XRT Status Report: Improvements of Ray Tracing Program
H. Kunieda, A. Furuzawa, M. Watanabe and the XRT Team
Several ways to analyze image data have been studied. One ideal way is the ray tracing program. The earlier version is not sufficient to reproduce the observed X-ray images accurately. The long exposure of Cyg X-1 observations provides us with high quality data to compare these programs. In this memo, we would like to report a recent effort to improve the ray tracing program. The introduction of broad tails at the ends of quadrants into the new version of ray tracing program gives much better fidelity in both PSF/EEF and azimuthal distributions. Stray light is also reproduced with certain accuracy. The long exposure Crab data also allow us to make fine tunings of the energy response. Though those processes are still on-going, the ray tracing program is becoming ready to be released to all users within a month or so.
1. Ray Tracing Program
Based on the pre-flight X-ray measurements of ASCA XRT, the ray tracing program has been developed by Nagoya group. It has been tested and compared with data by the XRT team and some collaborators. There are several problems and discrepancies have been reported. Some have been corrected and some are now being fixed.
The difficulties result from the extended profile at every 90 degrees of images, so-called "horns" at the ends of quadrants. As the first step, we only gave the radial distribution of flux averaged over the azimuthal angles. However, azimuthal information becomes necessary to examine asymmetry of diffuse sources such as clusters of galaxies. Since we know the foils in each quadrant have free ends and the images at these ends are much broader than other part of the mirror, a larger broadening parameter is given to the end sectors of quadrants, based on the data from 3C273 and GROJ1008. The off-axis angles of observations are summarized.
Qualitative comparison is possible in Figure 1a, 1b and 1c, where we show the observed Cyg X-1 images (P 0) and the ray traced images with/without "horns".
The quantitative comparison of PSF/EEF's from ray tracings and the Cyg X-1 data is shown in the next section. The radial profile at both ends and the middle part of quadrants are demonstrated in section 3.
2. Point Spread Function and Encircled Energy Function
2.1 Observed PSF of GROJ 1008 compared with Ray Tracings
The additional parameter (energy independent) for the ends was tuned for the GIS-2 X-ray images from GROJ1008, which was observed at the closest position to the optical axis. The point spread functions (PSF), flux density on the focal plane averaged over the azimuthal angles, are plotted against the angle from the image center. Figure 2a shows PSF for 2-6 keV band, and Figure 2b for 6-12 keV band. Crosses are the observed Cyg X-1 data and dashed lines are the ray tracing results.
|GROJ1008 g2 (2-6 keV)||GROJ1008 g2 (6-12 keV)|
The largest discrepancy of 10-20% is found near the center where the observed data exhibits dull and broad cores for almost all energies. It may be due to some mis-alignment of four quadrants. Ray tracing results are very similar to the data up to 20 arcmin radius with an accuracy of 20%.
2.2 Cyg X-1 (position 0)
The PSF of GIS-2 in 2-6 keV is shown in Figure 3a and that in 6-12 keV in Figure 3b ([[theta]]GIS2=8.1'). A difference of 10-20% is seen for r > 15 arcmin where the flux is 3.5 orders of magnitude less than the peak in both cases.
|Cyg X-1 P0 GIS2 (2-6 keV)||Cyg X-1 P0 GIS2 (6-12 keV)|
PSF's of GIS-3 in 2-6 and 6-12 keV are shown in Figures 4a and 4b ([[theta]]GIS3)=5.8'), respectively.
|Cyg X-1 P0 GIS3 (2-6 keV)||Cyg X-1 P0 GIS3 (6-12 keV)|
Ray tracing results are almost identical to the observed almost everywhere with an accuracy of 10% in both energy ranges.
2.3 Cyg X-1 (position 4)
PSF's of GIS-2 in 2-6 and 6-12 keV are shown in Figures 5a and 5b ([[theta]]GIS3)=17.0'), respectively.
|Cyg X-1 P4 GIS2 (2-6 keV)||Cyg X-1 P4 GIS2 (6-12 keV)|
PSF's of GIS-3 in 2-6 and 6-12 keV are shown in Figures 6a and 6b ([[theta]]GIS3)=12.8'), respectively.
|Cyg X-1 P4 GIS3 (2-6 keV)||Cyg X-1 P4 GIS3 (6-12 keV)|
In both telescopes, 10-20% systematic excess is clear at radii larger than 15 arcmin in low energies, while it becomes as large as 40-50% in 6-12 keV. Those excesses are all at the level of 1/1000 of the peak flux. It is more prominent for higher energies and larger off-axis angles.
In order to estimate the contribution of the systematic excess at larger angles found in Figures 5 and 6, an encircled energy function (EEF) is plotted against the radius normalized at 6 arcmin in Figures 7a and 7b for 2-6 keV and 6-12 keV, respectively. The deficit of ray tracing EEF from Cyg X-1 data at 15' is 1% for 2-6 keV and 2.1% for 6-12 keV. It becomes most prominent for the source off axis angle of 17' in the energy range 6-12 keV. The predicted EEF by the ray tracing program is 3.8% less than the Cyg X-1 data at radius of 15'.
3. Azimuthal Dependence of Radial Profile
Radial distributions are plotted for the middle and ends of quadrants, in order to demonstrate the accuracy of the reproduction.
3.1 Cyg X-1 (Position 0)
In Figures 8a, 8b, and 8c, flux density (2-6 keV band) is plotted against the radii for the ends (a, c) and middle (b) of a quadrant.
Another quadrant shows distribution shown in Figures 9a, 9b, 9c.
|90-105deg. (2-6 keV)||105-165deg. (2-6 keV)||165-180deg. (2-6 keV)|
The distributions by ray tracings are close to those of Cyg data within 20-30%. It has to be pointed out that the characteristic shapes of individual quadrants are recognized at the ends and sometimes even in the middle part of quadrants. The deviations are also 20% or so. Since such deviations are common for all energy bands, they are due to the mis-alignment of foils of each quadrant.
4. Stray Light
The ray tracing program is crucial for the estimation of the stray light effect on the CXB and largely extended clusters. The Crab observation on April 6, 1993 at an off axis angle of about 1 degree provides an image of stray light (Figure 10a) to be compared with ray tracing(Figure 10b) in all energy band for GIS-2.
|GIS2 simulation||GIS2 Crab data|
The pattern and flux are almost identical, though it is shifted by a few arcmin. If an extended bright source is placed out of the field of view, the contribution on the detector is well reproduced. However, the flux distribution due to a bright point source out of the field of view may have systematic errors of 30-50% in the worst case. If it is necessary to detect a faint source embedded in the stray light pattern, the ray traced results have to be shifted.
5. Energy Response
The basic idea in the energy calibration of XRT in orbit is to adjust the response, actually the optical constants, so that the high quality Crab spectrum can be explained by the nominal spectrum known so far. Since the GIS energy response is assumed to be relatively stable, we have started from GIS Crab data to tune the optical constants. At this moment, there is still some discrepancy around several keV, which is close to the boundary of previous tunings. Among the optical constants in this energy range [[beta]] is reliable, while d has ambiguities. ([[beta]] and d are refractive-index decrements.) The goal of error is 5% at any energy. The discrepancy at this moment appears at 5 keV and is being corrected.
6. How to Use the Ray Tracing Program
The input parameters are essentially photon energy, incident position and photon vector. The output is the position of the photon on the focal plane. If the photon energy and incident vectors are distributed according to the real astrophysical objects, the expected image and spectrum can be reproduced. It will be released with instructions, remarks, sample programs and their results. Earliest possible release will be July 1995. The old version of the ray tracing program has been tested in a frame work of SimASCA (see the report on "Extended Source Analysis with ASCA" in this ASCANews; in the chapter "Extended Source Analysis," section 1 ).
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