Photometry

In this Section, we detail how we obtained the photometric measurements at various wavelengths and combined them to construct the point-source catalogs. Although the procedures followed here are derived from the techniques developed by Khan et al. (2010) and Khan et al. (2013), there are some key differences, as we now carry out an inventory of all point-sources rather than targeting a particular sub-class with desired photometric properties.

Specifically, Khan et al. (2010) searched for very red mid-IR ( $m_{3.6}-m_{4.5}>1.5$) sources near or at the detection limit of the first two IRAC bands, and therefore included in their primary source-list objects that were detected in the $4.5\,\micron$ but not the $3.6\,\micron$ image, as well as objects that could only be detected in the $4.5\micron - 3.6\micron$ difference image but not in either of the individual images. Khan et al. (2013) focused on the most luminous mid-IR ( $L_{mIR}>10^{5}\,L_\odot$) sources with a spectral energy distribution (SED) that is either flat across the four IRAC bands or rising towards the longer wavelengths, and therefore included in the primary source-list all objects that had $\lambda L_\lambda>10^{4}\,L_\odot$ in any of the first three ( $3.6\,\micron, 4.5\,\micron, 5.8\,\micron$) IRAC bands.

In this work, we implement strict detection criteria by selecting all sources detected at $>3\sigma$ in both the $3.6\,\micron$ and $4.5\,\micron$ images within a certain matching radius as point-sources. Next, we search for $>3\sigma$ detections of these point-sources in the $5.8\,\micron$ and $8.0\,\micron$ images within the same matching radius. If no counterpart is found, we attempt to measure the flux at the location of the $3.6/4.5 \micron$ point-source through PSF fitting, and failing that, through aperture photometry. For the MIPS $24\,\micron$ images, we only use aperture photometry due to the much lower resolution and larger PSF size compared to the IRAC images. Finally, for all objects that do not have a $>3\,\sigma$ detection at $5.8\,\micron$, $8.0\,\micron$ and $24\,\micron$, we estimate the $3\sigma$ flux upper limits. The fluxes and upper limits are transformed to Vega-calibrated magnitudes using the flux zero-pointsand aperture corrections provided in the Spitzer Data Analysis Cookbook. Given this broad outline, we now describe the specific technical details of how we performed the measurements at the various stages of constructing the catalogs.

We used the DAOPHOT/ALLSTAR PSF-fitting and photometry package (Stetson1992) to construct the PSFs, to identify the $>3\sigma$ sources, and to measure their flux at all $4$ IRAC bands. The different roll-angles of the various Spitzer observations made it necessary to construct the PSFs for each galaxy in each band independently. Next, we empirically determined the optimal radius to match the $3.6\,\micron$ and $4.5\,\micron$ source-lists. Figure2 shows the distribution of distances to the nearest $3.6\,\micron$ source for each $4.5\,\micron$ source in M33. In this case, over $90\%$ have a match within $0.5$pixel. The density of nearest matches falls rapidly between $0.5-1.0$pixel ($<10\%$ additional matches), while the number of duplicates increases ($<0.5\%$ duplicate matches), and then the distribution essentially flattens. Similar distributions are observed for the other six galaxies (see Table1). We therefore adopted an empirically motivated matching radii of 1pixel in order to maximize the number of matches for a minimal number of duplicates.

We used the IRAF ApPhot/Phot tool for performing aperture photometry at the point-source locations for all IRAC bands and the MIPS $24\,\micron$ band. For the four IRAC bands, we use an extraction aperture of $2\farcs4$, a local background annulus of $2\farcs4 - 7\farcs2$, and aperture corrections of $1.213$, $1.234$, $1.379$, and $1.584$ respectively. For the MIPS $24\,\micron$ band, we use an extraction aperture of $3\farcs5$, a local background annulus of $6\farcs - 8\farcs$, and an aperture correction of $2.78$. We estimate the local background using a $2\sigma$ outlier rejection procedure in order to exclude sources located in the local sky annulus, and correct for the excluded pixels assuming a Gaussian background distribution. Using a background annulus immediately next to the signal aperture minimizes the effects of background variations in the crowded fields of the galaxies. We also determine the $3\sigma$ flux upper limit for each aperture location using the local background estimate.

Ideally, flux measurements of an isolated point-source through either aperture or PSF photometry would produce the same results after appropriate aperture corrections (in the first case) and small zero-point offsets (in the second case) to account for flux underestimation due to PSF fitting up to finite radii rather than to infinity. We derive this small (usually $\sim0.1$mag) offset for each image from the mean difference between the magnitudes of relatively isolated, unsaturated bright sources measured through aperture and PSF photometry. For fainter sources, especially in limited spatial resolution images of crowded fields, the aperture and PSF photometry measurements can vary significantly. Figure3 shows the differences between apparent magnitudes determined through aperture and PSF photometry as a function of PSF magnitude for the $m_{psf}<15$ sources in NGC6822 and M81. For the less crowded case of NGC6822, the two measurements generally agree for the very brightest sources in all four IRAC bands, with the scatter increasing for the fainter sources. The same is true for the $3.6\,\micron$ and $4.5\,\micron$ images of M81, but at $5.8\,\micron$, the scatter is much worse, although a sequence of bright sources with good agreement between the two sets of measurements can still be seen. However, for $8.0\,\micron$, such a sequence cannot be clearly identified, and we found this to be true for the other galaxies as well. Mismatches between the two magnitudes are a good indicator of when crowding is significantly effecting the magnitude estimates, and in the catalogs we list the difference between the PSF and aperture photometry magnitudes for each source.

Because of these crowding problems, we do not attempt to fine-tune the $8.0\,\micron$ PSF photometry measurements by applying the small linear offset, although we do this for the other three IRAC bands. For all IRAC bands, we universally prefer PSF photometry over aperture photometry, because PSF fitting is more successful at extracting relatively fainter sources in crowded fields. Aperture photometry can significantly over-subtract the sky and underestimate the source flux, or overestimate the source flux by failing to remove contamination from nearby brighter sources. Nevertheless, aperture photometry proves very useful for validating the PSF photometry measurements at the bright end in all IRAC bands, for estimating $5.8\,\micron$ and $8.0\,\micron$ fluxes where PSF fitting fails and $24\,\micron$ flux where the lower resolution makes PSF photometry infeasible, and for determining flux upper limits.

To summarize, we implement strict detection criteria by requiring a $>3\sigma$ detection of all cataloged sources at $3.6\,\micron$ and $4.5\,\micron$. We then complement those measurements at the $5.8\,\micron$, $8.0\,\micron$ and $24\,\micron$ bands through a combination of PSF and aperture photometry, preferring PSF fitting over aperture photometry at $5.8\,\micron$ and $8.0\,\micron$, and exclusively using aperture photometry at $24\,\micron$. For all objects that do not have a $>3\,\sigma$ detection at these three longer wavelengths, we estimate $3\sigma$ flux upper limits.