Testing new LSF_PARMS/RMF products with MARX simulated dataset



So after months of the fitting experiment (esp. proper addition of pixel randomization effects onto the MARX simulated datasets), the new LSF_PARMS products have finally matured into something useful. Let us illustrate how well it works and where it may fail. Our current focus is on ACIS-S/HETG; LETG will come in future.





Case 1: Spectral extraction width = +/- 1.99e-3 degrees



For the first example, a mono-energetic MARX simulation with 200,000 photons is run at various energy values and then processed through non-default CIAO reduction mode (however the scale of pixel_randomization is kept to 0.5 pixels). [This was done so since I was not yet familiar with rebinning within ISIS and it was just much easier to extract spectra with smaller binning sizes for both HEG and MEG. If a coarse binning is chosen, I had a hard time centering the model line spread function profile (i.e., it seems off by +/-0.5 pixels which is NOT due to bad LSFs or software -- just user (Bish) problems).] Spectral extraction width is set to +/-1.99e-3 degrees, which corresponds to encircled energy fraction value (EE_FRACS) of 99.75% for MEG. At any rate, each simulation shown here is fairly representative of what users might face when analyzing their CHANDRA/HETG spectra.

Here are the results of spectral fitting at various input energy values. We load both RMF (generated with new LSF_PARMS products) and ARF; single delta function is fitted onto each line. When available, both HEG and MEG plots are shown right next to each other for comparison. ISIS is chosen to do this process since it is highly capable of handling a batch processing written in S-Lang (hence saving my time).



Figure 3a: MARX simulated line profile (HEG) at E = 7keV fitted with single delta function. The bottom panel shows a delta-Chi to illustrate the goodness of fit.


Figure 3b: MARX simulated line profile (HEG) at E = 6.5keV fitted with single delta function.


Figure 3c: MARX simulated line profile (HEG) at E = 6keV fitted with single delta function.


Figure 3d: MARX simulated line profile at E = 4keV fitted with single delta function.
Left: HEG; Right: MEG


Figure 3e: MARX simulated line profile at E = 3keV fitted with single delta function.
Left: HEG; Right: MEG


Figure 3f: MARX simulated line profile at E = 2.5keV fitted with single delta function.
Left: HEG; Right: MEG


Figure 3g: MARX simulated line profile at E = 2keV fitted with single delta function.
Left: HEG; Right: MEG


Figure 3h: MARX simulated line profile at E = 1.8keV fitted with single delta function.
Some problem with fitting is present around here. The cause is yet known at this point.
Left: HEG; Right: MEG


Figure 3i: MARX simulated line profile at E = 1.4keV fitted with single delta function.
Left: HEG; Right: MEG


Figure 3j: MARX simulated line profile at E = 1keV fitted with single delta function.
Left: HEG; Right: MEG


Figure 3k: MARX simulated line profile (MEG) at E = 0.8keV fitted with single delta function.









Case 2: Spectral extraction width = +/- 1.22e-4 degrees



We have repeated the same procedure with a different extraction width. At this time we set the extraction width to be +/-1.22e-4 degrees, which corresponds to the EE_FRACS value of 60% for MEG.



Figure 4a: MARX simulated line profile (HEG) at E = 7keV fitted with single delta function. The bottom panel shows a delta-Chi to illustrate the goodness of fit.


Figure 4b: MARX simulated line profile (HEG) at E = 6.5keV fitted with single delta function.


Figure 4c: MARX simulated line profile (HEG) at E = 6keV fitted with single delta function.


Figure 4d: MARX simulated line profile at E = 4keV fitted with single delta function.
Left: HEG; Right: MEG


Figure 4e: MARX simulated line profile at E = 3keV fitted with single delta function.
Left: HEG; Right: MEG


Figure 4f: MARX simulated line profile at E = 2.5keV fitted with single delta function.
Left: HEG; Right: MEG


Figure 4g: MARX simulated line profile at E = 2keV fitted with single delta function.
Left: HEG; Right: MEG


Figure 4h: MARX simulated line profile at E = 1.8keV fitted with single delta function.
Some problem with fitting is present around here. The cause is yet known at this point.
Left: HEG; Right: MEG


Figure 4i: MARX simulated line profile at E = 1.4keV fitted with single delta function.
Left: HEG; Right: MEG


Figure 4j: MARX simulated line profile at E = 1keV fitted with single delta function.
Left: HEG; Right: MEG


Figure 4k: MARX simulated line profile (MEG) at E = 0.8keV fitted with single delta function.




As shown in these figures,a single delta function -- wrapped with new LSF parameters -- can adequately describe instrumental line profile at various energy values. There are other extraction widths that I have tested in the same way. If you're interested, please download PS files from the link below:









Line flux estimate (consistency check)



Suppose a mono-energetic emission line is present in a spectrum. Then at any given extraction width, an estimated model line flux should give the same value (c.f., a sum of events in the extracted line should vary with the extraction width). For example, suppose there is a single emission line with the photon flux 0.001 photons/s/cm2. Now even if the extraction width is chosen to be either 0.0001 or 0.002 degrees, the estimated model line fluxes should be about 0.001 photons/s/cm2 in either case, give or take a small statistical error. If this is not the case, then we may have a problem with the tabulated value of encircled energy fraction (EE_FRACS).

Here we test the new LSF_PARMS products on this issue with MARX simulated datasets. We use the same datasets used to test the profile fitting. The input photon flux is set to be 0.001 photons/s/cm2 for each mono-energetic beam. Since MARX does not have the information on QEU, we expect some small systematic offset in the flux estimate at low or high-energy ends of the HETG spectra. And in two cases, the available datasets are plain inadequate to perform this test (namely, beams with E = 0.45 and 0.60keV for MEG). At any rate, the derived model line fluxes measured at various extraction widths (per mono-energetic beam) should be the same values.

Let us look at good examples first. At E = 1.4 keV and some other energies, we confirm that the line fluxes are estimated correctly at various extraction widths.



Figure 5a: Extraction width vs. estimated flux: HEG line spectrum at E = 1.4keV.


Figure 5b: Extraction width vs. estimated flux: MEG line spectrum at E = 1.4keV.





The dotted line shows the intrinsic line flux (0.001 photons/s/cm2) specified in our MARX simulations. Clearly all the data points scatter around the intrinsic flux, which is one of two important factors that validate the accuracy of the derived EE_FRACS. Furthermore, it is also important to note that the model line fluxes are more or less the same at any extraction width used for measurements. This is the second point to watch out when validating the EE_FRACS values.

Now let's look at somewhat bad examples.


Figure 5a: Extraction width vs. estimated flux: HEG line spectrum at E = 0.8keV.

Note in Figure 5a that the measured fluxes are always lower than the intrinsic value (0.001 photons/s/cm2). Even worse, the estimated flux values decline at the two smallest widths.

Upon double-checking, the author (Bish) found nothing particularly wrong with the initial measurements on encircled energy fraction at E = 0.8 keV. We can explain that the data-point with the smallest width is due to poor extrapolation of EE_FRACS value between the width = 0 to the minimum EE_FRACS value measured (= 0.000122 x 2 degrees) for HEG. This is one of the caveats analyzing line fluxes. (Practically no user can afford to extract spectra from 1 ACIS-S CCD pixel. If it's a bright X-ray source, then pile-up will be their first problem anyway. If someone manages to obtain 1 Mega-sec observing time on HR1099 or something, then the user may try to extract spectra from one pixel. Oh I dare someone to try and sell that to any TAC). In any case, the lack of QEU in MARX simulations does not seem to explain the fluxes being underestimated consistently (at this energy, the QEU may amount to (conservatively) about 7% of difference). Either we missed something in measuring EE_FRACS, or something happened in MARX simulation or through CIAO processing. We are currently looking at OSIP procedures and how QE accounts for fluorescent escapes.


[Note: when the total number of photons was increased to 2,000,000 in MARX simulation at this energy (0.8keV), this problem disappeared and the measured fluxes became consistent with what we expected. This statement holds up to 3keV or so. For any X-ray photons harder than that, the problem persists. The fluxes above 6 keV are generally underestimated by a whooping 15% (see Figure 5b), which is not acceptable. Again, it is not certain that this is due to bad EE_FRACS measurements. Investigation is still pending on this issue.]

Figure 5b: Extraction width vs. estimated flux: HEG line spectrum at E = 6.0keV.



We have done many other measurements like the examples above. For your viewing pleasure, you may view them by downloading the following PS file:









Evaluating the accuracy of wavelength estimate



This analysis is still preliminary.

All we have done is to derive the measured centroid wavelength values upon fitting and compare them with the actual values. The following two figures show the offset (measured - real) vs. wavelength plot for both HEG and MEG. To derive more realistic uncertainties from this kind of experiment, we should repeat this process many times with different ensembles, i.e., by running multiple MARX simulations (generated under the same condition), perform the fitting in the identical way, and then record the measured wavelength.


Figure 6a: The offset vs. wavelength for the case of HEG

Figure 6b: The offset vs. wavelength for the case of MEG


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This page was last updated Aug 13, 2002 by Bish K. Ishibashi. Accessibility To comment on it or the material presented here, send email to bish@space.mit.edu.