2.1.

Electron Background in the Top-Layer DSSD

The background spectrum of the top-layer DSSD (layer 0; red circle in Fig. 2) was a hard power law extending up to high energies of $\sim 100\mathrm{keV}$. In spite of its very large energy deposit ($\sim 100\mathrm{keV}$), such a component was not seen in the other layers, indicating that the origin of this background component has a low penetrating power, while having energy of more than $\sim 100\mathrm{keV}$. This indicates that low-energy charged particles dominate the observed background.

In addition to the spectral properties, the variation of the count rate of this component with latitude and longitude of the satellite [Fig. 3(a)] matches well with the distribution of the geomagnetically-trapped electrons measured by the Instrument for Detecting Particles (IDP) onboard the Detection of Electro-Magnetic Emissions Transmitted from Earthquake Regions (DEMETER) satellite.⁸ This distribution is clearly different from that of the geomagnetically trapped protons, especially near the latitudes and longitudes corresponding to North America (latitude of $\gtrsim 20°$ and longitude of $\lesssim -100°$). Therefore, the background of the top-layer DSSD is considered to originate from the geomagnetically trapped low-energy electrons.

2.2.

Neutron Background in the Middle-Layer DSSDs

The most remarkable property of the background spectra of the middle-layer DSSDs (layer 1 to 3) is their similarity to each other. Such a property would be exhibited if the incident particle has a high penetrating power. Moreover, this component could not originate from the high-energy charged particles since the charged particles would be rejected because of anticoincidence with the BGO active shields or with the other layers in onboard/on-ground data screening.

The similarity of the configuration of the detector (Si detector surrounded by well-type BGO active shields) and that present in Suzaku/HXD^6,7 suggests that the background component of these detectors should also be similar. In addition, after scaling the HXD and HXI detectors with their corresponding thicknesses (0.2 and 0.05 cm, respectively), we find that the background of the HXD Si detector at 10 to 20 keV ($\sim 2\times {10}^{-4}\text{counts}{\mathrm{s}}^{-1}{\mathrm{keV}}^{-1}{\mathrm{cm}}^{-2}/0.2\mathrm{cm}\simeq 1\times {10}^{-3}\text{counts}{\mathrm{s}}^{-1}{\mathrm{keV}}^{-1}{\mathrm{cm}}^{-3}$) is consistent with that of the middle-layer DSSDs in HXI ($\sim 3\times {10}^{-5}\text{counts}{\mathrm{s}}^{-1}{\mathrm{keV}}^{-1}{\mathrm{cm}}^{-2}/0.05\mathrm{cm}\simeq 0.6\times {10}^{-3}\text{counts}{\mathrm{s}}^{-1}{\mathrm{keV}}^{-1}{\mathrm{cm}}^{-3}$) within a factor of two. In the case of the HXD Si detector, the background is thought to be dominated by albedo neutrons.^9,10 One of the supporting evidences is that it shows an anticorrelation with the cut-off rigidity. In other words, the background of the HXD Si detector is higher at the locations with lower cut-off rigidity. Since the cut-off rigidity is a parameter describing the geomagnetic shielding from the cosmic-ray particles, the lower cut-off rigidity means that there are a lot of cosmic-ray particles and their secondary particles such as albedo neutrons. As shown in Fig. 3(b), the middle-layer DSSDs in HXI also have such a property. Therefore, similar to the HXD Si detector, the background of the middle-layer DSSDs in HXI should also be dominated by albedo neutrons.

2.3.

Proton-Induced Radioactivation Background in the CdTe-DSD

Unlike the featureless spectrum of DSSDs, the background spectrum of CdTe-DSD (layer 4; green triangle in Fig. 2) is composed of many emission lines. Most of these lines originate from the radioactive isotopes arising from the activation of Cd and Te, induced by geomagnetically trapped protons in the South Atlantic Anomaly (SAA). Although this effect is inevitable, it is mitigated by the thick BGO shields with a typical thickness of $\sim 3\mathrm{cm}$, which stop protons with energies $\lesssim 100\mathrm{MeV}$.

The background of irradiated CdTe-DSD was thoroughly investigated with Monte Carlo simulations in our previous work.⁴ In that paper, we successfully reproduced the observed background of CdTe-DSD with the simulations, and revealed that it is dominated by the proton-induced radioactivation of the CdTe-DSD itself.

3.1.

Radiation Environment

The radiation environment assumed in this work is shown in Fig. 4. It is composed of albedo neutrons, geomagnetically trapped protons, low-energy electrons, cosmic x-rays, and albedo gamma-rays. The flux and spectral shapes of albedo neutrons, cosmic x-rays, and albedo gamma-rays were based on our previous study.¹⁰ Geomagnetically trapped protons were obtained from the Space Environment Information System (SPENVIS)¹⁶ AP-8 model at solar minimum.

Fig. 4

Radiation environment spectral model of the Monte Carlo simulations.

The spectral shape of the low-energy electrons was also obtained from the SPENVIS AE-8 model, but its flux was estimated from the observed trigger rate of the top-layer DSSD. Since we eliminated the SAA and the other high flux regions in the analysis (see Hagino et al. ¹⁵ for more details), the electron flux averaged over all the orbital phase obtained from AE-8 is an overestimation. Although the orbital dependence of the electron flux is implemented in the AE-8 model, the lower flux region included in our analysis is not fully reproduced in the model. Thus, we scale the AE-8 flux by a ratio of the observed trigger rate in the low flux region to the orbit-averaged trigger rate. The scaling factor is estimated to be $4.2\times {10}^{-4}$ to $6.7\times {10}^{-4}$. In the trapped electron spectrum in Fig. 4, the upper limit of the scaling factor is adopted because it gives a simulated background spectrum that matches well with the observed spectrum. It is worth noting that these radiation models except for the low-energy electrons were not optimized for the observed data of the HXI.

3.2.

Comparison with the Observed Spectra

The simulated background spectrum of each layer is shown in Fig. 5. The observed background spectra are well reproduced by the Monte Carlo simulations with albedo neutrons, low-energy electrons, trapped protons, cosmic x-rays, albedo gamma rays, and radioactivation of CdTe and BGO. In all the layers, the difference between the simulation results and observations is less than a factor of two, except for the line-like feature at 8 keV in the top-layer DSSD (layer 0). Although the origin of this small excess is unclear, it is possibly due to the fluorescence x-ray of copper at 8 keV induced by the radiation environment in space. These x-rays might be emitted from materials that are not implemented in the simulation, such as the wire harness and/or the extensible optical bench. The other two lines at 10 to 12 keV in the top-layer DSSD are the fluorescence x-rays from the Cosmic X-ray Background (CXB) shield made of lead.

Fig. 5

Simulated background spectra of top-layer DSSD (layer 0), middle-layer DSSDs (layer 1 to 3), and CdTe-DSD (layer 4) of the HXI (red solid lines), compared with the observed data (black points). The dashed lines represent the contributions from each component. Albedo neutrons and low-energy electrons are not shown in the bottom panel (layer 4) because their contribution is negligible.

According to the simulations, the background spectra of the top-layer DSSD (layer 0), middle-layer DSSDs (layer 1 to 3), and CdTe-DSD (layer 4) are dominated by low-energy electrons, albedo neutrons, and proton-induced radioactivation, respectively. These results confirm the validity of the hypothesis based on the spectral features of observational data analysis in Sec. 2.

4.1.

Incident Path of Low-Energy Electrons

In Secs. 2 and 3, we showed that the low-energy electrons with energies of $\sim 100\mathrm{keV}$ are the major background component of the top-layer DSSD. However, electrons with energies of 100 keV are easily stopped by Si with a thickness of $100\mu \mathrm{m}$. These electrons cannot enter the DSSD directly because the HXI is designed to block all such direct paths. Therefore, to reduce the electron component, it is necessary to understand the incident path of the low-energy electrons.

Figure 6(a) shows the intersections of a vertical plane crossing the detector center ($X=0$) and the initial path of the low-energy electrons entering the top-layer DSSD. This plot shows the path of the low-energy electrons on the vertical plane $X=0$, assuming that the electrons do not change their direction before reaching this plane. From this figure, we can infer that most of the electrons hit the entrance window (EW; two layers of $30\text{-}\mu \mathrm{m}$-thick poly-carbonate sheets). It becomes more apparent if we see the intersections of the electron paths with a horizontal plane placed at the height of the EW [Fig. 6(b)]. According to this plot, almost all incident paths intersect with the EW. This indicates that most of the low-energy electrons are scattered at the EW and then enter the top-layer DSSD. Since the EW needs to be thin to avoid absorbing x-rays at 5 keV, it is impossible to block the low-energy electrons at the EW. Therefore, to reduce the electron background, it is important to reduce the number of electrons hitting the EW.

Fig. 6

Incident path of the low-energy electrons. (a) Intersections of the initial electron paths and a vertical plane ($X=0$). (b) Intersections of the initial electron paths and a horizontal plane at the height of the EW ($Z=36.1\mathrm{cm}$).

4.2.

Cutting Electron Component

To reduce the low-energy electron background, the EW should be shielded from the low-energy electrons. The shield should have a density thickness more than $\sim {10}^{-2}\mathrm{g}{\mathrm{cm}}^{-2}$, corresponding to the continuous slowing down range of $\sim 100\text{-}\mathrm{keV}$ electrons. If carbon fiber reinforced polymer (density $\sim 1.5\mathrm{g}{\mathrm{cm}}^{-3}$) is chosen as the electron shield, the required thickness is $<\sim 100\mu \mathrm{m}$. It is worth mentioning that adding such a shield will not increase the instrumental background since the material from which it is made does not activate. Therefore, this requirement is relatively easy to satisfy.

In addition to the thickness, the electron shield must cover a large solid angle of the sky when seen from the EW. Figure 7 shows the requirement of an opening solid angle of the shield calculated from the simulation data. In this calculation, the shield is assumed to have a circular hole just above the EW. The horizontal axis is the distance between the hole and EW. According to this figure, the solid angle of the hole seen from the EW should be smaller than 0.05, 0.01, and 0.005 sr to reduce the electron background by $1/10$, $1/30$, and $1/100$, respectively.

Fig. 7

Opening solid angle of the shield required to reduce the electron background by 1/10, 1/30, and 1/100. The required solid angle depends on the distance from the EW because the size of the EW is not negligible at small distances.

As a demonstration, we show the electron background spectrum of the top-layer DSSD with an appropriate shield in Fig. 8. The shield is assumed to cover almost all of the solid angle except for a circular hole with a diameter of 10 cm at 1 m above the EW, corresponding to the opening solid angle of $\sim 0.008$. Here, all the electrons coming from the solid angle covered by the shield are assumed to be completely blocked. Since such a shield can efficiently reduce the number of low-energy electrons from outside of the field of view, the electron background spectrum with the shield is nearly two orders of magnitude lower than that without the shield. Hence, as demonstrated, the electron background can be reduced in future missions if an appropriate shielding is applied.

Fig. 8

Simulated electron background spectrum of the top-layer DSSD with shield. With an appropriate shield, the electron background can be reduced. The large fluctuation in the simulated spectrum with shield is due to the Monte Carlo noise.

Although we showed that the electron background can be reduced by adding an appropriate shield to the HXI, this design is not necessarily the best one for all hard x-ray missions. The best design must depend on the scientific objectives and constraints on the satellite design. When designing a future mission, a detailed quantitative analysis of the relative merits and demerits of the various possible detector designs would be needed.