2.5.4 Spectral Response Matrix

Using the ground-based data (see Figure 18) we constructed a spectral redistribution matrix for the HRI. The matrix is in OGIP FITS format, and can be used in XSPEC. We then fit the pulse height distributions of archival observations of HZ43 obtained between July 1990 and June 1992 and several observations of AR Lac. PSPC spectra of HZ43 are well fit with an unabsorbed blackbody spectrum with a temperature of 0.02 keV ($\chi^{2}_{}$ = 27 for 24 degrees of freedom). AR Lac PSPC data was fit by a Raymond-Smith plasma plus a powerlaw component (kT=0.87 and photon index 1.52). Table 7 lists the $\chi^{2}_{}$ values for selected observations with only the normalization treated as a free parameter. The minimum $\chi^{2}_{}$ values are extremely high because the instrument gain is different from the ground-based value.

To determine how well the ground-based response matrix can be corrected for the effect of spatial and temporal gain variations we repeated the fits to HZ43 and AR Lac, allowing the response matrix gain to change. This procedure involved fixing the input model source spectrum and allowing the response matrix to shift in channel space until a best fit was obtained ($\chi^{2}_{}$ was minimized; see Figure 23) The model normalization was also allowed to vary. These results are also shown in Table 7. Clearly, the fits are much improved. Figure 24 shows the response matrix shift (in channels) required to give a best fit plotted against the PHA maximum of the BE data at the time and position of the observation. There is a tight correlation between these two quantities, indicating that the BE data can be used to predict a response matrix gain shift. There is increasing scatter above a BE PHA maximum of $\sim$ 5. These points are all from observations > 8' offaxis, where the redistribution matrix changes. To obtain best results, only sources within 8' of the detector center should be used.

Work is in progress to provide these spectral capabilities to the community. Current plans involve a delivery to HEASARC by mid 1997.

  

Table 7: Spectral Fitting Results for HZ43

sequence	date	off-axis angle	$\chi^{2}_{}$	$\chi^{2}_{}$
		(arcmin)	ground-based	shifted
110196	7/2/90	1.7	247.3 (41.2)	4.420 (0.74)
110198	7/2/90	3.9	329.5 (54.9)	13.46 (2.24)
141809	12/11/91	1.3	28.94 (4.82)	3.99 (0.66)
110207B	03/07/90	10.3	302.1 (50.3)	9.15 (1.52)
110207A	03/07/90	10.3	1250 (208.3)	145.2 (24.2)

Note: A comparison of $\chi^{2}_{}$ values obtain by fitting selected HZ43 observations with the ground-based response matrix (column 4) and the response matrix shifted in channel space (column 5). Channels 4-10 were included in the fit, giving 6 degrees of freedom. The reduced $\chi^{2}_{}$ is shown in parentheses. The best fit is improved in all cases. The fit is still unacceptable more than $\sim$ 8' off-axis.

  

Figure 18: The pulse height distribution from ground-based measurements at 7 energies within a 1 ' x 5' strip centered on the detector. The dashed curve in the Boron panel is the PHA distribution of the Al data, and is included to show the full spectral range.

LINK TO POSTSCRIPT FILE for Figure 18

  

Figure 19: 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.

LINK TO POSTSCRIPT FILE for Figure 19

  

Figure 20: PCV phase observations of HZ43 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.

LINK TO POSTSCRIPT FILE for Figure 20

  

Figure 21: The pulse height distribution in 3 HRI observations of N132D. The highest gain observation (solid line) was taken during the PCV phase, the lowest gain observation was taken in April 1993, and the observation shown in the dot-dash line was taken in July 1994, 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 Table 3), 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.

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Figure 22: The temporal status of the mean PHA channel of N132D and the UV calibration lamp (a small area near the center of the detector). The mean PHA is plotted for many observations starting in July 1990 through April 1998. For N132D, the marker type specifies the high voltage level(HV).

LINK TO POSTSCRIPT FILE for Figure 22

  

Figure 23: The response matrix (solid line) convolved with a 0.02 keV blackbody shifted in channel space to give the best fit to an observation of HZ43 (crosses) in the top panel. The bottom panel displays the residuals.

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Figure 24: Response matrix shift (in channels) required to give a best fit plotted against the PHA maximum of the Bright Earth data for observations of two standards, AR Lac and HZ43.

LINK TO POSTSCRIPT FILE for Figure 24