Simulation Results

Photons were generated using the MARX [Wise et al.1997] package and Monte-Carlo simulations of the CCD physics were performed by software developed at Penn State. In order to meet the schedule for this report, these simulations had to be performed using MARX version 2.04, which uses PSF models which are known to differ significantly from the measured AXAF PSF. Thus, this work should be considered as a demonstration of an idea rather than as a calibrated recipe for pileup mitigation in ACIS. The ACIS team will repeat this analysis using a proper HRMA simulation when the corrected MARX version becomes available.

The relative motion that will occur between ACIS and the sky (``dither'' [ASC1997]) and the expected error in measuring that motion (aspect error^6.2) are simulated. Events with grade 255 are discarded^6.3. Each simulated event list contained $\sim 0.067$ detected events. For each of the three energies, the following eight simulations were performed:

• A Reference Simulation put exactly one photon on the CCD per frame, representing the behavior of the system with no pile-up (very low flux).
• A base flux level, F_B, which produced detected events per frame was determined empirically.
• With photons allowed to arrive randomly, seven simulations were run at the following flux levels: .

The width of the spectral line was measured in each reference event list: 20eV (O-K$\alpha$), 30eV (Al-K$\alpha$), 70eV (Cu-K$\alpha$). The event lists were filtered to extract those events which fell within  of the line peak and which had grades normally considered acceptable (ASCA grades 02346), producing eight in-band event lists. Each of these was then spatially filtered using various circular masks centered on the source, producing a large set of in-band event lists which explore the (flux, exclusion radius) parameter space. The fraction of photons detected in-band was calculated for each event list and those data are shown in Figure 6.42. The curves plainly demonstrate that many in-band events are lost at high fluxes when no masking is done (exclusion radius = 0) but that, for a given flux level, if you increase the exclusion radius you can approach the results of the reference simulation, i.e. reduce pile-up. The overall differences in the range of the Y axes and shape of the curves between the three energies reflects the energy dependence of the ACIS quantum efficiency and AXAF PSF size.

To quantify the reduction in pile-up effects that can be achieved by discarding events, a measure of pile-up effects is needed. Here, we concentrate on quantifying the spectral distortion effect remaining after an event list has been spatially masked by defining a ``quality'' metric in an obvious way: The ``quality'', Q, of an event list that has been filtered (e.g. by grade, spatial mask, etc.) is defined to be the number of events remaining divided by the number of events that would remain if the same photons had arrived at a very low rate (no pile-up) and the resulting events had been filtered in the same way. In our context, Q is the number of in-band events divided by the number of in-band events produced by a reference simulation (one photon per frame) that used the same number of incident photons. In Figure 6.42 dividing each of the seven curves by the reference curve (solid line) produces a plot of Q versus exclusion radius. For this study, we arbitrarily adopt a quality goal of 0.90 and plot the exclusion radius required to achieve this goal versus the relative flux level in Figure 6.43-left.
 
 

Figure 6.42:  In-band events with PSF core excluded for eight flux conditions.
The Base Flux level produced ~ 0.067 detected events per frame.

 

Figure 6.43:  Core masking (left) and efficiency reduction (right) required to achieve quality metric,  of 0.90.

 
 

If the exclusion radii shown in Figure 6.43-left are applied, then the quantum efficiency of ACIS will, of course, be reduced. The relative efficiency of the masked ACIS compared to a hypothetical ACIS that suffered no pile-up effects is shown in Figure 6.43-right. These values were determined empirically by computing the fraction of events from the Reference Simulation that survived the appropriate mask. An equivalent way to compute the relative efficiency would be to blur the AXAF mirror point spread function to account for aspect errors, then integrate the resulting PSF outside the exclusion radius. Figure 6.44 shows the results of applying the masking technique to the three most piled-up simulations (X 64 flux level).
 

Figure 6.44:  Grade-filtered piled-up spectra (X 64 flux level) shown both
with no masking, and with masking that achieves a quality level of 0.90.