundamen-tal di ff erences between photoelectron and background tracks.A straightforward comparison is shown in Fig. 3, which showstwo tracks with similar energy deposit in the detector but dif-ferent origin. The case (a) is a classical photoelectron trackfrom a 5.9 keV X-ray photon decayed from Fe . From theBethe formula, the energy loss increases as the particle velocityis decreased. Therefore, photoelectron tracks shows the max-imum charge density at its end, which is named Bragg peak.Dashed line presents the photoelectron eject direction. Thecase (b) shows, instead, a track generated by an energetic pro-ton (tens of GeV). The charge particle exits the gas leaving along, discontinuous string of electrons behind through ioniz-ing. Background tracks do not always look like Fig. 3 (b), theymay also be similar to photoelectron tracks, depending on theparticle type, the kinetic energy, the incident direction and theinteraction physics process. In the meanwhile, some photo-electron tracks also deviate from the ideal cases. The princi-ple for background rejection is to remove background events asmuch as possible while keeping source photons. This is done byparametrizing the properties e ffi cient in recognizing the back-ground tracks. We have studied most of the properties derived from the trackanalysis, for both genuine photoelectron tracks and backgroundevents. In this section, we introduce the beneficial parametersto be used for background rejection, with definitions listed asbelow:1.
Pulse Invariant (PI)
PI is the sum of the charge of the track, which is propor-tional to energy deposit. It is conventionally expressed inADC channels and it is intended to be correct for the possi-ble non-uniformity in the detector gain. When calculatingthe background rate, only tracks with energy depositing in2 to 8 keV, which is the IXPE energy range, are counted.2.
Track size
Track size is the number of pixels above the threshold inthe main cluster, that is, in the largest group of contiguouspixels of the event. With the same energy deposit, back-ground events usually leave larger track size than photo-electrons.3.
Skewness
Skewness, the third standardized moment, refers to theasymmetry of the energy distribution in the track alongthe major axis. The mean energy loss of a charged parti-cle varies inversely with its energy. For a photoelectron of4 able 1: Count rates for all the background components.
Component Rate in total [s − ] Rate in 2–8 keV [s − ] Reject e ffi ciency [%] Cosmic X-ray 3.19E-03 1.73E-03 45.76Albedo Gamma 3.39E-03 1.24E-03 63.48Albedo Neutron 1.14E-03 2.97E-04 74.01Primary Proton 9.77E-02 3.16E-02 67.65Primary Electron 8.67E-04 2.39E-04 72.43Primary Positron 7.45E-05 1.91E-05 74.34Primary Alpha 3.03E-02 1.09E-02 63.95Secondary Proton 4.50E-02 1.41E-02 68.63Secondary Electron 4.16E-02 1.11E-02 73.35Secondary Positron 1.32E-01 3.36E-02 74.61Total 3.56E-01 1.05E-01 70.51a few keV, at the very end of its path, the energy loss isprogressively increasing toward the end point, forming askewed track. On the contrary, for a background chargedparticle of the order of MeV or GeV, the energy loss andtherefore the ionization density is constant and the trackhas a low skewness. For example, in Fig. 3, photoelectrontrack (a) is more skewed (asymmetric) than backgroundtrack (b), and this is the usual case for them.4.
Elongation
Elongation is defined as √ M L / M T , where M2L andM2T are the longitudinal and transverse second momentsof the track, and their ratio refers to the eccentricity of thecharge distribution.5. Charge density
Charge density is defined as the energy (PI) divided bytrack size, which is expected to be lower for backgroundthan photoelectron. For example, the relativistic back-ground, known as minimum-ionizing particle (MIP), hasenergy losses about 2 MeV per g cm − in light material([20]), while the photoelectron energy density is about 10times larger than that of a charge particle ([21]). A com-parison is shown in Fig. 4. The position of the peak fromthe background is smaller than that of a source simulatedas a power-law spectrum with a photon index of 2. Thesignificant deviation benefits background identification.6. Cluster number
Cluster number is the number of clusters after apply-ing clustering algorithm in the ROI. For the same reasonabove, a long path length with low energy density frombackground particle is more likely discontinuous, there-fore more than one cluster may be grouped by the cluster-ing algorithm. On the contrary photoelectrons are mainlygrouped as single cluster only.7.
Border pixels
Border pixels is the number of pixels in the track whichare at the edge of the ASIC. Background entering in thegas from the side of the wall have a larger probability ofleaving a track with pixels on the border.
Before applying background rejection we need to quantifythe range of the parameters useful for this aim. For each readoutevent, all of these parameters are derived from the track analy-sis. For millions of events, there will be the probability distribu-tion of each parameter. We firstly determine the range of theseparameters from the source simulation, then apply the cuts tothe background events, and finally reject the background eventsif the parameters are not in the accepted range. The parametersof tracks from the photoelectrons vary significantly with theirkinetic energies. For example the track size of a 2 keV photon(see Fig. 5) has a most probable track size of 45 pixels, while an8 keV photon has a most probable track size of 126 pixels. Sep-arate such events into di ff erent energy bins helps to quantify therelevant parameters with a narrower range, therefore it is moree ffi cient in recognizing the background tracks. The followingsteps allow for developing the rejection methods:1) In consideration of the energy resolution of the GPD, wefirstly divide the full energy range 2–8 keV into 3 energy bins,2–3.4 keV, 3.4–5 keV and 5–8 keV (hereafter called Bin 1,Bin 2 and Bin 3). From the calibration, the energy resolutionis about 18% at 5.9 keV and at the other energies resolutionsare described approximately as a function that scales as E − / ,therefore three energy bins are a reasonable assumption. Whenquantifying the parameters, an independent study will be con-ducted in each of these energy bins.2) The second step is to convert the boundaries of the chosenenergy bins, i.e. 2 keV, 3.4 keV, 5 keV and 8 keV, to the corre-sponding ADC counts, which is the unit used in the simulationsfor the energy deposit and which is then used to apply eventsselection. In our simulator, the energies of the readout eventsare given in ADC counts, for the purpose of treating the energyresolution and noise suppression properly, which is important inthe step of reconstruction (track analysis). The correlations be-tween the deposited energy and ADC counts are well calibratedto be in excellent agreement with the laboratory measurement.Fig. 6 shows the energy distribution in ADC counts from thesimulation of 5.9 keV decay photons from the radioactive iso-tope Fe . The best Gaussian fitted peak value of 18395 ADCcounts equal to 5.9 keV, the resolution is defined as the ratio5 a )( b )Figure 3: Imaging of tracks with random electronic noises from the simulation.The dots represent the energy deposit 2D positions inside the gas recorded byGeant4. (a) : a track from a Fe decay X-ray photon and dashed line is thephotoelectron eject direction. (b) : a track from an energetic cosmic ray proton. of the full width at half maximum (FWHM) to the peak value.The connections between the bin-edge energies and the ADCcounts are listed in Table 2. Once the gain has been set, thesame correlation applies for both the simulation of source andbackground.3) The next step is to simulate genuine photons with a flatdistribution in each energy bin, and select the events in eachbin according to the PI of the event. We take the simulationfor Bin 1 as an example illustrated here, the procedure for theother bins are the same. A uniformly distributed photons in2–3.4 keV are generated impinging on detector along the tele-scope optical axis. After applying the reconstruction softwareon the readout data, a series of parameters is determined. Firstlywe apply the energy cuts on PI to select the good events. Eventhough all the readout events are originally from the photons inthe energy range of 2–3.4 keV, in reality nothing about the orig-inal energy of the particles is known, but the deposited energy Figure 4: Comparison of the charge density distributions expected from apower-law spectrum with the photon index of 2 (in blue) and the backgroundincluding all the simulated components (in red).Figure 5: Comparison of the track size distribution. Results from themonochromatic photons in four di ff erent energies are presented in di ff erent col-ors.Table 2: Connections between the bin-edge energies and the ADC counts, thepeak and sigma are the values from the Gaussian fitting, resolution is the ratioof FWHM to the peak value. Energy [keV] Peak Sigma Resolution [%] able 3: Parameters and the corresponding ranges applied for background rejection.
Energy bin PI Track size Skewness Elongation Charge density
Bin 1 (6092, 10485) (26, 67) (-0.383, 0.383) (1.023, 1.506) (116.702, 315.914)Bin 2 (10485, 15532) (34, 92) (-0.620, 0.620) (1.044, 2.414) (140.186, 315.930)Bin 3 (15532, 24950) (48, 156) (-1.013, 1.010) (1.112, 4.386) (134.936, 386.334)
Figure 6: PI distribution of 5.9 keV monochromatic photons, the red dashedline is the Gaussian fitting curve.
PI in ADC counts. From the previous step and correlations inTable 2, only events with PI in between 6092 and 10485 ADCcounts are taken into account in the case of Bin 1. As shownin the top panel of Fig. 7, the black line presents all the readout events, while only the hatched area are the selected events,which will subsequently be used for the data analysis.4) The last step is to identify the parameters for an e ffi cientbackground rejection and quantify their range. Parameters havebeen studied by comparing the distribution di ff erence betweenphotoelectron tracks and background tracks. From all the pos-sible parameters, we picked out the most e ffi cient ones: tracksize, skewness, elongation, charge density, cluster number, andborder pixels (see their definitions in Section 3.2.1). The widerthe range of the selected parameter, the less e ffi cient the back-ground rejection. We fixed the accepted range of each param-eter by removing 4% of the events (2% at the head and 2% atthe tail) in the distribution of that parameter for genuine eventfrom photons in the chosen energy bin. This is shown in fourbottom panels of Fig. 7. The black lines present the events afterenergy selection (hatched area from the top panel), blue and redlines define the two 2% boundary from the distribution of therelevant parameters. The quantified edges for all the three binsare listed in Table 3. We also request that the number of clustersis one and border pixels are zero for event acceptance. The results of this study may be used to optimize the signalto noise ratio, namely the sensitivity, of IXPE. This is based on
Figure 7: Parameters distribution for flat-distributed photons in Bin 1. Thehatched area in the top panel are the energy selection events. The head 2% andtail 2% are illustrated in blue and red lines. igure 8: Parameters distribution for background before (in blue) and after (inred) applying the rejection methods. Dashed lines in the top panel mark theedges of three energy bins. the rejection of some events with criteria (often referred to ascuts) that are not foreseen during on ground activities, when thenature and amount of background are totally di ff erent. Besidestudying these cuts following as guideline on the sensitivity, wemust verify whether any systematics is introduced. For this ac-tivity simulations are needed. The eventual validation of thesemethods will be done with flight data but always checked forsystematics by using the on-ground and in-flight calibrations.In this section, we evaluate the residual background after ap-plying the rejection methods introduced above. We aim at ahigh rejection e ffi ciency on background and at a low removal oftrue X-ray events from target source. Furthermore, this methodshould not induce a bias on the polarization detection. The fol-lowing steps allow us to perform the verification.1) We firstly apply the cuts to the background simulationdata. The total background spectra before and after rejec-tion are shown in Fig. 8, as well as the relevant parameters.More events from Bin 1 have been rejected, but still back-ground is dominated by low energy events. The residual back-ground levels for all the components are listed in Table 4.The total background reduces to 2 . × − counts s − , i.e.1 . × − counts s − cm − in 2–8 keV, with an extra rejectione ffi ciency of 75.0%, though it is still larger than the requirementby a factor of 2.9. The main components of background eventsafter applying the rejection methods are still the same. Com-pared to the rejection e ffi ciency for the other components (ex-cept for the CXB), the secondary electrons and positrons rejec-tion e ffi ciency is a bit lower. This is because the behavior of theleptons inside the gas are the same, no matter if they are photo-electrons or cosmic electrons. Therefore the rejection methodsare less e ffi cient for low energy electrons and positrons. Table 4: The residual rates after applying the rejection methods for all the back-ground components.
Component Residual rate [s − ] Reject e ffi ciency [%] Cosmic X-ray 5.77E-04 66.67Albedo Gamma 2.52E-04 79.61Albedo Neutron 5.24E-05 82.35Primary Proton 7.86E-03 75.12Primary Electron 5.52E-05 76.89Primary Positron 4.39E-06 77.00Primary Alpha 1.25E-03 88.59Secondary Proton 2.02E-03 85.56Secondary Electron 2.84E-03 74.35Secondary Positron 1.13E-02 66.50Total 2.62E-02 75.03The geometric shape of a typical track from a MIP penetrat-ing the gas cell is easy to be recognized, but in the close en-counters, electrons with su ffi cient kinetic energies may be gen-erated. These electrons, called delta rays, have energy of a fewkeV and are able to induce further ionization. The tracks fromdelta rays are similar to those of photoelectrons, become themain contributor of the background events, which is seen in oursimulation. For example, Fig. 9 is a residual background event8rom an energetic cosmic proton, (b) is the zoomed out view of(a). Trigger is generated by a delta ray with high-density en-ergy deposition in the center of the ROI (see Fig. 9 (a)), whileit’s mother particle passes through the active area and generatesa straight but less dense track nearby (see Fig. 9 (b)). We seefrom the simulation that primary tracks arriving quasi parallelto the readout plane do not trigger. Indeed if this was the caseROI should be much larger. It means that the energy densitydeposited from the MIP in this case is below the threshold.Fig. 10 shows the distribution of the reconstructed anglesfrom the background tracks. No preferential direction is pre-sented in the background simulated data, as we would expect,since the active area of the detector is far away from the sidewalls of the detector. Background may dilute the measured po-larization but according to our simulations, it is not introducingany spurious modulation.2) Then we apply the cuts to a polarized Crab-like pointsource simulation data (no background is included). A modelof power-law with the photon index of 2.05 and polarizationdegree of 100% is applied. Di ff erent from the isotropic back-ground, the source is simulated on-axis along the telescope op-tical axis. It is worth mentioning here that, as we will discussin the next section, background rejection is not needed for theobservation of point sources. Nevertheless, here we are inves-tigating how such rejection methods will a ff ect data which arerepresentative of a real astronomical source.Background rejection methods remove 14.9% events in 2–8 keV from such a Crab-like point source. Further study showsthat these removed events mainly have less deposited energyand less skewness, due to the tracks containing less informa-tion about the initial photoelectron directions, such as the eventsconverted in the Al coating of the Be window or in the top Culayer of the GEM. Depending on the spectrum of the particularcelestial source under study, these events may be removed toimprove the quality of polarization measurement. The possibleselections are consistent with the background rejection meth-ods, and this will reduce the impact of the latter. We will see inthe following paragraphs that simulations of the faint extendedsource suggests that background subtraction is needed to im-prove the quality of polarization measurement.The modulation factors before and after applying the rejec-tion methods in three bins are list in Table 5. We find that themodulation factors may change no more than a few percent, forexample, there is a relative variation of 2.7% for Bin 1. Never-theless, the di ff erence are barely consistent from the statisticalpoint of view (at 2.955 σ ), and we then conclude that the impactof the rejection technique on the modulation factor is minor, ifany. This is important because, when a selection of data hasbeen applied, strictly speaking the response function of the in-strument has been changed and new one has to be generated, atleast when changes are substantial.
4. Discussion
In imaging X-ray astronomy, background is expected to in-fluence the observations of very faint sources, depending on ( a )( b )Figure 9: A residual background event from an energetic cosmic ray protonwith energy deposition of 2.13 keV from the simulation. (a) represents the ROIwith window size of 572 pixels, (b) is the zoomed out view to illustrate the trackof the MIP better. Notice that the long and straight track out of the ROI from (b) is still inside the active volume just not triggering. Random electronic noiseare added and the green dots present the projected energy deposited positionsas Fig. 3.Figure 10: The reconstructed angle distribution from the track analysis of thebackground events. The dashed line is the result from the constant-fit of thehistograms. able 5: Modulation factor before and after applying the rejection methods onassumed 100% polarized source. Energy bin M before rejection M after rejection
Bin 1 25.10 ± ± ± ± ± ± . (cid:48)(cid:48) (full opening angle). Projected onto the readout plane, theHEW is a round area of ∼ with the mirror focal lengthof 4 m. For point-like sources the source signal to backgroundratio is relatively high enough, while for extended source thisratio is usually significantly smaller and has to be carefully eval-uated. Here we discuss how these considerations apply to twocases of very high interest for the IXPE program. We presentthe results of the simulated observations for a very faint pointsource, the magnetar AXP 1RXS J1708-4009 (flux ∼ . × − erg cm − s − in 2–8 keV) , and for an extended source, the Ty-cho supernova remnant (flux ∼ . × − erg cm − s − in 2–8 keV), using background levels derived from this paper (bothunrejected and residual level in the 2–8 keV energy range).The observation simulations are performed with IXPEOB-SSIM, a simulation framework specifically developed for theIXPE mission (see [22] for details). IXPEOBSSIM is a Python-based Monte Carlo framework that, takes the source models(including morphological, temporal, spectral and polarimetricinformation) as input, convolves them with the analytic instru-mental response functions (i.e. the e ff ective area, the energydispersion, the point-spread function and the modulation fac-tor), produces output files in a format widely used in X-raycommunity. Chandra images are supported as a model for thesource morphology.As the internal background is already defined in units ofcounts s − cm − keV − , there is no need to convolve this spec-trum with the response function of the optics or the e ffi ciencyof the detector. According to Fig. 10, background is assumed tospread on the readout plane evenly, polarization fraction is zeroand polarization angle is uniformly random in [0, 2 π ].Three separate cases are studied for comparison for both tar-gets (1RXS J1708 for short and Tycho SNR): • Case 1: Source-only • Case 2: Source plus the residual background (the spectrumas seen in Fig. 8, top panel, in red) • Case 3: Source plus the unrejected background (the spec-trum as seen in Fig. 8, top panel, in blue)For each case, 1000 independent runs with exposure of 1Ms, a typical observation duration planned for IXPE, have been done. Data analysis processes on point source and extendedsource are a bit di ff erent, which will be discussed more in thefollowing sections. Magnetars are isolated, pulsing magnetic-powered neutronstars with extremely strong magnetic fields. IXPE will enablethe direct measurement of magnetic field strength and geom-etry, as well as investigation of the quantum-electrodynamic(QED) e ff ect of vacuum birefringence that is detectable onlyin super-strong magnetic fields ([23]). As one of the brightestand the few potentially interesting magnetars, 1RXS J1708 istaken as an example here.From [23], we see that a simultaneous fit of the polarizationdegree, polarization angle, and phase-dependent flux recoversthe input model accurately. Fitted geometric parameters canalso be compared with those inferred from observation of hardX-rays and model fits based on a new coronal-outflow model.IXPE can readily discriminate between models with and with-out vacuum polarization, thus allowing confirmation of this re-markable QED prediction. Following the model introduced in[23], the magnetospheric parameters ∆Φ N − S = β = χ = ξ =
60 are set as primaries of the in-put model. The phase-dependent flux, polarization degree andpolarization angle of the input model are shown in Fig. 11. Po-larization angle is independent of the energy.
When dealing with the imaging of a point source, a selec-tion on the region with the encircled energy fraction (EEF)of 0.9 has been done. Here the EEF is the integral profile ofthe point-spread function (PSF) described as a Gaussian plusa King function, where EEF( ∞ ) =
1, and EEF(r) = on the readoutplane. By considering the PSF, the source detection rate is 0.29counts s − for 1RXS J1708, while the corresponding residualbackground is 8 . × − counts s − and the unrejected back-ground is 3 . × − counts s − , resulting to the source to back-ground ratio of 3422 and 873 respectively.In order to perform the phase-resolved observation, data arecollected in nine, equally divided phase bins. For each run andeach phase bin, a polarization degree and a polarization angleare derived, and a MDP (see Equation (1)) is calculated. Forexample, the results from the fifth phase bin [0.44, 0.56], whichhas the lowest polarization degree from the model (see Fig. 11middle panel), are shown in Fig. 12. In such a worst case, polar-ization degree has a relative change less than 0.05% when theresidual background is added, and this increases only to 0.25%if the unrejected background is added. Fitting results from allthe phase bins referring to these three cases are listed in Table 6in sequence. We see that MDPs show no di ff erence with back-ground added, and polarization degrees and angles are consis-tent in all the phase bins, as expected. The conclusion is that the10 igure 11: 1RXS J1708 source model ([23]). From the top to the bottom:source flux, polarization degree and polarization angle as functions of energyand phase.Figure 12: The distributions of polarization degrees (top) and polarization an-gles (bottom) in phase bin [0.44, 0.56] of 1RXS J1708. Red presents the source-only case, blue presents source plus the residual background, and green is forsource plus the unrejected background. The histograms are the binned distri-butions and the solid lines are the best Gaussian fitting. Notice that on the toppanel, the red line almost fully overlaps with the blue line. Table 6: Calculated MDPs, and the best fitted values of the polarization degreesand angles in each phase bin of 1RXS J1708. For each phase bin, from the topto bottom, results refer to three cases: source-only, source plus the residualbackground, source plus the unrejected background. Phase bin MDP [%] Degree [%] Angle [ ◦ ] [0.00, 0.11] 8.33 73.17 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± igure 13: Tycho SNR polarization map paired to the source model. The di-rection and the length of the arrows stand for polarization angle and degreerespectively. The maximum polarization degree on the external rim is up to50%. impact of background on point sources, even the faintest ones,is negligible. In the case of point sources, background rejectionis not needed, and therefore all the source counts could be keptfor further data analysis. The Tycho SNR is an extended, relatively faint object that ispart of the IXPE observing plan. The interest in the source liesin the possibility of observing a high polarization fraction (up to ∼ ff usive shock acceleration model(see for example [25, 26]).We use a 147 ks Chandra observation (obs ID 15998) as thestarting point for the Tycho SNR spectral and morphologicalmodel. Software ixpeobssim takes care of the conversion fromthe Chandra reprocessed data, an event list includes the ener-getic, spatial and temporal information, into a correspondingIXPE event list, through e ff ective area correcting, down sam-pling and events smearing with the instrument response func-tions. A simple polarization model which is a geometrical,radially-symmetric pattern with a maximum polarization de-gree of 50% on the SNR external rim, is paired to the sourcemodel, as shown in Fig. 13. The real measured polarization de-gree is expected to be lower than the model because of the mix-ing with the unpolarized emission from the thermal componentof the supernova remnant. However, this toy model fulfills thepurpose of this work, that is to evaluate the relative e ff ect of theinstrumental background on the measurement of polarization. Fig. 14 shows the simulated image of the Tycho SNR withour simulator, the rectangle of 100 (cid:48)(cid:48) × (cid:48)(cid:48) is the region we se-lected for the further data analysis. This region includes the nonthermal ”stripes” features ([27]) that are expected to be highlypolarized ([25]). Figure 14: The simulated image of the Tycho SNR with 1 Ms exposure derivedfrom ixpeobssim. The rectangle in green is the region selected for backgroundstudy.Table 7: Calculated MDPs, and the best fitted values of the polarization degreesand angles for the selected region of Tycho SNR. Results refer to three cases:source-only (Case 1), source plus the residual background (Case 2), source plusthe unrejected background (Case 3).
MDP [%] Degree [%] Angle [ ◦ ]Case 1 ± ± Case 2 ± ± Case 3 ± ± . × − counts s − ,the residual background is 6 . × − counts s − , and the un-rejected background is 6 . × − counts s − . Therefore thecorresponding source to background ratio are 16.6 and 1.77,much less than in the case of point sources. Obviously addingthe background have the e ff ect of diluting the measured po-larization degree. The uncorrected modulation amplitude forCase 2 in average is smaller by a factor of 5.5% with respectto the case with no background. This factor dramatically in-creases to 44.4% for Case 3. Though no significant shiftings onthe polarization angle, a widen e ff ect is clearly seen for Case3. Background subtraction is recommended for extended faintsources. Background data for subtraction can be acquired eitheras blank-sky or Earth occultation or with the filter and calibra-tion wheel in closed position ([28]).
5. Conclusion
The background of an instrument in orbit can be evaluatedthrough the comparison with previous space missions, as simi-lar as possible to the new instrument, and scaling the data withreasonable criteria. The GPD has many commonalities withproportional counters that have been used many times in X-ray astronomy, especially in early times. Unfortunately noneof them was filled with DME. The major contributors to the12 igure 15: The distributions of polarization degrees (top) and polarization an-gles (bottom) in the Tycho selected region. Red presents the source-only case,blue presents source plus the residual background, and green is for source plusthe unrejected background. The histograms are the binned distributions and thesolid lines are the best Gaussian fitting. background, to be accounted when scaling from one payloadto another one, are the orbit and the mass around the detector.The orbit determines the radiation environment. The mass de-termines how some components of the radiation are absorbed,so reducing the background, and some others are converted pro-ducing the reverse e ff ect.Given that the background of gas filled counters is very dif-ferent for di ff erent filling gases, in the past the comparison wasalways processed with measurements by detectors filled withlow atomic number gases flown on the OSO-8 satellite ([29]),which is also the initial reference for the estimation of IXPEbackground. It is not intuitive whether background levels fromNeon-filled detector or Methane-filled detector is more repre-sentative, Neon has a similar absorption coe ffi cient with theDME, while Methane is more similar in terms of atomic num-ber. For the sake of completeness we remind that the detector ofARIEL-6 was filled with Propane ([30]), likely the most similarmolecule to DME, but in literature only data up to 1.5 keV arereported. Anyway at the lower energy range the backgroundseems more similar to that of OSO-8 filled with Neon. Thebackground suppression methods applied for them were a com-bination of pulse height discrimination, pulse shape discrimina-tion (PSD) and anti-coincidence veto ([29], [30]), IXPE could,in principle, have better capability to remove background forthe following reasons: (1) PSD is used to identify the chargedparticles when they produce longer electron tracks than photonsdepositing the same energy inside the gas. The imaging capa-bility of GPD allows easy discrimination against these events;(2) Properties derived from the image, related to the shape orthe charge density of the track, work as the particle discrimi-nator; (3) A high ratio of the total gas volume to the active gasvolume is beneficial to prevent the background incidence fromthe side walls, and the peripheral region of the gas cell can serveas the anti-coincidence veto ([21]). From the Monte Carlo simulation, we understood that thelack of bottom anti-coincidence is responsible for a fair goodamount of un-rejected background. Fig. 16 shows the incidentdirections of the readout background events, including primarycosmic rays ( ∼ ∼
10 MeV–10 GeV) and photon-origin components ( < θ ) = θ = ∼ ff from the optical axis) andcrossing the gas, it likely losses energy about 3.2 keV per cm inDME, and in average generates 160 electrons inside the activevolume. This means every two holes of GEM along the cross-ing direction, there is one electron. Normally such low chargedensity will not be detected, because of the relatively low gainof the GPD (the level of ∼ ∼
50 elec-trons per pixel). So primary tracks are not detected. In somesense, that the detector is not triggered by the primary particleis a good thing, but not for removing signals generated by deltarays. This crucial di ff erence with respect to proportional coun-ters, which usually have a gain of the order of 5000–10000,could be the reason to explain the relatively high backgroundlevel.Recently a DME-filled GPD was flown aboard the Cube-Sat PolarLight. The filling gas was the same used for IXPE,however the di ff erence in spacecraft mass distribution and orbitare very significant. The PolarLight team published the back-ground result in paper [31] in 2021. In general, their results arein good agreement with ours: (1) The total background rate inthe energy range of 2–8 keV measured by PolarLight is about2 × − counts s − cm − in the central region. This is consis-13 igure 16: The distribution of background incident directions, where cos( θ ) = θ = Energy range Background [keV] [s − cm − keV − ] Methane / OSO-8 . × − Neon / OSO-8 . × − Neon / OSO-8 . × − DME / PolarLight . × − DME / IXPE . × − tent with our result of 4 . × − counts s − cm − , consideringthat many impact factors exist through the whole simulation.PolarLight works in a nearly polar orbit, and it is expected tosu ff er a higher flux of background, but from their result, theorbital variation of background is small for this type of detec-tor; (2) The dominant background for PolarLight is induced bythe electrons and positrons (they are discussed as a whole in[31]), and this is the same for IXPE (if you sum the contri-butions from electrons and positrons together from Table 1).We notice that the absolute values of the dominant component(1.52 counts s − cm − for PolarLight vs 1.98 counts s − cm − forIXPE) are very close, but their fractions with respect to the total(76% for PolarLight vs. 43% for IXPE) are di ff erent. This isbecause the second dominant component (background inducedfrom cosmic rays protons) is higher for IXPE. As we discussedbefore, background induced by the primary cosmic rays protonsmost likely come from the bottom of the detector (see Fig. 16),through the interaction with the massive materials below. WhilePolarLight doesn’t su ff er from it thanks to its light mass; (3)They reported that 72% background events in the 2–8 keV en-ergy range could be rejected with an e ff ective algorithm, andthis e ffi ciency is 75% from our work (see Table 4). The resid-ual events cannot be discriminated as they are generated by thesame process as the photoelectron of a few keV.The comparison of the backgrounds we have discussed areshown in Table 8, including measurements from Methane-filled detector, Neon-filled detector aboard OSO-8, DME-filledGPD aboard PolarLight, and the Monte Carlo simulated re-sult of IXPE from this work. With the background rejectionmethods developed in this work, we removed 92.6% of back-ground readout events, leaving a residual background level of1 . × − counts s − cm − in the 2–8 keV energy range. Thisresidual background is still 2.9 times higher than the require-ment 4 × − counts s − cm − , but the requirement is almostone order of magnitude above the value that can be toleratedwhen observing the most extended and faintest sources IXPEplanned (the X-ray reflected from the Sgr B2 molecular cloudsin the vicinity of the Galactic Center), where the surface bright-ness is 0.04 counts s − cm − per DU. We proved that this levelof background has no influence on point source observations:all the source counts could be kept without applying the back-ground rejection techniques, which come at the cost of a reduc-tion of the genuine counts from the source. But the dilutionof the polarization degree around a few percent may be impor-tant for the faint extended source, and in this case backgroundsubtraction is needed.We acknowledge the ’Accordo attuativo’ ASI-INAF n.2017-12-H.0 for funding the Italian contribution to the IXPE project.We thank Riccardo Campana for sharing the background sourcespectra. References [1] E. Costa, P. So ffi tta, R. Bellazzini, A. Brez, N. Lumb, G. Spandre, Ane ffi cient photoelectric X-ray polarimeter for the study of black holes andneutron stars, Nature 411 (6838) (2001) 662–665. arXiv:astro-ph/0107486 .
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