4.6 Pixel Phase-Dependent Photometric Correction for Point Sources
The flux density of a point source measured from an IRAC image depends on the exact location where the peak of the Point Spread Function (PSF) falls on a pixel. This effect is due to the variations in the quantum efficiency across a pixel, combined with the undersampling of the PSF. It is most severe in channel 1, partly due to the smallest PSF angular size. The correction for this effect can be as much as 4% peak to peak. Early in the cryogenic mission, the point source aperture flux was fit with a radial function in pixel phase (Reach et al. 2005). We define pixel phase as the offset between the centroid of a point source and the center of the pixel in which that centroid lies. Later, Mighell et al. (2008) found that the intrapixel sensitivity variation is better described by a two-dimensional function of (x,y) pixel phase, primarily because the peak of the response is not at the center of an IRAC channel 1 pixel. The effect is graphically shown in Figure 4.6. These images are subsampled in 0.01 pixel increments, starting at -0.5 and ending at +0.5 (in both xphase and yphase), and may be interpolated to the phase of a given stellar centroid and multiplied by the measured aperture flux. These correction images (the inverse of the response) that can be applied (multiplied) to the data can be downloaded in FITS format from IRSA’s Spitzer documentation website at
Figure 4.6: IRAC cryogenic pixel response model, showing intrapixel sensitivity variations as a function of pixel phase. Only channel 1 (3.6 μm) and channel 2 (4.5 μm) have significant variations.
At the beginning of the warm mission, we found that the pixel phase response peak-to-peak variation increased by a factor of about two in both channels 1 and 2. The larger dynamic range enabled us to model the intrapixel gain in terms of the sum of Gaussian functions in measured (xphase, yphase). See Section 8.3 and Appendix D for more details. See also the IDL code in the Contributed Spitzer software at IRSA about performing a simultaneous pixel phase and array location-dependent photometric correction to the observed fluxes.
4.7 IRAC Aperture Photometry Corrections
Because point source aperture photometry is often performed in apertures that have sizes that differ from the apertures used for the calibration stars (10 IRAC native BCD pixel radius aperture and a background measured between 12 and 20 IRAC native BCD pixel circular radii from the center of the source), an aperture correction is necessary. The native IRAC BCD pixel sizes are given in Table 2.1 (they are around 1.2 arcseconds).
The radius of the on-source aperture should be chosen in such a way that it includes as much of the flux from the star (thus, greater than 2 arcseconds) as possible, but it should be small enough that a nearby background annulus can be used to accurately subtract unrelated diffuse emission, and that other point sources are not contributing to the aperture. For calibration stars, an annulus of 12 arcseconds is used; such a wide aperture will often not be possible for crowded fields. The dominant background in regions of low interstellar medium (ISSA 100 μm brightness less than 10 MJy/sr) is zodiacal light, which is very smooth. In regions of significant interstellar emission, it is important to use a small aperture, especially in IRAC channels 3 and 4, where the interstellar PAH bands have highly-structured emission. For example, an aperture in a star-forming region might have a radius of 3 native pixels with a background annulus from 3 to 7 native pixels. The flux of a source can then be calculated in the standard way, taking the average over the background annulus, subtracting from the pixels in the on-source region, and then summing over the on-source region. Note that the calibration aperture did not capture all of the light from the calibration sources, so extended emission appears too bright in the delivered IRAC data products. See the more detailed discussion under Section 8.2.
Users should note that the spatial extent of the PSF in channels 3 and 4 was much larger than the subarray area. In other words, a large amount of the total power in the PSF is scattered onto arcminute size scales. As a result, special care needs to be taken when measuring fluxes in these channels, since accurate measurement of the “background” is difficult. Proper application of aperture corrections is very important.
For photometry using different aperture sizes, the aperture correction can be estimated with Table 4.8. All the radii in this table are in native pixels (≈ 1.2 arcseconds). Note that the post-BCD mosaics available at the Spitzer Heritage Archive use pixels that correspond to exactly 0.6 arcseconds x 0.6 arcseconds. The aperture corrections as written will increase the flux measured by the listed method, i.e., your measured brightness should be multiplied by the aperture corrections in the table. The third decimal place in these numbers is included only to illustrate the trends; the accuracy of these corrections is » 1% - 2%. The aperture corrections in Table 4.8 are the modes of the distributions of aperture flux ratios measured using stars at several different positions covering the whole arrays. Standard deviations (including measurement errors and true variations across the array) are less than 0.5% for all the entries except the smallest aperture, in which they are still less than 1%. The extended source (infinite) corrections in
Table 4.8 come from Reach et al. (2005). The measured flux densities can then be converted to magnitudes, if desired, using the zero-points in Table 4.2.
Table 4.8: Cryogenic and warm IRAC aperture corrections (warm corrections are given as the second set of values in channels 1 and 2). The radius is in native (≈ 1.2 arcsecond) pixels. To get arcseconds, multiply these numbers by the pixel size from Table 2.1.
