Distribution of corrected flux at different offset angles, shown in Figure 4.8 , suggests that the accurate estimation of a flux of a point source in the FOV is possible by using the distribution of the count rate from individual PIN detectors, if the position of the sources is given. The flux, the height of the triangle, can be calculated by solving a simple linear equation which consists of position of the peak and leaning of the data points. The calculation is afford to say as a simple imaging with a large PSF of 33′ and small FOV of several squares of minutes. We have developed a method to estimate the flux of the source even if the FOV is filled with another uniform emission such as the diffuse emission of the Galactic center region. As a summary, the flux estimation method introduced here is to solve the linear equations explained above for the individual PINs. When the FOV is filled with an uniform emission, an equation is provided as follows;
F[i] =R[i]f+B, (4.2)
where F is a flux arrived at the surface of the PIN detector, R is angular response, i is PIN’s ID, f is expected flux in the case that the target exists in the direction of light axis and B is an uniform background emission. In this equation, known parameters are F[i] and R[i], while unknown parameters f and B. Since the number of the unknown parameters is two, we are able to obtain values of the variables as long as two individual equations of equation 4.2 from the observational results of two PINs’ are given.
Since statistics of the two PIN’s fluxes are usually not enough to calculate f of the target, we utilized equations obtained from summed data of 64 PINs. In order to obtain the most effective statics, we define an equation
near
∑
i
F[i]−
far
∑
i
F[i] =
near
∑
i
R[i]f−
far
∑
i
R[i]f, (4.3)
where ”near” and ”far” are groups of PINs whose light axes are nearer and farer from a direction of the target. The flux of the target is given as below equation,
f = (
near
∑
i
F[i]−
far
∑
i
F[i]) /(
near
∑
i
R[i]−
far
∑
i
R[i]). (4.4)
It is assumed that the uniform background emission is constant for the individual PINs.
An example of a correlation between R and counting rates of the individual PINs are shown in Figure 4.12. The figure was created by using the actual data of one of the Crab scanning observations. The sequence number of the observation is ”10007020” whose position to the Crab is (X,Y) = (+3.5’, 0′). The position is counter side of the light axis of HXD-PIN for the Crab. It is expected that we are able to clearly confirm the correlation between the ratio of the angular response and the actual counting rates using the data of the position, in which the lean of the function is constant and the statics of the counting rates is good. In the figure, the horizontal axis means the ratio of the angular response of the individual PINs to the targets in the FOV. Meanwhile, the vertical axis means the counting rates of the individual PINs corrected with the relative effective areas.
An energy range of the counting rates is 16−40 keV. We confirmed that there are clear correlations between the ratio and the counting rates.
In order to confirm if the method can be utilized realistically, we calculated estimation limits of this method. An uncertainty of the calculated flux is determined by statistics of the NXB and fluxes from the source. And then, the detection limits are defined by the significance for the statics of the NXB.
At the observation of ”10007020”, an expected counting rate of the NXB is 0.26 counts/sec in an energy range of 16–40 keV, for example. From the rate, counting rate of each PIN is calculated to 4 ×10−3 counts/sec/PIN roughly. We assumed this rate as the typical counting rates and calculated the limits of the flux estimation method. When an exposure of an observation is EXP sec, an integration of count of the NXB is equal to 4 ×10−3×EXP counts/PIN. At the equation 4.4, the flux of the source is calculated by the counting rate F from the target and the ratio of the angular response R. In the actual analysis, F is calculated by subtracting counting rate of the NXB from the detected counting rate. Therefore, statics ofF are determined by the statics of the NXB and counting rate form the target. And then, the statical uncertainty of the component in the equation, ∑
iF[i], is calculated by√
32×(4×10−3 ×EXP) = √
0.13×EXP since the number of the PIN is 32 for each group. And then, changed to a unit of counts/sec,
√0.13/EXP. Finally, the uncertainty of the estimated flux, ∆f, is calculated as follows,
∆f =√
2×0.13/EXP / (
near
∑
i
R[i]−
far
∑
i
R[i]). (4.5)
The ratioR is calculated for each position, and a map of ∆f calculated for each meshed position is shown in Figure 4.13. We created the figure assuming that the exposure is 40 ksec. The units of the map is ”mCrab” which is corresponds to 4.6×10−4counts/secin the energy range of 16–40 keV. In an observation of exposure of 40 ksec, the uncertainty at the most sensitive position is ∼ 1 mCrab at 1 σ significance. In this figure, the sensitivity in the center of FOV is worse since the difference of counting rates between two groups,(∑near
i F[i]−∑f ar
i F[i]), is smaller because of the rounding top of the angular
Figure 4.8: Reconstructed shape of the angular response with the Crab scan-ning observations.
response While, the sensitivity around the end is worse since the transmittance is small and then the static of the detected counting rate is not good.
Utilizing this method, we estimated the flux of the Crab using the results of the scanning observations listed in Table 4.1. Figure 4.14 shows the estimated fluxes of the Crab compared among the scanning observations for X and Y-axis. We confirmed that the fluxes are estimated adequately within statistical uncertainty. Since the direction of light axis of HXD-PIN is (X,Y) = (−4.03′,−0.06′) and the rounding top of the angular response is positioned at the direction, the uncertainty of the observation in (X,Y) = (−3.5′,0′) is worse.
Performing the flux estimation method every energy bin, we are able to obtain spec-trum of the target source. Figure 4.15 shows spectra of the Crab extracted with the estimation method and regular means from the observational data of ”100023020” whose nominal position of the satellite is XIS-nominal of (X, Y) = (0′,0′). The regular means is described in chapter 6. An energy response of the spectrum with the regular means is summed for 64 PINs. Meanwhile spectrum with the estimation method is defined as that of a PIN detector. Therefore we scaled the spectrum with the estimation method by 64 times. We have confirmed that the two spectra is consistent with each other and we are able to obtain even a energy spectrum with this method if the target is bright enough for a static.
Figure 4.9: Distribution of the relative effective area among PINs’.
Figure 4.10: Cross sections of the angular responses. The line is an actual shape and the dashed line is an ideal shape.
-40 -30 -20 -10 0 10 20 30 40 -40
-30 -20 -10 0 10 20 30 40
0 0.2 0.4 0.6 0.8 1
DET-X (ʼ)
D ET -Y (ʼ)
Figure 4.11: Actual angular response of the HXD-PIN which is summed up responses of 64 PINs’.
Near Far
Figure 4.12: Correlation between ARF and count rate. (100007020)
-40 -30 -20 -10 0 10 20 30 40 -40
-30 -20 -10 0 10 20 30 40
0 2.5 5 7.5 10
DET-X (ʼ)
DET-Y(ʼ)
mCrab
Figure 4.13: Detection limit of the simple imaging method with an exposure of 40 ksec.
Figure 4.14: Fluxes of the Crab estimated with the imaging method.
0.110.20.525
normalized counts/sec/keV
0.511.52 20
ratio
channel energy (keV)
Figure 4.15: Spectrum of the Crab estimated with the imaging method.
Chapter 5
Suzaku Observations
5.1 Overview
Since the launch of Suzaku in 2005, we have performed thirty five observations the Galac-tic Center region (|l| < 2◦.0,|b| < 0.5◦). Most of the observations were performed in 4 terms; from 2005-09-23 to 2005-10-12, from 2006-02-20 to 2006-03-01, from 2006-09-09 to 2006-10-12 and from 2007-03-03 to 2007-03-18. The first two terms were done in SWG (Science Working Group) phase and the last two were done in AO-1 (1st Announcement of Oppotunity) phase. Total net exposure is amount be ∼1 Msec . The details of the observations, exposures, dates and positions of the observations, is listed in table 5.1.
The position of each pointing is show in figure 5.1 as an exposure map of the XIS.