DmpIRFs and DmpST: DAMPE Instrument Response Functions and Science Tools for Gamma-Ray Data Analysis
Kai-Kai Duan, Wei Jiang, Yun-Feng Liang, Zhao-Qiang Shen, Zun-Lei Xu, Yi-Zhong Fan, Fabio Gargano, Simone Garrappa, Dong-Ya Guo, Shi-Jun Lei, Xiang Li, Mario Nicola Mazziotta, Maria Fernanda Munoz Salinas, Meng Su, Valerio Vagelli, Qiang Yuan, Chuan Yue, Stephan Zimmer
DDmpIRFs and DmpST: DAMPE Instrument Response Functionsand Science Tools for Gamma-Ray Data Analysis
Kai-Kai Duan , † , Wei Jiang , , Yun-Feng Liang ‡ , Zhao-Qiang Shen , , Zun-Lei Xu ,Yi-Zhong Fan , , Fabio Gargano , Simone Garrappa , , Dong-Ya Guo , Shi-Jun Lei , XiangLi § , Mario Nicola Mazziotta , Maria Fernanda Munoz Salinas , Meng Su , , ValerioVagelli , , Qiang Yuan , , Chuan Yue , Stephan Zimmer Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, ChineseAcademy of Sciences, Nanjing 210008, China University of Chinese Academy of Sciences, Beijing 100049, China School of Astronomy and Space Science, University of Science and Technology of China, Hefei,Anhui 230026, China Istituto Nazionale di Fisica Nucleare Sezione di Bari, I-70125, Bari, Italy Istituto Nazionale di Fisica Nucleare Sezione di Perugia, I-06123 Perugia, Italy Dipartimento di Fisica e Geologia, Universit degli Studi di Perugia, I-06123 Perugia, Italy Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, 100049, China Department of Nuclear and Particle Physics, University of Geneva, CH-1211, Switzerland Department of Physics and Laboratory for Space Research, University of Hong Kong, Pok Fu Lam,Hong Kong, China
Abstract
GeV gamma ray is an important observation target of DArk Matter ParticleExplorer (DAMPE) for indirect dark matter searching and high energy astrophysics.We present in this work a set of accurate instrument response functions of DAMPE(DmpIRFs) including the effective area, point-spread function and energy dispersion thatare crucial for the gamma-ray data analysis based on the high statistics simulation data.A dedicated software named DmpST is developed to facilitate the scientific analyses ofDAMPE gamma-ray data. Considering the limited number of photons and the angularresolution of DAMPE, the maximum likelihood method is adopted in the DmpST to bet-ter disentangle different source components. The basic mathematics and the frameworkregarding this software are also introduced in this paper.
Key words:
DAMPE, gamma ray, IRFs, maximum likelihood analysis, software
DArk Matter Particle Explorer (DAMPE) is a high energy cosmic-ray and gamma-ray observatory(Chang 2014, Chang et al. 2017). It contains four sub-detectors: a Plastic Scintillation Detector (PSD), a † [email protected] ‡ [email protected] § [email protected] a r X i v : . [ a s t r o - ph . H E ] A p r K.-K. Duan et al.
Sillicon-Tungsten tracKer-converter (STK), a BGO calorimeter (BGO) and a NeUtron Detector (NUD).The PSD that measures the charge of particles also acts as anti-coincidence detector for gamma-rayobservation. The STK measures the trajectories of charged particles, as well as the photons that are con-verted into e + e − pairs. The BGO calorimeter measures the energies of incidence particles and is alsoable to distinguish the electron and hadron efficiently. The NUD provides an independent measurementand further improvement for the electron/hadron identification. The on-orbit calibration have adoptedfor DAMPE and is expected to operate stably during the next few years (Ambrosi et al. 2019, Ma et al.2018, Ding et al. 2019, Jiang et al. 2019).Based on the photon selection algorithm described in Xu et al. (2018), valuable gamma-ray datahave been accumulated. Further scientific analysis of high-level gamma-ray data, however, requiresdetailed knowledge about the instrument response functions (IRFs) of DAMPE, i.e., the effective area,the point-spread function (PSF) and the energy dispersion function. Using the high-statistics simulationdata, we have constructed the IRFs for DAMPE gamma-ray observation in the energy range from 1 GeVto 10 TeV and with the incidence angle from 0 ◦ to 60 ◦ .Limited by the relatively low statistics of DAMPE gamma-ray data, the chi square method is notsuitable for the data analysis, maximum likelihood method (Mattox et al. 1996) is adopted. Combiningthe IRFs and the model of gamma-ray sources, we can calculate the expected photon number recordedby the detector. The values, and also the uncertainties, of the parameters in the gamma-ray source modelthen can be estimated by comparing with the real DAMPE observation using the maximum likelihoodmethod.The data preparation, the convolution with the IRFs and the parameter inference are realized forDAMPE data analysis using a dedicated software named DmpST, which is also developed to facilitatethe scientific analysis. In this paper, we introduce both the DAMPE IRFs and the DmpST software.This paper is structured as the following. We first introduce the IRFs of DAMPE in Section 2. The observing time and exposure of DAMPE are then described in Section 3. In Section 4, we introduce themaximum likelihood method for DAMPE gamma-ray data analysis, followed by a description of thecode structures in Section 5. We summarize this work in Section 6. Instrument response functions (IRFs) are the parameterized representations of the instrument perfor-mance. The DAMPE IRFs can be factorized into three parts (Ackermann et al. 2012). The effectivearea, A eff ( E, ˆ v, s ) , is the product of the geometrical cross-section area, the probability of gamma-rayconversion and the efficiency of photon selection for a gamma-ray with energy E and direction ˆ v in thedetector reference frame. The s denotes the trigger type (see below). The Point-spread function (PSF), P (ˆ v (cid:48) ; E, ˆ v, s ) and the energy dispersion function, D ( E (cid:48) ; E, ˆ v, s ) are the probability distributions of thereconstructed direction ˆ v (cid:48) and the reconstructed energy E (cid:48) for a gamma-ray with energy E and direction ˆ v . Given the spatial and spectral model of the incidence gamma-ray sources, F ( E, ˆ p ) , where ˆ p refersto the celestial directions of the gamma-ray sources, we can convolve the model with the IRFs to predictthe distribution of observed photons: r ( E (cid:48) , ˆ p (cid:48) , s ) = (cid:90) (cid:90) (cid:90) F ( E, ˆ p ) A eff ( E, ˆ v ( t ; ˆ p ) , s ) × P (ˆ v (cid:48) ( t ; ˆ p (cid:48) ); E, ˆ v ( t ; ˆ p ) , s ) D ( E (cid:48) ; E, ˆ v ( t ; ˆ p ) , s )d E dΩd t, (1)where ˆ p (cid:48) is the reconstructed celestial directions of the gamma-rays. The integrals are over the time andenergy range of interest and the solid angle in the celestial reference frame.To evalute the DAMPE IRFs, we perform Geant4 -based Monte Carlo detector simulation to gener-ate pseudo-photons of DAMPE (MC data hereafter). We simulate gamma-rays with uniform distributionof incidence direction, that can be used to explore the instrument response across the entire field of view(FoV) of DAMPE. The MC data are generated with an E − counts spectrum uniformly in the logarithm mpIRFs and DmpST 3 energy, and from a sphere with 6 m cross-sectional area centered on the detector to cover the whole en-ergy range and the whole detector of DAMPE. The directions of the gamma rays are sampled uniformlyin solid angle with downward-going directions, leading to a semi-isotropic incidence flux of the simu-lated gamma rays. Here we ignore the back-entering events, because these events would have to traversea large amount of material and thus presumably lose a lot of energy along their way. Through the samereconstruction and gamma-ray selection algorithm as the on-orbit data, the MC data can describe theresponse of DAMPE for gamma-ray observation accurately (Xu et al. 2018).DAMPE uses two sets of trigger directives for physics data: the pre-scaled Low Energy Trigger(LET) and the Higt Energy Trigger (HET). The pre-scale factors of LET are different when the detectoris in different geographic latitude (Chang et al. 2017). When the detector is in the low latitude region( | φ g | < ◦ ), the Lower Energy trigger is pre-scaled with a factor of 8; and at high latitude region( | φ g | > ◦ ) it is 64 pre-scaled. The IRFs is also divided into two sub-sets, LET IRFs and HET IRFs. Effective area is a numerical function varying with the energy of gamma-ray photon and its incidencedirection in the instrument reference frame. We binned the MC data according to the event energy,incidence angle and trigger type. The effective area for each bin centered at E i , θ j , φ k with trigger type s is A eff ( E i , θ j , φ k , s ) = N i,j,k,s N sim ,i,j,k A sim , (2)where N sim ,i,j,k is the number of photons generated in the simulation in each bin, and N i,j,k,s is thenumber of photons that passing the selection algorithm with trigger type s = LET or HET . The A sim is the cross-section area of the generated sphere in the simulation.We divide the MC data into 20 energy bins from 1GeV to 100GeV (40 energy bins from 1 GeVto 10 TeV) and 10 angular bins from 0 ◦ to 60 ◦ for LET (HET) data. Fig. 1 shows the effective area ofDAMPE gamma-ray observation as a function of the energy and incidence direction. The reconstructed direction ( ˆ v (cid:48) ) of the photon may deviate from its true value ( ˆ v ), and the probabilitydistribution of the deviation δv = | ˆ v (cid:48) − ˆ v | is parameterized by the PSF. The PSF for the DAMPEis related to the inclination angle θ and the azimuth angle φ of the incidence photon in the detectorreference frame, and also the photon’s energy and trigger type. Because the φ dependence of the PSF ismuch weaker than the θ dependence, we ignore the φ dependence in the current version of the PSF.Based on the MC data, we construct a histogram of the angular deviations of the selected gamma-rays for each energy and incidence angle bin and for each trigger type. We find that the form of theFermi-LAT PSF (Ackermann et al. 2012) can accommodate DAMPE simulation data well. Accordingly,the PSF histogram is fitted with a double King function, P ( x ) = f core K ( x p ; σ core , γ core ) + (1 − f core ) K ( x p ; σ tail , γ tail ) , (3)where K ( x p ; σ, γ ) is King function defined as K ( x p ; σ, γ ) = 12 πσ (cid:18) − γ (cid:19) (cid:34) γ x p σ (cid:35) − γ , (4)and x p is the scaled angular deviation x p = δvS p ( E, θ ) . (5) K.-K. Duan et al. Energy [GeV] c o s LET Energy [GeV]
HET e ff e c t i v e a r e a [ c m ] Fig. 1
The effective area of DAMPE (in units of cm ) for gamma-ray observation at differentenergy and incidence direction. The energy is in 20 bins from 1 GeV to 100 GeV for LETphotons (left panel) and 40 bins to 10 TeV for HET photons (right panel). The incidence angleis in 10 bins from 0 ◦ to 60 ◦ . Note that the effective area presented here is averaged over φ .The S p ( E, θ ) is the angular resolution (defined as 68 % containment of the angular deviation) atenergy E and incidence angle θ . The functional form of the King profile originates from XMM Newton(Kirsch et al. 2004, Read et al. 2011) and was later adapted for the Fermi-LAT. Note that the Kingfunction is normalized, i.e., (cid:82) ∞ πxK ( x ; σ, γ )d x = 1 .We divide the MC data into 4 energy bins from 1GeV to 100GeV (8 energy bins from 1 GeV to10 TeV) and 5 angular bins from 0 ◦ to 60 ◦ for LET (HET) data. Fig. 2 shows the angular resolution ofDAMPE for gamma-ray observation at different energy and incidence direction. For each bin, the MCdata are fitted with above functions and the best-fit parameters of them are derived and stored in theDmpST. Fig. 3 shows an example of the best fit to the scaled angular deviation with the double Kingfunction in the bin of E ∈ [3 . ,
10] GeV and θ ∈ [25 . ◦ , . ◦ ] for HET photons. Energy dispersion function gives the probability of a photon with true energy ( E ) being allocated anenergy ( E (cid:48) ) after the events reconstruction. Similar to the PSF, we ignore the φ dependence and param-eterize the energy dispersion as function of scaled energy deviation x D = E (cid:48) − ES D ( E, θ ) E , (6)where the scale S D ( E, θ ) is the energy resolution (defined as the half-width of the 68 % containmentrange of the energy deviation) at the bin center of energy E and incidence angle θ . We fit the MC datawith three piecewise functions of the form D ( x D ) = N L R ( x D , x , σ L , γ L ) if ( x D − x ) < − ¯ xN l R ( x D , x , σ l , γ l ) if ( x D − x ) ∈ [ − ¯ x, N R R ( x D , x , σ R , γ R ) if ( x D − x ) > mpIRFs and DmpST 5 Energy [GeV] c o s LET Energy [GeV]
HET a n g l e r e s o l u t i o n [ d e g r ee ] Fig. 2
The angular resolution of DAMPE (in units of degree) for gamma-ray observation atdifferent energy and incidence direction. The energy is in 4 bins from 1 GeV to 100GeV forLET photons (left panel) and 8 bins to 10 TeV for HET photons (right panel). The incidenceangle is in 5 bins from 0 ◦ to 60 ◦ . Scaled angular deviation x10 x P ( x ) fitting functioncore King functiontail King functionsimulation data Fig. 3
The best fit to the scaled angular deviation with double King function in the energyrange [3.16, 10] GeV and incidence angle range [25.84 ◦ , 36.87 ◦ ] for HET photons. The pointsare the distribution of the scaled angular deviation of the MC data, the dash and dotted lineare the core and tail King functions respectively and the solid line is the sum of the twocomponents. The reduce χ of this fitting is 1.09. K.-K. Duan et al. Energy [GeV] c o s LET Energy [GeV]
HET e n e r g y r e s o l u t i o n Fig. 4
The energy resolution of DAMPE (dimensionless) for gamma-ray observation at dif-ferent energy and incidence direction. The energy is in 4 bins from 1 GeV to 100GeV for LETphotons (left panel) and 8 bins to 10 TeV for HET photons (right panel). The incidence angleis in 5 bins from 0 ◦ to 60 ◦ . R ( x D , x , σ, γ ) = N exp (cid:18) − (cid:12)(cid:12)(cid:12)(cid:12) x D − x σ (cid:12)(cid:12)(cid:12)(cid:12) γ (cid:19) . (7)We divided the MC data with the same binned method with the PSF. Fig. 4 shows the energyresolution of DAMPE for gamma-ray observation at different energy and incidence direction. And fitthe energy dispersion with above function in each bin. Fig. 5 shows an example of energy dispersionfitted with the function in the bin of E ∈ [3 . ,
10] GeV and θ ∈ [25 . ◦ , . ◦ ] for HET photons. For a particular source in the sky, its direction in the detector reference frame varies with the time. Sincethe IRFs various appreciably across the DAMPE field of view (FoV), we define the exposure (cid:15) for anygiven energy E and direction in the sky ˆ p as the integral of the effective area over the time range ofinterest, (cid:15) ( E, ˆ p ) = (cid:88) s (cid:90) A eff ( E, ˆ v ( t, ˆ p ) , s )d t. (8)The exposure can also be expressed as an integral over the solid angle in the detector referenceframe, (cid:15) ( E, ˆ p ) = (cid:88) s (cid:90) A eff ( E, ˆ v, s ) t obs (ˆ v ; ˆ p )dΩ= (cid:90) A LETeff t obs dΩ + (cid:90) A HETeff t obs dΩ , (9)here the t obs (ˆ v ; ˆ p ) is named observing time and defined as the total time in the range of interest duringwhich DAMPE have observed the direction ˆ p with detector frame direction ˆ v . The A LETeff and A HETeff mpIRFs and DmpST 7 D ( x ) fitting functionsimualtion data Fig. 5
The best fit to the scaled energy deviation with the energy dispersion function in theenergy range [3.16, 10] GeV and incidence angle range [25.84 ◦ , 36.87 ◦ ] for HET events. Thepoints are the scaled deviation distribution of the MC data, and the line is the best fit function.The reduce χ od this fitting is 1.05.in Eq. (9) are the effective area for LET and HET photons, respectively. As an example, we show theobserving time map in the detector reference frame for the Vela pulsar in Fig. 6. With the observingtime map and the DAMPE effective area, the exposure then can be calculated according to Eq. (9). Fig.7 shows the all-sky exposure map of DAMPE at 10 GeV for the first year of operation. Because DAMPEis in a sun-synchronous orbit, we can see that the exposure is not uniform over the sky. Analyzing the gamma-ray data from DAMPE requires the maximum likelihood method due to the lim-ited number of photons and the angular resolution. We characterize a source by its photon flux density F ( E, ˆ p, t ; λ ) . In order to reduce the computational burden, we assume the source is stationary duringthe time range in each likelihood analysis. The model of gamma-ray source then can be modeled by F ( E, ˆ p ; λ ) = S ( E ; λ ) M (ˆ p ) . (10)Here the M (ˆ p ) is a normalized function describing the spatial morphology of the source. For thepoint source, the spatial distribution can be described with the Dirac delta function, M (ˆ p ) = δ (ˆ p − ˆ p ) ,where ˆ p is the direction of the point source. The S ( E ; λ ) in Equation (10) is the spectrum of the sourcewith its parameters λ .To remove the θ dependence of the PSF and energy dispersion, we calculate the exposure-weightedPSF and energy dispersion for any sources included in the analysis: P ( δv ; E ) = (cid:80) s (cid:82) P ( δv ; E, θ, s ) A eff ( E, θ, φ, s ) t obs ( θ, φ )dΩ (cid:80) s (cid:82) A eff ( E, θ, φ, s ) t obs ( θ, φ )dΩ , (11) For the variable source, the time dependence of the flux can be achieved by repeating the analysis in finer time bins.
K.-K. Duan et al. deg ]0.50.60.70.80.91.0 c o s Fig. 6
The observing time map in the detector reference frame for DAMPE pointing to theVela pulsar in the first operation year. D ( E (cid:48) ; E ) = (cid:80) s (cid:82) D ( E (cid:48) ; E, θ, s ) A eff ( E, θ, φ, s ) t obs ( θ, φ )dΩ (cid:80) s (cid:82) A eff ( E, θ, φ, s ) t obs ( θ, φ )dΩ . (12)Considering the excellent energy resolution of DAMPE (i.e., ∼ at 1 GeV and ∼ at 100GeV (Chang et al. 2017)), the influence of energy dispersion can be ignored for most gamma-ray scienceanalysis. The only exception is the case of searching for narrow-line feature in the gamma-ray spectrum(Ackermann et al. 2015; Liang et al. 2016; Li et al. 2018), which will be performed with other dedicatedcode. So in the DmpST we ignore the energy dispersion and regard the measured energy as the truephoton energy in current version, and it will be considered in the future if the statistic allows.With the parameterized source model, the exposure and the exposure-weighted PSF, we can calcu-late the model predicted photon rate in the bin i (centered on E i , ˆ p (cid:48) i ) from the source j : r ij ( E i , ˆ p (cid:48) i ; λ j ) = (cid:90) dΩ F ij ( E i , ˆ p ; λ j ) (cid:15) ( E i , ˆ p ) ¯ P (ˆ p (cid:48) i ; ˆ p, E i ) . (13)The predicted photon rates are compared to the observation data to determine the model parameters.The information we can get from the DAMPE observation is the energy ( E ), the direction ( ˆ p (cid:48) ) and thetime of arrival ( t ) of each photon. We bin the photons in the region-of-interest (ROI) into a counts cubeaccording to their measured energies and directions. For each bin, the photon number N follows thePoisson distribution with unknown mean R : p ( N ; R ) = R N /N ! · exp( − R ) . Taking into account all thebins with numbers { N i } , the Poisson distribution becomes p ( { N i } ; { R i } ) = N bins (cid:89) i =1 R N i i N i ! exp( − R i ) . (14)Because of the broad PSF of DAMPE and the strong Galactic diffuse background, the photons ineach bin may originate from multiple sources, the parameters of which should be determined simultane-ously utilizing the likelihood fitting. With the model predicted photon rates and the real observed data, mpIRFs and DmpST 9 s] 1e9 Fig. 7
The exposure map of DAMPE at 10 GeV in the first year shown in a Hammer-Aitoffprojection in Galactic coordinates. The maximum value is at the two poles of the equatorialcoordinates, while the minimum value is at the equator.and based on the Poisson statistics, we construct the binned likelihood function (in logarithm form) bysumming over all N bins bins and all N s sources: log L ( λ ) = N bins (cid:88) i =1 − N s (cid:88) j =1 R ij + N i log N s (cid:88) j =1 R ij = N bins (cid:88) i =1 − (cid:90) d t (cid:90) d E (cid:90) dΩ (cid:48) N s (cid:88) j =1 r ij ( λ j ) + N i log (cid:90) d t (cid:90) d E (cid:90) dΩ (cid:48) N s (cid:88) j =1 r ij ( λ j ) , (15)where the R ij is the model expected photon number in the bin i from source j and the integral iscalculated in the corresponding bin i as well.When the bin widths are taken to be infinitesimal such that only 0 or 1 photon in each bin, thesummation over N bins bins becomes to an integral over the whole energy range and the ROI. Then weget the unbinned form of the likelihood function: log L ( λ ) = − (cid:90) d t (cid:90) d E (cid:90) ROI dΩ (cid:48) N s (cid:88) j =1 r j ( λ j ) + N events (cid:88) i =1 log N s (cid:88) j =1 r j ( λ j ) . (16)By maximizing the likelihood function of (15) or (16), we can get the best-fit values of all the freeparameters in the source models. The code is coded with Python, based on NumPy (van der Walt et al. 2011), SciPy , AstroPy (Robitailleet al. 2013) and iminuit (James & Roos 1984) packages. The structure of DmpST is shown in Fig. 8. SpaceCraft
DmpIRFsExposure DmpSkyObsSimuSky MapEvents SourceSpatialModelSpectrumModelLikelihood BaseLikelihood AnalysisBinned LikelihoodUnbinned Likelihood
Fig. 8
The structure of the DmpST. The blue, white and orange represent input, process andoutput modules, respectively.The input modules are
Events , SpaceCraft , DmpIRFs , Spatial Model , Spectrum and
Model (shown as blue in Fig. 8). The
Events module stores the information of photons that are se-lected from all the events detected by DAMPE using the photon selection algorithm (Xu et al. 2018).The information of a photon includes the arrive time ( t ), the reconstructed energy ( E ), the reconstructeddirection in the celestial coordinates ( α , δ , l , b ) and in the detector reference frame ( θ , φ ), andthe trigger type (s). The photons of interest in the analysis can be selected according to their times, en-ergies or directions utilizing the Events module and can be binned into a counts map or a counts cubewhich is managed by the
Sky Map module. The
SpaceCraft module stores the position, directionand livetime of DAMPE along with time, and can be used to calculate the observing time of DAMPE forany direction in the sky (see Section 3). The
DmpIRFs module is used to manage information of instru-ment response functions (IRFs), including the effective area matrix, the parameters of PSF and energydispersion function. With these parameters and the fitting functions described in Section 2, the distri-butions of PSF and energy dispersion can be reconstructed. The
Spatial Model and
Spectrum modules provide different kinds of spatial and spectral models of gamma-ray sources, respectively. The
Model module includes all the models of sources those will contribute photons to the ROI.The process modules comprise
Sky Map , Exposure , Source , Likelihood Base , BinnedLikelihood and
Unbinned Likelihood (white parts in Figure 8). The
Sky Map module man-ages the information of counts map or counts cube from the
Events module, such as the photon numberand celestial coordinates of each bin. The
Exposure module calculates the observing time, exposureand the exposure-weighted PSF and energy dispersion based on the information in
SpaceCraft and
DmpIRFs modules. The
Source module combines spatial and spectral models based on the
SpatialModel and
Spactrum modules for each source in the
Model module. The
Likelihood Base module convolves the PSF with the spatial model, integrals the spectrum over the energy to calculatethe expected photons number for each source based on the
Sky Map , Exposure and
Source mod-ules. The
Binned/Unbinned Likelihood modules construct the likelihood function described inSection 4.Finally, the
Likelihood Analysis module implements the maximum likelihood estimationwith the Minuit algorithm and the basic outputs are the best-fit values ( ˆ λ ) of source parameters, thesource fluxes and the corresponding statistic uncertainties. Also we can obtain the confidence level of mpIRFs and DmpST 11 /2Monte Carlo Results Fig. 9
The histogram is the normalized distribution of
T S values analyzed from simulateddata, and the dash line is the distribution following χ / . In the analysis, the null hypothesisis no point source and the alternative hypothesis is converse.each source defined as T S j = − L (ˆ λ ,j ) − log L (ˆ λ )) , (17)where ˆ λ ,j is the best-fit parameters without source j included in the model. The T S j follows χ distribution with h − m degrees of freedom (Wilks 1938), where h and m are the number of freeparameters in the model with/out source j . The DmpSkyObsSimu module simulates photons observedby DAMPE with the
DmpIRFs , SpaceCraft and
Source modules.Monte Carlo simulation has been done with the
DmpSkyObsSimu module with the Galactic dif-fuse emission and isotropic emission. With the
Likelihood Analysis module, we analyze thesimulated data to confirm the distribution of the
T S . The null hypothesis is there is no point source,only the background including the Galactic diffuse emission and isotropic emission. The alternativehypothesis is the converse: there is a point source with Power-Law spectrum with free normalizationparameter. For most point source analysis of DAMPE, the radii of ROI is ≈ × S p and the typicalnumber of photons N in the ROI is about 25. Fig 9 shows that for T S > , the distribution of T S isfollowing χ / , and the one-half of the simulations have TS = 0 (Mattox et al. 1996). The GeV gamma-ray sky is an important observation target of DAMPE. To facilitate analyzing theDAMPE gamma-ray data, we have developed a dedicated software named DmpST, which implementsmaximum likelihood analysis to extract the parameters of sources that attribute to the observed gamma-rays. The DAMPE IRFs that are essential to the gamma-ray data analysis, including the effective area,the PSF and the energy dispersion, are also derived based on high-statistics simulation data. Makinguse of the DmpIRFs and DmpST that are detailed in this paper, scientific analyses of the gamma-raydata could be carried out to obtain the best-fit spectral parameters, fluxes and corresponding statisticuncertainties, and further the spectral energy distribution and light curve of the gamma-ray sources,promoting our understanding the nature of high energy gamma-ray phenomena.
Acknowledgements
This work is supported in part by National Key Program for Research andDevelopment (No. 2016YFA0400200), the Strategic Priority Research Program of Chinese Academyof Sciences (No. XDB23040000), the 13th Five-year Informatization Plan of Chinese Academy ofSciences (No. XXH13506), the National Natural Science Foundation of China (Nos. U1631111,U1738123, U1738136, U1738210), Youth Innovation Promotion Association of Chinese Academy ofSciences, and the Young Elite Scientists Sponsorship Program. In Europe the activities and the dataanalysis are supported by the Swiss National Science Foundation (SNSF), Switzerland; the NationalInstitute for Nuclear Physics (INFN), Italy.