Resolved galaxies with apertures centered on the nucleus:
· For sources < 8 – 9 arcseconds in size, treat as point source (small aperture photometry, with local annular background subtraction)
· For sources > 8 – 9 arcseconds in size, apply extended source aperture corrections (see below).
Emission knots, embedded resolved sources
· If the source is small (compact, r < 7 – 8 arcseconds in size), treat as point source (small aperture photometry, with local annular background subtraction)
· If the source is large and fuzzy, use the extended source aperture corrections (see below). Beware that background structure will introduce large uncertainties (≈ 10%)
Surface Brightness (pixel-to-pixel measurements)
· For very extended sources (> 300 arcseconds) or flat, low surface brightness sources (e.g., Magellanic-type galaxies), use the maximum scaling factors given below.
Cross-comparing IRAC images (e.g., channel 1 versus channel 4), we recommend that you first cross-convolve the images. For the example above, convolve the channel 4 image with the channel 1 PSF, and convolve the channel 1 image with the channel 4 PSF. This operation will reduce the deleterious effects of the light scattering, but will not completely eliminate them. Be very conservative in interpreting colors as surface brightness measurements can be off by 5% – 10% in the short-wavelength channels and 30% in the long-wavelength channels.
8.2.2 Extended Source Aperture Correction
The following aperture corrections are intended to correct the photometry of extended sources (e.g., galaxies) whose absolute calibration is tied to point sources. These corrections not only account for the extended emission from the IRAC PSF itself, but also from the diffuse scattering of the emission across the IRAC focal plane. The curves were derived from a detailed analysis of elliptical galaxies (see related notes in Section 8.2.4). The curves may be applied to all types of galaxies, but beware that significant departures can be expected for sources that are morphologically different from elliptical galaxies (e.g., late-type LSB galaxies; see surface brightness recommendations above).
Figure 8.2: Extended source flux aperture correction factors; solid lines represent exponential function fits to the data. Also indicated are correction factors derived from zodiacal light tests, and Galactic HII region tests (e.g., GLIMPSE vs. MSX).
Figure 8.3: Extended source flux correction factors for galaxies (solid lines) versus the PSF aperture correction factors (dotted lines). The main difference between the two is the truly diffuse scattering internal to the array.
Aperture photometry should also include a background subtraction; we recommend that you use an annulus that is located just outside the boundary of your galaxy. Circular or elliptical apertures may be used.
The procedure for correcting extended source photometry is to apply the correction factor to the integrated flux measured from the IRAC image (subject to the standard or point source calibration). The correction factor is a function of the circular aperture radius or the effective circular aperture radius (if using ellipses). These corrections should be good to 10%. For convenience, we have converted the empirical curves into a functional form:
where radius is in arcseconds, and A, B, and C are the best fit coefficients tabulated below:
The coefficient C represents the infinite, asymptotic value.
8.2.3 Low Surface Brightness Measurements and the Maximum Scaling Factors
Photometry of diffuse emission or low surface brightness objects is also subject to a large calibration correction in the IRAC 5.8 and 8.0 μm channels. The way to think about flat extended objects is that any aperture you use to measure the integrated flux (or surface brightness) is equivalent to an infinitely large aperture applied to a point source (or galaxy). Hence, the appropriate aperture correction (or equivalently, surface brightness factor) is the large radius case of the above aperture corrections:
Surface Brightness = measured surface brightness * correction_factor, where the correction factors represent the infinite aperture value. Note that for IRAC channel 3 the recommended correction is somewhere between 0.66 and 0.73, depending on the downward curvature of the aperture corrections (which is highly uncertain). These aperture corrections should be good to 10%. Low surface brightness objects include large, late-type galaxies such as NGC 300, Magellanic-type galaxies such as NGC 6822, diffuse dwarf galaxies, such as M81 DwA, and HII regions that are larger than ≈ 100 arcseconds but not very centrally condensed.
8.2.4 Caveats & Cautionary Notes
At small radii, r < 7 – 8 arcseconds, the extended source aperture corrections should not be used. Instead, we recommend using the point source aperture corrections for small radii.
It remains uncertain how much the spectral shape of the extended object determines the flux corrections; the aperture corrections presented here were derived using relatively old spheroidal galaxies. To first order, the extended source aperture corrections apply to most types of galaxies.
Likewise, with the spectral color caveat, it remains uncertain how much the spatial distribution of the light determines the flux corrections; these corrections were derived using relatively high surface brightness spheroidal galaxies; it is unknown whether these corrections apply to lower surface brightness galaxies (e.g., late-type spirals, irregulars, Magellanic-types).
8.2.5 Faint Surface Brightness Behavior
Note that the discussion in this section applies only to warm mission IRAC data. For more detailed information, please see Krick et al. (2011).
Binning data by essentially making larger “pixels” should reduce the noise in the image linearly with binning length. Figure 8.4 and Figure 8.5 show a plot of noise versus binning length for a set of deep mapping data in the Virgo cluster (PID 60173). These data have been carefully corrected for the first-frame effect (See Section 7.1) using the data themselves. The measured noise does not achieve the expected linear relation with binning length, as elaborated in the following subsections.
Figure 8.4: Noise versus binning length in channel 1. To make this plot, the surface brightness was measured in nine regions across an object-masked mosaic. These regions are not near bright galaxies, stars, or diffuse plumes. The noise is defined as the standard deviation of those nine regions. The box size is incrementally increased until the box length is many hundreds of pixels. For reference the solid line shows the expected linear relation.
Figure 8.5: Similar to Figure 8.4 but for channel 2.
22.214.171.124 Small Scales
There is a discrepancy between the expected linear behavior and the data at short binning length scales of just a few pixels or a few arcseconds (mosaics only). This discrepancy occurs because we have correlated noise on a mosaicked image on small pixel scales (a few pixels), so the noise does not bin down appropriately.
126.96.36.199 Medium Scales
On 5 - 30 arcsecond scales much of the extra noise is due to sources in the image. The first level of masking used the SExtractor segmentation map as a mask. The resulting noise properties are shown with asterisks. Increasing the size of the masks to 1.5 (2.0) times the SExtractor-determined object radii produced noise properties shown with a square (triangle) symbol. Further increases in mask size are inconsequential. The discrepancy between the observed and expected behaviors in this binning length regime is dominated by noise from the wings of galaxies that are improperly masked. Even after increasing the mask sizes, extra sources of noise remain which prevent detection of ultra-low surface brightness. There appears to be a floor to the noise at roughly 0.0005 MJy/sr at 3.6 μm and 0.0008 MJy/sr at 4.5 μm.
188.8.131.52 Large Scales
Some of the large-scale (a few arcminutes) noise is caused by the mapping pattern used for the observations. On scales of roughly half a field of view there are differences in the total exposure time and hence the total number of electrons detected (not a dominant source of noise). There are remaining sources of noise on the large scales, both instrumental and astronomical, which are very hard to disentangle. Uncertainties in the flat-fielding and removal of the first frame effect are two instrumental effects that are contributing to the noise on large scales. The first-frame effect has a column-wise dependence that requires special calibration data to measure. Astrophysically, there is real structure in the zodiacal light and Galactic cirrus. There is also documented diffuse intracluster light in the Virgo cluster itself, and a small signal from the extragalactic background light that are both adding to the noise at low levels. There is potentially also noise due to the blue infrared color of intracluster light, while the zodiacal light from which the flats are made is red in near-IR (see Section 4.2). Differentiating between all of these sources of noise is difficult.
184.108.40.206 Increasing exposure time
The IRAC dark field was used to study whether the noise decreases with the square root of exposure time, as expected. The dark field has extremely low zodiacal light and low Galactic diffuse emission. Using all the warm mission dark calibration data through 2010, a mosaic was made from 300 dark frames (each with a 100 second frame time). Object masking was made with the SExtractor segmentation image. The noise on the distribution of pixel values is the standard deviation of the Gaussian fit to that distribution. Each distribution has > 750 pixels in it. For comparison the same analysis was performed on the dark field mosaics from the first year of the cryogenic mission. The results from both are in Figure 8.6 and Figure 8.7.
Figure 8.6: Noise as a function of exposure time (number of frames) in channel 1. The results from the warm mission data are shown with crosses and the expected behavior with the solid line. The results from the cryogenic mission are shown with open squares and the expected behavior with the dashed line.
Figure 8.7: Similar to Figure 8.6 but for channel 2.
These plots show that background noise in IRAC channels 1 and 2 does decrease roughly as expected with exposure time. The slight deviation at larger exposure times is likely caused by the first-frame effect (Section 7.1) and by residual source wings.