In-orbit calibration status of the Insight-HXMT

1. Energy scale and resolution calibration

1.1 HE

Figure 1 shows the detected background spectrum from seven hours of blank sky. The background is dominated by internal activation effects. Prominent background lines due to activation of iodine by cosmic and SAA protons are seen at 31, 56, 67 and 191 keV. These four lines can be used to calibrate the Energy-Channel (EC) relation or energy scale. Background line of 191 keV is also used to monitor the long-term stability of EC relation in-orbit as shown in Figure 2.

The energy resolution for 31keV is used to estimate the energy resolution in orbit.


Figure 1: The observed background spectrum detected by 18 PHOSWISH detectors of HE. Background lines due to activation of iodine by cosmic and SAA protons are evident at 31, 56, 67, and 191 keV.




Figure 2: The peak of 191 keV background line can be used to monitor the stability of energy scale for HE detectors.


1.2 ME

The working temperature of ME in-orbit changed between -50 and -5. In the calibration experiment on ground, we found the Energy-Channel (EC) relation is linear from 11 keV to 30 keV using the spectrum of 241Am source. The slopes and intercepts of E-C relation of all pixels are not a constant at different temperatures as shown in Figure 3. The slopes and intercepts will be achieved from the linear interpolation at two adjacent temperatures for each pixel. In-orbit, the pixels carried 241Am and other pixels which have Ag line are used to verify the change of EC relation on ground. All blank sky data are analyzed to get the peak of Ag line. We found that EC on ground is also suitable. As shown in Figure 4, the mean value of Ag peak is equaled to 22.5 keV, the same with the expected value.


Figure 3: The slope and intercept of Energy-Channel relation for 32 pixels of one ASIC at different temperatures.

The pixels carried 241Am in orbit can also be used to estimate the variation of FWHM. We found that change is very small.


Figure 4: The distribution of Ag line peak for about 1200 pixels


1.3 LE

Ground calibration experiments showed that the linearity of LE was very good, and the slopes and intercepts also differed at different temperatures. The same method for ME was used to obtain the slopes and intercepts at different temperatures.

In-orbit, Cas A was used to verify the change of EC relation. Here, we used the observed spectrum of Chandra to get the model of Cas A and fitted the measured spectrum of LE to check the shape of residual distribution of two instruments. If the shape of the residual distribution is same of the two instruments, we think that it comes from the systematic error of the source model. Otherwise, the EC of LE has changed compared with the result on ground. From the fit result in Figure 5, the EC relation from 1.8 keV to 4 keV has changed, the peaks in this energy range are used to update the EC relation in-orbit.


Figure 5: The red dot is the Cas A spectrum measured by Chandra. The black dot is the Cas A spectrum measured by LE. The EC relation from 1.8 keV to 4 keV was different with the on-ground results from the shape distribution of residual distribution.


2. Effective area calibration 

2.1  The crab pulsar as a calibration source

The Crab Nebula, with its pulsar has been served as a primary calibration target for many hard X-ray instruments because of its brightness, relative stability, and simple power-law spectrum. The Crab is too bright for most CCD based focusing X-ray instruments because of the pileup effect, but for LE, there are no problems of pileup.

As a collimated telescope, Insight-HXMT has to construct its background model to estimate the background level. There is no on/off observation and it is relatively hard for Insight-HXMT to estimate background because the particle-induced background varies significantly with time and orbit. In order to avoid the influence of background and independently obtain the systematic error of calibration, Crab Pulsar is used to calibrate the effective area of three payloads.

Figure 6 shows the pulse profiles of the Crab pulsar for the entire range of three payloads. The spectrum was generated with the whole pulse and the spectrum of the background is obtained from the phase between 0.6 and 0.8. To acquire the spectral parameter, the spectrum of the Crab pulsar observed by RXTE/PCA and RXTE/HEXTE in the year of 2011(Reference) was calculated with the same method. As shown in Figure 7, the model of the pulsed spectrum can be fitted by LOGPAR(Reference) according to the joint fitting result of two instruments. The fitting parameter alpha is equal to 1.52, beta is equal to 0.139, and norm is equal to 0.448.


Figure 6: X-ray profiles of Crab Pulsar detected by three payloads of Insight-HXMT. Phase 0 represents the position of the main radio peak. The un-pulsed component is subtracted from phase 0.6 to phase 0.8.



Figure 7: The Crab Pulsar spectrum observed by RXTE/PCA and HXTE in the year of 2011. They jointly determined the model of Crab Pulsar as LOGPAR.


2.2 Results of in-orbit effective areas

Pure Monte Carlo model of effective area is very difficult to fit the pulsar spectrum well because the absorption and scattering of anticoincidence detectors, non-uniform response of the detectors and so on.  Finally, it was decided to use an empirical function to modify the simulated effective areas. The comparisons of the simulated and modified effective areas are shown for three payloads are shown in Figure 8. With the new modified effective areas and fixed the parameters of Crab pulsar, the residual distributions of Crab Pulsar spectrum observed by the three payloads can be found in Figure 9.  There is no additional systematics added, 2% will be sufficient for a good fit.


Figure 8: The comparisons of the primary simulated and modified effective areas. The left one is one NaI(Tl) detector, the middle one is small FOV pixels of ME, and the right one is small FOV CCD236 of LE.


Figure 9: The residual distributions of Crab Pulsar spectrum observed by three payloads of Insight-HXMT with modified effective areas and fixed parameters of Crab Pulsar.


3. Timing calibration

The timing information of Insight was verified through observations of the Crab Pulsar based on the coordinated radio  and Fermi-LAT observations. Figure 10 shows the timing residuals of the Pulsar for Insight-HXMT, Radio Telescopes in Xinjiang and Yunnan and Fermi-LAT by TEMPO2. The timing residuals observed from Insight-HXMT are almost the same with the other two instruments. At the end, absolute time accuracy of HXMT is better than 100us from the root-mean-square of timing residual 51 us.


Figure 10: The residuals of TOA of Crab for Radio, Fermi/LAT, and HXMT. The absolute time accuracy of HXMT is better than 100us.









HE res 2

  • R(Ch)=(a+b∗Ch/kres+c√(Ch/kres))/(Ch/kres)
  • =(a∗kres+b∗Ch+c√(Ch∗kres))/Ch

3, 在轨RMF和ARF的标定

为了去除本底带来的影响,这里我们使用了Crab脉冲星的成分(Pulse on - Pulse off )进行了重新标定。

Crab Pular

利用RXTE的观测数据,得到了Crab脉冲星的谱模型及其参数。Crab Pulsar 可以利用logpar的模型进行拟合,谱参数分别为:alpha:1.58, beta:0.13











图1, HXMT卫星上的三个载荷及其分布




    HXMT的标定是将观测数据转化为科学成果的关键步骤,标定的难点在于标定模型和算法的研究上,体现在:各载荷的探测器单元众多(HE:18个,ME:1728个,LE:96个),视场复杂(大视场,小视场,盲探测器,摆放角度0度,±60度,±90度等),ME和LE在轨温度跨度很大,每个探测器之间存在不一致性(包括能标、能量分辨,探测效率,温度效应等)。这些为HXMT的标定数据库,用户标定软件的设计提出了很大的挑战。我们不能为每个探测器在每个温度范围内都提供一个能量响应矩阵,否则能量响应矩阵个数之庞大是不能接受的,而且会影响用户检索标定数据库的速度(HXMT的标定数据库采用了HEASARC提供的CALDB,它是一个文件系统)。因此这里我们将每个探测器在不同温度下的ADC道数都转换到PI空间(该空间严格和能量成线性关系PI=a*E+b),这样就可以修正不同探测器的能标、同一探测器在不同温度下的能标差异。然后关注每个探测器的能量分辨是否一致,根据能量分辨的差异为每个载荷提供几种能量响应矩阵,最后根据用户选择的探测器的个数提供一个带权重的响应矩阵。因此HXMT标定的两个核心功能是PHA到PI的转换及探测器响应文件RSP的产生,如图 2所示。这两个核心功能的实现所需要的输入来自标定数据库CALDB,如图 3所示。


图2 HXMT标定的核心问题及实现



图3 HXMT标定数据库的设计

    两个核心功能的实现依赖于载荷地面标定实验的结果及各载荷的性能模拟结果。实验结果和模拟结果为核心功能的设计和实现,为CALDB的设计提供强有力的依据。实验结果告诉我们各载荷的探测器单元在不同条件下的性能,体现在不同温度下的E-C关系,能量分辨,探测效率,能谱形状上。然而实验的能量点个数是有限的,必须依赖于MC模拟提供所有能量点的响应。为了验证MC模拟的可靠性,必须将MC 模拟的结果与实验结果进行比对,因此需要开发HXMT三个载荷单体及整星质量模型下的性能模拟软件,并与实验的数据进行比较,从而对模拟的输入参数进行优化后提供各载荷的PSF,RMF和ARF。