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Generation of Gain-Corrected "PI" bins

The Einstein Observatory was a satellite-based imaging X-ray telescope with sensitivity over the 0.2-3.5 keV energy range which operated from November 1978 to April 1981. Einstein had two associated imaging instruments located at the focal plane: the High Resolution Imager (HRI) and the Image Proportional Counter (IPC). The IPC has significant spectral response, that is the size of the pulse resulting from an incoming X-ray is proportional to the X-ray energy. After launch it was discovered that this constant of proportionality (i.e., the gain) varied both temporally and spatially. In order to remove the effects of variable gain, each photon is assigned a pulse height invariant (PI) value. By comparing the PI bins of photons, one can measure spectral variation in X-ray sources directly from processed data without doing spectral fits and free from the effects of variable gain. We have recently improved the method by which PI bins are assigned. In this article we describe the improved method, and show that use of the revised PI bins can lead to significantly better results.

To understand the nature of the improvement, we first need to review how a PI bin is assigned to a given photon. The spatial variation of the IPC gain was measured on the ground and the resulting image is known as the DGNI (Diffuse Gain Normalization Image). The temporal variations of the IPC gain were monitored by several on-board calibrators, most notably an aluminum line at 1.49 keV. The fundamental measure of the temporal gain is the BAL (Bin of ALuminum). This is the PH channel of the aluminum calibration source. The PI bin assigned to an incoming photon is therefore determined by its position in the detector (and hence its position on the DGNI) and the temporal BAL. Older versions of the Rev 1B processing system used sky coordinates rather than detector coordinates when accessing the DGNI resulting in erroneous spatial gain corrections. Significant improvements in the PI spectrum could be expected for sources which occur at a location on the detector where the DGNI has a value far from the average. This is how the error was first unearthed -- a source occurring at such a "hot spot" had a PI spectrum inconsistent with its fitted spectrum.

The improved PI binning algorithm has now been applied to all the standard IPC screened data and this data was released on the recent IPC Event List CD-ROMs. It is worth noting that spectral fitting involving PHA bins (for example fits made with PROS, XSPEC, and FINSPEC) are unaffected.

Improvements in Hardness Ratio

In order to obtain an idea of the effect of the improved PI bins we measured the hardness ratios of 100 sources with corrected and uncorrected data. The hardness ratio is a measure of the spectral slope of a source, and since it is calculated in terms of PI channels, it is sensitive to improved PI binning. It is defined in terms of the "soft" and "hard" PI bands as:

                        (1)

where PI is the number of counts in a standard circle radius 3 arcminutes minus the normalized background. The soft, hard and broad bands are defined as follows:

	BAND		PI BINS		ENERGY RANGE (keV)

	SOFT 		2-4 		0.2-0.8 
	HARD 		5-10 		0.8-3.5  
	BROAD		2-10 		0.2-3.5 

Results of Hardness Ratio Analysis

The results of this analysis are shown in Figures 1-3, which show the new hardness ratio using an improved PI spectrum plotted against the old hardness ratio, obtained from the old PI spectrum. Figure 1 shows data for all sources, while figures 2 and 3 show the data for the 50 medium and soft sources separately. It is clear that for most of the sources the hardness ratio does not change within the errors. Fifteen sources have new hardness ratios that are formally different from the old ones, and of those, two are more than three sigma away from the previous values. The Soft and Medium Surveys seem to be equally affected.

The effects of off-axis distance and roll angle on the change in hardness ratio are shown in Figures 4 and 5. Figure 4 shows the hardness ratio shift as a function of off-axis distance. The hardness ratio shift is defined as

              corrected hardness ratio - uncorrected hardness ratio        (2)
              -----------------------------------------------------
                                   error

From figure 4 it is clear that sources close to the center of the field (within approximately 10 pixels) do not have significantly improved hardness ratios. The scatter is larger further off-axis but there is no trend for the hardness ratio shift to increase with increasing off-axis distance. Figure 5 shows the hardness ratio shift as a function of roll angle. The spacecraft was constrained to have roll angles larger than 60 degrees to enable the solar panels to point toward the sun, so this region is blank in Figure 5. Figure 5 shows no evidence for a correlation between hardness ratio shift and roll angle, although the scatter may be smaller at smaller roll angle. These results may be understood with reference to the DGNI. The DGNI is relatively smooth with a few hot-spots. There are no spatial gradients that would introduce correlations between off-axis distance, roll angle and the hardness ratio shift. A significant hardness ratio shift may result if the sky and detector coordinates fall on two areas of the DGNI that have very different values. The scale of the change is a complicated function of the magnitude of the temporal BAL and the incident photon spectrum.

While these results are encouraging, the scope of this analysis was limited and users with specialized requirements may face further problems. For example, color ratios with narrower PI bands may provide more significant improvements and source detection on narrow PI bands may give improved results. However, it is clear that truly "pathological" sources are rare, and that the changes in the PI spectrum are smaller than the statistical errors for most sources.

Figure 1 Combined Soft and Medium Survey sources

Figure 2 Medium Survey sources

Figure 3 Soft sources

Figure 4 Off-axis distance (pixels)

Figure 5 Roll angle

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