IRAC-2MASS Stellar Density

Feasibility of using 2MASS Stars for IRAC Pointing Refinement

The blind pointing accuracy of SIRTF is expected to be on the order of the IRAC pixel size (1.2"). It would be desirable to refine this to subpixel accuracy by comparison to observed reference objects whose positions are known to high accuracy. 2MASS provides the best such catalog for pointing reconstruction. It covers the entire sky and it's longest wavelength (2.2 microns) is similar to IRAC's shortest wavelength (3.6 microns). It's positional accuracy is on the order of 0.2" (and may be further refined to 0.1"), which given the size of the IRAC PSF is probably close to the best positional accuracy we could ever hope to achieve.

In order to be usable, it must have a sufficient density of stars of appropriate magnitude to ensure a high likelihood of having reference objects in any given 5x5'IRAC field.

Fig. 1 - The current released 2MASS survey stellar density at K-band smoothed on spatial scales equivalent to the IRAC
field size.

Fig. 2 - A close-up view of the above figure. Note the current coverage non-uniformities and holes left
by bright stars.

John Carpenter has provided me with the above data for 2MASS at K-band, which has been boxcar smoothed to scales of 5x5', equivalent to the IRAC field size. As is expected the density of stars is very high in the galactic plane with a rapid decay at increasing galactic latitudes. The following figures show the stellar density in 5 galactic latitude "zones"


Figs. 3a and 3b - Histograms of the number of IRAC fields with a given stellar density. The histograms have been normalized to unity.


Figs. 4a and 4b - Normalized cumulative distribution functions of the number of IRAC fields with a given stellar density.

In Figure 3 one can see the most common number of stars found in an IRAC field in a given latitude band. The skew of the curve towards the high end is a result of the fact that for any given latitude band the low latitudes occupy a greater area on the celestial sphere, and also have higher stellar densities. The peak of the curve gives the most likely number of stars for that band, although the stellar density can vary by factors of several between the high and low latitude sides of the band.

Naturally, one needs at least one 2MASS star to get the pointing. Ideally, we would like two in order to also get the field rotation. More than this would recover the plate scale and distortion corrections, but these will already be accurately known since they are a fixed part of IRAC/SIRTF's construction. The extra stars will mostly improve the accuracy of the pointing and rotation refinement. Looking at the histograms, most often there will be two stars in the field even at the galactic cap. Far more informative are the cumulative distribution functions in Figure 4. Looking at Figure 4b we see that at galactic latitudes above 60 degrees there will be at least one star more than 70% of the time. Below 60 degrees this will be at least 95% of the time. At latitudes near the galactic plane (say, 40 degrees or so) there will be 4 or more stars more than 98% of the time. Moreover,the above only has stars down to K=14.5, which is the completeness limit of the 2MASS survey. The actual survey does contain more stars down to roughly K=16. Figure 5 shows K-band counts near the galactic pole and the galactic plane as a function of magnitude (derived from the internal 2MASS statistics server). The shape of both curves are essentially the same. Looking at the cumulative distribution functions we see that down to K=16.5 there are roughly twice as many stars as there are to a limit of K=14.5. Thus, Figures 3 and 4 underestimate the number of stars available by roughly a factor of 2. This is the difference between my earlier estimates and those indicated by the above figures. While these faint stars have degraded positional accuracy, it appears to typically be around 0.4".


Figs. 5a and 5b - Histogram and cumulative distribution function of K-band magnitudes in the 2MASS survey.

What about fluxes? Most 2MASS stars have H-K=(0.1-0.7), which is typical for late-type dwarfs with some dust thrown in. For these stars K-L is roughly similar. Hence, our 2MASS lower detection limit of K=16.5 is probably around L=16. If we assume a flux density for Vega of 250 Jy at 3.6 microns (which is for L and should be close for our passband), then this is roughly 100 microJy, or 7 sigma in a 12 second frame according to the sensitivity table in the SIRTF Observer's Manual. IRAC saturates in 12 sec on an L=9.3 star, and in 200 sec on an L=12.3 star. Assuming K-L=0.5 as we did above this is K=9.8 and K=12.8. Thus, we will always be able to detect a 2MASS star with fairly high confidence even in our shortest full-array frame time. 2MASS stars will saturate less than 1% of the time in the short IRAC frame times, and as often as 20% of the time in the longest frame times. Hence, 2MASS stars are in almost the ideal flux range for use with IRAC, albeit perhaps a little too bright by a factor of a few.

Conclusions:

2MASS stellar spatial densities are high enough that centering and rotation could be recovered over nearly the entire sky. Only in some places near the galactic caps would there be no stars.
2MASS stars are bright enough that we will always detect them.
2MASS stars are faint enough that saturation will not be a significant problem except at the very longest allowed frame time.

The refinement of positions from 2MASS stars for IRAC should be fairly straightforward. There are several important things that vastly simplify this task. First, the 3.6 micron channel is fairly similar in wavelength to the 2MASS K-band data. As a result, flux-matching can be enabled with a relatively tight window, perhaps a factor of 3 in each direction. Secondly, the positional offsets between IRAC channel 1 and it's other 3 channels will be accurately know, obviating the need to separately refine positions for each of the other 3 channels. Finally, the IRAC data will already have a fairly good pointing solution supplied by the SIRTF star tracker. Therefore, the search radius for positional matching can be quite small (<3").

Tom Megeath has pointed out a couple of other useful things. First, the colors of stars between 3.6 and 4.5 microns are likey to be pretty similar. This means that we probably can search the 4.5 micron array for matching stars as well, doubling the available search area and the number of stars available. In that case the expected number of stars for both FOVs and the full 2MASS database is fully 4x greater than that shown in figure 3. Furthermore, it is likely for maps that any IRAC field that has no stars will probably have neighboring fields with stars. Since the relative pointing offsets may be quite good, it is likely that the pointing solution for the adjacent frames can be interpolated to provide a pointing solution for the intervening star-less frame.