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|E||% photons outside|
|(keV)||a 10'' radius|
Figure 5.1: The point spread function from a long exposure of HZ 43. The surface brightness is in units of counts per pixel. To improve the statistics, the data were binned in increasingly larger annuli (0.5, 1, 2, 4, 10, and 60 arc seconds). The dashed line is the background rate in this observation determined between 8' and 12' off-axis. Also shown is the parametric form for the PSF.
Although the XRT PSF has a central core with a FWHM of 3'' (as determined by ground test), microroughness in the mirror surfaces leads to a slight but measurable scattering of X-rays and produces a small energy-dependent tail or wing in the PSF. As determined by ground test measurements, the fraction of imaged photons in the tail (beyond 10'') of the image of a point source is given in Tab. 5.2.
The HRI PSF has a central core with a FWHM of 1.7'' (as determined in the laboratory). In the absence of the electrostatic shield, the PSF has a near-Gaussian shape, but the electrostatic shield (introduced to reduce the background count rate) has broadened the PSF, creating a so-called ``halo''. X-rays interacting in the interchannel web in front of the MCPs produce electrons that are ``captured'' in microchannel pores a considerable distance from the initial event site, initiating an electron avalanche leading to a false position. Although the region between the shield and the MCP is, to first order, field free, fringe electrostatic fields deflect the web electrons back into the MCP. The magnitude of the effect is predicted to decrease with increasing energy, whereas mirror scattering increases with energy.
The in-flight, on-axis PSF, which includes aspect solution effects, has been determined from a 9.1 ksec exposure of HZ 43 which yielded 109,000 net counts. Figure 5.1 shows the azimuthally averaged surface brightness profile of this observation. The HRI halo is obvious in Fig. 5.1 and dominates the PSF beyond approximately 15''. The solid curve is a parametric representation of the in-flight, on-axis, PSF and consists of the sum of two Gaussians and an exponential. This functional form for the azimuthally averaged PSF, provides a good description of the PSF out to a radius of 2', and is given by:
where the radial distance, R, is in arc seconds, and:
|A = 0.9638||S = 2.1858 arcsec|
|A = 0.1798||S = 4.0419 arcsec|
|A = 0.00090||S = 31.69 arcsec|
Figure 5.2: A comparison of the point spread functions of HZ 43, LMC X-1, and AR Lac with arbitrary normalization. To improve the statistics, the data were binned in increasingly larger annuli (0.5, 1, 2, 5, 10, and 30 arc seconds). Also shown is the parametric form for the PSF normalized to the AR Lac observation.
Figure 5.3: The on-axis encircled energy function from a long exposure of HZ 43. The profile has been normalized to unity at 8'. This figure shows that approximately 15% of the power is scattered beyond 10'', 7% is scattered beyond 1', and less than 1% is scattered beyond 5'.
Figure 5.4: A comparison of the on-axis encircled energy functions for observations of HZ 43, LMC X-1, and AR Lac. Some extended emission is evident in the profile of LMC X-1. The error bars shown in the figure were all evaluated at 1', but were offset slightly on the graph for clarity.
Note the arbitrary normalization of the above expression for the azimuthally-averaged surface brightness. Figure 5.1 shows that there is an additional component in the PSF beyond 2', but this component will be well below the background in most observations. We have not fit this additional component, since we do not know at present how strongly it depends on energy.
The azimuthally averaged surface brightness for on-axis observation of HZ 43, AR Lac and LMC X-1 is shown in Figure 5.2. Since these sources represent a wide range of mean X-ray energies, this figure demonstrates that the combined PSF (HRI/XRT) is largely energy independent within 2'.
The integrated surface brightness (encircled energy function) for the long HZ 43 observation is shown in Figure 5.3. The extended HRI halo is evident in this figure and shows that approximately 15% of the total power is scattered beyond 10'', 7% beyond 1', and less than 1% beyond 5'. Figure 5.4 shows the encircled energy function for HZ 43, Ar Lac, and LMC X-1. This figure shows that the encircled energy function is consistent within the statistical errors for these three sources, and is not strongly dependent on the photon energy.
Figure 5.5: The best fit values of and to a sample of point sources observed nearly on-axis (within 3'). The pair of values in the on-axis PSF given above is shown as an open square. Observations of the meaty source are indicated by open circles.
Figure 5.6: Comparison of several nearly on-axis (within a few arc minutes) HRI images of point sources. While the core of the images are symmetrical, the surface brightness between 5'' - 8'' can exhibit some asymmetry. This feature is randomly oriented (i.e., it is not in the direction of the wobble) and depends on the date of the observation. The three images at the bottom of the figure show the WFC ``meaty'' source observed at three different times. Notice that the asymmetry is present in the first and last observation, but not in the intermediate observation.
The on-axis PSF given above is based on a single long observation of HZ 43 with excellent photon statistics. Such an observation is required in order to accurately parameterize the HRI halo. We have also looked at a number of shorter (nearly on-axis) observations of HZ 43, AR Lac, LMC X-1, and the meaty source taken throughout the mission in order to determine the reproducibility of the on-axis PSF. In general, there is no difference (within the statistics) beyond 10''. This indicates that the HRI halo is stable and approximately energy independent. However, due to random errors in the aspect solution, the width of the core of the HRI images can vary. Fitting the above functional formof the PSF to this sample (treating the width and normalizations of the two gaussians as free parameters) shows that the best fit value of varies from 1.9'' to 2.5'', and the best fit value of varies from 3.5'' to 4.1'' (see Figure 5.5). Variations in and between observations of the same source (eg. the meaty source) span almost the entire range of values shown in Figure 5.5.
Residual errors in the aspect solution also occasionally produce asymmetrical features in the PSF. Figure 5.6 displays images of the so-called ``meaty source'' (a white dwarf star newly discovered with the WFC) illustrating the inner core's appearance when the aspect solution is correct and when there are errors leading to an ellipsoidal image. The major axis of the ellipsoidal images are not aligned with the wobble direction. The asymmetry is the strongest between 5'' and 10'' from the centroid of the image and can have amplitudes up to 30%. When possible, the user should use the image of a known point source within 5' of their target as a template for the HRI PSF.
The actual two-dimensional PSF has a 16-fold-symmetrical pattern (``radial spokes'') caused by the shadowing of mirror-scattered X-rays by the mirror-support structure, as well as an ellipsoidal component due to an imperfect aspect solution. The radial spokes should only appear in images with large numbers of detected photons in observations which are not ``wobbled''.
Figure 5.7: HRI images of HZ 43 at nine different angles off-axis.
Figure 5.8: HRI images of LMC X-1 at nine different angles off-axis.