Ray tracing simulations for the Wide-field X-ray Telescope of the Einstein Probe mission based on Geant4 and XRTG4

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1 Ray tracing simulations for the Wide-field X-ray Telescope of the Einstein Probe mission based on Geant4 and XRTG4 Donghua Zhao a, Chen Zhang a,weiminyuan a, Richard Willingale b, Zhixing Ling a,hua Feng c,hongli c, Jianfeng Ji c,wenxinwang c and Shuangnan Zhang ad a National Astronomical Observatories, Chinese Academy of Sciences, No.0, Datun Road, Chaoyang District,001, Beijing, China; b Department of Physics and Astronomy, University of Leicester, Leicester, LE1 7RH, UK; c Department of Engineering Physics and Center for Astrophysics, Tsinghua University, Beijing 0084, China; d Institute of High Energy Physics, Chinese Academy of Sciences, No.19B, Yuquan Road, Shijingshan District, 0049, Beijing, China. ABSTRACT Einstein Probe (EP) is a proposed small scientific satellite dedicated to time-domain astrophysics working in the soft X-ray band. It will discover transients and monitor variable objects in kev, for which it will employ a very large instantaneous field-of-view (60 o 60 o ), along with moderate spatial resolution (FWHM 5 arcmin). Its wide-field imaging capability will be achieved by using established technology in novel lobster-eye optics. In this paper, we present Monte-Carlo simulations for the focusing capabilities of EP s Wide-field X-ray Telescope (WXT). The simulations are performed using Geant4 with an X-ray tracer which was developed by cosine ( to trace X-rays. Our work is the first step toward building a comprehensive model with which the design of the X-ray optics and the ultimate sensitivity of the instrument can be optimized by simulating the X-ray tracing and radiation environment of the system, including the focal plane detector and the shielding at the same time. Keywords: Monte-Carlo simulation, X-ray tracing, lobster-eye optics, telescope 1. INTRODUCTION Einstein Probe (EP) is a proposed small scientific satellite dedicated to time-domain astrophysics in the soft X-rays. Its scientific goals are to discover transients and monitor variable objects in the energy range of kev, for which it will employ a very large instantaneous Field-of-View (FoV) (60 o 60 o ), along with moderate spatial resolution (FWHM 5 arcmin). EP will offer unprecedentedly high sensitivity and large grasp, which would supersede previous and existing X-ray all-sky monitors. It was selected as one of the candidate missions (the so-called background missions ) for mission definition and technology development in the space science program of the Chinese Academy of Sciences. EP carries two scientific instruments and a fast alert downlink system. The primary instrument is a Widefield X-ray Telescope (WXT) with a FoV of 60 o 60 o, which is a lobster-eye type X-ray focusing telescope based on Micro-Pore Optics (MPO). The other is a Follow-up X-ray Telescope (FXT) with a smaller FoV (1 o 1 o ). In this paper, we present ray tracing Monte-Carlo simulations for WXT based on the Geant4 software and its extensions. Geant4 1 is a very powerfull toolkit for simulations of the passage of particles through matters and has remarkable ability to model complex geometrical configurations, and has been applied widely in space science. 4 However, the library of physical processes available in Geant4 lacks the description of the reflection at grazing incidence of X-ray photons from highly polished mirrors. Buis and Vacanti 5 developed Further author information: (Send correspondence to zhaodh@nao.cas.cn, chzhang@nao.cas.cn, wmy@nao.cas.cn ) Space Telescopes and Instrumentation 014: Ultraviolet to Gamma Ray, edited by Tadayuki Takahashi, Jan-Willem A. den Herder, Mark Bautz, Proc. of SPIE Vol. 9144, 91444E 014 SPIE CCC code: X/14/$18 doi:.1117/ Proc. of SPIE Vol E-1 Downloaded From: on /11/014 Terms of Use:

2 1IlI:ISrI:,P : I : rrrF1= '111N11 OI>`I1RI31A : / // /1 I1U mn1 V1/1-1lllil1111 Figure 1. Layout of WXT and FXT (in blue rectangle) of the Einstein Probe satellite. an extension to the Geant4 software package that allows Geant4 to be used to X-ray tracing simulations (thereafter we call it XRTG4). The physics of grazing angle scattering with this extension is realized through the implementation of three classes: (1) G4XrayRefractionIndex manages the refraction index data for specific materials; () G4XraySurfaceProperty is a derived object of G4SurfaceProperty and allows to define the logical surface for X-ray grazing incidence scattering and to describe the microscopic surface details; and (3) G4XrayGrazingAngleScattering implements the grazing angle scattering of X-rays on the surface during which the reflectivity changes with energy, incidence angle and the surface roughness. Geant4 has a powerful capability to build geometrical models of instruments. Accordingly, with this extension, Geant4 software allows one to do X-ray tracing simulations for arbitrary optics of complexity, as long as the geometrical model can be described by the geometry library available in Geant4.. WIDE-FIELD X-RAY TELESCOPE OF EP To achieve both a wide FoV and X-ray imaging with focusing, the MPO lobster-eye optics 6 is adopted for WXT. The lobster-eye optics comprises a thin spherical plate with numerous square micro pores, the axes of which all point radially to a common centre of curvature. The grazing incidence X-rays going through this type of optics will form a cruciform point-spread function on the enclosed sphere with a radius of half the curvature of the optics. The grazing incidence X-rays which reflect twice off two adjacent walls within the micro pores will form a focal point and those undergoing a single reflection within the pores will be redirected to form two linear images parallel to the pore sides and passing through the focal point. WXT consists of 8 modules, whose layout is shown in the Figure 1. All of the modules have a focal length of 375 mm. Modules 1-6 are identical, with different structures from that of modules 7-8. For each of the modules 1-6, the optics is composed of a 7 7 spherical lens array, and the supporting lens frame has an aperture of about 8 8 cm. Modules 7 and 8 have almost the same structures as modules 1-6; the only difference is that for each of modules 7 and 8 the optics is composed of 7 lens and, hence, a larger FoV and a larger focal plane. Each lens has a size of mm and a thickness of 1.5 mm. The micro pores in the lens have a size of mm and a length of 1.5 mm. The space between two adjacent pores is mm. The coating on the wall of pores is Iridium of 50 nm thickness. The frame between two adjacent lenses has a thickness of mm and a width of 3 mm. The main parameters of WXT are listed in the Table 1. The FoV is 0 o 0 o for each of the modules 1-6, and 0 o 30 o for each of the modules 7-8. Table 1. The main parameters of WXT. Module Num. Focal Length FoV Energy Range Angular Res. Energy Res. Temporal Res mm 60 o 60 o kev 5arcmin 40%@1 kev <=0 us Proc. of SPIE Vol E- Downloaded From: on /11/014 Terms of Use:

3 Case _--A.Window GEM Readout Plane Front -end electronics Figure. Sketch of the focal-plane detector of a WXT module. Figure shows a prototype of the gas detector of WXT for preliminary tests. The Gas Electron Multiplier (GEM) is the core component of the detector. The electrons produced in the photoelectric interactions of X-rays and the gas are multiplied in the holes in the GEM foil with a strong electric field, and finally are collected by the readout electrode. The detector has an area of cm for each of modules 1-6, and 14 0 cm for modules MASS MODEL OF WXT Because the 8 modules of WXT are independent with each other and have almost the same structure. We build a simulation model of WXT for one of the modules 1-6 with Geant4 toolkit (release 4.9.6p0) and do simulations. The main structure of WXT considered in the Monte-Carlo model is shown in Figure 3. The structure of the mass model mainly consists of a lobster-eye optics, a gas detector, supporting structures and some simple shielding. The dimensions of the lenses and the lens frame of the optics are set up according to the descriptions in the Section. The main material of the lens is SiO and PbO. Due to imperfection in the shaping and polishing processes, not all of the micro pores in the lenses point radially to the center of the curvature, and the coating surfaces on the walls of the micro pores have certain roughness. Therefore, we consider both the pore tilt and the surface roughness in the model. The gas detector in the model consists of a window comprising of a 40 nm thick Si 3 N 4 foil and a 30 nm thick Aluminum foil, and Xenon gas in an Aluminum holder. We set the volume of the gas 14 cm 14 cm 1 cm, the temperature 300 kelvin and the pressure 1.3 atmosphere. The gas holder is a five-sided box with side thickness of 5 mm. We take lead sheetings with a thickness of 0.5 mm as shielding and support structures around the optics and the detector. The process of the reflection of grazing incidence X-rays from surfaces based on XRTG4 is included in the simulation model besides physical electromagnetic interactions such as photo-electric effect, Compton scattering, gamma conversion, etc. Our aims are to understand the imaging processes of WXT and to obtain the parameters such as the effective area, the point spread function, and simulated source images, etc. 4. X-RAY TRACING SIMULATIONS FOR WXT Though the application of XRTG4 to X-ray tracing simulations had been validated by simulations on the X-ray telescope performance onboard the satellite XMM-Newton, 5 our work is the first time to apply this software to lobster-eye type telescopes. Therefore, before performing X-ray tracing simulations for WXT, we need to compare the results from Geant4 and XRTG4 and those from the Q software. The Q software is a sequential X-ray tracing package, which was developed by R. Willingale at the University of Leicester. This package has been used for simulations of different kinds of grazing incidence optics such as the conventional Proc. of SPIE Vol E-3 Downloaded From: on /11/014 Terms of Use:

4 Optics Micro pore and Coating Pb shielding Al 13 4 Xe Figure 3. Schematic diagram of a WXT model used in the simulations. Wolter I shells like the Swift XRT, Silicon Pore Optics (SPO) and the Wolter I optics implemented using square pore optics for MIXS-T aboard the Bepicolombo satellite. 7 We assume an ideal detector with 0% detection efficiency at any energy in the model, and compare the effective area values obtained with Geant4 and the Q software. The effective area is defined as the whole area of the lens array times the ratio of the photons reaching at the detector to incident photons at the lenses. For lobster-eye telescopes, the PSF comprises of 3 components arising from unreflected flux (diffuse transmission), single reflections and double reflections. Therefore, we calculate three effective areas: the focal area only from double reflections, the focal+arm area from both single and double reflections, and the total area for all of the three components. The comparison of the results obtained with Geant4 and the Q software are shown in Figure 4 (top). For each point, the number of incident photons is 7. In these simulations, both the surface roughness of the sidewalls of the micro pores and the tilt of the micro pores are zero. The left top panel of Figure 4 shows the results corresponding to the telescope with only one spherical lens located in the center of its FoV. The average difference between the results of Geant4 and the Q software is less than.0%. When we use the whole lens array described in Section, the average difference between the results of Geant4 and the Q software is less than.6% as shown Figure 4 (right top). The slope of the effective area curve for 7 7 lenses is much steeper than that for one lens below kev. This is because that the reflectivity decreases with increasing incident angle (Figure 4 (left bottom)), and decreases with increasing photon energy (Figure 4 (right bottom)). These comparisons verify the applicability of Geant4 and XRTG4 to lobster-eye telescopes. We thus conclude that the results given by the two softwares agree well with each other in general with an averaged deviation < 3%. Next, we carry out realistic simulations for WXT using Geant4 and XRTG4. Figure 5 (left) shows the effective area of WXT obtained. It shows that the maximum effective area is at around 0.6 kev and the maximum focal area is about.8 cm, while the the maximum focal+arm area is about 7.5 cm. The decrease of the effective area at 0.5 kev is due to the absorption of X-rays in the window of the detector (see Figure 5 (right)). Based on the computed effective area, we calculate the grasp of WXT, as shown in Figure 6. It shows that EP/WXT has much larger grasp than erosat, ROSAT and XMM-Newton, and is an ideal instrument for carrying out all-sky monitoring. The computed Point Spread Functions (PSF) of WXT at different energies are shown in Figure 7. The characteristic cruciform shape is clear, as anticipated. The size of the cruciform structure decreases with increasing photon energy. The blank areas in the PSF around 50 mm and 90 mm is due to the shadow of the lens frames. It should be noted that in these simulations, roughness of the surface (RMS= 0.55 nm) is taken Proc. of SPIE Vol E-4 Downloaded From: on /11/014 Terms of Use:

5 6 4-5 v T. m '-3 w t 0eant4, lorol Aree t Geant4, Focal.Arm Aree Geanl4, FOCal Aree --_r -- Q, Fatal Alea O, Fecal -Arm Area Q, Focal Area o 1 m 6 4 t 0eam4, Iota] Aree -0- Geam4, Focal \rm Area - Geanl4, Fecal Prey Q, Total Area --. O. FacalArnl Area O, Fecal Area,1, Í I Energy (kev) Energy (key) \ 1 kev O i Angle ((leg) ti O o Photon Energy (er) Figure 4. Verification of the grazing incidence X-ray scattering using Geant4 by comparing the effective area obtained from Geant4 (solid line with solid dots) and the Q software (dash line with solid triangles). (left top) the effective area varying with energy corresponding to one lens; (right top) the effective area varying with energy corresponding to the 7 7 lens array; (left bottom) the reflectivity of 1 kev X-ray on Ir surface (roughness=0, thickness=50 nm, the substrate material is SiO ) changing with grazing incidence angles; (right bottom) the reflectivity of X-rays at different energy on Ir surface (roughness=0, thickness=50 nm, the substrate material is SiO ) with a grazing incident angle of deg. Proc. of SPIE Vol E-5 Downloaded From: on /11/014 Terms of Use:

6 Energy (kev) Energy (kev) Figure 5. (left) Effective area of WXT with considering the surface roughness of about 0.55 nm and channel tilt of lenses which follows a Gaussian distribution function with σ=0.85 arcmin.(right) The transmission of the entrance window for X-ray. ) deg Effective Area*FoV (cm 4 3 EP,Considering Focus+Arm Area EP, Considering Focal Area erosat, 7 Tel ROSAT, PSPC XMM_Newton, PN+MOS Thin Energy (kev) Figure 6. The grasp of WXT, defined as the product of FoV times effective area, as a function of energy. For comparison, the grasp 11 of 7 erosita telescopes, ROSAT PSPC and XMM-Newton PN+MOS thin filter are shown. into account, which can reduce the reflectivity of X-rays. The pore tilt of lenses is also considered, leading to degraded spatial resolution. The pore tilts are assumed to follow a Gaussian distribution with a zero mean and σ=0.85 arcmin. The incident direction of the X-ray is on axis in the simulations. We also simulate observations of a patch of the X-ray sky with one WXT module with inputs from the ROSAT All-Sky Survey Bright Source Catalogue (RASS-BSC). 1 Figure 8 (left) shows the simulated observed X-ray image of the sky region centered at (RA=5 o, Dec=-50 o ) within the FoV (0 0 square degrees) of one WXT module, with an exposure time of 0 kilo-seconds. There are about sources located in this region, as indicated by open circles. It can be seen that there is no noticeable vignetting effect across the FoV, and the cruciform shape of the PSF may cause confusion for faint sources in the vicinity of bright ones. For demonstration purpose, the simulation is performed only for known RASS bright sources without any background (e.g. cosmic X-ray background, diffuse Galactic emission, internal background of the detector). As shown in Figure 8 (right), more than 80% sources can be detected 50 photons at least even considering only the focal points of their images. Proc. of SPIE Vol E-6 Downloaded From: on /11/014 Terms of Use:

7 kév 0 E X (mm) 11; X (mm) Figure 7. PSF of WXT for different energies with considering the surface roughness of about 0.55 nm and channel tilt of lenses which follows a Gaussian distribution with σ=0.85 arcmin. (left top) the surface plot of the normalized PSF at 1.0 kev. (right top, left bottom and right bottom) the contour plots of the PSF at 1.0 kev,.0 kev and 4.0 kev, respectively whole detector whole cruciform structure only Focus Y (mm) Number of Sources X (mm) Photon Counts Figure 8. (left) Simulated X-ray image of a sky region (centered at RA=5 o,dec=-50 o ) with one WXT module of a FoV of 0 o 0 o and an exposure time of 0 ks. The sources are taken from the RASS bright source catalogue. Note that no background is included in the simulation and the color code is on logarithmic scale. (right) Histogram of the number of detected photons for RASS-BSC with WXT. 4 5 Proc. of SPIE Vol E-7 Downloaded From: on /11/014 Terms of Use:

8 5. SUMMARY The proposed Einstein Probe mission is a small scientific satellite dedicated to monitoring X-ray transients and variable objects in the soft X-rays. Its primary instrument, the Wide-field X-ray Telescope, which employs the established novel MPO Lobster-eye X-ray focusing technology, has unprecedentedly high sensitivity and large grasp. In order to understand and characterize the imaging properties of EP s WXT, ray-tracing simulations are carried out by making use of the Geant4 and XRTG4 softwares. In this paper, results of the simulations on the performance of WXT are presented. The application of simulations based on Geant4 and XRTG4 to MPO X-ray focusing optics is validated by comparing the results with those given by the Q software. The effective area and the PSFs at various energies obtained from the simulations are given, along with simulated X-ray image of the sky based on the ROSAT all-sky survey. This work is the first step toward building a comprehensive Monte-Carlo model, in which the X-ray tracing, X-ray detection and particle interaction are all incorporated. Such a model can be used to understand and characterize the instrument performance, such as effective area, sensitivity, angular resolution and various types of background, which are critical to optimizing the instrument design. ACKNOWLEDGMENTS This work is supported by the Strategic Priority Research Program on Space Science, the Chinese Academy of Sciences, Grant No. XDA040610, the program of National Natural Science Foundation of China under the Grant No , and the Young Researcher Grant of National Astronomical Observatories, Chinese Academy of Science. REFERENCES [1] Agostinelli, S., and 17 colleagues 003. GEANT4 a simulation toolkit. Nuclear Instruments and Methods in Physics Research A 506, [] Daly, E., Evans, H., Lei, F., Longo, F., Magni, S., Nartallo, R., Nieminen, P., Pia, M. G., Truscott, P. R Space Applications of the Geant4 Simulation Toolkit. Advanced Monte Carlo for Radiation Physics, Particle Transport Simulation and Applications [3] Zhao, D., Cordier, B., Sizun, P., Wu, B., Dong, Y., Schanne, S., Song, L., Liu, J. 01. Influence of the Earth on the background and the sensitivity of the GRM and ECLAIRs instruments aboard the Chinese-French mission SVOM. Experimental Astronomy 34, [4] Zhao, D.-H., Wu, B.-B., Song, L.-M., Dong, Y.-W., Schanne, S., Cordier, B., Liu, J.-T Onboard GRB trigger algorithms of SVOM-GRM. Research in Astronomy and Astrophysics 13, [5] Buis, E. J., Vacanti, G X-ray tracing using Geant4. Nuclear Instruments and Methods in Physics Research A 599, [6] Angel, J. R. P Lobster eyes as X-ray telescopes. The Astrophysical Journal 33, [7] Short, A. D., Ambrosi, R. M., Hutchinson, I. B., Willingale, R., Abbey, A. F., Wells, A. A., Hill, J. E., Burrows, D. N., Tagliaferri, G., Citterio, O Performance of the Swift X-ray Telescope (XRT) Mirror/Detector Combination. Gamma-Ray Burst and Afterglow Astronomy 001: A Workshop Celebrating the First Year of the HETE Mission 66, [8] Spaan, F. H. P., Willingale, R The point spread function of silicon pore x-ray optics. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series [9] Martindale, A., and 18 colleagues 009. The Mercury Imaging X-ray Spectrometer: optics design and characterisation. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series [] Willingale, R., Fraser, G. W., Brunton, A. N., Martin, A. P Hard X-ray imaging with microchannel plate optics. Experimental Astronomy 8, [11] Merloni, A., and 4 colleagues 01. erosita Science Book: Mapping the Structure of the Energetic Universe. ArXiv e-prints arxiv: [1] Voges, W., and 19 colleagues The ROSAT all-sky survey bright source catalogue. Astronomy and Astrophysics 349, Proc. of SPIE Vol E-8 Downloaded From: on /11/014 Terms of Use: