Point source fitting of IRAC images using a PRF

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Photometry of moderately-resolved sources

Point source fitting is most appropriate for true point sources, the flux of astronomical objects that are extended will be underestimated by such a procedure. Nearly all fields observed by IRAC have a substantial population of faint (10s of microJy) background sources, which are in fact galaxies, and in a typical 100-second exposure these can approach 100 galaxies per IRAC frame at 3.6 microns. Although a casual visual inspection of the IRAC data would seem to indicate that the majority of these sources are compact and point-like, in fact treating them as such will lead to substantial errors in photometry, as these objects are typically resolved on a scale of ~1 arcsecond (e.g. Lacy et al. 2005).

This issue has been studied in substantial detail in the IRAC Dark Field, which is the dark current calibration field for IRAC. This is an extremely deep IRAC pointing of approximately 200 square arcminutes near the north ecliptic pole, and which reaches the confusion limit in all IRAC bands. More importantly, there is also deep high spatial resolution HST optical imaging over the same field, which can provide prior information on true source sizes and shapes.

Point source fitting was used to extract photometry for the IRAC Dark Field. An examination of the point-source subtracted residual image shows clearly that the residuals mimic the HST source morphology, conclusively demonstrating that IRAC does in fact resolve the majority of the faint galaxies. This result is strongest at the shorter IRAC wavelengths, where the spatial resolution is higher and the galaxies may be slightly more extended. This result was hardly unexpected - calculations of expected galaxy angular sizes assuming a modern cosmology indicated that most galaxies would be marginally resolved by IRAC almost regardless of distance, modulo changes in galaxy morphology with redshift and the ability to detect faint extended emission.

Curves of growth were generated for the galaxies, and when used in conjunction with the optical priors, the amount of error associated with point source fitting was quantified. Sources below a few microJy start to be affected by confusion issues, so we describe here results for galaxies brighter that this. At 3.6 microns, roughly 50% of all galaxies are demonstrably resolved by IRAC. In 20% of the objects, the use of point source fitting will underestimate the true flux by a factor of two or more.

A much more effective solution is to use aperture photometry for such sources. The SWIRE survey performed detailed analyses to determine an "ideal" extraction aperture such that it minimized noise. This aperture was 1.9 arcseconds in radius, or roughly twice the FWHM. Most other survey groups have found similar results, and this mirrors well-known ideas about aperture photometry of small sources. When such an aperture is used, even though some objects may be larger than this the number where the flux differs by a factor of 2 falls to only 3%. This improvement over the PSF-fitting reflects the fact that the summation over an aperture larger than the PSF FWHM will always capture a better representation of the true flux of an extended object, even if that is more extended than the aperture itself. A more ideal solution is to use Kron-like apertures (which are dynamically sized based on moments derived from the image) which are either derived from the data itself or from image priors in some other band.

We may thus conclude that for the extragalactic background, which is present in nearly all IRAC data, at least half the objects are resolved by IRAC in a meaningful fashion. Ideally, measurements should dynamically use shape information determined from the data itself, or from priors derived from other, higher resolution datasets. Barring the use of shape parameters, use of aperture photometry in circular apertures somewhat larger than the PSF provides a more accurate result than PSF fitting.