4.4 HXD-PIN Detector Response Matrix
4.4.2 Crab Nebula
The Crab nebula is the product of the supernova explosion occurred in 1054. The ex-plosion itself was historically observed optically by Chinese astronomers. In the X-ray region, Gursky et al. (1963) discovered the source. Currently, the Crab occupies an elliptical region of 180′′×120′′ in the optical while it is slightly smaller in the X-ray band.
Toor & Seward (1974) argued that the Crab can be interpreted as a constant intensity source, since most of the emission is from the diffuse part of the nebula rather than the
Figure 4.13: The geometry model of the PIN diode implemented insimHXD.
Each black number is the size in the unit of mm, and each red number indicates charge collection efficiency.
Figure 4.14: Spectral feature of the PIN diode. The spectrum was obtained in on-ground experiment when we irradiated the HXD with X-rays from 133Ba.
central pulser. The X-ray nebula is extended over a diameter of four light years, and hence the flux of the nebula should not vary on time scale shorter than a few years. Furthermore, the energy source of the emission is consistent with the spin-down luminosity of the central rotation neutron star, the Crab pulsar. For this reason and its brightness, the Crab nebula has been used as a calibration target for many X-ray/soft gamma-ray detectors.
The X-ray spectrum of the Crab is well reproduced with a simple absorbed power-law model. Kirsch et al. (2005) summarize the best-fit parameters obtained with various recent missions such as ASCA,XMM-Newton, RXTE, Beppo-SAX, etc. They also fitted all data simultaneously in various ranges. They obtained photon index of 2.12 when they fitted the data in an energy range of 10–50 keV, which almost completely covers the bandpass of HXD-PIN.
4.4.3 Response Matrix Generation
The response matrices of HXD-PIN are generated by using outputs from simHXD. If we input a number of photons with fixed energy into the detector model of simHXD, we can obtain probability distribution of output spectra for the relevant input energy.
Therefore, by inputing photons with energies fully covering the bandpass, we can obtain the response matrices of the PIN detectors.
One of the important factors for the response matrix is the thickness of the depletion layers of the PIN diodes. The first version of the response matrix were constructed using the model of the PIN diode shown in Figure 4.13 with a depletion layer thickness of 1.75 mm. The PIN diodes is so thick, ∼ 2.0 mm, that their full depletion needs a bias voltage around 700 V (Ota et al. 1999). At the nominal operation voltage of ∼ 500 V, the actual thickness of the depletion layer can vary among the 64 PINs.
We determined the depletion layer thickness was performed in the following two steps.
Firstly, we analyzed the Crab spectrum for its slope in an energy range of 50–70 keV, where the diode thickness has little effects on the energy dependence of the detection efficiency (see Figure 4.15). The slope is determined solely by the Crab’s slope and the energy dependence of the interaction cross-section of silicon. This analysis gives the Crab photon index of Γ = 2.12, consistent with the canonical value, indicating that the energy scales established in §4.1 are correct. Then, the overall 15–70 keV Crab spectra were fitted individually by a single power-law model, and the effective thickness were adjusted so that every PIN spectrum can be reproduced by the relevant photon index obtained at 50–70 keV band. Further fine tunings were introduced to properly model the shape of the efficiency decrease toward lower energies, which is mainly determined by the 64 analog LD levels.
By combining the 64 response matrices into a single one, 64 PIN summed spectra were collectively examined. Since there are two nominal positions, the XIS-nominal and the HXD-nominal, as nominal pointing modes of Suzaku (see §3.2), corresponding two response matrices were constructed (ae hxd pin[xi/hx]nom 20060814.rsp).
Two-Figure 4.15: Ratio of photoelectric absorption probability of 1.20 mm thick silicon to that of 1.75 mm thick silicon. This curve is constant within 1%
in an energy range of 50–70 keV even in this extreme case. The calculation was performed using the photon cross section database supplied by NIST (http://physics.nist.gov/PhysRefData/Xcom/xcom1.html).
dimensional image of the response matrix for the XIS-nominal position is shown in Fig-ure 4.16. Fitting of the Crab spectra were performed in an energy range of 12–70 keV using these response matrices. Figure 4.17 shows the spectra with the best-fit power-law models and the model parameters are summarized in Table 4.1. The spectra are well reproduced within a few % over the entire range used in the fitting, while the deviation becomes larger up to ∼10% around 10 keV, where the effective area is rapidly changing with the energy. There is also an artificial structure at around the characteristic energy of gadolinium, suggesting that the modeling of the effect of the active shields is yet to be optimized.
One of the characteristic of the Suzaku observatory is its wide-energy-band coverage by the combination of the XIS and the HXD. Therefore, it is also essential to confirm the calibration results of these two detector systems jointly. The in-orbit calibrations of XIS and XRT were extensively performed in parallel with those of the HXD. The details are reported in Koyama et al. (2007) and Serlemitsos et al. (2007). The two instruments have been independently calibrated, and no artificial “adjustment” has been performed. Even though the XIS and HXD always simultaneously observe the Crab nebula, individual spectral fittings result slight differences between individual best-fit parameters, on both the photon index and absolute flux at a level of ∼ 0.04 and ∼ 15%, respectively. As shown in Figure 4.18, the overall spectra can still be fitted with power-law models having a common photon index and different normalizations between the XIS and HXD-PIN.
Simultaneous fittings with a single power-law model give higher absolute fluxes from PIN diodes than those of the three FI chips of the XIS. The relative increase is ∼ 13%
Incident Photon Energy [keV]
10 20 30 40 50 60 70 80 90
PI [ch]
0 50 100 150 200 250
10-1
1 10
Figure 4.16: Two-dimensional image of response matrix of HXD-PIN.
Energy (keV)
Counts s-1 keV-1 Counts s-1 keV-1ratioratio
Energy (keV)
Figure 4.17: The HXD-PIN spectra of the Crab nebula obtained at the XIS-nominal (left) and the HXD-XIS-nominal (right) position, compared with predic-tions (red) by the best-fit power-law model of which the parameters are given in Table 4.1. The fitting was carried out in a range of 12–70 keV, and then remaining channels were retrieved. The lower panels are the data-to-model ratio.
Table 4.1: Best-fit parameters and 90% confidence errors for the spectra of the Crab nebulaa.
Target position Photon Index Normalizationb χ2ν (ν) XIS-nominalb 2.11±0.01 11.7±0.1 1.03 (152) HXD-nominalc 2.10±0.01 11.2±0.1 1.24 (152)
aThe fitted model is an absorbed power law with the column density for the interstellar absorption of 3×1021cm−2(fixed).
bPower-law normalization in a unit of photons cm−2s−1keV−1 at 1 keV.
cObservation performed on 2005 Sep.15 19:50–Sep.16 02:10 (UT).
dObservation performed on 2006 Apr.05 12:47–Apr.06 14:13 (UT).
as an issue to be further investigated.
Table 4.2: Best-fit parameters and 90% confidence errors for the spectra of the Crab Nebula at the XIS and the HXD-nominal positions.
Target position NHa Photon Index Normalizationb Constant Factorc XIS-nominald 0.32±0.01 2.10±0.01 10.0±0.1 1.13±0.01±0.02 HXD-nominale 0.30±0.01 2.09±0.01 9.5±0.1 1.15±0.01±0.02
aHydrogen column density in a unit of 1022 cm−2.
bPower-law normalization in a unit of photons cm−2s−1keV−1 at 1 keV.
cRelative normalization of PIN above XIS.
dObservation performed on 2005 Sep.15 19:50–Sep.16 02:10 (UT).
eObservation performed on 2005 Sep.15 14:00–19:50 (UT).
Energy (keV)
Counts s-1 keV-1 Counts s-1 keV-1
Energy (keV)
Figure 4.18: The background-subtracted Crab spectrum of XIS (summed over the three XIS-FIs) and PIN, compared with the best-fit ab-sorbed power-law model. An energy range of 1.7–1.9 keV is ex-cluded from the XIS spectra, due to large systematic uncertain-ties of the current response matrices (ae xi[023] 20060213.rmf and ae xi[023] [xis/hxd]nom6 20060615.arf).
4.4.4 Detector Response to Diffuse Emission
In the previous subsection, we have shown that the Crab spectra are well reproduced with the response matrices for both the XIS-nominal position and the HXD-nominal position. Here, we consider about the response of the HXD to diffuse emission. Below, we demonstrate that the spectral shape does not depend on the extent of the source, point-like or extended. It is important because the targets dealt within this thesis are diffuse sources.
The Crab Nebula was observed at various angles in August and September 2005 in order to determine the optical axis of each detector system. Here, these data are used to demonstrate observations and simulations give consistent results for a point source at various positions. Table 4.3 summarize the information about the Crab observations.
The positions of the Crab Nebula are expressed in the detector coordinate system of the XIS (the XIS-nominal position corresponds to (0′, 0′), and the HXD-nominal position corresponds to (−3′.5, 0′)). We simulated the spectra from all these observations with simHXD, assuming the best-fit model obtained for the HXD-nominal position (see Ta-ble 4.1 for the parameters). Figure 4.19 shows the observational spectrum, the simulated spectrum, and ratio of the two plotted in the range of 12–40 keV. Here are plotted only the data when the Crab is located at (0′, 20′). See Appendix A. As seen in this figure, the normalization and the spectral shape are consistent between the observations and the simulations.
Since the simHXD are shown to be accurate also for off-center sources, we then simulated a diffuse emission assuming the same power-law spectrum. We simulated the uniform emission radiating from the region of 2◦×2◦ centered on the optical axis of the HXD. Figure 4.20 shows the simulated spectra from a diffuse source (red) and a point source at the XIS-nominal position (black). This figure shows the spectral shape does not change even if we assume diffuse emission. The difference of the spectral shape is so small that it corresponds to the difference of photon index of 0.01 when fitted with a power-law model using the same response matrix. Thus, diffuse emission distribution does not cause any spectral steepening or flattening at least below 40 keV. This is reasonable because the fine collimators made of 50 µm thick phosphor bronze sheets are almost completely optically thick below 80 keV.
Based on the study above, we fit the HXD spectra with response matrix for a point source at the XIS-nominal position, ae hxd pinxinom 20060814.rsp, throughout this thesis. Only when absolute flux is needed, appropriate scaling is introduced considering expected emission distribution and the angular response of the HXD-PIN (see §5.5 and
§6.5).
Table 4.3: Summary of the Crab observations of various angles.
Obs. ID Angle of the Crab Date 100007010 (0′, 0′) 2005/08/22 100007020 (−10′, 0′) 2005/08/22 100007030 (+10′, 0′) 2005/08/22 100007040 (0′, + 10′) 2005/08/22 100007050 (0′, −10′) 2005/08/22 100010010 (−3′.5, 0′) 2005/08/24 100010020 (+3′.5, 0′) 2005/08/25 100010030 (−20′, 0′) 2005/08/25 100010040 (+20′, 0′) 2005/08/25 100010050 (0′, + 20′) 2005/08/25 100010060 (0′, + 3′.5) 2005/08/25 100010070 (0′, −3′.5) 2005/08/26 100010080 (−7′, 0′) 2005/08/26 100010100 (0′, −20′) 2005/08/26 100010120 (+7′, 0′) 2005/08/26 100010130 (0′, + 7′) 2005/08/27 100010140 (0′, −7′) 2005/08/27 100015010 (−4′.74, −0′.79) 2005/08/31 100015020 (−9′.74, −0′.79) 2005/08/31 100015030 (−0′.26, −0′.79) 2005/09/01 100015050 (−4′.74, + 4′.21) 2005/09/01 100015060 (−4′.74, −5′.79) 2005/09/02
Figure 4.19: The Crab spectra obtained from observations (black) and simu-lations (red) when the Crab is located at (0′, 20′). The lower panel shows the ratio of the observational data to the simulated data.
Figure 4.20: The simulated HXD-PIN spectra for a point source at the XIS-nominal position (black) and a uniformly diffuse source (red). The lower panel shows the ratio of the point source spectrum to the diffuse source spectrum.