Two-level (aka "Fluffy") Contamination Model

FAQs - February 2, 2004 - dd
What the heck is this all about?

The ACIS detector on the Chadra X-ray Observatory has a slowly growing layer of contamination on it. The contamination absorbs X-rays, especially lower energy ones. The absorption of X-rays at around 700 eV has been determined and monitored using an on-borad "External Calibration Source" or ECS. The time dependance of this absorption was fit with a simple analytical form by A. Tennant of Chandra Project Science group. The contaminant absorption can also be seen and measured by looking at the size of absorption edges in the spectra of bright continuum sources. A model and coresponding calibration file, number N0001, was constructed from these edge measurements by H. Marshall in the CXC Calibration group. The 'N0001 correction could be applied to an un-corrected arf using a piece of s/w called "contamarf", created by D. Huenemoerder of the CXC SDS group.

The edge-based model did a very good job over-all but predicted an absorption at ~700 eV that is not quite as much absorption as the ECS measurements indicate - an additional factor of about ~0.88 is needed in the 'N0001 edge model at ~700 eV at time 2002.82, the time of a very deep Markarian 421 observation.
How can this correction factor be included in a physical way while retaining the size of the well-modeled edges in the 'N0001 contamination file ?

Note that there are differences between these two contamination measurement methods: the ECS measures the absolute change in the QE of the system at ~700 eV, whereas the edge depths seen in high-resolution spectra are a relative measure or ratio of the QE above and below the edge, in particular the Carbon edge.

This work (linked below) shows that if the contamination layer is non-uniform in thickness or density by about a factor of two or three then it is possible to create a physical model that has the same edge structure and depths as the 'N0001 model and yet has an additional factor of ~0.88 absorption at ~700 eV. The model then predicts how this additional absorption factor will behave at other energies, see the green curve in the figure below.

Original 'N0001 model (black) and an example modified "two-level" model (red).
Their ratio is shown in green. The two-level model adds more
absorption at ~700 eV (specifically the blue vertical lines) while retaining
the same edge structure, shown by the smoothness of their ratio (green.)

Is there an easy way to understand the basic idea?

Yes, maybe...

We'd like to add thickness to the edge-based model in order to match the transmision at ~700 eV, but adding this thickness will make the Carbon edge (ratio) larger. If, however, we allow thin and thick regions in the contaminant then we have another two "knob"s to turn: an additional thickness and the filling-factor, or covering fraction, of the thick material. The depth of the carbon edge depends very much on the thickness of the thin, more transmissive, component whereas the absorption at ~700 eV depends more on the total amount of material in both thin and thick regions. In this way it is possible to match the transmission at ~700 eV while retaining the same Carbon edge depth.

How could we physically have different thicknesses of material?

Well, the contaminant could vary in thickness with position as, for examples, drops on a surface or ripples on sand, giving actual thickness differences with position...
Another realization would be to have varying density of the contaminant, e.g., a fluffy contaminant perhaps like frost in a freezer or the web of warm-hot matter in the universe(!) The result is that X-rays traveling through it see differences in column density by ~factor of two or more from location to location.

Has a similar model ever been used in the past?

"There are no new ideas [including this one.]" - Keith Arnaud.

Well, the "ice" model on the Einstein Solid State Spectrometer, SSS, was modelled as "made up of two thicknesses of granules or snow flakes" in a partial covering model like this one! They even got more complex with a four parameter two-kinds-of-clumps model, see:
"The Einstein Solid State Spectrometer Calibration"
by Christian, Swank, Szymkowiak, and White for some details. Of course we have mostly Carbon building up so it may not be as flaky as H2O building up... or more so?

Does this two-level model reconcile the ECS curvature with the linear edge-depth growth?

[ The tau (thickness) of contaminant at ~700 eV measured with the ECS is well fit to a step exponential-decay curve whereas the Carbon edge thickness has been fit with a straight line indicating constant thickness growth. ]

Answers: No. Perhaps. We'll see... Yes!

No: The two-level model itself does not introduce curvature in the ~700 eV tau value with time if the two-level thicknesses themselves grow linearly with time, so curvature is not automatically added due to the model per se.

Comparing tau at ~700 eV due to the 'N0001 model(green)
with the ECS best-fit curve (blue). The difference between
these two curves is what the two-level model is meant to fix (see next plot.)

Perhaps: Because the tau of the two measurements differed in value by a significant amount there was no impetous or ability to jointly fit them and see if a common thickness-vs-time curve would agree with both data sets. However, now that they can be made to agree in value it is worth trying to jointly fit them and see if a common thickness vs time is allowed by the data.

Comparing tau at ~700 eV due to the Two-level model(green)
with the ECS best-fit curve (blue). Note that the two-level model,
a modification of the 'N0001 model, has not added any curvature
to the green curve so this difference remains. However the values
are very close and a common thickness-growth curve may be made to
agree with both data sets. A new Carbon-edge measurement at ~2004.0
may be a useful additional data point to settle this issue.

We'll see: As the plot above shows, the straight-line two-level model and the curved ECS model agree at 2003.0 but should deviate significantly by 2004.0.

Yes! : A 50 ks observation of PKS 2155-304 was taken on Dec. 16, 2003 and shows a roll-off in the C-K edge linear trend with time(!), suggesting that the carbon edge growth may reasonably track the ECS measured absorption changes.

This is all nice, but what's in it for the Chandra observer?

A new calibration product, 'N0003, for the contaminant on ACIS-S has been created by combining three items:

The first two are well known, the third, "Fluffium", is constructed as the ratio of the 'N0001 model to a two-level model, i.e., it is the ratio(green) curve in the figure at the top of the page. Although this ratio or correction term does not behave exactly as another element, that is by varying simply as a power of the thickness, it is a good approximation especially in the region above 0.5 keV.

The exact steps of creating the files to generate the 'N0003 product are excruciatingly detailed in the following linked notes - note that a first beta version 'N9998 was created and evaluated and then a second beta version, 'N9997, was created and is now the released 'N0003 version. In this iterative creation it was more clearly realized that the 'N0001 product includes (warranted) modifications to the near-edge structure of the carbon response - in a sense aspects of Fluffium have already been included at some level by these changes. Hence the Fluffium used in 'N0003 has minimal effects to the carbon response shape below 0.5 keV.

Most recent products on top:

A plot of the "tau"s ( -ln(transmission) ) of the N0003 element components, C, O, and F, and the Fluffium component is given below as a function of wavelength at t=2002.8 :

(Courtesty D. Huenemoerder)

The change in the time dependance to match the ECS curve is shown in these two figures which plot the effective tau of the model or 'N0003 versus time (green) as well as the ECS tau curve (blue):
The two-level model (left plot) agrees with the ECS at t=2002.82 but still has the 'N0001 time dependence in it. The 'N0003 version (right plot) is matched to and here indistinquishable from the ECS time dependance, as intentionally constructed (within 0.2%).

So, we have a real physical model of the real contaminant?

Well, maybe not... H. Marshall refering to this new 'N0003 product wrote on Jan. 29, '04:

It should be clear that the original justification for [the two-level] model is out of favor with the contamination chemistry expert, Adam Hitchcock. He feels that it is very unlikely that the contaminant layer is crystalline or anything but slowly thickening uniform layer. [In which case], we have a nonphysical model. I'm still in favor of releasing the model but no one should have the impression that the adjustments to the contamination model have a [plausible] physical basis. [The] adjustment does what it takes to make the ECS and LETG/ACIS edges agree, so I endorse it.

Well, what next?

The addition of the "fluffium" contamination component and the adoption of the ECS time variation into the contaminant model as encoded in the 'N0003 contamination file go a long way toward creating a useful, physics-based calibration product. But there is still more work to be done that is beyond the scope of this note, for example:

Can we measure spatial variations in the density of the contaminant?


Since the ACIS has a pixel size of 24 um this sets a lower practical limit for spatial scales we can measure on the OBF. Of course it is worse than this because both the HRMA beams and ECS "beams" coming to a pixel actually sample a larger size on the OBF which is ~12 mm above the CCD surface. The "sampling foot-print" is described below for these two measurement cases.

- - -

The HRMA has an f-ratio of about f/8.3 for the outer shell 1. Thus the beam diameter intercepting the OBF is ~ 12.0/8.3 or 1.44 mm. Simulations for ~700 eV X-rays and grating=NONE are presented here to show the specific distribution of events on the OBF without and with dither on. (Note that other energies and/or the use of the HETG/LETG may change the relative intensity of the different shell contributions.)

The figure below left shows a MARX simulation of photons being detected when the focal plane is moved 12 mm towards the HRMA, i.e., this is the "foot print" of rays going through the OBF from a point source instantaneously and/or with no dither. (Specifically, the plot here is of the Sky X and Y coordinates which have aspect motion removed.) The plot frame has a size of 2mm x 2mm here (+/-42 pixels on each axis) and the four HRMA shells are clearly visible.

The figure below right is the same simulation except that TDETX and TDETY coordinates are plotted (with one pixel randomization) and thus show the effects of dither motion in moving around the HRMA shell pattern on the OBF. A square of 2mm size is plotted as well for comparison with the frame of the figure at left. The 16 arc second peak-to-peak dither corresponds to a physical distance of almost 0.8 mm which causes a substantial spreading of the HRMA pattern on the OBF.

- - -

When looking at the ECS the amount of the OBF sampled depends on the sizes (1mm, 8mm) and distance (~500 mm) of the ECS sources, values provided by Mark Bautz. The result is that X-rays arriving at a specific point on the CCD array have sampled a circular region on the OBF of diameter 0.024 mm for the Mn/Fe source and 0.19 mm for the Al and Ti sources. For the Fe ~700 eV measurements 2x2 pixel cells would see largely independant OBF regions and so variations on scales of ~50 um and larger can be measured (subject to enough counts!)

Note that when looking at the ECS, if the ACIS is translated in SIM-Z by a distance of ~40 mm then the "shadow" of the OBF contamination pattern will be shifted on the devices by ~ 1 mm. By making ECS measurements with ACIS offset it may be possible to see the OBF variations shift with respect to the CCD coordinates and separate OBF variations (if visible) from CCD pixel-pixel/column-column variations...

* The following write-up dates from October/November 2003 *
and is included for its specific description of the two-level model. -dd

Initial Two-level model write-up

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