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Improved IPC PI-binning
and Hardness Ratios
A. Prestwich, J. McDowell and K. Manning
SAO/CfA
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
Fifty of the test sources were taken from the Medium Survey and 50 from the
Soft Survey. All sources were removed from each sequence in the sample and the
remaining photons used as background. This background was normalized by the
appropriate area and subtracted from source counts in the standard 3-arcminute
circle centered on the source. All of the data analysis (on both improved and
original data) was performed within PROS to avoid introducing numerical errors
from different software/hardware systems.
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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