THE NEWFIRM MEDIUM-BAND SURVEY: PHOTOMETRIC CATALOGS, REDSHIFTS, AND THE BIMODAL COLOR DISTRIBUTION OF GALAXIES OUT TO z ∼ 3

The survey targets two fields within COSMOS (Scoville 2007) and the All-wavelength Extended Groth strip International Survey (AEGIS; Davis et al. 2007), chosen to take advantage of the wealth of publicly available ancillary data over a broad wavelength range (see Section 3.6). The NEWFIRM 276×276 pointing within the COSMOS field is centered at α = 9^h59^m533, δ = +02°24^m08^s (J2000). This pointing overlaps with the zCOSMOS deep redshift survey (Lilly et al. 2007) and the upcoming Ultra-VISTA survey.¹¹ The pointing in the AEGIS field is centered at α = 14^h18^m00^s, δ = +52°36^m07^s (J2000).

The observations were carried out with Mayall using the NEWFIRM camera with the J₁, J₂, J₃, H₁, and H₂ medium-bandwidth filters and the K broadband filter. Data were taken over the 2008A, 2008B, and 2009A semesters, for a total of 75 nights. The two main fields were observed whenever conditions were reasonable (i.e., no significant cirrus and seeing typically <15), and they were available at an airmass <2 and >20° away from the moon.

Due to the dominance and short-term variability of the sky background, ground-based NIR imaging requires many short dithered exposures. This observing procedure is well established (see, e.g., Labbé et al. 2003; Quadri et al. 2007), and facilitates the removal of artifacts remaining from bright objects that can leave residual images in subsequent exposures. The telescope follows a semi-random dither pattern with a dither box of 90'', enabling good background subtraction without significantly reducing the area with maximal exposure. The dither box is sufficiently large to "fill in" the gaps between the four NEWFIRM arrays.

At each dither position, the exposure times were typically 1 × 60 s (co-adds × individual exposure time) for J₁, J₂, and J₃, 3 × 20 s for H₁ and H₂, and 5 × 12 s for K. The internally co-added frames make longer exposure times possible at each dither position while staying in the linear regime of the array.

We obtained a total on-sky integration time between 17 and 31 hr in each filter in each field over the three semesters (see Table 1 for details). This represents all usable data, including aborted sequences or frames that were outside weather specifications or seeing constraints; the total on-sky time was 294 hr. When tallying only those frames that get included in the final combined images, the total integration times range from 12 to 24 hr (a loss of ∼10%–30% of the data).

An overview of the median seeing and background levels measured in each observing sequence (ranging from 10 to 90 minutes, typically 60 minutes) is given in Figure 2. The median seeing is measured from bright stars in the individual frames that are fit with a two-dimensional (2D) Moffat model using the robust, nonlinear least-squares curve-fitting algorithm mpfit in IDL (Markwardt 2009). The data are of excellent quality with clean images that have no obvious systematic problems.

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Every individual raw frame was visually inspected to identify any poor quality frames. To fall into this category, the frame must either (1) contain artifacts such as satellite streaks, ghost pupils or other transient features on the detector, (2) have a strongly varying background across the detector, (3) have severe elongation of the point-spread function (PSF), or (4) have double images of all objects due to "jumps" of the telescope or wind shake. Between 10% and 30% of the raw data was discarded for each filter, resulting in final combined mosaics with negligible artifacts.

The dark current is non-negligible in NIR cameras and thus dark images with the appropriate exposure times relative to the co-added science images are subtracted. Next, the raw images must be divided by the flat-field image to remove variations in the sensitivity across the array.

We constructed flat fields from dome flats in combination with observations of the open cluster M67, accounting for both the small- and large-scale variations across the arrays, respectively. First, we determined the pixel-to-pixel response from dome flats. The large-scale structure in the dome flats was removed by median filtering using a 51 × 51 pixel box, fitting a seventh-order 2D Legendre polynomial to the median-filtered image, and dividing by this fit. It was verified that subtracting rather than dividing by the fit changes the resulting residual image by <1% (except for the K band, where differences can be up to ∼5% in the corners of the arrays).

The simple flat fields are not enough to correct to the large-scale sensitivity of the array due to imperfect illumination corrections. We therefore determine the sensitivity variations across each array from observations of the open cluster M67 in an 8 × 8 grid of positions spanning 28' × 28'; this way, many stars were observed on many array positions. The M67 data were dark-subtracted, flat-fielded using the "flattened" dome flat (i.e., the dome flat with large-scale structure removed), and sky-subtracted. The fluxes of stars in M67 were measured using SExtractor (Bertin & Arnouts 1996) with a 4'' diameter aperture. Using the R.A. and decl. of the detected objects, sequences of unique stars imaged on multiple positions were identified. From these stars, a response image was generated reflecting the large-scale response of the arrays. The scatter in the best-fit response was typically 1%–3%, with larger errors possible in small areas for some array/filter combinations. These "response images" were then multiplied by the flattened dome flat to create the flat fields.

The individual dark-subtracted and flat-fielded frames are combined in two passes. During the first pass, the sky background is created for each science frame from a running median of the dithered sequence of the four preceding and four subsequent science images. Next, the dithered sky-subtracted images are cross-correlated with the central frame to determine the relative shifts of the individual frames. The relative flux scaling between the images is determined by measuring the flux of stars spread across the field. Finally, the images are shifted to a common reference frame using linear interpolation and are combined. All objects in the combined image are detected using a simple thresholding algorithm to generate an object mask. This mask is then shifted back into the reference frame of each individual science exposure, and the background subtraction process described above is repeated in a second pass, using a mean combined with cubic interpolation. The second pass is optimal for the background subtraction as the objects are masked out during the calculation of the running median.

In the reduction, we mask out any dead or hot pixels (or generically "bad" pixels) using a custom master bad pixel file. Bad pixels have a nonlinear response and these bad pixels can be easily separated from "normal" functioning pixels during twilight. The signal of good pixels increases or decreases linearly with time, and so we fit the average flux of each quadrant as a function of the time with a linear function. Any dead or hot pixels will exhibit variable behavior, resulting in drastically different best-fit slopes compared to properly functioning pixels. We flag any pixels with deviations >15%. The final bad pixel file contains a flag for any pixel that has been flagged in at least two of the twilight sequences, in addition to the original bad pixel file from the NEWFIRM calibration library. Although we are conservative with the bad pixel file, the total fraction of bad pixels is still small (∼7%). Any remaining bad pixels in each individual science frame are removed with a sigma-clipping algorithm before combining the images within the reduction.

The nonlinearity of the NEWFIRM arrays increases with additional signal, reaching ∼5% at 10,000 ADU. Beyond this level, the nonlinearity increases very steeply as the detector approaches saturation at 12,000 ADU. Co-adding frames allows us to keep exposure times short, thereby avoiding this nonlinear regime, as does observing when the sky levels are relatively low in a particular filter. A nonlinearity correction is applied to all individual frames, using the following empirical equation:

$$\begin{equation} y=x\left(1 + \frac{6.64\times 10^{-6}}{nx}\right), \end{equation} \tag{ 1 }$$

where x is the nonlinear (raw) frame, y is the nonlinearity corrected frame, n is the number of internally co-added frames, and 6.64 × 10⁻⁶ is the average coefficient for the four arrays.¹⁴ The nonlinearity correction to the photometry is typically <1% for the majority of frames.

Another issue in NIR detectors is persistence images of bright objects, where the array has not completely recovered from the previous exposures. To alleviate this problem, we create a second object mask of the cores of the brightest objects. These are used to mask the pixels that contained the brightest objects in the previous two exposures in the final pass of the reduction. The detectors also exhibit bias residuals that are constant along rows. After masking all sources, the residual bias is removed by subtracting the median of each row in the individual sky-subtracted frames.

The final major optimization of the image combination includes weighting the individual sky-subtracted frames to maximize the signal-to-noise ratio (S/N; see, e.g., Labbé et al. 2003; Quadri et al. 2007). This method substantially improves the final image depth and quality by assigning weights to the individual frames that take into account variations in the seeing, sky transparency, background noise, and PSF ellipticity. To optimize the S/N, the weight is proportional to the square of the flux scale (scale_i) divided by the median sky background (sky_i) and the median size of the seeing disk (FWHM_i), penalized for ellipticity:

$$\begin{equation} w_{i}=\frac{\mathrm{scale}_{i}^{2}}{\mathrm{sky}_{i}\times \frac{\mathrm{FWHM}_{i}^{2}}{\sqrt{1-e^{2}}}}. \end{equation} \tag{ 2 }$$

The weighted, sky-subtracted individual frames are combined into a single mosaic with a pixel scale of 03 pixel⁻¹ (resampled from the native NEWFIRM pixel scale of 04 pixel⁻¹). The combined NMBS mosaics are aligned with the Canada–France–Hawaii Telescope (CFHT) I-band images (see Section 3.6), with an astrometric precision of ≲01 over the entire field of view. The relative registration between the NMBS and CFHT images must be precise to allow for accurate colors and cross-identification of sources.

The initial registration within the code is performed using a linear transformation in the first pass of the reduction. The rms variation in the position of individual sources is about 01–02 (0.3–0.7 pixels) in most cases, but can be as high as ≳0.5''–1'' (2–3 pixels) in the corners of the arrays. We fit the residual distortions with a second-order polynomial and combine this fit with the original transformation. This combined distortion correction is then applied to the images, which are registered using a cubic interpolation. The resulting rms variation in position of the individual sources in the final combined images is ≲01 (0.3 pixels).

NIR spectro-photometric standard stars from the Calibration Database System¹⁵ were observed in wide five-point dither patterns on photometric nights in the 2008A semester. All of the other data were directly tied to the photometric data from 2008A. Synthetic magnitudes of these stars were calculated by integrating their observed (Hubble Space Telescope (HST)/NICMOS) spectra in the five medium-bandwidth filters (see Table 2 in van Dokkum et al. 2009). We adopt the mean zero points from these observations, listed in Table 1. The zero points derived from these standard stars are remarkably stable, with variations of ≲0.02 mag throughout the observing program.

A Galactic extinction correction has been applied to the photometry within the catalogs, as estimated from Schlegel et al. (1998). The corrections ranged from 4.5% to 0.3% for the u – K photometry in the AEGIS field, with slightly larger values of 8%–0.6% in the COSMOS field due to its lower Galactic latitude.

The final combined J₁, J₂, J₃, H₁, H₂, and K images constructed from the individually registered, distortion-corrected weighted averages of all frames are of excellent quality. The flatness of the background is readily visible in the final combined K-band images shown in Figures 3 and 4. Furthermore, the relatively deep and wide images are rich in compact sources. The combined images are slightly shallower near the edges and center of the image where there are gaps between the NEWFIRM arrays, as these areas receive less exposure time in the dither pattern. This is reflected in the weight maps containing the total exposure time per pixel. The reduced NMBS images and weight maps will be made publicly available through the NOAO archive.¹⁶

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Well-understood noise properties are important both for calculating the depths of the final combined images and for measuring accurate photometric uncertainties. Although the noise properties of the raw images are well described by the variance of the signal per pixel, the reduction process introduces correlations between neighboring pixels. Additionally, small errors in the background subtraction may contribute to the noise.

To estimate the noise, we follow Labbé et al. (2005) and empirically fit the dependence of the normalized median absolute deviation (nmad) of the background as a function of the linear size N of an aperture with area A, where $N=\sqrt{A}$. We measure the fluxes in >1000 independent circular apertures randomly placed on the registered, sky-subtracted convolved images (see Section 4.1 for a description of the PSF matching) in a range of aperture sizes. Any apertures that overlap with the detection image segmentation map are excluded.

As described in Quadri et al. (2007), the scaling of the background noise with aperture size will be proportional to N² in the limiting case of perfect correlations between the pixels within an aperture. In the other extreme case of uncorrelated adjacent pixels within an aperture, the background noise scales with the linear size N. The latter standard relation is unrealistic given the correlations between pixels that were introduced by the imperfect background subtraction but also by undetected sources, resampling of the pixels, etc. The true scaling between the background and the linear size falls somewhere between these two extremes. Following Quadri et al. (2007), we parameterize the noise properties as

$$\begin{equation} \sigma _{\mathrm{nmad}} = \sigma _{1}\alpha N^{\beta }, \end{equation} \tag{ 3 }$$

where 1 < β < 2, σ₁ is the standard deviation of the background pixels, and α is the normalization. In Figure 5, we see that the width of the noise distribution within an aperture increases with increasing aperture size. The best-fit scaling of the background fluctuations falls roughly between the two extremes of no correlation and a perfect correlation from pixel to pixel, with a best-fit power-law index of β = 1.37 in COSMOS (β = 1.35 in AEGIS).

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The background noise measurements are used to estimate the depths of the images. In Table 1, we list the 5σ limiting depths. These values are calculated using the background fluctuations within a 15 "color" aperture (see Section 4.1). An additional aperture correction determined from the growth curves must be applied to these values to convert to total fluxes (see Column 7 of Table 1). The typical aperture correction for a point source is 1.9 for a typical seeing of ∼11.

The survey catalog combines the data taken with the NEWFIRM camera with publicly available optical ugriz broadband images of both survey fields from the Deep Canada–France–Hawaii Telescope Legacy Survey (CFHTLS),¹⁷ using image versions reduced by the CARS team (Erben et al. 2009; Hildebrandt et al. 2009), and JHK_S broadband imaging from the WIRCam Deep Survey (WIRDS; McCracken et al. 2010; R. Bielby et al. 2010, in preparation). Additionally, we include deep Subaru Telescope images with the B_J, V_J, r⁺, i⁺, and z⁺ broadband filters and 12 medium-band filters in the COSMOS field (Taniguchi et al. 2007; Y. Taniguchi et al. 2008, in preparation).¹⁸ We include mid-IR images in the Spitzer/IRAC bands over the entire COSMOS pointing that are provided by the S-COSMOS survey (Sanders et al. 2007), and partial coverage of the AEGIS pointing (∼0.15 deg²) overlapping with the Extended Groth Strip (EGS; Barmby et al. 2008). The catalogs include Spitzer/MIPS fluxes at 24 μm that are derived from images provided by the S-COSMOS and Far-Infrared Deep Extragalactic Legacy¹⁹ surveys, with the same coverage as the IRAC data. Finally, we incorporate near-UV (NUV) and Far-UV (FUV) Galaxy Evolution Explorer (GALEX; Martin et al. 2005) data in both fields from the Multimission Archive at the Space Telescope Science Institute into the catalogs (see also Zamojski et al. 2007 for a description of the COSMOS GALEX data).

All ancillary images are matched to the same pixel scale (03 pixel⁻¹) and pointing of the NMBS images using the IRAF task wregister. The details of the source detection and extraction of photometry can be found in Section 4.2. In general, for objects that have flat spectra in F_λ, all of the ancillary data are deeper than the NMBS images with typical FWHM values of 08 for the optical images. For consistent photometry in all (optical to NIR) bands, the images have all been convolved to the broadest PSF as determined from the growth curves (see Section 4.1 for more details).

The FWHM of the PSF varies significantly between the optical and NIR bands; point sources in the optical images typically have FWHM of approximately 08, whereas the point sources in the medium-band NIR images have FWHM of 10–12. Directly performing aperture photometry on these images would lead to different fractions of the flux falling within the aperture for different bands, thereby resulting in systematic color errors.

To minimize this problem, we degrade all of the optical and NIR images for each field to the broadest PSF. We produce high S/N PSFs for each band from bright (unsaturated) stars covering the entire field. Square postage stamps (32 pixels on a side or 96) of the PSF stars are created, masking any nearby objects and averaged to create empirical PSFs. A kernel is then generated using the Lucy-Richardson method algorithm (lucy in IRAF) to convolve the empirical PSF to the broadest PSF (H₁ in AEGIS and H₂ in COSMOS).

Growth curves were determined for the empirical PSFs in each band, measuring the enclosed flux as a function of the aperture size. In the top panels of Figure 6, we show the ratio of the growth curves of each band relative to the broadest PSF in both fields before degrading the PSF (dashed lines). Generally, the broadest PSFs (the slowest-growing growth curves) are the longer wavelength bands. The bottom panels of Figure 6 show the ratio of the growth curves once they have been smoothed to the worst seeing. For "perfect" PSF matching, this ratio should be unity at all aperture diameters. At the aperture size used for the flux measurements (solid black line), the PSFs of all bands are matched within <2% for both fields.

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Given the noise properties of the images (see Section 3.5) and the growth curve of the PSFs, we estimate the aperture size that optimizes the S/N for point sources in Figure 7. This optimization enables accurate color measurements, which are necessary for photometric redshift calculations and modeling of the stellar populations. We adopt an aperture of 5 pixels (15), defining the color aperture as

$$\begin{equation} F_{\mathrm{color},i}=\sum \limits _{\sqrt{x^2+y^2}<0\farcs 75}F_{i}(x,y), \end{equation} \tag{ 4 }$$

where F_{color, i} is the flux for each band i within a circular aperture with a radius $r=\sqrt{x^2+y^2}$ of 075. The color aperture defined in Equation (4) is small enough to give a nearly optimal S/N for point sources and large enough to minimize possible systematics from residual astrometric or PSF matching uncertainties. We note that the K band has a relatively flat slope in S/N, whereas the improvements are most prominent for the J₁ band (shown in Figure 7). There is a 20%–30% loss of S/N when using larger apertures of 2''–3'' in bands blueward of the K band.

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The empirical estimate of the background noise σ_nmad described in Section 3.5 was repeated for all optical and NIR images within the color aperture of 15. From these values, we estimate the flux uncertainties for each object in each band as

$$\begin{equation} \sigma _{\mathrm{color},i}^2=\left(\frac{\sigma _{\mathrm{nmad},i}}{\sqrt{w_i/w_{\mathrm{median},i}}}\right)^2+\frac{F_{\mathrm{color},i}}{g_i}. \end{equation} \tag{ 5 }$$

The photometric error for each band i is the sum in quadrature of the background uncertainty (σ_{nmad, i}; defined in Equation (3)) weighted by the fractional exposure w_i at each object's location relative to the median w_{median, i}, and the source Poisson noise F_i/g_i for each band, with the former dominating the noise for faint sources and the latter for bright sources. F_i is the flux of the object in ADU within a 15 aperture and g_i is the total effective gain. Note that these are the uncertainties of the aperture fluxes, not the total fluxes. The uncertainty in the total fluxes listed in the catalogs is

$$\begin{equation} \sigma _{\mathrm{total},i}=\sigma _{\mathrm{color},i}\times \frac{K_{\mathrm{total}}}{K_{\mathrm{color}}}. \end{equation} \tag{ 6 }$$

The K-band total magnitude is calculated from the SExtractor AUTO photometry (see Equation (9)), with an uncertainty calculated as

$$\begin{equation} \sigma _{K_{{\rm tot}}}^{2}=\left(\frac{\sigma _{1}\alpha \left(\pi R_{\mathrm{Kron}}^{2}\right)^\frac{\beta }{2}}{\sqrt{w_K/w_{\mathrm{median},K}}}\right)^{2}+\frac{K_{\mathrm{AUTO}}}{g_K}, \end{equation} \tag{ 7 }$$

where R_Kron is the circularized Kron radius (Kron 1980) and σ₁, α, and β are defined in Equation (3), weighted by the fractional exposure time. The circularized Kron radius is calculated from the semimajor and semiminor axes as $R_{\mathrm{Kron}}=\sqrt{\mathrm{A\_IMAGE}\times \mathrm{B\_IMAGE}\times \mathrm{KRON\_RADIUS}^2}$, using the output SExtractor parameters. The following equation can be used to determine the full error in the total magnitude for a single band in isolation, including systematics:

$$\begin{equation} \sigma _{\mathrm{full},i}^2=\sigma _{\mathrm{total},i}^2+\sigma _{K_{{\rm tot}}}^2-\sigma _{\mathrm{total},K}^2. \end{equation} \tag{ 8 }$$

The derivation of the uncertainties for the UV and mid-IR data is described in Sections 4.3 and 4.4.

The sources are detected in a noise-equalized K-band image using SExtractor in dual-image mode, where the aperture photometry is simultaneously measured on the PSF-matched u – K images. In both fields, the K-band detection image is the unsmoothed (pre-PSF matching) NEWFIRM K-band image multiplied by the square root of the weight map (based on fractional exposure time per pixel). The input SExtractor parameters were optimized so as to find all faint objects while limiting the number of spurious detections. The optimal setting for the minimum number of pixels above the threshold to trigger a detection was 5 pixels, with a detection threshold of 1.2σ and 32 deblending sub-thresholds. We use a Gaussian filter for the detections with an FWHM of 4 pixels, first performing a global background subtraction in all optical–NIR images with a background mesh size of 32 pixels and a smoothing filter of 3 pixels. We note that we used a minimum Kron radius of 3 pixels, compared to the default value of 3.5 pixels. A fixed aperture diameter of 15 (5 pixels) was used to enclose a significant fraction of a given object's flux while minimizing uncertainties due to background fluctuations (see Section 4.1, Figure 7).

Total fluxes were determined using the SExtractor AUTO photometry, which uses a flexible elliptical aperture. This aperture contains the majority of the flux for bright objects but may be missing a large fraction of the light for fainter objects. Therefore, an aperture correction is applied to convert the AUTO flux to total flux (see, e.g., Labbé et al. 2003). The K-band total flux is calculated as follows:

$$\begin{equation} K_{\mathrm{total}}=K_{\mathrm{AUTO}}\times \frac{1}{f_{\mathrm{R<AUTO}}}, \end{equation} \tag{ 9 }$$

where K_AUTO is the AUTO flux and f is the fraction of light enclosed within the K-band growth curve generated during the PSF matching described in Section 4.1 for a circular aperture with the same area as the AUTO aperture. We force a minimum size of the AUTO aperture equal to the size of the color aperture, affecting <0.1% of the sources. The aperture correction to the AUTO fluxes is typically on the order of 5%–10%, extending to higher values for the faint, extended sources. The total flux for each band i is calculated as

$$\begin{equation} F_{\mathrm{total},i}=F_{\mathrm{color},i}\times \frac{K_{\mathrm{total}}}{K_{\mathrm{color}}}, \end{equation} \tag{ 10 }$$

where F_{color, i} is the flux within a color aperture of 15 diameter (see Equation (4)).

The FWHM of the IRAC and MIPS images are a factor of about two and about five broader, respectively, than the PSF-matched images. Furthermore, the IRAC and MIPS images contain significant non-Gaussian structure that results from point-source diffraction. Smoothing the optical-to-NIR photometry to the IRAC PSF shape would substantially reduce the S/N and cause significant blending issues in the deep optical data in addition to the IRAC/MIPS images.

We use a source-fitting algorithm developed by one of us (I.L.) that is designed for heavily confused images to extract the photometry from the IRAC and MIPS images (see, e.g., Labbé et al. 2006; Wuyts et al. 2007; Marchesini et al. 2009; Williams et al. 2009). As sources that are bright in K are also typically bright in the IRAC images (and to a lesser extent MIPS images), the K band can be used as a high-resolution template to deblend the IRAC/MIPS photometry. The information on position and extent of the sources based on the higher resolution K-band segmentation map is therefore used to model the lower resolution IRAC 3.6–8.0 μm and MIPS 24 μm images. This technique is similar to Laidler et al. (2007), with one important difference. Laidler et al. (2007) use the best-fit fluxes to calculate flux ratios (colors) directly, whereas our method adds back in the residuals of the fit before performing aperture photometry.

Each source is extracted separately from the K-band image and, under the assumption of negligible morphological K-corrections, convolved to the IRAC/MIPS resolution using local kernel coefficients. The convolution kernels are constructed using bright, isolated, and unsaturated sources in the K and IRAC/MIPS bands, derived by fitting a series of Gaussian-weighted Hermite functions to the Fourier transform of the sources. Outlying or poorly fit kernels are rejected and a smoothed 2D map of the kernel coefficients is stored. All sources in each IRAC/MIPS image are fit simultaneously, with the flux left as a free parameter. The modeled light of neighboring objects is subtracted, thereby leaving a clean IRAC/MIPS image to perform aperture photometry in fixed 3'' apertures for IRAC and 6'' apertures for MIPS. For an illustration of this technique, see Figure 1 in Wuyts et al. (2007).

In order to compute a consistent K-IRAC color, we measure the flux of the objects on a cleaned K-band image convolved to the IRAC resolution within the same aperture to correct the photometry for flux that falls outside of the aperture due to the large PSF size. We then scale the photometry to total fluxes by measuring the ratio of the total K-band flux to the convolved K-band flux within a 3'' aperture for each object:

$$\begin{equation} F_{\mathrm{IRAC,catalog}}=F_{\mathrm{IRAC,cleaned}}(3^{\prime \prime })\times \frac{K_{\mathrm{total}}}{K_{\mathrm{conv}}(3^{\prime \prime })}, \end{equation} \tag{ 11 }$$

where F_{IRAC, cleaned} is the flux of the object measured with the modeled light of the neighbors removed, K_conv is the flux of the object measured in the K-band image after smoothing it to the IRAC resolution, and K_total is the total K-band flux. The F_IRAC catalog flux is the total flux that would have been measured in a 15 aperture with an aperture correction if IRAC had the same PSF as the other data.

The uncertainties in the measured fluxes are derived from the residual contamination of the subtracted neighbors. The normalized convolved K-band image of each neighboring source is scaled by the formal 1σ error in the fitted flux as computed from the covariance matrix produced by least-squares minimization. By performing aperture photometry on the image of the residual neighbor contamination, we get the error corresponding to the source flux measured within an aperture of the same size.

The catalog includes the 24 μm flux within fixed 6'' apertures and total fluxes. To measure the total 24 μm flux, we create a MIPS growth curve from several bright, isolated, and unsaturated point sources within each field. These square postage stamps are 126 on a side, and we derive an aperture correction from 6'' to 126 of a factor of 2.8. To convert to total flux, we include an additional aperture correction for the 17% of the flux that falls outside 13''.²⁰

The GALEX FUV band (1350–1750 Å) and NUV band (1750–2800 Å) have 45–6'' resolution (FWHM), roughly ∼4–5 times broader than the PSF-matched optical-to-NIR photometry. The same method described in Section 4.3 is used to extract the GALEX photometry. In this case, however, the higher resolution prior is the CFHT u-band image.

As the u band contains many blue galaxies not in the K-band detection image, a new segmentation map was generated with SExtractor for the u band and matched to the K-selected catalog. This allows for all of the objects within the field of view to be modeled to clean the GALEX images for aperture photometry, regardless of whether these objects are in the NMBS K-selected catalog.

Following Section 4.3, we measure an aperture correction from the flux of the objects on the cleaned u-band image convolved to the GALEX resolution in order to compute a consistent GALEX u color. We then scale the photometry to the same color apertures used for the optical-to-NIR photometry by measuring the ratio of the convolved u-band flux within a 6'' aperture and our catalog aperture size for each object, analogous to Equation (11).

A significant fraction of the objects detected by SExtractor are actually blended objects, although classified as single objects. Although SExtractor implements a deblending algorithm, there is no set of parameters that will enable the splitting of close pairs while also detecting faint objects, which requires pre-smoothing. Deblending the photometry is particularly important when studying the most luminous galaxies; the fraction of sources that are deblended increases from ∼10% at K = 22 mag to ∼40% at K = 20 mag, reaching as high as ∼80% of sources with K = 18 mag. In this section, we describe the method used to deblend the photometry of the single "parent" object into its constituent "children," based on the technique described by Lupton et al. (2001).

The deblending is done using the WIRDS K_S-band image (07 seeing) in COSMOS and a combination of the WIRDS K_S-band image (07 seeing) where the exposure is greater than 30% of the maximum and the non-PSF-matched K-band image in AEGIS (11) in the remaining area. Using this criterion, roughly half of the AEGIS deblending image is from the higher resolution WIRDS data. Peaks are found after applying a difference of Gaussian bandpass filter that preserves scales similar to the seeing size. Object templates are created by comparing pairs of pixels symmetrically around the peak and replacing both by the lower value. False peaks are rejected if the total template S/N < 3 or if the template peak value is less than two times the combined pixel value of all other templates at that location. Finally, we solve for the template weights by a linear fit of the templates to the image, and then assign flux to every pixel of each child according to the relative contribution of the weighted templates. The segmentation map is updated, assigning each pixel to the child with the largest contribution.

Using the peaks previously found in the high-resolution image, the deblending procedure is repeated for each u – K background-subtracted, PSF-matched image. Aperture photometry in 15 color apertures is then performed on the "deblended" children. Total fluxes are computed by dividing the parent total flux according to the aperture flux ratio of the children, thus conserving the total flux of the parent. The IRAC and MIPS photometry of the children is remeasured using the method described in Section 4.3, but now using the new deblended segmentation map and the positions of the children. Due to the large PSF size of the GALEX data and the lack of a deblended u-band segmentation map, no attempt was made to deblend the NUV and FUV data.

2186 and 3017 objects in the original catalogs were split into 5019 and 6803 children in AEGIS and COSMOS, respectively. New identification numbers of the children start at ID = 30000. On average, the difference between the total K-band flux of the brightest child relative to the parent increases with redshift, with a median difference of 0.1 mag at z ∼ 0.5 and 0.3–0.4 mag at z > 1.5.

Figure 8 shows an example of an object that has been deblended with the above algorithm. Although classified as a single object by SExtractor, there is clearly a faint neighbor. The deblending technique recovers a well-described SED of the faint neighbor, with a notably different shape and photometric redshift compared to the brighter galaxy. It is worthwhile to note that, in the case of a fainter neighboring object (e.g., child 2 in Figure 8), the photometric redshift of the brighter object (child 1) is generally not significantly different from the parent, even though the children can have vastly different spectral shapes and photometric redshifts.

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It is important to distinguish between galaxies and objects that are likely stars in the photometric catalog. Stellar SEDs have a characteristically steep rise and fall in their spectra, resulting in a tight stellar sequence in their u – J and J – K colors relative to the colors of galaxies. This is shown in Figure 9: stars (red) form a distinctive sequence with blue J – K colors for a wide range of u – J colors as compared to galaxies (black).

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Stars are flagged based on the u – J₁ and J₁ – K colors of all objects, where any objects satisfying the following limits (corresponding to the red line in Figure 9) will be classified as a star:

$$\begin{eqnarray} &&J_{1}\,{-}\,K\,{<}\,{-}0.74\,{+}\,0.26(u\,{-}\,J_{1})\quad [u\,{-}\,J_{1}\,{<}\,3]\nonumber \\ &&J_{1}\,{-}\,K\,{<}\,{-}0.55\,{+}\,0.19(u\,{-}\,J_{1})\quad [3<u\,{-}\,J_{1}\,{<}\,4]\nonumber\\ && J_{1}\,{-}\,K\,{<}\,{-}0.16\,{+}\,0.10(u\,{-}\,J_{1})\quad [u\,{-}\,J_{1}\,{>}\,4]. \end{eqnarray} \tag{ 12 }$$

The middle panel in Figure 9 shows the χ² values for the stars (red) and galaxies (black) when fit with the Pickles (1998) stellar template library compared to the default set of EAZY galaxy templates. The vast majority of objects that are classified as stars through their u – J and J₁ – K colors are better fit with the stellar templates. The fraction of objects that are classified as stars relative to the total number of objects as a function of K-band magnitude is shown in the right panel of Figure 9 for both fields. Almost all objects brighter than K ∼ 16 mag are stars.

We have compared our star classification to the COSMOS HST Advanced Camera for Surveys catalog,²¹ matching objects within a radius of 1''. We find that >90% of the objects classified as stars using the higher resolution I-band data also fall within our u – J₁ and J₁ – K color selection limit in Equation (13). The star classification method seems robust, although we note that there may be a small fraction of objects (<10% of stars and <1% of galaxies) that are misclassified, especially close to the detection limit.

The final K-selected catalog consists of 24,739 and 27,520 objects detected by SExtractor in the AEGIS and COSMOS mosaics, with a total of 27,572 and 31,306 objects in the deblended catalogs. Photometry in the FUV through the MIPS 24 μm band is included, with additional optical broadband and medium-band photometry in the COSMOS field. The catalog fluxes can be converted into total magnitudes as follows:

$$\begin{equation} m = -2.5\log {F}+25, \end{equation} \tag{ 13 }$$

where F is the total flux density of the object with a magnitude m normalized to a zero point of 25 in the AB system, corresponding to a flux density of 3.631 × 10⁻³⁰ erg s⁻¹ Hz⁻¹ cm⁻² (or 0.3631 μJy). To convert from total magnitudes to the color aperture magnitude, the fluxes and errors should be multiplied by the ratio of the K-band aperture flux (Kaper) to the total K-band flux. A description of the columns included in the version 5.1 catalogs can be found in Table 2.

A standard selection of galaxies can be obtained by selecting use = 1 for either the original SExtractor catalog or the deblended catalog, which is equivalent to wmin >0.3 and star_flag = 0. An additional cut on the S/N of the galaxies may be optimal.

We estimate the (point-source) completeness of our catalogs as a function of magnitude by attempting to recover simulated sources within the K-band noise-equalized detection images. The simulated point sources were generated from the K-band empirical PSF described in Section 4.1, before smoothing. The empirical PSF is scaled to the desired flux level and inserted at random locations within the entire image. We then run SExtractor using the same settings described in Section 4.2, determining the fraction of recovered sources as a function of input K-band total magnitude. Figure 10 shows the resulting completeness curves from this analysis. The completeness curves qualitatively agree with the raw number counts of galaxies within the fields shown in the inset plot.

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A fraction of the simulated point sources will fall on or close to other objects and these blended objects may not be properly handled by SExtractor. We have also repeated the simulations by inserting the point sources in locations that do not overlap with the segmentation map, thereby "masking" the original detected sources (dotted lines in Figure 10). We include the 90% and 50% completeness limits for both the masked and unmasked simulations in Table 3. We note that about 10% of the objects are blended within the original catalogs produced by SExtractor, as determined by the additional deblending algorithm described in Section 4.5. When using the deblended catalogs, these completeness limits may therefore be slightly conservative. As the NMBS K-band fields are not overly crowded, the completeness limits for both simulations are similar.

Figure 11 shows the surface density of galaxies as a function of magnitude in the NMBS fields compared to other galaxy number-count analyses drawn from the literature. Objects that are classified as stars (see Section 4.6) have been excluded from this calculation. The number counts are calculated in 0.4 mag bins using objects within the image area with >30% of the total K-band exposure time (∼0.21 deg² in both fields).

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The number counts of the NMBS fields have been corrected for incompleteness using the simulations without masking, as calculated in Section 4.8. We note that the completeness values only provide a simplistic correction to the surface density of objects, whereas a more sophisticated analysis would account for the difference between measured and intrinsic fluxes of the synthetic sources. Due to the potential biases in the photometry of the faintest sources, we only extend the average number counts to K ∼ 22.7, where the completeness correction begins to become significant (Figure 10).

The number counts of the NMBS fields agree with the large compilation of data sets within the scatter due to field-to-field variations. We note that the COSMOS field appears to have a relatively high density of objects at K < 18 mag. We refer the reader to Wake et al. (2011) for a detailed analysis of the relative densities and galaxy clustering in the NMBS fields.

We have compared our K- and K_S-band flux measurements to the COSMOS survey catalog (Capak et al. 2008; Ilbert et al. 2009).²² The COSMOS catalog is I-selected and quotes fluxes within a 3'' aperture with an aperture correction provided to convert to AUTO fluxes (see Capak et al. 2007, 2008). The K_S-band data in the COSMOS catalog is derived from an earlier CFHT K_S image taken during the 2004–2005 observing season, whereas we include the publicly available K_S image with photometry from the 2005–2007 observing seasons for this analysis. As the COSMOS K_S image used to make the publicly available COSMOS catalog has 15 seeing (compared to ∼08 seeing in the image version used in the NMBS catalogs), we smooth our K_S image with a Gaussian kernel to 15 and compare the fluxes between the catalogs.

Figure 12 shows the difference in K_S-band magnitude between the smoothed NMBS K_S image and the magnitude quoted within a 3'' aperture in the COSMOS catalog (black points) for all objects. The results indicate that there are no significant systematic zero-point offsets between the NMBS and COSMOS catalogs.

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We have also compared the GALEX and IRAC flux measurements to publicly available catalogs, finding excellent agreement. We exclude comparisons to catalogs where it is unclear how aperture corrections are applied as the interpretation is difficult, but note that there were not any large systematic offsets. The COSMOS GALEX NUV and FUV catalog fluxes within 3'' apertures agree within ∼0.05 mag with the public catalogs available through the Multimission Archive.²³ The AEGIS NMBS IRAC photometry within 35 apertures has a median difference of <0.03 mag for all channels when compared to the EGS catalog.²⁴ Finally, we have also compared the MIPS total fluxes in COSMOS to the S-COSMOS GO3 catalog, finding excellent agreement with a median offset of <1%. In general, the photometry of the NMBS catalogs agrees well with all publicly available catalogs within the fields.