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Spectral Response Matrix


G. Fraser [Fraser1992] has analyzed the on-axis ground based data by fitting Pearson functions to the 7 pulse height distributions shown in Fig. 5.16. A detailed analysis of his results are given in his report. The relative FWHM of the fitted pulse height distributions vary from 66% (for the Al-K and Fe-K lines) to 107%(for the B-K line).    Fraser concludes that ``the average pulse height per pixel has very little dynamic range and is a very poor indicator of photon energy''. However, he also notes that ``the softness ratio, (counts in channels 1-5)/(counts in channels 6-11), used by [Wilson et al.1992] does seem the most sensitive energy indicator that can be constructed.'' (As noted below, the actual channels fulfilling this purpose will change as a function of the temporally-dependent gain.)

Figure 5.17: The spatial variation in the centroid of the pulse height distribution in the ground based Cu(0.93 keV) flat field image. The image was first blocked by a factor of 64, producing 32'' pixels with 1% statistical errors. The contours are at PHA values of 4.0, 4.25, 4.5, 5.0, 5.5, 6.0, 7.0 and increase outward.

Figure 5.18: PVC phase observations of HZ 43 and AR Lac were taken at many positions on the detector surface. The observed mean PHA of the calibration source measurements are plotted with errors against the expected mean PHA from the ground based measurements of copper (0.93 keV). The line represents the best least squares fit of the data points.

Figure 5.19: The pulse height distribution in 3 HRI observations of N132D. The highest gain observation (solid line) was taken during the PVC phase, the lowest gain observation was taken in 1993 April, and the observation shown in the dot-dash line was taken in 1994 July, just after the HV increase. Also shown (dashed lines) are the pulse height distributions of the Al-K (1.49 keV) and B-K (0.18 keV) lines obtained during the ground based tests. Although the total count rate (in all PHA channels) has remained nearly constant (see Tab. 5.4), the earlier observations show a downward trend in the peak of the distribution. The latest observation shows that the HV increase has restored the peak to within 0.5 channels of the original.

Using the ground-based data (see Fig. 5.16) we constructed a spectral redistribution matrix for the HRI. We then fit the pulse height distributions of several observations of HZ 43 and one observation of 3C273. PSPC spectra of HZ 43 are well fit with an unabsorbed black body spectrum with a temperature of 0.02keV ( tex2html_wrap_inline17503 for 24 degrees of freedom). Table 5.8 lists the tex2html_wrap_inline17505 values obtained by fitting the HRI observations of HZ 43 with the same unabsorbed black body spectrum, with only the normalization treated as a free parameter. The minimum tex2html_wrap_inline17507 values are extremely high no matter what PHA channels are included in the fit. The best fit absorbed power-law model to the PSPC spectrum of 3C273 is obtained with tex2html_wrap_inline17509  cm tex2html_wrap_inline17511 and an energy index of tex2html_wrap_inline17513 . Since the HRI observation of 3C273 has 30,000 net counts we fit the HRI spectra with 0, 2, and 5% systematic errors, added in quadrature with the statistical errors.   Table 5.9 lists the minimum tex2html_wrap_inline17515 values obtained by fitting the HRI\ observation of 3C273 with tex2html_wrap_inline17517 and tex2html_wrap_inline17519 fixed. We also fit the HRI pulse height distribution treating tex2html_wrap_inline17521 as a free parameter. The best fit energy index so obtained for 3C273 is significantly steeper than that obtained from the PSPC observation.

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