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Appendix C: Example of application to real data


C.1 Presentation of the data

The XMM/EPIC-MOS Flight Model 1 was calibrated at the Panter facility in January 1998 behind the XMM mirrors (Sembay 1998), giving data with the spatial distribution of a point source in flight. Several runs were performed with the aim of calibrating pile-up. I have used the data taken with the Fe L source at varying beam intensity (runs 01343 to 01346), and the night-long run at low intensity (01351), in full-frame mode. The centering was the same in all these runs.

The data was cleaned as thoroughly as possible of bad pixels and background (using energy selection). The observed pattern distribution (outside the core, in order to be free of pile-up contamination) was [0.8834, 0.1040, 0.0061, 0.0065]. Patterns more complicated than quadripixels were negligible. The idea is not here to analyse in any detail the data itself, but simply to illustrate the relevance of the model to real data.

C.2 Construction of the Point Spread Function

  This was not so easy for three reasons. Firstly there were clear deviations in the data from the ideal King profile. Secondly even the low intensity run could not be considered totally free of pile-up. Thirdly the number of counts in the wings of the low intensity run was inadequate to model the high intensity data. The problems were tackled in the following way:

C.3 Model comparison with piled-up data

The comparison was performed for monopixels only. The events from runs 01343 to 01346 were projected onto an image and divided by the number of frames. The spatial domain was limited to a window of $201 \times 201$ pixels centered on the maximum. For each run Eq. (6) was solved for the incoming flux $\Lambda$ in the window, using the PSF constructed as described in C.2. Then the radial profiles, and profiles projected onto the X and Y axes, were compared with those expected from the pile-up model applied locally.

The comparison was fully satisfactory. It indicated that the fit was significantly better when one used Eqs. (9) than (2), and Fig. C1, illustrating the comparison, was obtained using (9). It is not clear, however, whether the improvement is due to the fact that even for XMM/EPIC-MOS the pixels are not small enough to allow using (2) with a high precision, or that the statistical fluctuations in the model PSF lead to the wrong pile-up corrections (as described in C.2). Data with higher statistical significance in the PSF core would be required to decide.

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