1) Overview

Derivation of the IRAC flat-field is problematic in the two InSb channels due to the extremely low background levels of the IR sky at these wavelengths. A possible alternative is to observe high surface brightness extended objects in order to get adequate flux levels for deriving the flat-field.

Elliptical galaxies are some of the better candidates. The SAO and SSC IRAC groups have identified approximately 20-30 big, bright elliptical galaxies which could conceivably be targets. None of the targets lies in the CVZ, and as a result a network of such targets would have to be established to allow for the flat-fielding of IRAC on a campaign basis (see the following visibilities).

Figure 1 shows 2MASS K-band images of some of these galaxies - the most important point being that unfortunately the galaxies are typically significantly smaller than the IRAC FOV (the images are displayed in a 5 arcminute frame). Only a couple of the galaxies (M49 and the core of M31) are large enough to expose a significant fraction of the FOV. This will be dealt with in more detail below.

To investigate how easily the derivation of this flat-field would be, we simulated observations of an elliptical galaxy using the ISDS and attempted to derive the the flat.

M 49	M 31	NGC 205
NGC 1344	NGC 4125	NGC 4697
NGC 5322	NGC 1404	NGC 4589
Fig. 1 - 2MASS images of large elliptical galaxies.

2) Input Data

The input data were a set of of simulations generated by Myungshin Im based on simulated truth images of NGC 4589. This was chosen because it's size and brightness are fairly "typical" of the candidate galaxies from which a flat-field network might be constructed. This simulation used a model profile based on 2MASS data, to which were added 2MASS stars, along with an extension of the stellar luminosity function to fainter flux levels than covered by 2MASS. Two observing strategies were investigated in detail (see Figure 2):

• An observation of the galaxy in each band using the Realeaux dither pattern. There are 24 12-second frames on the galaxy.
• A 5x5 map which placed the target in a grid pattern over the entire array. There are a total of 50 30-second frames.

The simulated data were produced using the ISDS. The ISDS was run with most instrumental effects turned off, with the exception of the gain and dark. This will produce a product similar to what we will have in flight, where the pipeline will preprocess the data before special handling for producing calibrations.

Fig. 2 - Mapping patterns used for simulations, as illustrated by the sum of all the input images.

3) Fixsen Reduction

Because the galaxy covers a substantial portion of each frame, it is difficult (or impossible) to use any kind of masking approach for combining the frames. Fixsen is much more ideal because it creates a simultaneous estimate of the sky, and thus the separation between the sky and gain/dark is handled.

Simultaneous Solution for Flat and Dark

Here I tried to solve for the flat and dark simultaneously.

Results were clearly mixed. The Reuleaux pattern at least produces a relatively uniform result, although the derived values are considerably different from the known input to the simulation. In all cases it is aparrent that the elliptical galaxy was too small to adequately expose all the pixels. For the Reuleaux triangle dither patterns a fairly uniform solution is acheived for the pixels with S/N > 8. The grid map, though, isn't very good. It is clear that the solution is on erroneous on spatial frequencies that are the same as the mapping frquency.

5x5 Mapping Pattern	Reuleaux Triangle
Fig. 3 - Band 1 Simultaneous Gain (top) and Offset (bottom)

Gain-Only

Using Fixsen to derive just the gain essentially reduces it to a way of separating the structure in the sky from the gain. This requires that one supply a "dark", if not, the derived gain will have a strong component from the dark.

Where, then, does one get the dark? I used a dark derived directly from the data itself. This dark (illustrated in Figure 4) was created with a judicious approach to median combining with outlier rejection, and prior knowledge of the background level.

Fig. 4 - Raw elliptical galaxy data (left), dark derived by median combining the 5x5 map pattern data (center), and the dark-subtracted data (right).

Results of processing with Fixsen using the median dark are shown in Figure 5. The resulting flat has a pixel-to-pixel uncertainty of about 7%, and there are large-scale errors of 5-10%. It does, however, reproduce the vignetting at left fairly well. A lot of this may be due to using an inaccurate dark. As an exercise, I show in Figure 6 the results of the same experiment, only using a ground-based dark which was fit to the data frames. This mimics a possible flight situation, where we might try to use lab darks taken at a different epoch than the sky data.

Fig. 5 - Input simulated flat (left), derived flat (middle), and percent difference (right).

Fig. 6 - Input simulated flat (left), lab dark-subtracted derived flat (middle), and percent difference (right).

The resulting derived flat has a pixel-to-pixel noise of about 2%. Large scale deviations are about 5-10%. The major residuals are the result of erroneous dark subtraction along the left edge of the image. Shown below is the skymap derived via fixsen for band 1 in the case of using a dark derived directly from the data. Cosmetically the skymap (Figure 7) looks quite good.

Fig. 7 - Fixsen derived skymap of NGC 4589 in band 1.

A considerable problem in deriving the IRAC flat is getting adequate flux to beat down photometric noise in the solution. The above 5x5 mapping AOR required 34 minutes to do just 1 FOV, while the Reuleaux triangle required 45 minutes to do both. It is clear for the Reuleaux case that the galaxy was too small to acheive adequate S/N over the entire array, so mapping of the galaxy (or much longer total integration times) would be required. Therefore, I instead examine the 5x5 mapping case. If we map over the entire array with something like the 5x5 pattern, though, the typical pixel spends most of it's time during the AOR looking at the sky, not the galaxy. Even though the peak of the galaxy has a count rate over 400 DN/sec, if we look at the median count rate on the array from the galaxy per time spent integrating, this is only 0.38 DN/sec. If we look at the count level per total wall clock time this is even lower, more around 0.24 DN/sec. This is actually an order of magnitude lower than the high zodiacal background. If we consider just the pixels that happen to lie in the core of the galaxy, the resulting count rate is only (400 / 25 (map points)) = 16 DN/sec, and accounting for slew overheads 11 DN/sec, which is just a factor of 3-4 greater than the background. Furthermore, the times just given are for just one FOV. To get the 2nd InSb channel requires repeating the process with the galaxy steered onto the second FOV. The efficiency thus falls by another factor of 2.

Since the zodiacal background covers every pixel in every frame and both FOVs simultaneously, I conclude that only galaxies signficantly larger than NGC 4589, which cover most of the array and therefore might require at most 4 mapping positions, offer a clear advantage over using the extended zodical background. Obviously, it would also help if they were signficantly brighter than NGC 4589. NGC 4589 has a B-band magnitude = 11.6. From above, the "average" pixel has a count rate of only 0.24 DN/sec. This is 15x fainter than the high zody background. Ideally we want something 5-10x brighter than the high zody. This implies we need galaxies that are 4.5-5.5 magnitudes brighter, which is B<7. If they were significantly larger than NGC 4589, then we could probably use B<9. Two such systems are M 31 and M 49. These lie at ecliptic longitudes of 27 and 182 degrees, respectively. Unfortunately, these will have similar visibilities since they are on nearly opposite sides of the ecliptic sky (their exact visibilities lie near mid-summer and mid-winter). More precisely, their visibilities are:

M49                             M31
2002 Dec 19 - 2003 Jan 29     2002 Dec 17 - 2003 Feb 3
2003 May 28 - 2003 Jul 10     2003 Jul 12 - 2003 Sep 02
2003 Dec 26 - 2004 Feb 05     2003 Dec 23 - 2004 Feb 10
2004 Jun 04 - 2004 Jul 17     2004 Jul 19 - 2004 Sep 09

Several conclusions can be drawn:

• Derivation of the gain alone from the elliptical galaxy data is probably quite doable, subject to the limits of photon statistics and the accuracy of the dark-current subtraction. Derivation of both the offset and gain is more problematic, and will require a different weighting scheme than that used here.

• The ideal targets need to be very large and bright to make the efficiency of this approach significantly better than the zodiacal background observations, which have the additional benefit that they can be reduced via more conventional means.

• The elliptical galaxy approach is probably not feasble for routine derivation of the flat-field. It could, however, be used twice a year as an alternate approach to the high zody technique, and thus provide a check on the derived routine flats.