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 (tens of micro-Jy) 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 µm. 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 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 channels. 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 images 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 micro-Jy start to be affected by confusion issues, so we describe here results for galaxies brighter that this. At 3.6 µm, 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 two 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 themselves 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 themselves, 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 PRF fitting.
C.3.6 Positional Accuracy
Tests were performed on GLIMPSE AORKEY 9225728, which contained approximately 10000 point sources in channels 1 and 2. Comparisons were made with respect to SExtractor Gaussian-windowed centroids XWIN_WORLD, YWIN_WORLD using both the pipeline mosaics, and mosaics made with the original pointing. Using the 100x oversampled PRFs recentered as previously described we found that the source positions agreed with SExtractor to within ≈ 0.1 arcseconds. Systematic shifts with respect to 2MASS are ≈ 0.2 arcseconds in the pipeline (superboresight) pointing, and ≈ 0.4 arcseconds in the original pointing. Recentering the PRF has no effect on photometry but is required for use in APEX. The shifted and unshifted PRFs gave nearly identical photometric results in channels 1 – 4.
C.3.7 A How-To-Guide for IRAC Point Source Photometry with APEX
It is recommended that APEX in point source fitting mode should be used only directly on the BCD data using the Hoffmann PRFs modified for use with APEX as described above. Trying to fit point sources on the mosaic is not recommended as the mosaicking process both blurs the undersampled point sources, and loses the pixel phase information. Therefore, the fitting should be done to individual (C)BCD frames whereas a mosaic should only be used to find the point sources. We also do not recommend using the prf_estimate tool to derive a PRF from IRAC data, as it does not deal correctly with the undersampling of the PRF.
We list below the steps towards producing a point source list using APEX in multiframe mode (i.e., on the stack of individual [C]BCDs).
1. Source fitting versus aperture fluxes: ask yourself if point source photometry is appropriate for your sources of interest. If in doubt after reading about photometry of moderately resolved sources above, use aperture photometry with APEX or SExtractor.
2. Artifact correction: use CBCDs or preprocess your IRAC BCD data to remove or mask artifacts as necessary.
3. Rmasks: assuming the data were taken with overlapping (C)BCDs, make a mosaic with MOPEX, doing outlier rejection, and creating rmasks. Then include the appropriate rmasks with your input data to APEX.
4. PRF: put the center Hoffmann 100x PRF (the one with ...col129_row129...) in your MOPEX cal/ subdirectory for command-line (this will be PRF_FILE_NAME in the namelist file), or type it into the GUI. Although you can run APEX with just the center PRF, we recommend using the whole PRF Map set, as it noticeably improves the quality of the fits for sources outside of the central region of the arrays. To do this, create a table like the one linked from the PSF/PRF section of IRSA’s IRAC web pages (substituting appropriate filenames and paths). PRF position refers to the bottom-left corner of the region of size NAXIS1, NAXIS2 over which the PRF is valid (in native pixels). This will be PRFMAP_FILE_NAME in a namelist, or you can type it into the GUI. Figure C.5 shows how the PRFs are distributed over the arrays.
5. Normalization Radius: the Hoffmann PRFs require a normalization that matches the IRAC calibration radius. In the Sourcestimate block, set Normalization_Radius = 1000 (since it is in PRF pixels and the sampling is 100x).
6. Run APEX. If doing command-line for IRAC1, edit the default namelist for your data and run: apex.pl -n apex_I1_yourdata.nl
7. PRF Flux: The PRF flux column is called “flux” in the extract.tbl output file, and the units are micro-Jy. These need to be divided by the appropriate photometric correction factors from Table C.1: 1.021 (IRAC 1), 1.012 (IRAC2), 1.022 (IRAC3), and 1.014 (IRAC4).
8. PRF Flux Uncertainty: The column labelled “delta_flux” is the formal uncertainty from the least-squares fit. It will in general underestimate the flux uncertainty. Do not use the column labelled “SNR” for IRAC, as it only takes into account the background noise, and ignores the Poisson (shot) noise term which typically dominates the error. The best estimate is the aperture uncertainty (calculated from the data uncertainties) in a 3 pixel radius. This covers the majority of the PSF without going too far out. (For the default namelist, the relevant uncertainty is in column “ap_unc2” [microJy].)
9. Array Location-Dependent Photometric Corrections: Use MOPEX to make an array location-dependent photometric correction mosaic and correct APEX-produced fluxes by the values at the locations of source centroids in the correction mosaic. The fluxes will be correct for blue sources that have colors of an early-type stellar photosphere. For red sources with colors close to that of the zodiacal light, use fluxes derived from running APEX on unmodified CBCDs.
10. Color Correction: This is the correction needed to get the right monochromatic flux if your source spectrum is different from the reference spectrum used to calibrate the IRAC filters (constant). There is a good discussion of this in Chapter 4 of this Handbook.
If all these steps are followed, then the systematic error in the flux measurement for bright, isolated point sources should be ≈ 1%. A comparable systematic error exists in the flux density scale. Background estimation errors will contribute significantly to the error budget for fainter sources and in confused fields.