Simulations of expected signal and background of gamma-ray sources by large field-of-view detectors aboard CubeSats
Gábor Galgóczi, Jakub ?ípa, Riccardo Campana, Norbert Werner, András Pál, Masanori Ohno, László Mészáros, Tsunefumi Mizuno, Norbert Tarcai, Kento Torigoe, Nagomi Uchida, Yasushi Fukazawa, Hiromitsu Takahashi, Kazuhiro Nakazawa, Naoyoshi Hirade, Kengo Hirose, Syohei Hisadomi, Teruaki Enoto, Hirokazu Odaka, Yuto Ichinohe, Zsolt Frei, László Kiss
SSimulations of expected signal and background of gamma-raysources by large field-of-view detectors aboard CubeSats
G´abor Galg´oczi a,b,* , Jakub ˇR´ıpa a,c,d,e, , Riccardo Campana f , Norbert Werner e,g,c , Andr´asP´al h , Masanori Ohno a,c,g , L´aszl´o M´esz´aros h , Tsunefumi Mizuno i , Norbert Tarcai j , KentoTorigoe g , Nagomi Uchida g , Yasushi Fukazawa g , Hiromitsu Takahashi g , KazuhiroNakazawa k , Naoyoshi Hirade g , Kengo Hirose g , Syohei Hisadomi k , Teruaki Enoto l , HirokazuOdaka m , Yuto Ichinohe n , Zsolt Frei a , L´aszl´o Kiss g a E¨otv¨os University, Institute of Physics, P´azm´any P´eter s´et´any 1/A, Budapest, Hungary, 1117 b Wigner Research Centre, Konkoly-Thege Mikl´os ´ut 29-33., Budapest, Hungary, 1121 c MTA-E¨ot¨vos University Lend¨ulet Hot Universe Research Group, P´azm´any P´eter s´et´any 1/A, Budapest, Hungary,1117 d Charles University, Faculty of Mathematics and Physics, Astronomical Institute, V Holeˇsoviˇck´ach 2, Prague 8,Czech Republic, 180 00 e Masaryk University, Faculty of Science, Department of Theoretical Physics and Astrophysics, Kotl´aˇrsk´a 2, Brno,Czech Republic, 611 37 f INAF - Astrophysical and Space Science Observatory (OAS), Via Gobetti 101, Bologna, Italy, 40129 g Hiroshima University, School of Science, 1-3-1 Kagamiyama, Higashi-Hiroshima, Japan, 739-8526 h Konkoly Observatory of the Hungarian Academy of Sciences, Konkoly-Thege ut 15-17, Budapest, Hungary, 1121 i Hiroshima University, Hiroshima Astrophysical Science Center, 1-3-1 Kagamiyama, Higashi-Hiroshima, Japan,739-8526 j C3S Electronics Development LLC., K¨onyves K´alm´an krt. 12-14., Budapest, Hungary, 1097 k Nagoya University, Department of Physics, Furo-cho, Chikusa-ku, Nagoya, Aichi, Japan, 464-8602 l Kyoto University, The Hakubi Center for Advanced Research and Department of Astronomy, Kyoto, Japan,606-8302 m University of Tokyo, Department of Physics, 7-3-1 Hongo, Bunkyo, Tokyo, Japan, 113-0033 n Rikkyo University, Department of Physics, Nishi Ikebukuro 3-34-1, Toshimaku, Tokyo, Japan, 171-8501
Abstract.
In recent years the number of CubeSats (U-class spacecrafts) launched into space has increased exponen-tially marking the dawn of the nanosatellite technology. In general these satellites have a much smaller mass budgetcompared to conventional scientific satellites which limits shielding of scientific instruments against direct and indirectradiation in space.In this paper we present a simulation framework to quantify the signal in large field-of-view gamma-ray scintilla-tion detectors of satellites induced by X-ray/gamma-ray transients, by taking into account the response of the detector.Furthermore, we quantify the signal induced by X-ray and particle background sources at a Low-Earth Orbit outsideSouth Atlantic Anomaly and polar regions. Finally, we calculate the signal-to-noise ratio taking into account differentenergy threshold levels. Our simulation can be used to optimize material composition and predict detectability ofvarious astrophysical sources by CubeSats.We apply the developed simulation to a satellite belonging to a planned
CAMELOT
CubeSat constellation. Thisproject mainly aims to detect short and long gamma-ray bursts (GRBs) and as a secondary science objective, todetect soft gamma-ray repeaters (SGRs) and terrestrial gamma-ray flashes (TGFs). The simulation includes a detailedcomputer-aided design (CAD) model of the satellite to take into account the interaction of particles with the materialof the satellite as accurately as possible.Results of our simulations predict that CubeSats can complement the large space observatories in high-energyastrophysics for observations of GRBs, SGRs and TGFs. For the detectors planned to be on board of the
CAMELOT
CubeSats the simulations show that detections with signal-to-noise ratio of at least 9 for median GRB and SGR fluxesare achievable.
Keywords:
Geant4, GRB, gamma-rays, satellite, cosmic background. * G´abor Galg´oczi, [email protected]
Jakub ˇR´ıpa, [email protected] a r X i v : . [ a s t r o - ph . I M ] F e b Introduction
Particle background is a considerable constraint for satellites, particularly those aiming to in-vestigate the high-energy Universe. It is especially important for instruments without an anti-coincidence shield, e.g. for the increasingly large number of CubeSats which have recently beenproposed for scientific missions.A dedicated Geant4 software has been developed including the simulation of the optical lightpropagation inside the scintillators used as detectors. This way the detector response can be takeninto account. In order to include the effects of scattering, photon conversion and other interac-tions happening between background particles, X-ray photons and the materials of the satellite, acomputer-aided design (CAD) model of the whole satellite was included in the simulations.The spectra of high energy photons and particles which contribute to the overall detected back-ground were used as an input to the Geant4 simulations. These components of the external back-ground include cosmic X-rays/ γ -rays, cosmic ray particles, geomagnetically trapped particles andalbedo (secondary) particles produced in the Earth’s atmosphere.In order to validate the background simulations, a set of dedicated experiments were carried outat the Hiroshima University in order to obtain the scintillator optical parameters (e.g. reflectivity ofthe surfaces and absorption length) which determine the position dependence of signal collectionefficiency.The developed simulation, spectra of the X/ γ -rays and particle background as well as ex-ample spectra of high-energy photon transients were applied on one 3U CubeSat belonging tothe planned Cubesats Applied for MEasuring and LOcalising Transients ( CAMELOT ) constella-tion.
This simulation framework can be also helpful for other CubeSat and SmallSat missions2ith gamma-ray detectors in preparation by other teams, e.g.
BurstCube ,
5, 6
BlackCAT , Gravita-tional wave high-energy Electromagnetic Counterpart All-sky Monitor (
GECAM ), Gamma-RayIntegrated Detectors (GRID), Glowbug , High Energy Rapid Modular Ensemble of Satellites -Scientific Pathfinder (
HERMES-SP ), Satellite Polarimeter for High eNergy X-rays (
SPHiNX ), SkyHopper , Space Industry Responsive Intelligent Thermal satellite, ( SpIRIT ) .The paper is organized as follows: Sec. 2 describes the astrophysical sources whose detectabil-ity is investigated, Sec. 3 overviews various background components, Sec. 4 describes the CAMELOT satellites and the detector system, Sec. 5 details the validation of Geant4 simulations and the cal-ibration of the detector’s optical parameters, Sec. 6 describes the performed Geant4 simulations,Sec. 7 presents the results of Geant4 simulations and Sec. 9 summarizes the conclusions. γ -ray Transient Sources The main scientific objective of the proposed
CAMELOT satellites is the detection of GRBs.
13, 14
Short GRBs (sGRBs) originate from a merger of two neutron stars and possibly also from a mergerof a neutron star and a black hole.
The typical duration T (the time during which the cumula-tive counts increase from 5 % to 95 %) of their prompt gamma-ray emission is (cid:46) s in the observerframe and their gamma-ray energy flux peaks at ∼ keV. Long GRBs (lGRBs) originate in thegravitational collapse of fast-spinning massive stars and their typical duration is (cid:38) s. The promptspectra of lGRBs are on average softer then the sGRB spectra with their energy flux peaking at ∼ keV.The CAMELOT satellites might be sensitive also to other astrophysical X-ray transients suchas soft gamma repeaters with typical duration of individual peaks in their light curves ∼ . s and https://skyhopper.research.unimelb.edu.au https://spirit.research.unimelb.edu.au
20, 21
Also the gamma-ray phenomena produced in the Earth’satmosphere during thunderstorms called terrestrial gamma-ray flashes might be observed. Theseevents are typically shorter than 1 ms and have gamma-ray spectra reaching energies of severalMeV. The following subsections describe in detail the fluxes expected from these sources. Fig. 1summarizes the spectra of the X-ray/ γ -ray transient sources which we study in this paper. Fig 1
Differential (left) and integral (right) spectra of typical GRBs, SGR and TGF. The black solid curve shows atypical peak spectrum of a sGRB. The black dotted curve shows a typical peak spectrum of a lGRB and the blackdashed line shows a typical fluence spectrum of a lGRB accumulated over the duration of the burst. The blue solidcurve shows an average spectrum of a TGF based on measurements from the
AGILE satellite. The red solid curveshows a typical spectrum of a burst from a SGR based on measurements from the Konus experiment. The shadedregions correspond to 68 % CL.
Since the main objective of the
CAMELOT mission is the detection of GRBs, we run Monte Carlo(MC) simulations using the typical spectra of sGRBs and lGRBs in order to estimate the expectedsignal-to-noise ratio. The typical spectra were constructed using the
Fermi
GBM Burst Catalog(FERMIGBRST ). For detailed information about the catalog see Ref. 24–27. For sGRBs, weused the so called peak flux spectrum which is accumulated over the peak of the GRB (typically https://heasarc.gsfc.nasa.gov/W3Browse/fermi/fermigbrst.html Fermi /GBM. The triggering system employs 120possible sets of trigger algorithms (not all actively employed at a time and approximately 60 triggeralgorithms are currently active ) consisting of eight set of energy bands, ten time scales 16, 32,64, 128, 256, 512, 1024, 2048, 4096, 8192 ms and different time offsets for two phases of selectedtime interval. Most frequently, GBM triggers on 5 time scales from 16 to 4096 ms. The typical spectra of sGRB and lGRB were constructed in the following way. First, wechecked what was the most common best fit spectral model in the catalog. For peak flux spectraof sGRBs it was the power law model (PL). For the peak flux and fluence spectra of lGRBs it wasthe Comptonized model (CPL, exponential cutoff power law). For detailed information about thedifferent spectral models see Ref. 24.Although PL model was the most frequent one for peak spectra of sGRBs in the FERMIGBRSTcatalog, we use the second most frequent model, i.e. CPL. The reason is that sGRBs dim in peakflux are most frequently best fit by PL whereas brighter sGRBs are most frequently fit by CPLmodel. A likely explanation is that short GRB have Comptonized spectra, and that weak sGRBsproduce insufficient signal in the instrument to distinguish the models.Then in case of the peak spectra, we used the median best fit spectral parameters and then wetuned the normalizations A of the spectra to obtain the values of the integral fluxes in the rangeof − keV equal to the median 1024 ms, 256 ms and 64 ms timescale peak fluxes obtainedfrom the catalog. The median peak fluxes for sGRBs for 1024 ms, 256 ms and 64 ms time scalesand in the − keV range are 2.0, 4.8 and 7.5 ph cm − s − , respectively. Note that the median5ower law index for PL model for sGRBs peak spectra is α = − . which is unphysical and thatis also the reason why we use CPL model for sGRB spectra. In case of lGRBs the median peakfluxes for 1024 ms, 256 ms and 64 ms time scales and in the same energy range are 4.1, 5.2 and 6.7ph cm − s − , respectively. For the fluence spectra of lGRBs, we used the median best fit spectralparameters, including the normalization, from the catalog. The obtained spectral parameters arein Table 1. The pivot energy E piv is fixed at 100 keV. Figure 1 shows the typical GRB spectrawith shaded regions corresponding to 68 % CL. These 68 % CL were obtained from the measuredspectral parameters separately for short and long GRBs in the FERMIGBRST catalog and usingthe CPL spectral model. Table 1
Spectral parameters of typical GRB spectra.
GRB Spec. A A A A α E peak type type (keV)sGRB pflx . +0 . − . . +0 . − . . +0 . − . — − . +0 . − . +574 − lGRB pflx . +0 . − . . +0 . − . . +0 . − . — − . +0 . − . +269 − lGRB flnc — — — . +0 . − . − . +0 . − . +250 − The spectral parameters are for the peak flux spectra (pflx) and the fluence spectra (flnc) of typicalshort and long GRBs. The normalizations A , A and A are for the 1024 ms, 256 ms and64 ms timescale peaks, respectively, A is the normalization for the fluence spectrum and all nor-malizations are in units of ph cm − s − keV − . Parameters α and E peak are respectively the powerlaw index and the peak energy of the Comptonized model. The uncertainties correspond to 68 %CL. Soft gamma repeaters and anomalous X-ray pulsars (AXPs) are believed to be neutron stars withextremely strong magnetic fields of up to B ∼ − G called “magnetars”.
For reviewssee Refs. 20, 32–34. First observations date to 1979 with several magnetar bursts detected up tonow, see e.g. Refs. 21,36–38. For example a giant flare of magnetar SGR 1806-20 on 27 December,6004 was observed by several satellites and it was so bright that it saturated detectors.SGR giant flares are rare and it is essential for their better understanding to observe and monitorall of them. The all sky coverage provided by future networks of nano-satellites will ensure thatall future SGR outbursts will be detected and their behaviour will be monitored.The SGR spectra are in soft gamma-ray region and well represented by a single blackbody(BB) or two-temperature BB model. Above ∼ keV the spectra are well modeled by opticallythin thermal bremsstrahlung (OTTB). In our simulations we analyze the response to regular SGR bursts. For an example spectrum ofa regular SGR we utilize the Konus catalog of SGRs detected from 1978 to 2000. The catalogcontains bursts from SGR 0526-66, 1627-41, 1801-23, 1806-20 and 1900+14 observed using de-tectors on board Venera 11–14, Wind, and Kosmos 2326 spacecrafts. The SGR photon spectra inthe catalog are modeled by optically thin thermal bremsstrahlung using: F ( E ) = AE − e − EkT , (1)where kT (keV) is the spectral parameter, E (keV) is the photon energy and A (ph cm − s − ) is thenormalization factor.We took 81 spectral fits from the catalog and derived the normalization factor A from eachspectrum. Figure 2 shows the distribution of the kT parameter and the normalization A . Themedian values are kT = 22 +8 − keV and A = 384 +493 − ph cm − s − . The uncertainties correspond to68 % CL. The typical duration of SGR bursts in the catalog is ∼ . s. We use these parametersfor an example SGR spectrum used in our MC simulations in the energy range of − keV.The spectrum is shown in Figure 1 with the shaded region corresponding to 68 % CL which was7alculated using MC simulations and the aforementioned values of kT and A parameters with theiruncertainties. Fig 2
Distribution of the spectral parameter kT (left) and normalization A (right) from the Konus SGR catalog for81 spectral fits. The dashed lines mark the median values and the regions delimited by dotted lines correspond to 68 %CL. Terrestrial gamma-ray flashes, brief bright bursts of multi-MeV gamma-rays, which are believedto be emitted by thunderclouds and generated, via bremsstrahlung, by the relativistic runawayelectrons accelerated by electric fields in the atmosphere. They were discovered by the Burst andTransient Source Experiment (BATSE) aboard Compton Gamma-ray Observatory (
CGRO ). Plen-tiful observations have also been provided by other astrophysical instruments such as the ReuvenRamaty High Energy Solar Spectroscopic Imager (
RHESSI ),
46, 47 the Gamma Ray Burst Monitor(GBM) on board the
Fermi satellite, and the Astrorivelatore Gamma ad Immagini Leggero(
AGILE ) satellite.
The
AGILE satellite was launched to 550 km altitude with inclination of . ◦ . The Mini-Calorimeter (MCAL) is composed of 30 CsI(Tl) scintillator bars with each crystalof dimension of × × mm giving the detector a sensitivity from 300 keV to 200 MeV andthe effective area of − cm . Although this makes
AGILE /MCAL a more sensitive instru-8ent for TGF detection than what is foreseen for
CAMELOT , which is expected to be launched topolar LEO with detectors composed of 5 mm thick CsI(Tl) crystals, we use the
AGILE /MCAL ob-servations of TGFs as a reference for our simulations because the mission accumulated a large andhigh quality TGF database in orbit. For their TGF observations see the 3rd
AGILE
TGF catalog
22, 55 and the corresponding online catalog .The duration of TGFs is typically below 1 ms with the peak of the distribution around − µ s. AGILE measurements show that the cumulative spectrum of 228 single-pulse TGFs inthe range . − MeV can be fitted by a power law with exponential cutoff: F ( E ) = K (cid:18) E MeV (cid:19) − α e − EE C , (2)where α = 0 . +0 . − . and E C = 5 . +0 . − . MeV. The cumulative spectrum is a rough approxima-tion because of the effects due to atmospheric absorption from different source regions and due tothe direction-dependent detector response which in the cumulative spectrum are smeared out. Foranalysis of instrumental effects and their impact on energy spectra see. The fluence distribution can be represented with a power law with an index of − −
52, 57
Therefore, there is no typical observed TGF fluence. However, for a reference we can con-sider a typical TGF fluence at the threshold level of
AGILE which is around 0.05 ph cm − overthe full energy range of AGILE /MCAL . − MeV and this typical fluence is emitted overan average duration T of less than µs (M. Marisaldi, private communication). The nor-malization K corresponding to this fluence integrated over . − MeV and within µs is K = 123 ph cm − s − MeV − . We assume this normalization in our MC simulations. The spectrum α and E C parame-ters with their uncertainties. We assume that the published uncertainties of α and E C correspond to68 % CL. Normalization K was kept fixed because it corresponds to the fluence detection thresholdof TGFs by AGILE . There are several external background components at Low-Earth Orbits (LEO) which need tobe considered in a study of the expected detected background count rate by an instrument withlarge field-of-view (FOV). The various components include extragalactic gamma-rays, cosmic-rayparticles, secondary gamma-rays and particles produced in the Earth’s atmosphere and the Galacticgamma emission. For overview see publications Refs. 58–70 and technical notes Refs. 71, 72. Thefollowing subsections describe each component in detail and Fig. 3 shows a comparison of thein-orbit expected background fluxes which we use in our Geant4 simulations involving the massmodel of one 3U
CAMELOT
CubeSat and its detectors. γ -ray Background The cosmic X-ray/ γ -ray background (CXB) was discovered by a sounding rocket in 1962. It isnearly isotropic emission detected over a wide range of energies from few keV to few 100 GeV.
60, 61, 63, 64, 66, 74–88
It is composed of high-energy emission from various extragalactic sources (active galactic nuclei,quasi-stellar objects, supernovae Ia, galaxy clusters, starburst galaxies, X-ray binaries, hot inter-galactic gas).
61, 81, 84, 89–101
Some authors also argue that the diffuse γ -ray radiation originates inCosmic Microwave Background being inverse Compton scattered on cosmic-ray electrons. ig 3 An overview of various background components.
Left:
The differential photon flux multiplied by the solidangles of the incident radiation valid for the expected altitude of the satellite of 500 km and for all-sky field-of-view.Trapped particle, primary CR H and He fluxes are for the orbital inclination i = 20 ◦ . Primary CR e − and e + fluxesare for the geomagnetic latitude θ M = 29 . ◦ . Secondary p + flux was obtained from the combination of data for . rad ≤ θ M ≤ . rad and for . ≤ L-shell ≤ . , where L-shell is the McIlwain L-parameter. Secondary e − ande + fluxes were obtained from the combination of data for rad ≤ θ M ≤ . rad and for . ≤ L-shell ≤ . . Albedo γ flux is for i = 20 . ◦ . Albedo n is for cutoff rigidity R cut = 5 GV or θ M = 37 ◦ . Details are described in Sec. 3. Right:
The integral photon flux for the same models also multiplied by the same solid angles.
There are several empirical models used to describe the measured flux.
60, 69, 74, 84, 105
In oursimulations we compare two models: the model introduced by Gruber et al. (1999) and the onederived by Ajello et al. (2008) (see Sec. 7).The Gruber et al. (1999) model fits the low-energy as well as the high-energy part of theCXB measurements obtained by HEAO-1 , CGRO /COMPTEL and
CGRO /EGRET instru-ments across a wide energy range spanning from 3 keV to 100 GeV. This empirical model is usedas a standard in modeling of the CXB flux for planning space missions. The differential photonflux F ( E ) ≡ dN/dE in units of ph cm − s − sr − keV − is:for energies E = 3 − keV F ( E ) = 7 . (cid:18) E (cid:19) − . e − E .
13 keV (3)11nd for energies
E > keV it is F ( E ) = 0 . (cid:18) E
60 keV (cid:19) − . + 0 . (cid:18) E
60 keV (cid:19) − . + 0 . (cid:18) E
60 keV (cid:19) − . . (4)Ajello et al. (2008) derived a CXB model which is in a good agreement with measure-ments from Swift /BAT, HEAO-1 , INTEGRAL , BeppoSAX instruments and other missionsin the 2 keV – 2 MeV energy range. The differential photon flux F ( E ) ≡ dN/dE in units ofph cm − s − sr − keV − is: F ( E ) = C ( E/E B ) Γ + ( E/E B ) Γ , (5)where the parameters with 1 σ errors are C = (10 . ± . × − , Γ = 1 . ± . , Γ = 2 . ± . and E B = 29 . ± . keV.The CXB flux is omnidirectional and for 500 km altitude it irradiates a satellite from a solidangle of 8.64 sr (3.93 sr are occulted by the Earth). The CXB spectra for different models, includingthe two previously discussed, are shown in Figure 4. The integral flux, i.e. the integrated flux forenergies above a given energy threshold, for the Gruber et al. (1999) model and for E > keVis 30.3 ph cm − s − whereas for the Ajello et al. (2008) model the integral flux at the same low-energy threshold is 33.7 ph cm − s − .Concerning the CAMELOT
CubeSats, the detectors are 5 mm thick CsI(Tl) scintillators (asdescribed in Sec. 4) with effective area having maximum at ∼ keV (see Figure 18). Thescintillator is relatively transparent to gamma-rays above 2 MeV. For example the effective area at1 MeV is a factor of about 7 lower than at 100 keV. Although some gamma-rays can cause pair-production or Compton scatter in the material of the satellite and then lower-energy gamma-rays12an reach the scintillator, the CXB flux above 2 MeV is much lower than at few tens of keV orat 100 keV. Therefore, the high-energy gamma-ray component (above few MeV) included in theGruber et al. (1999) model is not essential for the CAMELOT ’s detectors.Ajello et al. (2008) discusses that the normalization of the Swift /BAT CXB spectrum at30 keV (CXB peak) is ∼ % higher than the HEAO-1 measurement and consistent with the
IN-TEGRAL one. Also, the HEAO-1 measurement has 10 % precision at the CXB peak. Therefore,we use both CXB models to simulate the expected detected background by
CAMELOT , however,for a more detailed analysis, e.g. detected count rate as a function of energy threshold, we choosea more conservative approach and use the Ajello et al. (2008) model which gives ∼ % higherintegral flux in the energy range of − keV, which is approximately the sensitivity range of CAMELOT ’s detectors.
Fig 4
The CXB spectra for different models.
Left:
The differential photon flux.
Right:
The integral photon flux forthe same models. The integral flux is multiplied by a solid angle of the radiation illuminating the satellite at 500 kmaltitude.
The Galactic gamma emission which consists of diffuse continuum and resolved sourceshas been widely observed by many instruments, e.g. by
SAS-2 ,
77, 111–113
OSO-3 , COS B , NTEGRAL
82, 87, 116–120 satellites, COMPTEL, EGRET and OSSE instruments
81, 121–124 aboard the
CGRO satellite,
Fermi /LAT,
88, 125–127
RXTE /PCA and
Swift /BAT instruments.For our MC simulations (Sec. 7) we took the X-ray/gamma-ray fluxes of the inner Galac-tic region from Figures 10 and 11 as published in Ref. 87 in EF E flux density representation.Ref. 87 summarizes measurements from RXTE /PCA,
INTEGRAL /SPI,
INTEGRAL /IBIS,
87, 116
CGRO /COMPTEL and
CGRO /EGRET instruments and show the fluxes renormalized to thecentral radian of the Milky Way defined by | l | < ◦ and | b | < ◦ .The emission from the inner Galactic region irradiates a satellite from the solid angle of0.542 sr. The differential and integral photon spectra are shown in Figure 5. The integral fluxfor energy E > keV is 0.2 ph cm − s − . However, it should be noted that the Galactic emis-sion is not spatially uniform and has a brightness structure peaked at the Galactic center (see e.g.Ref. 115). Figure 5 also shows measurements done by Fermi /LAT taken from Figure 4 of Ref. 125for smaller region of | l | < ◦ and | b | < ◦ . We do not include these Fermi /LAT measurementsin our MC simulations because the region of the inner Galaxy is not exactly the same as the oneused for the other aforementioned data sets. This does not effect our results because the photonflux at these very high energies is very small.
The fluxes of the geomagnetically trapped electrons and protons inside the inner van Allen ra-diation belt contribute to the overall detected instrumental background and they are especiallyimportant when a satellite at LEO passes the polar regions or the South Atlantic Anomaly(SAA). Details about the Earth’s radiation environment can be found in, for example, Ref. 58, 64,133–139. 14 ig 5
The spectra of the inner Galaxy emission.
Left:
The differential photon flux observed by
RXTE /PCA,
INTE-GRAL /SPI,
INTEGRAL /IBIS,
CGRO /COMPTEL and
CGRO /EGRET for the region defined by | l | < ◦ , | b | < ◦ and Fermi /LAT for the region defined by | l | < ◦ , | b | < ◦ . The gray solid line marks the flux takenfor our MC simulations. Right:
The integral photon flux. The integral flux is multiplied by 0.542 sr solid angle of theinner Galaxy region.
Several models describing the fluxes of the trapped particles around the Earth based on mea-surements from tens of space missions have been developed over last decades, e.g. the NationalAeronautics and Space Administration’s (NASA) AE8 and AP8 models, EuropeanSpace Agency’s (ESA) AE-8 update ESA-SEE1 model, or model based on the measurementsfrom Proton/Electron Telescope (PET) onboard the Solar, Anomalous, and Magnetospheric Parti-cle Explorer (
SAMPEX ) satellite - the
SAMPEX /PET PSB97 model.
In our on-board background simulations (Sec. 7) we employ the fluxes of trapped electronsand protons prescribed by the recent AE9 and AP9 models as they are implemented in ESA’sSPace ENVironment Information System (SPENVIS ). SPENVIS is an Internet interface to modelsof the space environment and its effects, developed by a consortium led by the Royal BelgianInstitute for Space Aeronomy (BIRA-IASB). The AE9/AP9 models are based on 33 satellite datasets from 1976 to 2011 and they are provided by the U.S. Air Force Research Laboratory (AFRL)
15n their software package .The AE8/AP8 models available in SPENVIS or in the AFRL package do not compute fluxeslower than 1 particle cm − s − , whereas the AE9/AP9 models provide fluxes below 1 particle cm − s − .That is important for our purpose, because we want to estimate the detected background count ratein the regions outside SAA and polar regions. However, the current version of the AP9/AE9 modelprovided in SPENVIS is recommended for evaluation purposes only and there have been reporteddiscrepancies between the AE8/AP8 and the AE9/AP9 models, e.g. see Ref. 149 and referencestherein.Figure 6 shows orbit-averaged integral spectra of trapped electrons and protons averaged over60 days of orbiting (including SAA passages) with sampling of 10 s obtained for different modelsby the AFRL package. It demonstrates that AE9/AP9 models gives much higher electron andproton fluxes compared to the AE8/AP8 models at low inclinations and low energies. Thereforethe detected background count rate due to the trapped particles calculated by our simulation mayoverestimate the real level.Figure 7 shows maps of integral fluxes (flux of particles with energy higher than E ) of trappedelectrons and protons for the AE9 and AP9 models with Monte Carlo (MC) mode, 100 runs and50 % confidence level (CL) at 500 km altitude. The MC mode accounts for the uncertainty due tothe random perturbations as well as the flux variations due to the space weather. We calculated spectra of electrons and protons averaged along the trajectory of a satellite ataltitude 500 km with inclination of i = 20 ◦ and orbiting 30 days with flux sampling every 10 s.Only the regions with the integral flux ≤ particle cm − s − were used ( E > keV for electronsand E > keV for protons). These conditions give a duty cycle, i.e. the fraction of time a ig 6 Comparison of orbit-averaged integral fluxes of trapped electron models AE8 MAX (solar maximum), AE950 % and 90 % confidence levels (CL); and trapped proton models AP8 MIN (solar minimum), AP9 50 % and 90 %CL for different altitudes and inclinations. satellite spends in a region with particle flux lower than a given flux threshold, of 80 %. If theorbital inclination is ◦ the duty cycle would be 76 %. Details about the duty cycle for differentinclinations, altitudes at LEO, flux and energy thresholds for AE8, AP8, AE9 and AP9 models canbe found in Ref. 150.In this way we were able to obtain averaged spectra outside of SAA. The differential and in-tegral fluxes are shown in Figure 8. The differential flux per solid angle has been calculated forsimplicity assuming the radiation is illuminating a satellite isotropically from the solid angle of π because, for example, in case of CAMELOT satellites the pointing strategy is not established yet.17 ig 7
A map of the integral flux of geomagnetically trapped electrons (left) and protons (right) at 500 km altitudeaccording to the AE9 and AP9 models (MC mode, 50 % CL), respectively, obtained by the AFRL package.
The trapped particles can collide with the detector from various directions and we are interested ina long-term average. Also, the assumption of the isotropy of the trapped particle flux is a simplifi-cation because of the well known “East-West” effect.
The integral flux for trapped electrons is0.41 cm − s − ( E > keV) and for trapped protons is 0.14 cm − s − ( E > keV) as obtainedfrom the model.
Fig 8
Differential fluxes (left) and integral fluxes (right) of geomagnetically trapped electrons and protons averagedalong the trajectory of a satellite at altitude 500 km with inclination i = 20 ◦ and orbiting 30 days. The models wereAE9 and AP9, MC mode with 100 runs and the spectra were derived from the 50 % CL of the fluxes. Only the regionsavoiding SAA were used. The differential flux per solid angle has been calculated for simplicity assuming the radiationis illuminating the satellite isotropically from the solid angle of π . .4 Primary Cosmic-Rays The spectra of the primary particles of cosmic-rays (CRs) used in our simulations are describedbelow. For the assumed 500 km altitude the fluxes irradiate the satellite from the solid angle of8.64 sr. The origin of CRs is extraterrestrial consisting mainly of protons. Other components ofCRs such as electrons, positrons, alpha particles and nuclei of heavier elements have been de-tected as well. Several experiments have been performed to study CRs, e.g. AMS,
BESS,
CREAM,
Fermi /LAT,
HESS,
PAMELA.
We considered two models for the spectra of primary particles. The first one was the ISO-15390 model, which is the international standard for estimating the radiation impact of CRs onhardware in space and which describes the fluxes of primary protons, alpha particles, and nuclei ofheavier elements.The second model which we considered was described by Mizuno et al. (2004), see Ref. 63,and it was based on measurements done by BESS and AMS experiments (see also Ref. 66). Theflux of primary CRs in interstellar space can be modeled by a power law function: F U ( E k ) = A (cid:20) R ( E k )GV (cid:21) − a , (6)where R = pc/Ze is the rigidity of the particle as a function of its kinetic energy E k or momentum p and its charge Ze . The flux constant A and the exponent a are determined by fitting of thefollowing model to the measurements.The flux of primary CRs for a given phase of the solar cycle and in a given position in the19arth’s magnetosphere according to the model described in Ref. 63 is: F ( E k ) = F U ( E k + Zeφ ) × F M ( E k , M, Z, φ ) × F C ( R, h, θ M ) , (7)where M is the mass of the particle, φ is a solar modulation potential, h is the altitude of thesatellite’s orbit and θ M is the geomagnetic latitude.By applying an effective shift of energy of the primary particles due to the deceleration by thesolar wind the first function F U in Eq. (7) gets form: F U ( E k + Zeφ ) = A (cid:20) R ( E k + Zeφ )GV (cid:21) − a . (8)The second function F M accounts for the flux modulation due to the solar cycle and is givenby: F M ( E k , M, Z, φ ) = ( E k + M c ) − ( M c ) ( E k + Zeφ + M c ) − ( M c ) , (9)where the solar modulation potential varies between φ = 0 . GV for solar minimum and φ =1 . GV for solar maximum.The third term is the geomagnetic cutoff function F C given by: F C ( R, h, θ M ) = 11 + ( R/R cut ) − r , (10)where r = 12 for p + or α particles, r = 6 for e − or e + , and the cutoff rigidity R cut is given by theSt¨ormer equation: R cut = 14 . (cid:18) hR E (cid:19) − cos θ M GV , (11)20here R E is the Earth’s radius.We want to estimate a long term average of the flux, therefore we assume that the flux hasuniform angular distribution for the zenith angle ◦ ≤ θ ≤ θ cut and the flux is zero for θ cut ≤ θ ≤ ◦ , where the θ cut is the zenith angle of the Earth’s horizon and it is ◦ for the altitude of500 km. For primary protons and alpha particles we compared the model ISO-15390 and the model Mizunoet al. (2004) described in Ref. 63.For the ISO-15390 model we employed SPENVIS where we generated the orbit-averaged spec-tra for circular orbit with inclination i = 20 ◦ , duration 30 days and sampling 60 s. The followingparameters setting was applied: solar minimum activity (May 1996), magnetic shielding on, stormyand quite magnetosphere, Størmer with eccentric dipole method and magnetic field moment un-changed.For the model described in Ref. 63 we used the following parameters: solar minimum cyclewith the solar modulation potential φ = 0 . GV, altitude 500 km, and two geomagnetic latitudes θ M = 0 ◦ and θ M = 20 ◦ (orbital inclination) + . ◦ (tilt between the geomagnetic dipole axis andthe Earth’s rotational axis).For primary protons the values of A = 23 . particle m − s − sr − MeV − and a = 2 . wereadopted. For primary alpha particles the values of A = 1 . particle m − s − sr − MeV − and a =2 . were adopted.Figure 9 and 10 show fluxes of primary protons and alpha particles, respectively, at 500 kmaltitude obtained by the ISO-15390 model for quiet and stormy magnetosphere and obtained by the21izuno et al. (2004) model for fixed geomagnetic latitudes θ M = 0 ◦ and θ M = 29 . ◦ . This modelpredicts the integral flux of primary protons of kinetic energies E > GeV being 0.11 cm − s − (for θ M = 0 ◦ ) or 0.29 cm − s − (for θ M = 29 . ◦ ) and the integral flux of primary alpha particles ofkinetic energies per nucleon E > GeV/n being 0.016 cm − s − (for θ M = 0 ◦ ) or 0.041 cm − s − ( θ M = 29 . ◦ ).For our Geant4 simulations of the expected on-board background by a CAMELOT satellite(Sec. 7) we use the ISO-15390 model with stormy magnetosphere, because it is the internationalstandard for CR flux and because it was obtained for a fixed orbital inclination of i = 20 ◦ meaningcrossing the range of geomagnetic latitudes between − ◦ and ∼ ◦ , . It predicts the integralflux of primary protons of kinetic energies
E > GeV being 0.095 cm − s − (for quite magneto-sphere) or 0.099 cm − s − (for stormy magnetosphere) and the integral flux of primary alpha parti-cles of kinetic energies per nucleon E > GeV/n being 0.017 cm − s − (for quite magnetosphere)or 0.018 cm − s − (for stormy magnetosphere). For the spectra of the primary e − and e + we used the model described by Mizuno et al. (2004) with references to the flux measurements by. The measurements of the ratio of positrons andelectrons e + /(e − +e + ) are given by. We adopt the model of the primary interstellar particles Eq. (6) with following parameters: A =0 . particle m − s − sr − MeV − and a = 3 . for electrons and A = 0 . particle m − s − sr − MeV − with the same exponent a for positrons.Same as for the primary protons and alpha particles we used the following conditions of the https://spawx.nwra.com/spawx/maps/maplats.html ig 9 Differential fluxes (left) and integral fluxes (right) of primary CR protons. Solid lines mark model introducedby Mizuno et al. (2004) for geomagnetic latitudes θ M = 0 ◦ and θ M = 29 . ◦ . Dashed lines mark galactic CRmodel ISO-15390 for quiet and stormy magnetosphere obtained in SPENVIS for circular orbit with inclination i = 20 ◦ . Spectra from both models were obtained for altitude of 500 km. The integral flux is multiplied by a solidangle corresponding to the radiation illuminating the satellite at this altitude. Fig 10
Differential fluxes (left) and integral fluxes (right) of primary CR alpha particles as a function of energy pernucleon. Solid lines mark model introduced by Mizuno et al. (2004) for geomagnetic latitudes θ M = 0 ◦ and θ M = 29 . ◦ . Dashed lines mark galactic CR model ISO-15390 for quiet and stormy magnetosphere obtained inSPENVIS for circular orbit with inclination i = 20 ◦ . Spectra from both models were obtained for altitude of 500 km.The integral flux is multiplied by a solid angle corresponding to the radiation illuminating the satellite at this altitude. solar cycle and the orbit: solar minimum with the modulation potential φ = 0 . GV, altitude500 km, and two geomagnetic latitudes θ M = 0 ◦ and θ M = 29 . ◦ . Figure 11 and 12 show thefluxes of the primary electrons and positrons.For our simulations of the expected detected background (Sec. 7) we use the spectrum for23 M = 29 . ◦ . We also assume that the angular distribution of the flux is incoming uniformlyfrom the solid angle unocculted by the Earth. Then the integral flux ( E > GeV) for e − is × − cm − s − and for e + it is . × − cm − s − . Fig 11
Differential fluxes (left) and integral fluxes (right) of primary CR electrons modeled by Mizuno et al. (2004) for geomagnetic latitudes θ M = 0 ◦ and θ M = 29 . ◦ and altitude of 500 km. The integral flux is multiplied by a solidangle corresponding to the radiation illuminating the satellite at this altitude. Fig 12
Differential fluxes (left) and integral fluxes (right) of primary CR positrons modeled by Mizuno et al. (2004) for geomagnetic latitudes θ M = 0 ◦ and θ M = 29 . ◦ and altitude of 500 km. The integral flux is multiplied by a solidangle corresponding to the radiation illuminating the satellite at this altitude. .5 Secondary Particles and Radiation Secondary (albedo) particles and radiation are created by interaction of primary CRs with theEarth’s atmosphere.
58, 64
For secondary p + and for energy above 100 MeV we use the model based on the measurementsdone by the Alpha Magnetic Spectrometer (AMS) from 380 km altitude for the geomagneticlatitude . rad ≤ θ M ≤ . rad. For energy below 100 MeV we use the fit to MITA /NINA-2 data from 450 km altitude and for . ≤ L-shell ≤ . , where L-shell is the McIlwain L-parameter. For details see the LAT Technical Note LAT-TD-08316-01 of the Fermi satellite.
There is onlysmall dependence of the flux on altitude therefore it can be used as an approximation to theflux at altitude of 500 km.The differential flux F ( E ) in units of particle m − s − sr − MeV − is modeled as: F ( E ) = . (cid:0) E MeV (cid:1) . for MeV ≤ E ≤ MeV . (cid:0) E MeV (cid:1) − . for MeV ≤ E ≤ E brk . (cid:0) E brk MeV (cid:1) − . (cid:16) EE brk (cid:17) − . for E ≥ E brk , (12)where E brk = 600 MeV is break energy. Figure 13 shows the modeled flux together with themeasurements.The same model is used for the upward and downward component of the flux and it is assumedthat secondary protons irradiate the satellite from the solid angle of π sr without zenith-angledependence of the flux. The integral flux ( E ≥ MeV) is 0.037 cm − s − .25 ig 13 Differential fluxes (left) and integral fluxes (right) of secondary protons modeled by Eq. (12) are marked by theblack curve. The measurements from the AMS and
MITA /NINA-2 experiments for the given geomagnetic position areshown as well. The integral flux is multiplied by the solid angle of π sr. For secondary e − and e + and for energy above 100 MeV we use the model based on the mea-surements done by AMS from 380 km altitude for the geomagnetic latitude ≤ θ M ≤ . rad.For energy below 100 MeV we use the fit to Mir /MARIA-2 data from 400 km altitude andfor . ≤ L-shell ≤ . . For details see the LAT Technical Note LAT-TD-08316-01. For secondary e − the differential flux F ( E ) in units of particle m − s − sr − MeV − is modeledas: F ( E ) = . (cid:0) E MeV (cid:1) − . for MeV ≤ E ≤ MeV . (cid:0) E MeV (cid:1) − . for MeV ≤ E ≤ E brk . (cid:0) E brk MeV (cid:1) − . (cid:16) EE brk (cid:17) − . for E ≥ E brk , (13)where the break energy E brk = 3000 MeV. Figure 14 shows the modeled flux together with themeasurements.For secondary e + the differential flux F ( E ) in units of particle m − s − sr − MeV − is modeled26 ig 14 Differential fluxes (left) and integral fluxes (right) of secondary electrons modeled by Eq. (13) are marked bythe black curve. The measurements from the AMS and
Mir /MARIA-2 experiments for the given geomagnetic positionare shown as well. The integral flux is multiplied by the solid angle of π sr. as: F ( E ) = (cid:0) E MeV (cid:1) − . for MeV ≤ E ≤ MeV . (cid:0) E MeV (cid:1) − . for MeV ≤ E ≤ MeV . (cid:0) E MeV (cid:1) − . for MeV ≤ E ≤ E brk . (cid:0) E brk MeV (cid:1) − . (cid:16) EE brk (cid:17) − . for E ≥ E brk , (14)where the break energy E brk = 3000 MeV. Figure 15 shows the modeled flux together with themeasurements.The same model is used for the upward and downward component of the flux and it is assumedthat secondary e − and e + irradiate the satellite from the solid angle of π sr without zenith-angledependence of the flux. The integral flux ( E ≥ MeV) is 0.18 cm − s − for e − and 0.23 cm − s − for e + . 27 ig 15 Differential fluxes (left) and integral fluxes (right) of secondary positrons modeled by Eq. (14) are marked bythe black curve. The measurements from the AMS and
Mir /MARIA-2 experiments for the given geomagnetic positionare shown as well. The integral flux is multiplied by the solid angle of π sr. γ -rays The secondary (albedo) X-ray and γ -ray flux is due to interaction of primary CRs with the Earth’satmosphere. It is produced by decay of π pions (mainly above 50 MeV), by bremsstrahlung fromprimary and secondary electrons (mainly below 50 MeV), and also by the reflection of CXB and ithas been measured by several satellites and balloon experiments.
60, 61, 63, 64, 69, 75, 76, 78, 82, 87, 172–177
Theintensity depends on the geomagnetic latitude.
We utilize a model reported by Ajello et al. (2008) based on the Swift /BAT measurementsfrom ∼ keV to ∼ keV for altitude of h ∼ km and inclination of i = 20 . ◦ and whichis compatible with measurements from BeppoSAX ( h ∼ km and i = 4 ◦ ) and after somecorrections with measurements by the polar-orbiting satellite 1972-076B ( h ∼ km). MCsimulations show that this model is a very good approximation of the Earth albedo X-ray emissionup to 300 keV.
84, 179
We assume the Ajello et al. (2008) model in the energy range of E = 10 − keV andhence the differential photon flux F ( E ) given by Eq. (5), where the model parameters and their280 % CL errors are Γ =-5 (fixed), Γ =1.72 ± . , E b =33.7 ± . keV and C = 1 . +0 . − . × − .For higher energies we assume a model reported by Mizuno et al. (2004) based on measure-ments by and Kosmos 461 satellites and by balloon flights.
Particularly, weconsider only energies E = 0 . − MeV where we assume the differential photon flux F ( E ) inunits of ph cm − s − sr − keV − to be a simple power law function: F ( E ) = 719 (cid:18) E keV (cid:19) − . , (15)where we normalized the Mizuno et al. (2004) model, their Eq. (21), in order to obtain the samedifferential flux at 300 keV as predicted by the Ajello et al. (2008) model. The spectrum is shownin Figure 16. According to MC simulations there is only a small dependence of the albedo X-rayflux ( − keV) on the solar cycle and geomagnetic latitude below ∼ ◦ for an instrument atLEO with large FOV which covers the whole terrestrial disc. Fig 16
The albedo X-ray/ γ -ray spectra. For energies from 10 keV to 300 keV modeled by Ajello et al. (2008) and forenergies from 300 keV to 20 MeV modeled by Eq. (15). Left:
The differential photon flux.
Right:
The integral photonflux integrated up to 20 MeV. The integral flux is multiplied by the Earth-subtended solid angle of 3.93 sr at an altitudeof 500 km.
A zenith angle dependence of the albedo γ -ray flux has been measured in the − MeV29egion.
63, 75, 76
See also Ref. 61, 114, 172, 174–178, 180 and references therein for the zenith angledependence of the albedo γ -ray flux at other energies. In the energy range − keV, coveredby the Ajello et al. (2008) model, the MC simulations suggest that there is no zenith angledependence. However, for the higher-energy part . − MeV one can expect a zenith angledependence of the flux. In case of
CAMELOT satellites, they will have detectors with all-sky FOVwhich can be illuminated from various directions and we are interested in a long term average flux,therefore, for simplicity, we do not assume any zenith angle dependence in our Geant4 simulationsinvolving a
CAMELOT satellite mass model.At an altitude of 500 km the photons would irradiate the satellite from a solid angle of 3.93 sr.The integral flux (
E > keV) is 3.1 ph cm − s − . The albedo neutrons are produced in hadronic showers created by CRs interacting with the Earth’satmosphere and they can reach a satellite at LEO. For the albedo neutrons we use the predictionsof the QinetiQ Atmospheric Radiation Model (QARM), based on MC radiation transport code, asreported in the ESA document ECSS-E-ST-10-04C. The model has been validated against severalmeasurements and is also consistent with other MC simulations.
59, 65
For other models andmeasurements see Ref. 61, 69, 185, 186 and references therein.Figure 17 shows the fluxes of secondary neutrons for the cutoff rigidity R cut = 16 . GV and R cut = 5 GV for solar minimum. The fluxes were scaled from the altitude of 100 km to 500 km asdescribed in the ECSS-E-ST-10-04C document.In our simulations of the expected detected background (Sec. 7) we use the spectrum for thesolar minimum and for the cutoff rigidity R cut = 5 GV which corresponds to the geomagnetic30atitude θ M = 37 ◦ following from the St ¨ormer equation Eq. (11) or latitude between ∼ ◦ and ∼ ◦ , see Figure 7 of Ref. 161.The integral flux is 0.61 cm − s − for E > eV, for R cut = 5 GV, altitude of 500 km andassuming that all neutrons are coming from the solid angle of 3.93 sr which corresponds to theangular size of the Earth observed from that altitude.
Fig 17
Differential fluxes (left) and integral fluxes (right) of albedo neutrons predicted by the QARM model for twovalues of cutoff rigidity and scaled to the altitude of 500 km. The integral flux is multiplied by the solid angle of3.93 sr.
CAMELOT
CubeSats
We study in particular the expected on-board background for the proposed
CAMELOT mission,expected to be launched to LEO with the main objective of all-sky monitoring and timing-basedlocalization of GRBs. The at least nine satellites are considered to be placed on orbits with altitudeof ∼ − km with inclination of ◦ or at Sun-synchronous orbits of inclination . ◦ . Oneof the options for the
CAMELOT satellite platform is the one being developed by C3S LLC inBudapest, therefore we apply its mass model in our Geant4 simulations.31 .1 The Detector System
The constellation of at least nine 3U CubeSats is proposed to be equipped with large and thinCsI(Tl) scintillators, of size × × mm each, read out by Hamamatsu Multi-Pixel PhotonCounters (MPPC). There would most likely be four scintillators on each satellite with two scin-tillators placed on two neighbouring sides of the satellite. The scintillators will be wrapped inthe enhanced specular reflector (ESR) foil and enclosed in a support structure made either fromaluminium or carbon fiber-reinforced plastic (CFRP). For details about the detector system seeRef. 187. The effective area of four detectors on board one CAMELOT satellite as a function ofenergy and for different directions, obtained from Geant4 simulations, is shown in Figure 18.In order to understand and characterize the behaviour of the large-area CsI(Tl) scintillator de-tector and the MPPC readout, an experimental setup was built in Hiroshima, Japan. The experi-mental setup provided vital information for the simulation, mostly for the position dependence ofthe scintillator effective light yield. Different γ sources were used in the tests, mostly an Amsource.
A dedicated set of measurements were carried out with Am γ source with an activity of 471 kBqwhich was collimated to irradiate different positions on the scintillator. The experiments werecarried out with a single MPPC very similarly to the measurements presented in Ref. 188. Thecollimation was achieved with two lead sheets each containing holes in nine positions. In order toobtain the optical parameters of the scintillators as precisely as possible, the effect of reflectivityand absorption length on photon light yield was maximized by utilizing one MPPC in the middle ofthe shorter side of the scintillator. Spectra were recorded in nine cases by moving the Am source32 ig 18
The effective area of four detectors on board one
CAMELOT satellite as a function of energy and for differentangles α and β defining the source direction in respect to the satellite. For the exact definition of these angles seeFig. 21. in the nine positions where holes were present. Figure 19 shows the simulation of the experimentalset-up.The measured and simulated spectra for the irradiation point closest to the MPPC and in thefarthest corner are compared in Figure 20. The same number of X-rays were simulated, whichwere emitted in 2 minutes of data acquisition for each spectrum. The difference between thesespectra is the largest of all. The main reason for this is the difference in the mean path of opticalphotons, which is the shortest when the source is in front of the MPPC and the largest when thesource is placed in the corner. 33 ig 19 Simulation of 50 X-rays originating from a collimated X-ray source placed above the middle of the scintillator.Blue tracks are X-rays, green tracks are optical photons and the red square marks the MPPC. Only optical photonswhich are detected were drawn.
Two distinct peaks are visible in the measured and simulated spectra (Figure 20). The peak withthe higher energy corresponds to the Am γ peak at 59.5 keV. The lower-energy one is the K α X-ray fluoresence peak of the Cesium in the scintillator.
The results of the Geant4 simulationwere smeared by a Gaussian function with a standard deviation σ of 5 channels for the closestpoint of irradiation and 15 channels for the farthest to match them with the measured ones. Thehistogram of the number of photons detected in the simulation were scaled up by 1.35 and 1.39respectively to match them with the measurements. This way assuming a linear detector response,all amplification factors were treated together. The fact that the scaling factor is almost the samefor all parts of the scintillator translates to a good light collection efficiency. The main aim of themeasurements was to determine the number of detected optical photons for an energy deposition of1 keV in the scintillator (on average). For the measurements taken at the farthest position from theMPPC the 59.5 keV Am peak was at ADC channel 180. The number of detected photons in thesimulations had to be scaled up by roughly 1.37 to match the measurements. For the measurementstaken at the closest point to the MPPC the same scaling parameter was used. For the farthest34osition from the MPPC this implicates that an energy deposition of 1 keV yields 4.11 detectedoptical photons on average.
Fig 20
Simulated spectra of number of scintillation photons detected compared to the measurements. At the closestposition to the MPPC (right) and at one of the farthest corners (left). The simulated spectra were smeard by 5 and 15channels respectively.
The light yield in the simulation for the scintillator was fixed at 54 photons/keV, which is theyield for CsI(Tl) scintillators produced by Saint-Gobain which is similar to our scintillator pro-duced by AMCRYS . The absorption length and the reflectivity of the surface of the scintillatorwas varied until the simulation agreed with the measurements for the two extreme spectra, the onein front of the MPPC and the one in the farthest corner. The best fitting reflectivity was 99.99 %and the absorption length determined from the fit was 60 cm. These values were used in the latersimulations.In this way of calibration the energy resolution and noise of the electronics are taken intoaccount in the simulations. Although pileup is not included but during operation we do not expectsuch high count rates from regular sources where it could be relevant. Description of Geant4 Simulations
A Geant4 MC based simulation was developed in order to understand how the
CAMELOT
Cube-Sat constellation would detect γ -rays originating from short GRBs, long GRBs and TGFs. Thisrequired dedicated simulations of each background component as well as response to the γ -raysources and calculation of the signal-to-noise ratio. The repository containing the simulationsource code and analysis code are shared on GitHub (with a GNU General Public License). , .As the first step, the experimental setup that was used to calibrate the optical parameters ofthe CsI(Tl) scintillator – the γ -ray detector of the satellite – that with its casing was implementedin Geant4. Details are in Sec. 5. Afterwards the complex CAD model (Sec. 6.2) of the satellite –consisting of 7 modules, each with a given average material composition – was imported to Geant4with CADMESH. Four scintillators, each read out by 8 MPPCs were placed on two sides of thesatellite.In order to keep computation time at a reasonable level, the simulation of each primary particleis stopped if the number of detected optical photons reaches 10 000. Heavy ions can create severalhundred thousands of scintillation photons. This limitation made it possible to run the codes onpersonal computers with a few cores. The signal of the 8 MPPCs is planned to be grouped into twogroups of 4 MPPCs. In the following simulations the signal of all 32 MPPCs belonging to the fourscintillators is summed up. This way we give a conservative signal-to-noise ratio (SNR) estimationsince a more sophisticated trigger algorithm will decrease the chance of the background to exceedthe threshold in each channel. The energy deposition is calculated from the number of detectedoptical photons. As described in Sec. 5, 1 keV energy deposition corresponds to 4.11 optical https://github.com/ggalgoczi/szimulacio/tree/master/Bck_4.10.6 https://github.com/ggalgoczi/szimulacio/tree/master/GRB The simulations presented in this paper can be split into two main groups based on whether we aresimulating the source of the background or an astrophysical source. The latter are the target objects:sGRBs, lGRBs and TGFs, which can be considered as point sources very far away, thereforephotons coming from these sources are treated in the simulations as parallel.The other main group is the background (eg. CXB, albedo particles, trapped electrons). Thebackground particles and γ -rays mainly hit the satellite from large solid angles or isotropically.The pointing strategy of the CAMELOT satellites is not established yet and the detector has all-skyFOV. We are interested in the estimation of a long-term average background at the regions of lowgeomagnetic latitude and outside SAA as mentioned in Sec. 3. Therefore, as an approximation,we assume that all components of the background flux of particles and γ -rays irradiate the satelliteisotropically.In order to realize this in the simulations the background particles were placed randomly on asphere with a radius R around the model of the satellite. To maintain isotropy their direction wasalso randomly chosen. To boost up the simulation a source biasing was used to limit the numberof primary particles simulated to the ones which would hit the satellite. Due to the biasing, thenumber of detections in the simulation had to be normalized to determine the detection rate wewould actually have. 37he expected detection rate N det . rate for CAMELOT in space can be calculated as follows: N det . rate = 4 f Ω π R (sin θ max − sin θ min )Φ N det . sim /N prim , (16)where f Ω = Ω / π is the factor which takes into account the solid angle Ω of the type ofthe background. For instance albedo particles originate only from the atmosphere beneath thesatellite. This corresponds to 3.95 sr for our orbit. R is the radius of the sphere upon whichthe primary particles are distributed. This radius needs to be much larger than the size of thetarget object to maintain isotropy. θ stands for the angle that is formed by the initial directionof the simulated primary particle and the vector pointing to the center of the satellite from theorigin of the simulated primary particle. By limiting θ we are able to simulate only those particleswhich would hit the satellite. In our case R = 50 m. θ min and θ max are the upper and lowerbounds for the chosen interval of the emission angle in the simulation. In our case θ min = 0 and θ max = 0 . ◦ . Φ is the flux in units of cm − s − sr − . N det . sim is the number of detectionsin the given simulation. N prim is the number of primary particles shot in the simulation. Thefactor π R (sin θ max − sin θ min ) = 24668 cm . Table 2 summarizes the values of Ω and thenormalization factor f norm = 4Ω π R (sin θ max − sin θ min ) for the background models describedin Sec. 3. Table 2
Summary of solid angles Ω of background flux and normalization factor f norm . CXB and Galactic Trapped and charged Albedoprimary CR γ secondary particles γ and n Ω (sr) 8.64 0.542 π f norm (cm sr) . × . × . × . × .2 Satellite’s Mass Model In order to include all parts of the satellite including even the smallest volumes, the detailed CADmodel of the satellite was read into Geant4 directly with CADMESH that utilizes TETGEN and ASSIMP software libraries to directly read in STL files into Geant4. The satellite consists ofseven modules including the structure of the satellite, the communications module, the payload etc.The only volume that was not included were the antennas. The material of each of the volumeswas averaged (as described in Table 7. and Table 8.). The complete list of alloys used in eachvolume are listed in Sec. 10 together with their composition. Figure 21 shows the mass model ofthe CAMELOT satellite. Figure 30 in the Appendix presents the individual volumes of the satellite.
In this section the simulation results of the satellite response to each of 14 external backgroundcomponents is presented. The results are for one
CAMELOT satellite. The count rate is summedfor all detectors. By far the most relevant background is CXB. Therefore we chose to simulate twodifferent CXB models introduced by Gruber et al. (1999) and Ajello et al. (2008) describedin Sec. 3.1. The input energy spectra of each background component used for the simulations aredescribed in the corresponding subsection of section 3. The model of the satellite was irradiatedisotropically as shown in Figure 22.Four possible aluminium detector support structure (shortly detector casing or just casing)thicknesses were investigated. The same material and thickness is on all sides of the detectorhousing, including the back side. In order to give an idea of the contribution of each component a ig 21 The mass model used for the Geant4 simulations. The CAD model of the satellite was read into Geant4 and4 scintillators (green rectangles) with their respective read out were placed on two sides of the satellite. The angles α and β refer to the angles shown in the figure of the detector’s effective area. β is rotation around the Y axis, countedfrom the -Z axis and it increases towards +X axis. α is rotation around the Z axis, counted from the +X axis andincreasing towards -Y axis. The highest effective area is for a source at direction ( α , β ) = (135 ◦ , 270 ◦ ). realistic 20 keV low-energy threshold was chosen. The five components which contribute the mostto the background for the casing thickness of 0.5 mm thick Al with this low-energy threshold are:CXB ( ∼ − counts per second (cps)), albedo γ ( ∼ cps), primary CR protons (27 cps),albedo protons (45 cps) and albedo positrons (28 cps). Tables 3 and 4 summarize the backgrounddetection rate predicted by the simulation.By summing up the contribution of each background component we derived a total backgroundrate of 1550 cps for 0.5 mm, 1400 cps for 1 mm, 1270 cps for 1.5 mm and 1100 cps for 2 mm of thecasing thickness assuming a low-energy threshold of 20 keV. From the two CXB models simu-lated, the Ajello et al. (2008) model was chosen since it gives a more conservative estimate. TheAjello et al. (2008) and Gruber et al. (1999) models have integral fluxes of 33.7 ph cm − s − and40 ig 22 The mass model of the satellite is isotropically irradiated with X-rays (blue tracks). All four scintillatorsonboard appear green as they are filled with the tracks of optical photons which have green colour. The effect of thedirectional biasing (described in Sec. 6.1) can be seen.
Table 3
Simulated detection rate induced by cosmic and trapped particle background components.
Thickness CXB CXB CR CR Galactic Trapped CR CR Trapped(mm) A08 G99 α p + γ p + e − e + e − and by Ajello et al. (2008) (denoted asG99 and A08) were simulated for the CXB. For the primary CR p + and α particles we used theISO-15390 model with stormy magnetosphere and inclination of i = 20 ◦ . For primary CR e − ande + we used the model described by Mizuno et al. (2004) for solar minimum, θ M = 29 . ◦ . Fortrapped e − and p + we used the AE9 and AP9 models, respectively, for inclination of i = 20 ◦ , MCmode and derived from the 50 % CL of the fluxes. Altitude of 500 km was chosen.30.3 ph cm − s − for E > keV and give background rates of 1020 cps and 893 cps for 1 mmthick Al detector casing, respectively.The low-energy threshold onboard the CAMELOT satellites is planned to be a tunable pa-rameter and changeable upon a ground command. Laboratory experiments show that low-energy41 able 4
Simulated detection rate induced by background components originating in the atmosphere.
Thickness (mm) Albedo γ Secondary e + Secondary e − Secondary p + Albedo n R cut = 5 GV was used.threshold for our detectors is around − keV. In Figure 23 the detection rate is shown fordifferent casing thicknesses and low energy thresholds. The low energy part of the backgroundspectrum is dominated by CXB X-rays which are stopped by thicker detector casing. The higherenergy part is dominated mostly by hadrons and albedo gamma rays (hard spectrum) which caneasily cross aluminium and deposit high energies in the scintillator. Energy threshold [keV]0500100015002000 C o un t r a t e [ c p s ] Fig 23
Background count rate for three aluminium detector support structure thicknesses versus low-energy thresholds.Above a threshold of ∼
50 keV the thickness of the support structure does not change the background rate. .2 Simulation of a Typical Short GRB from Different Directions In order to quantify if
CAMELOT is capable of detecting X-ray sources we need to investigate theX-ray absorption by the satellite structures themselves. The four scintillators are placed on twosides of the satellite. Therefore the X-rays from half of the objects need to cross a certain part ofthe satellite before arriving to the detectors.
Fig 24
The satellite hit by parallel X-rays, such as the ones originating in short GRBs. Only one of the four scintillatorswere triggered in this case. Blue tracks are X-rays, green tracks are optical photons which were detected by the MPPCs.
To quantify the X-ray absorption of the satellite and to determine the count rate expected fromsGRBs, different source directions were simulated. First, the satellite was rotated around its majoraxis by 10 ◦
35 times to cover all directions around this axis. Afterwards the same was repeatedfor the minor axis of the satellite. A 1024 ms peak spectrum of a typical sGRB was used in thesimulation. Details of typical sGRB spectra are described in subsection 2.1.43 .2.1 Rotating Around Major Axis for Short GRB
The satellite was rotated around its major axis (Z in Figure 24) by ◦ between each simulation.The simulated primary X-rays originated from the direction of the X axis. ◦ case corresponds tothe scenario when X-rays arrive perpendicular to the surface of two of the scintillators. The countrate is the highest for ◦ when the angle between the direction of the photons and the surfacenormal of both detectors is ◦ . The combined projected area of the four scintillators is the largestin this scenario. The least favored direction is ◦ (see Figure 25). ∘ ]200250300350∘00∘50500550 C o un t r a t e [ c p s ] Count rate with thresholdCount rate without threshold
Fig 25
Count rate of a typical sGRB (for 1024 ms peak spectrum) for different source directions. The satellite wasrotated around its major axis. An arbitrary but possible low-energy threshold of 20 keV was utilized. The detectorsupport structure thickness of the scintillator was 2 mm.
In Figure 26 the spectra of two directions are shown. As expected for the least optimal direction( ◦ ) the low energy part of the spectrum is suppressed. These are the X-ray photons which arenot able to cross the material of the satellite.Different low-energy thresholds are possible to be set. Therefore, it is important to understand44
200 400 600 800 1000 1200 1400Energy [keV]10 −2 −1 C o un t r a t e [ c p s ] Simulated scintillation spectrum for 45 ∘ Simulated scintillation spectrum for 270 ∘ Fig 26
Typical short GRB spectra (for 1024 ms peak) for the most optimal direction and the least optimal directionamong the investigated cases. The lower energy band is suppressed for 270 ◦ , since GRB X-rays need to cross thematerial of the satellite for this scenario to be detected. Thickness of the detector support structure was 2 mm in thiscase. how the count rate of X-rays from sGRBs would change by varying the low-energy threshold. InFigure 27 the count rate for the most and least optimal direction is shown depending on the low-energy threshold. Up to about 100 keV the count rate does not decrease significantly. Also it isimportant to notice that the direction of the source is much more important than the thickness ofthe detector casing. The same procedure as described in subsection 7.2.1 was followed for investigating sGRB (for1024 ms peak spectrum) directions around the minor axis (X in Figure 24). X-ray were simulatedas a parallel beam coming from the Z direction. In Figure 28 the count rate for each direction isshown. ◦ is the least optimal. It corresponds to the case when all scintillators are seen from theiredge. In this case the cross-section of the four scintillators combined is 7.5 cm , which is about45 Energy threshold [keV]10 C o un t r a t e [ c p s ] Fig 27
Count rate for a typical sGRB (for 1024 ms peak spectrum) versus detection low-energy threshold. Two sourcedirections and thicknesses of the detector support structure are shown from the 70 investigated scenarios. σ . Therefore from the directionsinvestigated with the rotation of the minor axis the interval between ◦ and ◦ is suitable forthe detection of sGRBs. γ -ray Transients For the detection of astrophysical objects, the final figure of merit is the SNR. It is importantto mention that for the localization accuracy not only the SNR but also the number of detectedphotons is important for the cross-correlation of light curves. Electronic noise was neglected inthe following calculations as the planned low-energy threshold set for detection is higher than theamplitude of the electronic noise. 46
50 100 150 200 250 300 350Direction of the GRB [ ∘ ]50100150200250300 ∘ o un t r a t e [ c p s ] ∘ount rate with threshold∘ount rate without threshold Fig 28
Count rate of a typical sGRB (for 1024 ms peak spectrum) for different source directions. The satellite wasrotated around its minor axis. An arbitrary but possible low-energy threshold of 20 keV was utilized. The aluminiumdetector support structure was 2 mm thick in this case.
Detection low-energy threshold can be set onboard the satellite. Therefore SNR was quantifiedfor each astrophysical object in the function of low-energy threshold. The following equation wasused to determine SNR:
SN R = ∆ t E (cid:80) E f ( E ) (cid:115) ∆ t E (cid:80) E g ( E ) , (17)where f ( E ) is the detected count rate spectrum of the signal, g ( E ) stands for the detected countrate background spectrum, E is the low-energy threshold, E is the high-energy threshold and ∆ t is the exposure time. In our simulations we did not put boundary on the high-energy threshold, butthe triggering algorithm onboard CAMELOT satellites will have capability to set both the low- andthe high-energy thresholds. 47he main aim of the
CAMELOT mission is the detection and localization of sGRBs. Thereforeit is important to understand with what significance could
CAMELOT satellites detect these objects.Among the direction, when the satellite was rotated around its major axis SNR is the highest whenthe angle between X-rays from a GRB and the surface normal of both detectors is ◦ . We havethe lowest SNR for the angle of ◦ (see Figure 25). S i g n a l - t o - n o i s e r a t i o Fig 29
Signal-to-noise ratio of short GRBs versus low-energy detection threshold. Two detector support structurethicknesses and two GRB directions (rotating around Z axis) are shown among the directions investigated in Sec. . . .Among these investigated directions, highest signal is achieved when the direction of the GRB is ◦ . For ◦ thesignal from a typical sGRB is the smallest (see Figure 25). When the simulated typical sGRB (for 1024 ms peak spectrum) is in the most optimal directionan SNR of > can be achieved. SNR stays above 10 within the low-energy detection thresholdrange from up to 100 keV. The thickness of the aluminium detector casing affects SNR mostly forlow values of the low-energy detection thresholds, since the main background component, CXBhas a rather soft spectrum. For the least optimal direction among the directions investigated anSNR of 6 can be achieved. This characteristic is shown in Figure 29. The other directions, when48he satellite was rotated around its minor axis (Figure. 28), are less favored. In these cases thecross section of the detectors are significantly lower.Tables 5 and 6 summarize the simulated detection count rate induced by the X-ray/ γ -ray tran-sient sources and the expected SNR. For GRBs four different exposure times ∆ t were used: 64, 256and 1024 ms for sGRBs and 4096 ms for lGRBs. It should be noted that long triggering timescalesof the order of several seconds or tens of seconds are readily affected by the time variation ofbackground due to geomagnetic latitude (cutoff rigidity) change during the orbit and the activationbackground varying with time since SAA passages. The SNR calculated for such long integrationtime is effected by the background systematics. Varying background can cause false triggers anddetectors with larger effective area are more vulnerable unless a sophisticated background model-ing is part of the trigger algorithm.Different missions has employed different triggering timescales. BeppoSAX /GRBM used ad-justable timescale in the range from 7.8125 ms to 4 s in 10 steps.
CGRO /BATSE used timewindows of 64 ms, 256 ms and 1024 ms.
Suzaku /WAM used triggering timescales of 1/4 s and1 s. HETE-2 /WXM and FREGATE used timescales from 80 ms up to 10.5 s or longer, but theymodeled background to remove trends which can cause false triggers.
Swift /BAT uses two typesof rate triggers: i) “short” rate triggers with timescales 4, 8, 16, 32 and 64 ms which are tradi-tional triggers employing single background period of fixed duration; ii) “long” rate triggers withtimescales from 64 ms to 64 s which fit multiple background intervals to remove trends as pio-neered by
HETE-II . Fermi /GBM uses triggering timescales of 16, 32, 64, 128, 256, 512, 1024,2048, 4096 and 8192 ms. In case of
AGILE /MCAL, transients are searched using time windowsof duration of sub-millisecond, 1, 16, 64 , 256, 1024 and 8192 ms.
From Table 6 it is also seen that in contrary to one’s expectation, TGF SNR increases with49hicker detector casing. The reason for this is the hardness of TGF spectrum. The median energyof X-ray photons originating in TGFs is 2 MeV. These have a few per cent chance to interactwith the scintillator material. The thicker detector casing provides more material in which theseenergetic photons can interact and produce secondary particles. Therefore thicker casing yieldsin higher SNR. This study is important in order to understand sensitivity of different trigger timewindow durations necessary for designing efficient GRB trigger algorithm.
Table 5
Simulated detection rate induced by X-ray/ γ -ray transient sources. Al sGRB peak spectrum lGRB peak spectrum lGRB TGF SGR(mm) 64 ms 256 ms 1024 ms 64 ms 256 ms 1024 ms fln. sp.0.5 1440 910 385 1190 924 758 326 34600 162001.0 1390 911 367 1139 908 715 309 38900 140001.5 1300 890 367 1110 840 674 292 37600 119002.0 1320 839 355 1058 815 662 277 38600 10500The detection rate is in counts per second, assumes a low-energy threshold of 20 keV and is sim-ulated for different thicknesses of the aluminium support structure of the detector. For short andlong GRBs the 64 ms, 256 ms and 1024 ms peak spectra were used. For long GRB also the fluencespectrum (fln. sp.) was used.
Table 6
Simulated detection signal-to-noise ratio for X-ray/ γ -ray transient sources. Al sGRB peak spectrum lGRB peak spectrum lGRB fln. sp. TGF SGR(mm) 64 ms 256 ms 1024 ms 64 ms 256 ms 1024 ms 4096 ms 0.1 ms 0.2 s0.5 9.27 11.7 9.91 7.66 11.9 19.5 16.8 8.79 1851.0 9.35 12.3 9.87 7.66 12.2 19.2 16.7 10.3 1671.5 9.23 12.6 10.4 7.89 11.9 19.2 16.6 10.6 1492.0 10.1 12.8 10.8 8.08 12.5 20.2 16.0 11.6 142The detection SNR has been calculated for different thicknesses of the aluminium support structureof the detector. The assumed background count rate is the sum of all components as described inRef. 7.1. For the GRB peak spectra were used the exposure time ∆ t =
64 ms, 256 ms and 1024 ms.For the fluence spectrum (fln. sp.) of long GRB we used ∆ t = 4096 ms. For TGF we assumeexposure time ∆ t = 0 . ms and for SGR ∆ t = 0 . s. For this TGF spectrum the SNR is only atheoretical value following from the formula. For example, for 1 mm thicknesses of the Al detectorcasing the expected detected number of counts within 0.1 ms from is 3.9 cnt, whereas the expectednumber of background counts is below 1 cnt (only 0.14 cnt).50 Discussion
The background count rates obtained in our MC simulations were derived from models of fluxes ofgamma-rays and particles averaged over various latitudes, depending on the particular flux com-ponent, below ◦ and outside SAA. The reason is that we aim to obtain an expected “mean”background rate in parts of orbit which are suitable for gamma-ray transient scientific data collec-tion. However, in reality, the background rate will have time variation due to geomagnetic latitude(cutoff rigidity) change within the orbit and due to the activation background varying with timesince SAA passages.The foreseen orbital inclination of the CAMELOT satellites is above ∼ ◦ and option of polarorbits is also likely. Therefore significant background variation is expected as well. We investigatedbackground count rates measured by Fermi /GBM,
RHESSI and
Lomonosov /BDRG gamma-ray instruments throughout their orbits to learn what background variations are expected. In caseof
Fermi /GBM (altitude 560 km and inclination 26 ◦ ) the background rate outside SAA for oneNaI detector module in − keV range varied throughout the orbit between ∼ cps and ∼ − cps, i.e. ∼ . − × change (about two months after the launch), see also Ref. 199.In case of the RHESSI spectrometer (altitude 500 km and inclination 38 ◦ ) the background rateoutside SAA for one rear detector segment in −
20 000 keV range varied throughout the orbitbetween ∼ cps and ∼ cps, .i.e. ∼ . × change (about three years after the launch) . Fora detector on a polar orbit the background rate can increase dramatically more when passing thepolar regions of trapped particles in the van Allen radiation belt. The Lomonosov /BDRG (altitude550 km and inclination 98 ◦ ) measurements show that the rate outside SAA, in − keV rangeincreases ∼ × inside the polar regions compared to the rates near equator (about 5 months http://sprg.ssl.berkeley.edu/˜tohban/browser/ ∼ × the value near the equator for detectors on boardthe CAMELOT satellites are also foreseen. Inside the polar regions the rate increase can be muchhigher.Since CubeSats which are not on equatorial orbit (currently most of them) are subject to highproton flux upon SAA passages, these protons have enough energy to activate the material ofthe satellite. Short term activation is important as decaying isotopes can cause a strongly time-variable background for a few minutes after the end of SAA passes. Long term activation canincrease the background significantly in a matter of months.
To quantify the effects of protoninduced activation, we plan to conduct simulations in the near future. Emission lines of radioactiveisotopes could also be used for energy calibration. As an example for our scintillators
I will becreated which emit γ -rays with an energy of 159 keV. In order to discuss how our estimated background rates of
CAMELOT detectors scale to theobservations of
Fermi /GBM,
AGILE /MCAL and
Suzaku /WAM we consider the surface area of thescintillators of these instruments and assume that these surface areas can be used as rough scalingfactors. For CAMELOT (CsI):
15 cm × . × scintillators giving the area of ∼ cm . For Fermi /GBM (NaI): . × (12 . / giving the area of ∼ cm for one detector module (theeffective area around 0.4 MeV is ∼ cm ). For
AGILE /MCAL (CsI): . × . × detectors giving the area of ∼ cm (the effective area at . − MeV is ∼ − cm ). For
Suzaku /WAM (BGO) the area is ∼ cm . The estimated background rates of
CAMELOT detectors for 0.5 mm Al support structure are ∼ . , ∼ . and ∼ . kHz respectively for E > keV, E > keV and E > keV (seeFig. 23). The observed background rates of one detector module of
Fermi /GBM ( ∼ months52fter the launch, altitude h = 560 km and inclination i = 26 ◦ ) are ∼ kHz and ∼ . kHz for E > keV and E > keV, respectively. For
AGILE /MCAL ( h = 550 km and i = 2 . ◦ ) therate is ∼ . kHz for E > keV. In case of
Suzaku /WAM ( h = 570 km and i = 31 ◦ ) the rate is − kHz for E > keV.If we use the surface area of scintillators as a scaling factor than the background rate scal-ing between Fermi /GBM and
Suzaku /WAM or
Fermi /GBM and
AGILE /MCAL is in a good ap-proximation. The current simulated
CAMELOT background is smaller than that of
Fermi /GBMand
Suzaku /WAM observations. For example, if we scale the
CAMELOT background to the
Fermi /GBM, it would be ∼ . kHz, which is lower than the observed value of ∼ kHz for E > keV. This is of course due to the activation background component, which is not includedin the CAMELOT simulated background and the scaling would be reasonable if we consider theactivation background component for
CAMELOT around − kHz. The same applies when wescale CAMELOT background to
Suzaku /WAM observations. Scaling
CAMELOT background to
AGILE /MCAL is in a good agreement even without accounting for the activation component for
CAMELOT . The
AGILE /MCAL satellite is in an equatorial orbit with an inclination of only . ◦ with low particle background which causes material activation.Having the simulation results of the detection background count rate and GRB count rate wecan discuss an approximate number of expected short and long GRB detections per year by asingle CAMELOT satellite. For 1 mm Al casing and the best gamma-ray incident angle ( ◦ tothe surface normals of perpendicular detectors) the simulation detection count rate is 911 cps and715 cps for sGRB 256 ms and lGRB 1024 ms median peak spectrum, respectively. GRBs willnot always be seen under this most preferred direction therefore we scale this rate by a factorof / √ which corresponds to the rate expected from GRBs seen perpendicular to the largest53cintillator side (644 cps for sGRB and and 506 cps for lGRB). There will be GRBs seen undermore preferred direction as well as under less preferred direction therefore this is a compromisedirection. Furthermore we can assume a detection SNR threshold to be 5 and a mean backgroundcount rate to be 3 000 cps (1 500 cps from external background flux and 1 500 cps from materialactivation).Therefore for the above-mentioned integration times we obtain detection count rate thresholdsof 541 cps and 271 cps, respectively for sGRBs and lGRBs with median spectral shapes. By scalingthe spectral normalizations A and A of typical Fermi /GBM sGRB and lGRB from Table 1by factors of / for sGRB and by / for lGRB and by integrating those amplitude-scaled typical spectra one obtains the threshold photon peak fluxes of 4.03 ph cm − s − for sGRB(or fluence of . × − erg cm − for 256 ms) and 2.22 ph cm − s − for lGRB (or fluence of . × − erg cm − for 1024 ms). These thresholds together with the expected duty cycle can beused to estimate an approximate number of GRB detections per year from the distribution of GRBphoton peak fluxes from the FERMIGBRST catalog. Fermi /GBM surveys the entire sky, that is not occulted by the Earth, with the observing dutycycle of ∼ %. Following the trapped particle maps the duty cycle would be 76 % for orbitalinclination of ◦ (polar orbit is an option for CAMELOT
CubeSats) and integral particle flux ≤ particle cm − s − (see Sec. 3.3 and Ref. 150). However, we examined background data measuredby a GRB instrument Lomonosov /BDRG at polar LEO and it suggests that due to high backgroundvariation the duty cycle can be expected to be lower, i.e. about %. Therefore we assumethis more conservative value of ∼ % as a duty cycle for a single CAMELOT
CubeSat. Fromthese calculations we obtain an approximate number of sGRBs detectable by a single
CAMELOT
CubeSat, i.e. with photon peak flux higher than the aforementioned thresholds, to be 18/year. In54ase of lGRBs we obtained 115/year.In the same way we proceeded with SGRs. By using the simulated detection count rate of atypical SGR for the aluminium detector casing thickness of 1 mm from Table 5 and the typicalSGR spectral parameters calculated in Sec. 2.2 we obtained SGR detection threshold photon fluxof 9.19 ph cm − s − or threshold fluence of . × − erg cm − for 0.2 s and energy range of − keV. This means that all bursts listed in the Konus catalog of SGRs between 1978 and2000 would be detectable also by a CAMELOT
CubeSat.A difficulty is to estimate the SGR annual detection rate using this catalog because it wascomposed of measurements from several interplanetary spacecrafts and one LEO satellite whichmeans it is difficult to know the exact duty cycle for the SGR measurements. Therefore we ex-amined the five year
Fermi /GBM SGR catalog and calculated the detection thresholds also forthe time scale of 0.1 ms and energy range of − keV which are the median SGR durationand energy range used in this catalog. For these conditions we obtained CAMELOT
SGR photonflux detection threshold of 18.2 ph cm − s − or fluence threshold of . × − erg cm − . Usingthis fluence threshold, the SGR fluence distribution reported in the Fermi /GBM SGR catalog andthe aforementioned assumed duty cycle of a single
CAMELOT
CubeSat we obtained a predictionof 46 SGRs detectable by one
CAMELOT satellite annually. Note that the annual number of de-tected SGRs will be subject to large fluctuations since SGR bursts tend to occur in clusters whenparticular magnetars become active.Concerning the used SNR calculation it should be noted that it is rather simplistic for TGF de-tection. The large number of 0.1 ms intervals (large number of trials) during the mission examinedby the trigger algorithm (note that the rate trigger algorithm for
CAMELOT is yet under develop-ment) as well as the fact that a cosmic ray could easily cause a count in two detectors needs to be55aken into account. If other background sources by chance produce one or two additional countsin the same 0.1 ms interval, then a false trigger would be issued.Specific conditions of the trigger algorithm to efficiently detect TGFs by
CAMELOT
CubeSatsare yet to be determined. For example one option is to aim to detect brighter but less frequentTGFs.
AGILE /MCAL observes 2780 TGFs within 3.5 years which is ∼ TGFs/year. Thefluence distribution follows a power low of − This means that TGFs with 5 times greaterfluence will be 3 % in number. The spectrum of a typical TGF used in our simulations is based onthe TGF fluence at the threshold level of
AGILE /MCAL. Therefore if a
CAMELOT satellite hadequtorial orbit as
AGILE then this scaling would give 23 TGFs/year/CubeSat with 19.5 cnts/TGF.However,
CAMELOT satellites will likely have polar or other high-inclination orbits. Fromobservations most, if not all, TGFs has been detected at latitude lower than ◦ north and southby CGRO /BATSE,
RHESSI , AGILE /MCAL,
Fermi /GBM and ASIM instruments.
One ofthe good distribution maps was obtained from the recent ASIM instrument.
As relativelyyoung (operational for ∼ years yet), the TGF number is not high, but with 51.6 ◦ on ISS , it has arelatively uniform coverage of the TGF positional distribution. There are three major TGF sites:around Central America, around Central Africa and around South East Asia. A good comparisonof the expected TGF detections by
CAMELOT can be done with the
TARANIS /XGRE instrumentwhich was supposed to operate on Sun-synchronous orbit with 700 km altitude. According toRef. 208
TARANIS (unfortunately lost due to the VEGA launch failure) was expected to detect ∼ TGFs/year. A
CAMELOT satellite will have about 1/10 of the effective area, but if correctedfor the 500 km vs. 700 km altitude difference, this would be converted into ∼ / . Then × %(for × brighter TGFs) give ∼ TGFs/year for a single satellite. With 9 satellites in a constellationCAMELOT would provide ∼ TGFs/year. 56s shown in Fig. 25, the
CAMELOT detectors can observe gamma-ray sources also for di-rections when the photons need to pass through the body of the satellite (rear direction). Thismeans that also gamma-ray photons scattered off the Earth’s atmosphere and entering the detec-tor from the side not facing the source can produce signal. In this sense the
CAMELOT satelliteswill have omnidirectional FOV although the sensitivity for the rear direction is lower. Comptonscatter of the burst flux off the Earth’s atmosphere into the detector is known effect and observedalready by the
CGRO /BATSE instrument.
Correction for this effect has been included in theBATSE’s response matrices and in the trigger efficiency calculation.
See also Refs. 212, 213with spectrum of GRB 021206 measured by the RHESSI satellite which shows significant Earth’satmospheric backscatter of photons below 300 keV. Moreover, a method which employs the at-mospheric scattering of GRB flux for the polarisation measurements in the prompt gamma-rayemission has been published in Ref. 214 and Ref. 215. The atmospheric scattering might affectthe
CAMELOT measurements and it might be necessary to do careful modeling of this effect inthe future in order to reduce the systematic uncertainties. A detailed simulation of this effect isbeyond the scope of this paper, however such an analysis might be useful to improve the timingbased localization in LEO.
A Geant4 based simulation was developed to understand the capabilities of the planned
CAMELOT
CubeSat constellation to detect short and long GRBs, TGFs. The CAD model of the satellite wasimported directly to Geant4 with CADMesh. Since the scintillators onboard
CAMELOT have aconsiderably large size, optical light propagation is important. To take this into account, scin-tillation light propagation was simulated in Geant4 by tracking each optical photon created by57cintillation.The simulation was validated and its optical parameters were calibrated with an
Am X-raysource. The calibrated reflectivity of the surface of the scintillator turned out to be 99.99 % andabsorption length 60 cm.Thirteen background components were simulated to determine their contribution to the overallbackground spectrum. The five components which contribute the most to background are: CXB(1000 cps), albedo X-rays (200 cps), cosmic-ray α particles (49 cps), albedo protons (44 cps) andalbedo positrons (27 cps). These count rates were calculated by assuming a 20 keV low-energythreshold and 1 mm of aluminium detector support structure thickness.The total simulated background rate was 1545 cps for a detector casing thickness of 0.5 mm.By increasing the casing thickness to 1 mm the total background decreased to 1410 cps and byincreasing it more to 1.5 mm it turned out to be 1270 cps. Finally for 2 mm it was 1100 cps. Theserates were obtained from models of fluxes of gamma-rays and particles averaged over variouslatitudes, depending on the particular flux component, below ◦ and outside SAA, because ourgoal was to obtain an expected “mean” background rate in parts of orbit which are suitable forgamma-ray transient scientific data collection.Since the four scintillators of the CAMELOT
CubeSat are placed on its two sides the direc-tion of the source influences the signal-to-noise ratio. A typical short GRB was simulated in 70directions. 35 directions were investigated by rotating the satellite around its major axis by 10 ◦ between simulations. The SNR of the detection of the typical short GRB (with integral fluxesbetween 8.15 ph cm − s − and 2.21 ph cm − s − for E > keV and for 64 and 1024 ms integrationwindow respectively) varied between 5 and ∼ . Other 35 directions were simulated by rotatingthe satellite around its minor axis. This resulted in less favorable directions, since the cross section58ith respect to the direction of X-rays from the sGRB is much smaller in this case. An SNR of atleast 5 was determined for the range from 50 ◦ to 150 ◦ .The simulations show that CubeSats equipped with large area scintillators are able to detectsGRBs, lGRBs, TGFs and SGRs. In our case for the CAMELOT
CubeSats an average sGRB(256 ms peak spectrum) could be detected with an SNR of > in the most favoured direction.lGRBs (with an integral flux of 2.54 ph cm − s − for E > keV) yield an SNR of > for 4096 msexposure. TGFs despite their very short duration of 0.1 ms could also be detected because, forexample, for 1 mm thicknesses of the Al detector casing the expected detected number of countswithin 0.1 ms from a TGF (with fluence at the threshold level of AGILE /MCAL) is 3.9 cnt, whereasthe expected number of background counts is only 0.14 cnt. SGRs due to their very large X-rayflux yield in an SNR of > Acknowledgments
The research has been supported by the European Union, co-financed by the European Social Fund(Research and development activities at the E¨otv¨os Lor´and University’s Campus in Szombathely,EFOP-3.6.1-16-2016-00023). This work was partially supported by the GINOP-2.3.2-15-2016-00033 project which is funded by the Hungarian National Research, Development and InnovationFund together with the European Union. This research was partially supported by JSPS and HASunder Japan - Hungary Research Cooperative Program. The research has been also supported bythe Lend ¨ulet LP2016-11 grant awarded by the Hungarian Academy of Sciences. The authors wouldlike express their sincere gratitude to Martino Marisaldi for the fruitful discussions on TGFs. Theuseful remarks of the anonymous referees are kindly acknowledged. Also the authors would like59o thank at last but not least the engineers at C3S LLC for the support they provided with the CADmodel of the satellite. 60
Table 7
The mass ratio of materials that are used for the satellite (Courtesy of C3S LLC).
Name of module mass [g] Type of material Mass ratio [%]ADCS 710 Aluminum 6061-T6 50Copper Electric 25Glass Borosilicate 25COM 90 Stainless Steel 2Brass Generic 25Aluminum 7075-T73 40FR4 Glass-Epoxy sheet 33EPS 750 FR4 Glass-Epoxy sheet 25Aluminum 6061-T6 75OBC 50 FR4 Glass-Epoxy sheet 100STRU 980 Aluminum 6061-T6 100SP 570 Solar Panel 100Payload 100 Aluminum 7075-T73 100
Table 8
The chemical composition of materials in mass fraction that are used for the satellite (Courtesy of C3S LLC).
Material nameAluminum 6061-T6 Al 96.90 Mg 1.20 Si 0.80 Fe 0.70 Cu 0.40Aluminum 7075-T73 Al 88.60 Zn 6.10 Mg 2.90 Cu 2.00 Si 0.40Stainless Steel Fe 66.50 Cr 20.00 Ni 10.50 Mn 2.00 Si 1.00Copper Electric Cu 100.00Glass Borosilicate Si 42.10 O 54.80 B 3.10FR4 Glass-Epoxy Si 23.39 O 36.02 C 37.04 H 3.55Brass Generic Cu 85.00 Zn 15.00Solar Panel Ge 38.00 Si 24.00 O 20.00 C 13.00 H 4.00 B 1.0061 ig 30
The individual volumes of the simulated satellite. The CAD model of the satellite was read into Geant4 and4 scintillators (not displayed on this figure) with their respective read out were placed on two sides of the satellite(Courtesy of C3S LLC).
References et al. , “Recent developments in Geant4,”
Nuclear Instruments andMethods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Asso-ciated Equipment , 186–225 (2016).2 N. Werner, J. ˇR´ıpa, A. P´al, et al. , “CAMELOT: Cubesats Applied for MEasuring and LO-calising Transients mission overview,” in
Proceedings of the SPIE , Society of Photo-OpticalInstrumentation Engineers (SPIE) Conference Series , 106992P (2018).3 A. P´al, L. M´esz´aros, N. Tarcai, et al. , “CAMELOT - Concept study and early results foronboard data processing and GPS-based timestamping,” arXiv e-prints , arXiv:1806.03685(2018).4 J. ˇR´ıpa, N. Werner, M. Ohno, et al. , “Monitoring of gamma-ray bursts with a fleetof nanosatellites,” in , IAC–18,B4,2,8,x46335(2018). 62 J. Smith, “BurstCube: Mission Concept, Performance, and Status,” in , International Cosmic Ray Conference , 604 (2019).6 J. S. Perkins, J. Racusin, M. S. Briggs, et al. , “BurstCube: A CubeSat for Gravitational WaveCounterparts,” in , InternationalCosmic Ray Conference , 760 (2017).7 T. Chattopadhyay, A. D. Falcon, D. N. Burrows, et al. , “BlackCAT CubeSat: a soft x-ray sky monitor, transient finder, and burst detector for high-energy and multimessengerastophysics,” in
Space Telescopes and Instrumentation 2018: Ultraviolet to Gamma Ray ,J.-W. A. den Herder, S. Nikzad, and K. Nakazawa, Eds.,
Society of Photo-Optical Instru-mentation Engineers (SPIE) Conference Series , 106995S (2018).8 S. Zheng, “The status of GECAM mission,” in
The Extragalactic Explosive Universe: theNew Era of Transient Surveys and Data-Driven Discovery , 63 (2019).9 J. Wen, X. Long, X. Zheng, et al. , “GRID: a student project to monitor the transient gamma-ray sky in the multi-messenger astronomy era,”
Experimental Astronomy , 77–95 (2019).10 J. E. Grove, C. C. Cheung, M. Kerr, et al. , “Glowbug, a Low-Cost, High-Sensitivity Gamma-Ray Burst Telescope,” in Gamma-ray Bursts in the Gravitational Wave Era 2019 , 57–59(2020).11 F. Fuschino, R. Campana, C. Labanti, et al. , “HERMES: An ultra-wide band X and gamma-ray transient monitor on board a nano-satellite constellation,”
Nuclear Instruments andMethods in Physics Research A , 199–203 (2019).12 M. Pearce, L. Eliasson, N. Kumar Iyer, et al. , “Science prospects for SPHiNX - A smallsatellite GRB polarimetry mission,”
Astroparticle Physics , 54–63 (2019).633 J. ˇR´ıpa, G. Galg´oczi, N. Werner, et al. , “Estimation of the detected background by thefuture gamma ray transient mission CAMELOT,”
Astronomische Nachrichten , 666–673 (2019).14 Z. Bagoly, L. G. Bal´azs, G. Galg´oczi, et al. , “Transient detection capabilities of small satel-lite gamma-ray detectors,”
Astronomische Nachrichten , 681–689 (2019).15 G. Vedrenne and J.-L. Atteia,
Gamma-Ray Bursts: The brightest explosions in the Universe ,Springer, Berlin (2009).16 C. Kouveliotou, R. A. M. J. Wijers, and S. Woosley,
Gamma-ray Bursts , Cambridge Uni-versity Press, Cambridge (2012).17 A. Levan,
Gamma-Ray Bursts , IOP Publishing, Bristol (2018).18 B. Zhang,
The Physics of Gamma-Ray Bursts , Cambridge University Press, Cambridge(2019).19 C. Kouveliotou, C. A. Meegan, G. J. Fishman, et al. , “Identification of two classes ofgamma-ray bursts,”
The Astrophysical Journal , L101–L104 (1993).20 S. Mereghetti, “The strongest cosmic magnets: soft gamma-ray repeaters and anomalousX-ray pulsars,”
The Astronomy and Astrophysics Review , 225–287 (2008).21 K. Yamaoka, M. Ohno, M. S. Tashiro, et al. , “Suzaku Wide-band All-sky Monitor (WAM)observations of GRBs and SGRs,” Publications of the Astronomical Society of Japan , R2(2017).22 A. Lindanger, M. Marisaldi, C. Maiorana, et al. , “The 3rd agile terrestrial gamma ray flashcatalog. part i: Association to lightning sferics,” Journal of Geophysical Research: Atmo-spheres , e2019JD031985 (2020). 643 J. R. Dwyer, D. M. Smith, and S. A. Cummer, “High-Energy Atmospheric Physics: Terres-trial Gamma-Ray Flashes and Related Phenomena,”
Space Science Reviews , 133–196(2012).24 D. Gruber, A. Goldstein, V. Weller von Ahlefeld, et al. , “The fermi gbm gamma-ray burstspectral catalog: Four years of data,”
The Astrophysical Journal Supplement (1), 12(2014).25 A. von Kienlin, C. A. Meegan, W. S. Paciesas, et al. , “The Second Fermi GBM Gamma-Ray Burst Catalog: The First Four Years,”
The Astrophysical Journal Supplement (1),13 (2014).26 P. Narayana Bhat, C. A. Meegan, A. von Kienlin, et al. , “The Third Fermi GBM Gamma-Ray Burst Catalog: The First Six Years,”
The Astrophysical Journal Supplement (2), 28(2016).27 A. von Kienlin, C. A. Meegan, W. S. Paciesas, et al. , “The Fourth Fermi-GBM Gamma-RayBurst Catalog: A Decade of Data,”
The Astrophysical Journal , 46 (2020).28 A. Goldstein, E. Burns, R. Hamburg, et al. , “Updates to the Fermi-GBM Short GRB Tar-geted Offline Search in Preparation for LIGO’s Second Observing Run,” arXiv e-prints ,arXiv:1612.02395 (2016).29 R. C. Duncan and C. Thompson, “Formation of Very Strongly Magnetized Neutron Stars:Implications for Gamma-Ray Bursts,”
The Astrophysical Journal Letters , L9 (1992).30 C. Thompson and R. C. Duncan, “The soft gamma repeaters as very strongly magnetizedneutron stars - I. Radiative mechanism for outbursts,”
Monthly Notices of the Royal Astro-nomical Society , 255–300 (1995). 651 C. Thompson and R. C. Duncan, “The Soft Gamma Repeaters as Very Strongly MagnetizedNeutron Stars. II. Quiescent Neutrino, X-Ray, and Alfven Wave Emission,”
The Astrophys-ical Journal , 322 (1996).32 W. H. G. Lewin and M. van der Klis,
Compact Stellar X-ray Sources , Cambridge UniversityPress, Cambridge, UK (2006).33 V. M. Kaspi, “Recent progress on anomalous X-ray pulsars,”
Astrophysics and Space Sci-ence , 1–11 (2007).34 T. Enoto, S. Kisaka, and S. Shibata, “Observational diversity of magnetized neutron stars,”
Reports on Progress in Physics , 106901 (2019).35 E. P. Mazets, S. V. Golentskii, V. N. Ilinskii, et al. , “Observations of a flaring X-ray pulsarin Dorado,” Nature , 587–589 (1979).36 C. Kouveliotou, S. Dieters, T. Strohmayer, et al. , “An X-ray pulsar with a superstrong mag-netic field in the soft γ -ray repeater SGR1806 - 20,” Nature , 235–237 (1998).37 S. Mereghetti, D. G¨otz, I. F. Mirabel, et al. , “INTEGRAL discovery of persistent hard X-rayemission from the Soft Gamma-ray Repeater SGR 1806-20,”
Astronomy and Astrophysics , L9–L12 (2005).38 S. Molkov, K. Hurley, R. Sunyaev, et al. , “The broad-band spectrum of the persistent emis-sion from SGR 1806-20,”
Astronomy and Astrophysics , L13–L16 (2005).39 K. Hurley, S. E. Boggs, D. M. Smith, et al. , “An exceptionally bright flare from SGR 1806-20 and the origins of short-duration γ -ray bursts,” Nature , 1098–1103 (2005).40 E. P. Mazets, T. L. Cline, R. L. Aptekar, et al. , “The Konus-Wind and Helicon-Coronas-F66etection of the giant γ -ray flare from the soft γ -ray repeater SGR 1806-20,” arXiv e-prints , astro–ph/0502541 (2005).41 S. Mereghetti, D. G¨otz, A. von Kienlin, et al. , “The First Giant Flare from SGR 1806-20:Observations Using the Anticoincidence Shield of the Spectrometer on INTEGRAL,” TheAstrophysical Journal Letters , L105–L108 (2005).42 D. M. Palmer, S. Barthelmy, N. Gehrels, et al. , “A giant γ -ray flare from the magnetar SGR1806 - 20,” Nature , 1107–1109 (2005).43 T. Terasawa, Y. T. Tanaka, Y. Takei, et al. , “Repeated injections of energy in the first 600msof the giant flare of SGR1806 - 20,”
Nature , 1110–1111 (2005).44 R. L. Aptekar, D. D. Frederiks, S. V. Golenetskii, et al. , “Konus Catalog of Soft GammaRepeater Activity: 1978 to 2000,”
The Astrophysical Journal Supplement , 227–277(2001).45 G. J. Fishman, P. N. Bhat, R. Mallozzi, et al. , “Discovery of Intense Gamma-Ray Flashes ofAtmospheric Origin,”
Science , 1313–1316 (1994).46 D. M. Smith, L. I. Lopez, R. P. Lin, et al. , “Terrestrial Gamma-Ray Flashes Observed up to20 MeV,”
Science , 1085–1088 (2005).47 B. W. Grefenstette, D. M. Smith, B. J. Hazelton, et al. , “First RHESSI terrestrial gamma rayflash catalog,”
Journal of Geophysical Research (Space Physics) , A02314 (2009).48 M. S. Briggs, G. J. Fishman, V. Connaughton, et al. , “First results on terrestrial gammaray flashes from the Fermi Gamma-ray Burst Monitor,”
Journal of Geophysical Research(Space Physics) , A07323 (2010). 679 G. J. Fishman, M. S. Briggs, V. Connaughton, et al. , “Temporal properties of the terrestrialgamma-ray flashes from the Gamma-Ray Burst Monitor on the Fermi Observatory,”
Journalof Geophysical Research (Space Physics) , A07304 (2011).50 O. J. Roberts, G. Fitzpatrick, M. Stanbro, et al. , “The First Fermi-GBM Terrestrial GammaRay Flash Catalog,”
Journal of Geophysical Research (Space Physics) , 4381–4401(2018).51 M. Marisaldi, F. Fuschino, C. Labanti, et al. , “AGILE Observations of Terrestrial Gamma-Ray Flashes,” , arXiv:1111.2188(2011).52 M. Marisaldi, F. Fuschino, M. Tavani, et al. , “Properties of terrestrial gamma ray flashes de-tected by AGILE MCAL below 30 MeV,”
Journal of Geophysical Research (Space Physics) , 1337–1355 (2014).53 M. Marisaldi, A. Argan, A. Ursi, et al. , “Enhanced detection of terrestrial gamma-ray flashesby AGILE,”
Geophysical Research Letters , 9481–9487 (2015).54 C. Labanti, M. Marisaldi, F. Fuschino, et al. , “Design and construction of the Mini-Calorimeter of the AGILE satellite,” Nuclear Instruments and Methods in Physics ResearchA , 470–479 (2009).55 C. Maiorana, M. Marisaldi, A. Lindanger, et al. , “The 3rd agile terrestrial gamma-ray flashescatalog. part ii: Optimized selection criteria and characteristics of the new sample,”
Journalof Geophysical Research: Atmospheres , e2019JD031986 (2020).56 M. Marisaldi, M. Galli, C. Labanti, et al. , “On the high-energy spectral component and fine68ime structure of terrestrial gamma ray flashes,”
Journal of Geophysical Research: Atmo-spheres , 7484–7497 (2019).57 D. Tierney, M. S. Briggs, G. Fitzpatrick, et al. , “Fluence distribution of terrestrial gamma rayflashes observed by the Fermi Gamma-ray Burst Monitor,”
Journal of Geophysical Research(Space Physics) , 6644–6650 (2013).58 A. S. Jursa,
Handbook of geophysics and the space environment , Air Force Geophysics Lab-oratory, Air Force Systems Command, United States Air Force, Springfield, USA (1985).59 T. W. Armstrong and B. L. Colborn, “Predictions of induced radioactivity for spacecraftin low Earth orbit,”
International Journal of Radiation Applications and Instrumentation.Part D. Nuclear Tracks and Radiation Measurements (1), 101–130 (1992). Special IssueSpace Radiation.60 N. Gehrels, “Instrumental background in gamma-ray spectrometers flown in low earth or-bit,” Nuclear Instruments and Methods in Physics Research, Section A , 513–528 (1992).61 A. J. Dean, A. J. Bird, N. Diallo, et al. , “The Modelling of Background Noise in Astronom-ical Gamma Ray Telescopes,”
Space Science Reviews , 285–376 (2003).62 J. L. Barth, C. S. Dyer, and E. G. Stassinopoulos, “Space, atmospheric, and terrestrial radi-ation environments,”
IEEE Transactions on Nuclear Science , 466–482 (2003).63 T. Mizuno, T. Kamae, G. Godfrey, et al. , “Cosmic-Ray Background Flux Model Basedon a Gamma-Ray Large Area Space Telescope Balloon Flight Engineering Model,” TheAstrophysical Journal , 1113–1123 (2004).64 M. Zombeck,
Handbook of Space Astronomy and Astrophysics: Third Edition , CambridgeUniversity Press, Cambridge, UK (2007).695 V. Fioretti, A. Bulgarelli, G. Malaguti, et al. , “The low Earth orbit radiation environmentand its impact on the prompt background of hard x-ray focusing telescopes,” in
Proceedingsof the SPIE , Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series , 845331 (2012).66 R. Campana, M. Feroci, E. Del Monte, et al. , “Background simulations for the Large AreaDetector onboard LOFT,”
Experimental Astronomy , 451–477 (2013).67 M. A. Xapsos, P. M. O’Neill, and T. P. O’Brien, “Near-Earth Space Radiation Models,” IEEE Transactions on Nuclear Science , 1691–1705 (2013).68 B. Zabori, A. Hirn, J. Eastwood, et al. , “Space radiation and magnetic field environmentspecification for the radcube space weather related cubesat mission,” in , IAC–18,A1,5,2,x42514 (2018).69 P. Cumani, M. Hernanz, J. Kiener, et al. , “Background for a gamma-ray satellite on a low-Earth orbit,” Experimental Astronomy , 273–302 (2019).70 S. Mate, L. Bouchet, J.-L. Atteia, et al. , “Simulations of the SVOM/ECLAIRs dynamicbackground: a fast, accurate and general approach for wide-field hard X-ray instruments,” Experimental Astronomy , 171–198 (2019).71 ESA, “Space engineering - Space environment,” Tech. Rep. ECSS-E-ST-10-04C, ESA Re-quirements and Standards Division (2008).72 J. F. Ormes, T. Burnett, E. Grove, et al. , “GLAST LAT Background Review,” Tech. Rep.LAT-TD-08316-01, NASA (2006).73 R. Giacconi, H. Gursky, F. R. Paolini, et al. , “Evidence for x Rays From Sources Outsidethe Solar System,” Physical Review Letters , 439–443 (1962).704 K. Kasturirangan and U. R. Rao, “Spectrum of the Cosmic X- and Gamma Ray Backgroundin the Energy Range 1 keV-1 MeV,” Astrophysics and Space Science , 161–166 (1972).75 D. A. Schwartz and L. E. Peterson, “The Spectrum of Diffuse Cosmic X-Rays Observed byOSO-3 Between 7 and 100 KEV,” The Astrophysical Journal , 297–304 (1974).76 V. Schoenfelder, U. Graser, and J. Daugherty, “Diffuse cosmic and atmospheric MeVgamma radiation from balloon observations.,”
The Astrophysical Journal , 306–319(1977).77 C. E. Fichtel, G. A. Simpson, and D. J. Thompson, “Diffuse gamma radiation.,”
The Astro-physical Journal , 833–849 (1978).78 V. Schoenfelder, F. Graml, and F. P. Penningsfeld, “The vertical component of 1-20 MeVgamma rays at balloon altitudes,”
The Astrophysical Journal , 350–362 (1980).79 E. Boldt, “The Cosmic X-Ray Background,”
Comments on Astrophysics , 97 (1981).80 H. M. Horstman, G. Cavallo, and E. Moretti-Horstman, “The X and gamma diffuse back-ground.,” Nuovo Cimento Rivista Serie , 255–311 (1975).81 P. Sreekumar, D. L. Bertsch, B. L. Dingus, et al. , “EGRET Observations of the ExtragalacticGamma-Ray Emission,” The Astrophysical Journal , 523–534 (1998).82 E. Churazov, R. Sunyaev, M. Revnivtsev, et al. , “INTEGRAL observations of the cosmicX-ray background in the 5-100 keV range via occultation by the Earth,”
Astronomy andAstrophysics , 529–540 (2007).83 F. Frontera, M. Orlandini, R. Landi, et al. , “The Cosmic X-Ray Background and the Popu-lation of the Most Heavily Obscured AGNs,”
The Astrophysical Journal , 86–95 (2007).714 M. Ajello, J. Greiner, G. Sato, et al. , “Cosmic X-Ray Background and Earth Albedo Spectrawith Swift BAT,”
The Astrophysical Journal , 666–677 (2008).85 M. Ajello, L. Costamante, R. M. Sambruna, et al. , “The Evolution of Swift/BAT Blazarsand the Origin of the MeV Background,”
The Astrophysical Journal , 603–625 (2009).86 A. Moretti, C. Pagani, G. Cusumano, et al. , “A new measurement of the cosmic X-raybackground,”
Astronomy and Astrophysics , 501–509 (2009).87 M. T ¨urler, M. Chernyakova, T. J. L. Courvoisier, et al. , “INTEGRAL hard X-ray spectraof the cosmic X-ray background and Galactic ridge emission,”
Astronomy and Astrophysics , A49 (2010).88 M. Ackermann, M. Ajello, A. Albert, et al. , “The Spectrum of Isotropic Diffuse Gamma-Ray Emission between 100 MeV and 820 GeV,”
The Astrophysical Journal , 86 (2015).89 Z. Bagoly, A. Meszaros, and P. Meszaros, “Cosmological Constraints on the Clustering ofX-Ray Background Sources,”
The Astrophysical Journal , 54 (1988).90 A. Meszaros and P. Meszaros, “Large-Scale Structure of the Universe: Constraints from theX-Ray Background,”
The Astrophysical Journal , 25 (1988).91 H. G. Bi, A. Meszaros, and P. Meszaros, “On the large scale structure of X-ray backgroundsources,”
Astronomy and Astrophysics , 16–22 (1991).92 K. Jahoda, O. Lahav, R. F. Mushotzky, et al. , “Cross-Correlation of the X-Ray Backgroundwith Nearby Galaxies,”
The Astrophysical Journal , L37 (1991).93 T. Shanks, I. Georgantopoulos, G. C. Stewart, et al. , “The origin of the cosmic X-ray back-ground,”
Nature , 315–320 (1991). 724 A. C. Fabian and X. Barcons, “The origin of the X-ray background.,”
Annual Review ofAstron and Astrophys , 429–456 (1992).95 A. Comastri, G. Setti, G. Zamorani, et al. , “The contribution of AGNs to the X-ray back-ground.,” Astronomy and Astrophysics , 1 (1995).96 A. A. Zdziarski, “Contributions of AGNs and SNe IA to the cosmic X-ray and gamma-raybackgrounds,”
Monthly Notices of the Royal Astronomical Society , L9 (1996).97 W. N. Brandt and G. Hasinger, “Deep Extragalactic X-Ray Surveys,”
Annual Review ofAstron and Astrophys , 827–859 (2005).98 N. Cappelluti, P. Ranalli, M. Roncarelli, et al. , “The nature of the unresolved extragalacticcosmic soft X-ray background,” Monthly Notices of the Royal Astronomical Society ,651–663 (2012).99 K. Helgason, N. Cappelluti, G. Hasinger, et al. , “The Contribution of z <˜6 Sources tothe Spatial Coherence in the Unresolved Cosmic Near-infrared and X-Ray Backgrounds,”
The Astrophysical Journal , 38 (2014).100 N. Cappelluti, Y. Li, A. Ricarte, et al. , “The Chandra COSMOS Legacy Survey: EnergySpectrum of the Cosmic X-Ray Background and Constraints on Undetected Populations,”
The Astrophysical Journal , 19 (2017).101 Q. Ma, B. Ciardi, M. B. Eide, et al. , “X-ray background and its correlation with the 21 cmsignal,”
Monthly Notices of the Royal Astronomical Society , 26–34 (2018).102 A. A. Penzias and R. W. Wilson, “A Measurement of Excess Antenna Temperature at 4080Mc/s.,”
The Astrophysical Journal , 419–421 (1965).7303 I. V. Moskalenko and A. W. Strong, “Anisotropic Inverse Compton Scattering in theGalaxy,”
The Astrophysical Journal , 357–367 (2000).104 A. Dar and A. De R´ujula, “Is the diffuse gamma background radiation generated by Galacticcosmic rays?,”
Monthly Notices of the Royal Astronomical Society , 391–401 (2001).105 D. E. Gruber, J. L. Matteson, L. E. Peterson, et al. , “The Spectrum of Diffuse Cosmic HardX-Rays Measured with HEAO 1,”
The Astrophysical Journal , 124–129 (1999).106 R. Rothschild, E. Boldt, S. Holt, et al. , “The cosmic X-ray experiment aboard HEAO-1.,”
Space Science Instrumentation , 269–301 (1979).107 N. Gehrels, E. Chipman, and D. A. Kniffen, “The Compton Gamma Ray Observatory.,” Astronomy and Astrophysics Supplement Series , 5–12 (1993).108 F. Melia, High-Energy Astrophysics , Princeton University Press, New Jersey (2009).109 V. Sch¨onfelder,
The Universe in Gamma Rays , Springer, Berlin (2001).110 A. W. Strong, I. V. Moskalenko, and O. Reimer, “Diffuse Continuum Gamma Rays fromthe Galaxy,”
The Astrophysical Journal , 763–784 (2000).111 C. E. Fichtel, R. C. Hartman, D. A. Kniffen, et al. , “High-energy gamma-ray results fromthe second Small Astronomy Satellite.,”
The Astrophysical Journal , 163–182 (1975).112 C. E. Fichtel, R. C. Hartman, D. A. Kniffen, et al. , “Tabulated data from the SAS-2 highenergy gamma ray telescope,” Tech. Rep. NASA-TM-79650, NASA Goddard Space FlightCenter (1978).113 D. L. Bertsch, T. M. Dame, C. E. Fichtel, et al. , “Diffuse Gamma-Ray Emission in theGalactic Plane from Cosmic-Ray, Matter, and Photon Interactions,”
The Astrophysical Jour-nal , 587 (1993). 7414 W. L. Kraushaar, G. W. Clark, G. P. Garmire, et al. , “High-Energy Cosmic Gamma-RayObservations from the OSO-3 Satellite,”
The Astrophysical Journal , 341 (1972).115 H. A. Mayer-Hasselwander, K. Bennett, G. F. Bignami, et al. , “Large-scale distribution ofgalactic gamma radiation observed by COS-B,”
Astronomy and Astrophysics , 164–175(1982).116 R. Krivonos, M. Revnivtsev, E. Churazov, et al. , “Hard X-ray emission from the Galacticridge,”
Astronomy and Astrophysics , 957–967 (2007).117 T. A. Porter, I. V. Moskalenko, A. W. Strong, et al. , “Inverse Compton Origin of the HardX-Ray and Soft Gamma-Ray Emission from the Galactic Ridge,”
The Astrophysical Journal , 400–407 (2008).118 L. Bouchet, E. Jourdain, J. P. Roques, et al. , “INTEGRAL SPI All-Sky View in Soft GammaRays: A Study of Point-Source and Galactic Diffuse Emission,”
The Astrophysical Journal , 1315–1326 (2008).119 R. Krivonos, M. Revnivtsev, S. Tsygankov, et al. , “INTEGRAL/IBIS 7-year All-Sky HardX-ray Survey. I. Image reconstruction,”
Astronomy and Astrophysics , A107 (2010).120 R. Krivonos, S. Tsygankov, A. Lutovinov, et al. , “INTEGRAL 11-year hard X-ray sur-vey above 100 keV,”
Monthly Notices of the Royal Astronomical Society , 3766–3774(2015).121 S. D. Hunter, D. L. Bertsch, J. R. Catelli, et al. , “EGRET Observations of the DiffuseGamma-Ray Emission from the Galactic Plane,”
The Astrophysical Journal , 205–240(1997). 7522 A. W. Strong, H. Bloemen, R. Diehl, et al. , “COMPTEL Skymapping: a New ApproachUsing Parallel Computing,”
Astrophysical Letters and Communications , 209 (1999).123 A. W. Strong, I. V. Moskalenko, and O. Reimer, “Diffuse Galactic Continuum Gamma Rays:A Model Compatible with EGRET Data and Cosmic-Ray Measurements,” The Astrophysi-cal Journal , 962–976 (2004).124 N. Prantzos, C. Boehm, A. M. Bykov, et al. , “The 511 keV emission from positron annihi-lation in the Galaxy,”
Reviews of Modern Physics , 1001–1056 (2011).125 A. W. Strong, “Interstellar Gamma Rays and Cosmic Rays:. New Insights from Fermi-Latand Integral,” in Cosmic Rays for Particle and Astroparticle Physics , S. Giani, C. Leroy,and P. G. Rancoita, Eds., 473–481, Scientific Publishing Co. Pte. Ltd. (Singapore) (2011).126 A. A. Abdo, M. Ackermann, M. Ajello, et al. , “Spectrum of the Isotropic Diffuse Gamma-Ray Emission Derived from First-Year Fermi Large Area Telescope Data,”
Physical ReviewLetters , 101101 (2010).127 M. Ajello, A. Albert, W. B. Atwood, et al. , “Fermi-LAT Observations of High-EnergyGamma-Ray Emission toward the Galactic Center,”
The Astrophysical Journal , 44(2016).128 M. Revnivtsev, S. Sazonov, M. Gilfanov, et al. , “Origin of the Galactic ridge X-ray emis-sion,”
Astronomy and Astrophysics , 169–178 (2006).129 K. Oh, M. Koss, C. B. Markwardt, et al. , “The 105-Month Swift-BAT All-sky Hard X-RaySurvey,”
The Astrophysical Journals Supplement , 4 (2018).130 J. A. van Allen, “Observation of high intensity radiation by satellites 1958 alpha andgamma,”
Journal of Jet Propulsion (9), 588–592 (1958).7631 S. I. Svertilov, M. I. Panasyuk, V. V. Bogomolov, et al. , “Wide-Field Gamma-SpectrometerBDRG: GRB Monitor On-Board the Lomonosov Mission,” Space Science Reviews , 8(2018).132 M. I. Panasyuk, V. M. Lipunov, I. Pack, et al. , “Complete set of detectors for studyingcosmic gamma-ray bursts onboard the Lomonosov satellite,”
Physics of Particles and Nuclei , 109–112 (2018).133 J. G. Roederer, Dynamics of geomagnetically trapped radiation , Springer-Verlag, NewYork, USA (1970).134 M. G. Kivelson and C. T. Russell,
Introduction to Space Physics , Cambridge UniversityPress, Cambridge, UK (1995).135 M. Walt,
Introduction to Geomagnetically Trapped Radiation , Cambridge University Press,Cambridge, UK (2005).136 M. Qin, X. Zhang, B. Ni, et al. , “Solar cycle variations of trapped proton flux in the innerradiation belt,”
Journal of Geophysical Research (Space Physics) , 9658–9669 (2014).137 O. Adriani, G. C. Barbarino, G. A. Bazilevskaya, et al. , “Trapped Proton Fluxes at LowEarth Orbits Measured by the PAMELA Experiment,”
The Astrophysical Journal , L4(2015).138 V. V. Benghin, O. Y. Nechaev, I. A. Zolotarev, et al. , “An Experiment in Radiation Mea-surement Using the Depron Instrument,”
Space Science Reviews , 9 (2018).139 Y. Y. Shprits, V. Angelopoulos, C. T. Russell, et al. , “Scientific Objectives of Electron Lossesand Fields INvestigation Onboard Lomonosov Satellite,”
Space Science Reviews , 25(2018). 7740 J. I. Vette, “The AE-8 trapped electron model environment,” Tech. Rep. NSSDC/WDC-A-R&S 91-24, The NASA/National Space Science Data Center (1991a).141 J. I. Vette, “Trapped Radiation Environment Model Program (1964-1991),” Tech. Rep.NSSDC/WDC-A-R&S 91-29, The NASA/National Space Science Data Center (1991b).142 D. M. Sawyer and J. I. Vette, “Trapped Proton Environment for Solar Maximum and SolarMinimum,” Tech. Rep. NSSDC/WDC-A-R&S 76-06, The NASA/National Space ScienceData Center (1976).143 A. L. Vampola, “The ESA Outer Zone Electron Model Update,” in
Environment Modelingfor Space-Based Applications , T. D. Guyenne and A. Hilgers, Eds.,
ESA Special Publication , 151 (1996).144 D. Heynderickx, M. Kruglanski, V. Pierrard, et al. , “A low altitude trapped proton model forsolar minimum conditions based on SAMPEX/PET data,”
IEEE Transactions on NuclearScience , 1475–1480 (1999).145 G. P. Ginet, T. P. O’Brien, S. L. Huston, et al. , “AE9, AP9 and SPM: New Models forSpecifying the Trapped Energetic Particle and Space Plasma Environment,” Space ScienceReviews , 579–615 (2013).146 W. R. Johnston, T. P. O’Brien, G. P. Ginet, et al. , “AE9/AP9/SPM: new models for radiationbelt and space plasma specification,” in
Proceedings of the SPIE , Society of Photo-OpticalInstrumentation Engineers (SPIE) Conference Series , 908508 (2014).147 W. R. Johnston, T. P. O’Brien, S. L. Huston, et al. , “Recent Updates to the AE9/AP9/SPMRadiation Belt and Space Plasma Specification Model,”
IEEE Transactions on Nuclear Sci-ence , 2760–2766 (2015). 7848 T. P. O’Brien, W. R. Johnston, S. L. Huston, et al. , “Changes in AE9/AP9-IRENE Version1.5,” IEEE Transactions on Nuclear Science , 462–466 (2018).149 M. de Soria-Santacruz Pich, I. Jun, and R. Evans, “Empirical radiation belt models: Com-parison with in situ data and implications for environment definition,” Space Weather ,1165–1176 (2017).150 J. ˇR´ıpa, G. Dilillo, R. Campana, et al. , “A comparison of trapped particle models in lowEarth orbit,” in Space Telescopes and Instrumentation 2020: Ultraviolet to Gamma Ray , J.-W. A. den Herder, S. Nikzad, and K. Nakazawa, Eds., , 114443P, International Societyfor Optics and Photonics, SPIE (2020).151 G. P. Ginet, B. K. Dichter, D. H. Brautigam, et al. , “Proton Flux Anisotropy in Low EarthOrbit,”
IEEE Transactions on Nuclear Science , 1975–1980 (2007).152 J. Alcaraz, D. Alvisi, B. Alpat, et al. , “Protons in near earth orbit,” Physics Letters B ,215–226 (2000).153 J. Alcaraz, B. Alpat, G. Ambrosi, et al. , “Leptons in near earth orbit,”
Physics Letters B ,10–22 (2000).154 T. Sanuki, M. Motoki, H. Matsumoto, et al. , “Precise Measurement of Cosmic-Ray Protonand Helium Spectra with the BESS Spectrometer,”
The Astrophysical Journal , 1135–1142 (2000).155 Y. S. Yoon, H. S. Ahn, P. S. Allison, et al. , “Cosmic-ray Proton and Helium Spectra fromthe First CREAM Flight,”
The Astrophysical Journal , 122 (2011).156 M. Ackermann, M. Ajello, W. B. Atwood, et al. , “Fermi LAT observations of cosmic-rayelectrons from 7 GeV to 1 TeV,”
Physical Review D , 092004 (2010).7957 M. Ackermann, M. Ajello, A. Albert, et al. , “Inferred Cosmic-Ray Spectrum from FermiLarge Area Telescope γ -Ray Observations of Earth’s Limb,” Physical Review Letters ,151103 (2014).158 F. Aharonian, A. G. Akhperjanian, U. Barres de Almeida, et al. , “Energy Spectrum ofCosmic-Ray Electrons at TeV Energies,”
Physical Review Letters , 261104 (2008).159 M. Martucci, R. Munini, M. Boezio, et al. , “Proton Fluxes Measured by the PAMELAExperiment from the Minimum to the Maximum Solar Activity for Solar Cycle 24,”
TheAstrophysical Journal Letters , L2 (2018).160 “Space environment (natural and artificial) - Galactic cosmic ray model,” Tech. Rep. ISO-15390, International Organization for Standardization (2004).161 D. F. Smart and M. A. Shea, “A review of geomagnetic cutoff rigidities for earth-orbitingspacecraft,”
Advances in Space Research , 2012–2020 (2005).162 T. E. VanZandt, W. L. Clark, and J. M. Warnock, “Magnetic apex coordinates: A magneticcoordinate system for the ionospheric F layer,” Journal of Geophysical Research , 2406(1972).163 W. R. Webber, “Cosmic ray electrons and positrons - A review of current measurements andsome implications,” in NATO Advanced Science Institutes (ASI) Series C , M. M. Shapiro,Ed.,
NATO Advanced Science Institutes (ASI) Series C , 83–100 (1983).164 I. V. Moskalenko and A. W. Strong, “Production and Propagation of Cosmic-Ray Positronsand Electrons,”
The Astrophysical Journal , 694–707 (1998).165 R. L. Golden, C. Grimani, B. L. Kimbell, et al. , “Observations of Cosmic-Ray Electronsand Positrons Using an Imaging Calorimeter,”
The Astrophysical Journal , 769 (1994).8066 V. Bidoli, M. Casolino, M. de Pascale, et al. , “Energy spectrum of secondary protons abovethe atmosphere measured by the instruments nina and nina-2,”
Annales Geophysicae (10),1693 (2002).167 C. E. McIlwain, “Coordinates for Mapping the Distribution of Magnetically Trapped Parti-cles,” Journal of Geophysical Research , 3681–3691 (1961).168 W. B. Atwood, A. A. Abdo, M. Ackermann, et al. , “The Large Area Telescope on the FermiGamma-Ray Space Telescope Mission,” The Astrophysical Journal (2), 1071 (2009).169 P. Zuccon, B. Bertucci, B. Alpat, et al. , “A calculation of the radiation environment forsatellite experiments operating below the van allen belts,” in
Proceedings of the 28th Inter-national Cosmic Ray Conference , , 4249 (2003).170 S. A. Voronov, A. M. Gal’Per, S. V. Koldashov, et al. , “Energy spectra of high-energyelectrons and positrons under the earth’s radiation belt,” Kosmicheskie Issledovaniia ,567 (1991).171 V. V. Mikhailov, “Low Energy Electron and Positron Spectra in the Earth Orbit Measuredby Maria-2 Instrument,” International Journal of Modern Physics A , 1695–1704 (2002).172 D. J. Thompson, “A three-dimensional study of 30- to 300-MeV atmospheric gamma rays,” Journal of Geophysical Research , 1309–1320 (1974).173 I. A. Gurian, E. P. Mazets, M. P. Proskura, et al. , “Investigation of hard gamma radiation ofthe atmosphere on Cosmos 461.,” Geomagnetism and Aeronomy , 11–17 (1979).174 J. M. Ryan, M. C. Jennings, M. D. Radwin, et al. , “Atmospheric gamma ray angle andenergy distributions from sea level to 3.5 g/cm and 2 to 25 MeV,” Journal of GeophysicalResearch , 5279–5288 (1979). 8175 A. Aky ¨uz, D. Bhattacharya, K. W. Chuang, et al. , “Atmospheric gamma rays at geomagneticlatitudes of -29 ◦ and +43 ◦ ,” Journal of Geophysical Research , 17,359–17,364 (1997).176 D. Petry, “The Earth’s Gamma-ray Albedo as observed by EGRET,” in
High EnergyGamma-Ray Astronomy , F. A. Aharonian, H. J. V¨olk, and D. Horns, Eds.,
American In-stitute of Physics Conference Series , 709–714 (2005).177 A. A. Abdo, M. Ackermann, M. Ajello, et al. , “Fermi large area telescope observations ofthe cosmic-ray induced γ -ray emission of the Earth’s atmosphere,” Physical Review D ,122004 (2009).178 W. L. Imhof, G. H. Nakano, and J. B. Reagan, “High-Resolution Measurements of Atmo-spheric Gamma Rays from a Satellite,” Journal of Geophysical Research , 2835 (1976).179 S. Sazonov, E. Churazov, R. Sunyaev, et al. , “Hard X-ray emission of the Earth’s atmo-sphere: Monte Carlo simulations,” Monthly Notices of the Royal Astronomical Society ,1726–1736 (2007).180 D. J. Thompson, G. A. Simpson, and M. E. Ozel, “SAS 2 Observations of the EarthAlbedo Gamma Radiation Above 35 MeV,”
Journal of Geophysical Research , 1265–1270 (1981).181 F. Ait-Ouamer, A. D. Zych, and R. S. White, “Atmospheric neutrons at 8.5-GV cutoff in thesouthern hemisphere,” Journal of Geophysical Research , 2499–2510 (1988).182 D. J. Morris, H. Aarts, K. Bennett, et al. , “Neutron measurements in near-Earth orbit withCOMPTEL,” Journal of Geophysical Research , 12243–12250 (1995).183 F. Lei, S. Clucas, C. Dyer, et al. , “An Atmospheric Radiation Model Based on Response Ma-82rices Generated by Detailed Monte Carlo Simulations of Cosmic Ray Interactions,”
IEEETransactions on Nuclear Science , 3442–3451 (2004).184 F. Lei, A. Hands, S. Clucas, et al. , “Improvement to and Validations of the QinetiQ Atmo-spheric Radiation Model (QARM),” IEEE Transactions on Nuclear Science , 1851–1858(2006).185 R. E. Lingenfelter, “The Cosmic-Ray Neutron Leakage Flux,” Journal of Geophysical Re-search , 5633 (1963).186 M. Kole, M. Pearce, and M. Mu˜noz Salinas, “A model of the cosmic ray induced atmo-spheric neutron environment,” Astroparticle Physics , 230–240 (2015).187 M. Ohno, N. Werner, A. P´al, et al. , “CAMELOT: design and performance verification of thedetector concept and localization capability,” in Proceedings of the SPIE , Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series , 1069964 (2018).188 K. Torigoe, Y. Fukazawa, G. Galg´oczi, et al. , “Performance study of a large CsI(Tl) scintil-lator with an MPPC readout for nanosatellites used to localize gamma-ray bursts,”
NuclearInstruments and Methods in Physics Research A , 316–320 (2019).189 C. M. Poole, I. Cornelius, J. V. Trapp, et al. , “A CAD Interface for GEANT4,”
AustralasianPhysical & Engineering Science in Medicine , 329–334 (2012).190 J. D. Sullivan, “Geometrical factor and directional response of single and multi-elementparticle telescopes,” Nuclear Instruments and Methods , 5–11 (1971).191 H. Si, “TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator,” ACM Trans. onMathematical Software , 11 (2015). 8392 M. Feroci, F. Frontera, E. Costa, et al. , “In-flight performances of the BeppoSAX gamma-ray burst monitor,” in EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII ,O. H. Siegmund and M. A. Gummin, Eds.,
Society of Photo-Optical Instrumentation Engi-neers (SPIE) Conference Series , 186–197 (1997).193 D. L. Band, “A Gamma-Ray Burst Trigger Tool Kit,”
The Astrophysical Journal , 806–811 (2002).194 E. E. Fenimore and M. Galassi, “The HETE Triggering Algorithm,” in
Gamma-ray Burstsin the Afterglow Era , E. Costa, F. Frontera, and J. Hjorth, Eds.,
ESO Astrophysics Symposia ,393, Springer-Verlag (2001).195 E. E. Fenimore, D. Palmer, M. Galassi, et al. , “The Trigger Algorithm for the Burst AlertTelescope on Swift,” in
Gamma-Ray Burst and Afterglow Astronomy 2001: A WorkshopCelebrating the First Year of the HETE Mission , G. R. Ricker and R. K. Vanderspek, Eds.,
American Institute of Physics Conference Series , 491–493 (2003).196 M. Feroci, E. Costa, P. Soffitta, et al. , “SuperAGILE: The hard X-ray imager for the AGILEspace mission,”
Nuclear Instruments and Methods in Physics Research A , 728–754(2007).197 F. Fuschino, C. Labanti, M. Galli, et al. , “Search of GRB with AGILE Minicalorimeter,”
Nuclear Instruments and Methods in Physics Research A , 17–21 (2008).198 D. M. Smith, R. P. Lin, P. Turin, et al. , “The RHESSI Spectrometer,”
Solar Physics ,33–60 (2002).199 G. Fitzpatrick, S. McBreen, V. Connaughton, et al. , “Background estimation in a wide-fieldbackground-limited instrument such as Fermi GBM,” in
Space Telescopes and Instrumenta- ion 2012: Ultraviolet to Gamma Ray , T. Takahashi, S. S. Murray, and J.-W. A. den Herder,Eds., Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series ,84433B (2012).200 M. Kokubun, Y. Fukazawa, E. Idesawa, et al. , “Activation of the ASTRO-E hard X-raydetector in low Earth orbit,”
IEEE Transactions on Nuclear Science , 371–376 (1999).201 D. E. Gruber, G. V. Jung, and J. L. Matteson, “Radioactivity observed in scintillation coun-ters during the HEAO-1 mission,” in High-Energy Radiation Background in Space , J. Rester,A. C. and J. I. Trombka, Eds.,
American Institute of Physics Conference Series , 232–242(1989).202 C. Meegan, G. Lichti, P. N. Bhat, et al. , “The Fermi Gamma-ray Burst Monitor,”
The Astro-physical Journal , 791–804 (2009).203 A. Goldstein, “The Importance of Fermi GBM in the Era of Gravitational-Wave Astron-omy,” in
AAS/High Energy Astrophysics Division , AAS/High Energy Astrophysics Division , 203.04 (2019).204 A. C. Collazzi, C. Kouveliotou, A. J. van der Horst, et al. , “The Five Year Fermi/GBMMagnetar Burst Catalog,” The Astrophysical Journal Supplement Series , 11 (2015).205 N. Østgaard, T. Neubert, V. Reglero, et al. , “First 10 Months of TGF Observations byASIM,”
Journal of Geophysical Research (Atmospheres) , 14,024–14,036 (2019).206 A. Ursi, M. Marisaldi, M. Tavani, et al. , “Detection of terrestrial gamma-ray flashes with theAGILE satellite,” in
Journal of Physics Conference Series , Journal of Physics ConferenceSeries , 012029 (2017). 8507 T. Neubert, N. Østgaard, V. Reglero, et al. , “The asim mission on the international spacestation,”
Space Science Reviews (2), 26 (2019).208 D. Sarria, F. Lebrun, P.-L. Blelly, et al. , “TARANIS XGRE and IDEE detection capability ofterrestrial gamma-ray flashes and associated electron beams,”
Geoscientific Instrumentation,Methods and Data Systems , 239–256 (2017).209 G. N. Pendleton, R. S. Mallozzi, W. S. Paciesas, et al. , “The Intensity Distribution forGamma-Ray Bursts Observed with BATSE,” The Astrophysical Journal , 606 (1996).210 W. S. Paciesas, C. A. Meegan, G. N. Pendleton, et al. , “The Fourth BATSE Gamma-Ray Burst Catalog (Revised),”
The Astrophysical Journal Supplement Series , 465–495(1999).211 G. N. Pendleton, J. Hakkila, and C. A. Meegan, “The BATSE trigger efficiency as a functionof intensity and energy range,” in
Gamma-Ray Bursts, 4th Hunstville Symposium , C. A.Meegan, R. D. Preece, and T. M. Koshut, Eds.,
American Institute of Physics ConferenceSeries , 899–903 (1998).212 C. Wigger, O. Wigger, E. Bellm, et al. , “Observation of an Unexpected Hardening in theSpectrum of GRB 021206,”
The Astrophysical Journal , 553–565 (2008).213 C. Wigger, W. Hajdas, A. Zehnder, et al. , “Spectral analysis of GRBs measured byRHESSI,”
Nuovo Cimento B Serie , 1117–1121 (2006).214 D. R. Willis, E. J. Barlow, A. J. Bird, et al. , “Evidence of polarisation in the prompt gamma-ray emission from GRB 930131 and GRB 960924,”
Astronomy and Astrophysics , 245–253 (2005).215 M. McConnell, D. Forrest, W. T. Vestrand, et al. , “Using BATSE to measure gamma-ray86urst polarization,” in
Gamma-ray Bursts: 3rd Huntsville Symposium , C. Kouveliotou, M. F.Briggs, and G. J. Fishman, Eds.,
American Institute of Physics Conference Series384