ULTRA-DEEP K_S-BAND IMAGING OF THE HUBBLE FRONTIER FIELDS

K_s-band observations of the Abell 2744 and MACS-0416 fields were obtained between 2013 October and 2014 February with the High Acuity Wide-field K-band Imager (HAWK-I; Pirard et al. 2004; Kissler-Patig et al. 2008) on the 8.2 m UT4 telescope at the ESO Very Large Telescope (ESO program 092.A-0472). HAWK-I K_s-band observations of the Abell S1063 and Abell 370 fields were obtained between 2015 July and 2016 January from a subsequent program (095.A-0533). HAWK-I is composed of four chips with 2048 × 2048 $0\buildrel{\prime\prime}\over{.} 106$ pixels, and the full $7\buildrel{\,\prime}\over{.} 5\times 7\buildrel{\,\prime}\over{.} 5$ HAWK-I field of view is perfectly suited for covering both the primary and parallel HST ACS optical and WFC3 IR fields simultaneously in a single pointing (see Figure 1).

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The HAWK-I observations were divided into individual service mode Observation Blocks (OBs); typically one or two OBs of a given field were observed per night as conditions allowed, and occasionally multiple fields were observed on the same night. The execution of each OB lasted either 60 or 90 minutes, depending on how many exposures were obtained in the block. The exposures were roughly one minute each, with multiple coadds of shorter reads making up the exposure ($\mathrm{NDIT}\times \mathrm{DIT}\,=4\times 15$ s = 60 s for Abell 2744, 7 × 8 s = 56 s for MACS-0416, 8 × 12 s = 96 s for Abell S1063 and 8 × 12 s = 96 s for Abell 370).¹⁸ The telescope was offset with random dithers between each exposure to facilitate sky subtraction; observations taken before 2013 November 4 were dithered within a $20^{\prime\prime}$ box, which was subsequently increased to $40^{\prime\prime}$ to improve sky subtraction in the cluster cores crowded with bright galaxies and intra-cluster light. The total on-sky integration times for the Abell 2744, MACS-0416, Abell S1063, and Abell 370 fields are 29.3, 25.8, 27.9, and 28.3 hr, respectively. This includes some time taken with unfavorable image quality or transparency conditions in service mode; all on-sky exposures are included in the final mosaics, with relative weighting designed to favor the optimal observing conditions (see Section 3 and Equation (1)).

Imaging observations of the MACS-0717 and MACS-1149 fields in the K_s filter were obtained on 2015 January 26/27 and 2015 February 24 (program N097M), respectively, and both fields again on 2016 January 21/22 (program N135M), with the Multi-Object Spectrometer For Infra-Red Exploration (MOSFIRE; McLean et al. 2012) on the 10 m Keck I telescope. The MOSFIRE detector consists of 2048 × 2048 $0\buildrel{\prime\prime}\over{.} 1798$ pixels; the resulting $6\buildrel{\,\prime}\over{.} 1\times 6\buildrel{\,\prime}\over{.} 1$ field of view is unfortunately slightly too small to cover both HST fields simultaneously and therefore requires two pointings to cover the entire deep HST Frontier Fields imaging area (Figure 1). MOSFIRE exposures were obtained in a 3 × 3 "Box9" dither pattern spaced roughly $40^{\prime\prime}$ between offset positions. The total integration times on the MOSFIRE survey fields are summarized in Table 1. The individual detector integration times (DIT) were adjusted on the fly during the observing run to keep the total counts within the linear regime of the detector, while maintaining $\mathrm{NDIT}\times \mathrm{DIT}\sim 40\,{\rm{s}}$.

Additional archival HAWK-I imaging of the MACS-1149 fields was obtained from the program 090.A-0458. These data were obtained with one HAWK-I chip centered on the z = 9.7 candidate from Zheng et al. (2012); they largely cover the HFF cluster field, but the pointing was not optimized to also include the parallel field whose location was defined later (see Figure 1). The MACS-1149 HAWK-I observations were obtained in Service Mode at the ESO/VLT in between 2013 March 21 and 2014 June 9. The 20 × 15 s = 300 s exposures were taken at nine dithered positions offset within a $30^{\prime\prime}$ box; the on-source exposure time of the final MACS-1149 HAWK-I mosaic is 5.3 hr.

The HAWK-I and MOSFIRE observations were reduced with a pipeline that has been developed for previous surveys with the NEWFIRM (NMBS; Whitaker et al. 2011) and FOURSTAR (ZFOURGE; Spitler et al. 2012; Straatman et al, submitted) infrared imaging instruments. Treating each detector individually, the pipeline is easily modified for the different instrument configurations of the four HAWK-I and single MOSFIRE chips. The primary task of the pipeline is removing the bright, time-variable sky background from the individual exposures, which is often some 10⁴ times brighter than the distant galaxies of interest in the field. With such a bright background, we first determine an empirical "sky flat" that is a median of all of the science exposures in a HAWK-I OB or MOSFIRE group, after rejecting the brightest 12 exposures at each pixel position to remove the contribution of bright objects. We find these empirical flats to be preferable to external twilight or dome flats, given the difficulty of obtaining a truly flat illumination pattern over such large detector fields of view.

After dividing by the flat, the background of each exposure is determined in a first pass from the simple median of the four exposures that came both immediately before and after it. The first-pass background-subtracted exposures are combined into a mosaic, and objects are identified as pixels with values greater than five times the robust standard deviation (Beers et al. 1990) of the combined image. A buffer with a radius of 3 pixels is grown around each "object" pixel that satisfies this 5σ criterion. The final refined background of each exposure is determined in a second "mask pass" from a median again from the four exposures before and after it but now masking all pixels that contain flux from the detected objects.

As the archival HAWK-I images of the MACS-1149 field were obtained with longer individual exposures and with fewer exposures per sequence, the mask pass technique described above did not produce satisfactory results. In this case, for each raw exposure we divide by the empirical sky flat and then subtract a third-order polynomial fit to the background.

For the HAWK-I observations, a single 90 minute Service Mode OB was obtained in each of the fields requiring photometric transparency conditions, and these OBs were followed immediately by an observation of a photometric standard star at a similar airmass, with single exposures on each of the four chips. The standard star exposures were processed with empirical sky flats derived from the science exposures as described above, and the observed fluxes of the standard stars yield absolute photometric zeropoints for each chip. Correction factors were then computed to scale the OBs obtained at varying transparency levels to the calibrated photometric OB; the additional service mode OBs were obtained under generally satisfactory (i.e., "clear") weather conditions and the scale factors typically differ from unity by only a few percent. The photometric calibration of the MOSFIRE observations was determined from standard star observations taken the same night as the science exposures, again with the standard exposures reduced in the same way as the science exposures.

The 2-Micron All Sky Survey (2MASS; Skrutskie et al. 2006) provides an additional check on the photometric calibration, though the comparison is limited due to relatively little brightness overlap between the faint end of reliable 2MASS photometry and the bright end where stars are in the linear regime of the detectors on the 8–10 m telescopes. A comparison of the observed photometry in the four survey fields to the 2MASS catalog magnitudes is shown in Figure 2. The stellar photometry on the deep K_s-band mosaics is measured within $1^{\prime\prime}$ apertures corrected to infinity with the curves of growth described below. The error bars on the points in Figure 2 come from the 2MASS catalog; the photometric uncertainties are negligible for such bright stars in the deep images (${\rm{S}}/{\rm{N}}\gt 100$). The 2MASS comparison suggests a systematic zeropoint offset of −0.09 mag for the Abell S1063 field. However, the exposure time for that field was similar to those of the additional deep HAWK-I fields and the derived depths of all deep HAWK-I fields are nearly identical (Table 1). Therefore, we do not apply this offset to the S1063 zeropoint, since if it is real it should be reflected in the derived depth of that field, as compared to the others. Given the overall good agreement with the 2MASS photometry, we estimate that the systematic uncertainty of the absolute photometric calibration is ${\sigma }_{\mathrm{sys}}\leqslant 0.05$ mag.

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Similar to Fontana et al. (2014), we do not apply any correction for nonlinearity effects of the HAWK-I or MOSFIRE detectors. For the case of HAWK-I the user manual suggests that the detector is linear at the 1% level up to 30 000 detector counts (ADUs). For a 2MASS star in the Abell 2744 field with K = 17.3, the brightest pixel reaches ∼31 000 ADUs, including the bright sky background. Therefore, there could be a linearity correction of up to a few percent between the bright 2MASS stars used for the photometric comparison and galaxies in the field some 8–9 magnitudes fainter, though the stars in Figure 2 do not show any significant slope in the 2MASS magnitude residuals across ∼1.5 mag of dynamic range. For the fainter galaxies, empirical "zeropoint corrections" are often computed as part of the photometric redshift analysis (e.g., Skelton et al. 2014), and these would compensate for relatively small linearity effects.

In order to simplify measurements from the K_s-band images in concert with space-based HST and Spitzer mosaics, the astrometry of the ground-based mosaics must be refined. Absolute astrometric reference catalogs were generated from HST images when available (i.e., the chips overlapping the cluster and parallel HST fields) and public Subaru Suprime-Cam r_c-band images otherwise.¹⁹ Next, object catalogs were generated with the SEXtractor software (Bertin & Arnouts 1996) for each individual background-subtracted exposure and transformations to the reference frame (shift, rotation, and scale) were computed with the stsci.stimage.xyxymatch and scikit-image.transform ²⁰ Python software tools. For the HAWK-I exposures, we fit a third-order polynomial to the geometric distortion model determined by Libralato et al. (2014) and specified the polynomial terms as "Simple Imaging Polynomial" (SIP) coefficients (Shupe et al. 2005) in the individual exposure FITS files. The SIP FITS header that is generally applicable for HAWK-I is provided in the Appendix. We note that the HAWK-I distortion is generally small, reaching ∼2 pixels ($0\buildrel{\prime\prime}\over{.} 2$) at the image corners, but that the distortion corrections are necessary, in particular, given the excellent overall image quality of the observations.

Figure 4 shows the curves of growth for stars identified by the tight relationship between their brightness and half-light radii (see, e.g., Figure 13 of Skelton et al. 2014). The image quality of the K_s-band mosaics is excellent with stellar FWHM $\lesssim 0\buildrel{\prime\prime}\over{.} 4$ for the deep HAWK-I fields, thanks in large part to the execution of the HAWK-I observations in service mode, ensuring optimal and uniform image quality across the many hours of integration on the survey fields. The classical scheduling of the MOSFIRE observations does not allow such control over the seeing conditions. The result is that the image quality of the MACS-0717 and MACS-1149 fields is somewhat degraded in comparison, at $0\buildrel{\prime\prime}\over{.} 42$–$0\buildrel{\prime\prime}\over{.} 54$, and the image quality differs measurably between the two MOSFIRE pointings in the MACS-0717 field. Despite the compact cores of the stellar PSFs, the curves of growth shown in Figure 4 deviate from Gaussian profiles with significantly higher flux in the outer wings, with a shape more consistent with a Moffat profile (Trujillo et al. 2001) with $\beta \sim 2$. We caution that these extended profiles will yield significantly shallower final image depths than would be predicted with Exposure Time Calculators that may assume Gaussian profiles. Nevertheless, the deep K_s mosaics have excellent image quality that is much closer to the resolution of the HST IR imaging and the typical apparent size of distant galaxies (median ${r}_{e}\sim 0\buildrel{\prime\prime}\over{.} 1$–$0\buildrel{\prime\prime}\over{.} 2$ at $z\gt 4;$ Shibuya et al. 2015) than the redder Spitzer IRAC bands (PSF FWHM∼$1\buildrel{\prime\prime}\over{.} 7$–2'').

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The image quality obtained here with HAWK-I demonstrates the excellent natural seeing conditions of the VLT site at Cerro Paranal. We note here that HAWK-I will soon be upgraded with a ground layer adaptive optics module (GRAAL; Paufique et al. 2010) that will improve the image quality by factors of 1.5–2 over the natural seeing over the wide HAWK-I field of view. Schirmer et al. (2015) recently presented deep AO-corrected K_s-band imaging of the MACS-0416 cluster field obtained with the Gemini South Adaptive Optics Imager (GSAOI; Carrasco et al. 2012). Thanks to the availability of a bright guide star near the center of the cluster field, GSAOI provided exquisite image quality (FWHM $\sim \,0\buildrel{\prime\prime}\over{.} 09$) better than even that of HST WFC3/IR. Though somewhat shallower (${K}_{s}\,\sim$ 25.6, 5σ) and covering a smaller field of view ($1\buildrel{\,\prime}\over{.} 7\times 1\buildrel{\,\prime}\over{.} 8$, Figure 1) than the HAWK-I mosaics, the GSAOI images provide an auspicious demonstration of the power of wide-field AO-corrected imaging for deep extragalactic science.

Along with practical benefits mentioned above, the most dramatic benefit of using the drizzle algorithm comes from the fact that the raw detector pixels are only resampled once in the process of generating the output mosaic. Furthermore, with a large number of dithered raw images we can use drizzle to shrink the raw input pixels by a factor of 10 before dropping them into the output grid,²² and the result is dramatically reduced correlations between neighboring pixels, particularly for output pixel sizes that are somewhat smaller than the native HAWK-I or MOSFIRE detector pixels.

A comparison of the final combined images created with output $0\buildrel{\prime\prime}\over{.} 1$ and $0\buildrel{\prime\prime}\over{.} 06$ pixel grids using the drizzle implementation, to versions created with the SWarp software (Bertin et al. 2002), is shown in Figure 5. In the later case, the raw pixels are resampled twice before making the final mosaic, once combining the raw exposures in each OB and a second time combining the separate OBs into the final stack with an arbitrary pixel grid. One could avoid the second resampling and combine all of the raw exposures at once, though SWarp is still limited to dropping the original pixels into the output mosaic preserving the input native pixel grid and therefore a single input pixel maps onto multiple (perhaps many) output pixels.

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The fact that the drizzle-combined images in Figure 5 (panels (a) and (b)) appear to the eye to be noisier than their SWarped counterparts (panels (c) and (d)) is simply the result of a smoothing of the pixel noise in the latter case rather than reflecting true underlying differences in their pixel-to-pixel variance. Casertano et al. (2000) discuss how the noise properties of correlated output pixels are affected by the relative sizes of the input and output pixel grids and the adopted drizzle parameters. With the drizzle algorithm and a small pixfrac, a given input pixel will map to only a single output pixel and therefore correlations between the output pixels should be minimal.²³

We explore these correlations between the output pixels in Figure 6. For the black and red curves in each panel, we measure value differences between random pairs of pixels sorted by the separation between the pixels for the drizzled and SWarped images, respectively. For perfectly uncorrelated pixels, these curves will be flat and will reflect the intrinsic noise of the image pixels. In the presence of correlations between adjacent pixels, however, the curves will show a depression at small separations. As expected, the SWarp-combined images show exactly such a depression for pairs of pixels 1–2 pixels apart. The yellow curves in Figure 6 show the same pairwise differences for the drizzled images now convolved by small Gaussian kernels as indicated, which agree very well with the curves for the images with correlated pixels.

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In terms of understanding the noise properties of the images, a key point here is not only that depression at small separations indicates the presence of correlations between adjacent pixels but also the fact that correlations cause the apparent overall rms to be decreased at all separations. That the pixel variances cannot be used directly in the presence of such correlations (Casertano et al. 2000) is the primary reason why significant effort has been devoted to placing random "empty apertures" across images in order to characterize their noise properties (e.g., Labbé et al. 2003; Förster Schreiber et al. 2006; Quadri et al. 2007a; Whitaker et al. 2011; Skelton et al. 2014). Now by eliminating the pixel correlations with the drizzle image combination technique (with a small pixfrac) we have shown that the pixel statistics are robust and it is now trivial to compute the expected variance within an arbitrary photometric aperture, for example:

$$\begin{eqnarray}&&{\sigma }_{\mathrm{aper},D}^{2}={\sigma }_{\mathrm{pix}}^{2}\cdot \pi /4\cdot {D}^{2},\end{eqnarray} \tag{ 2 }$$

for circular apertures with diameter, D, in pixels, and where ${\sigma }_{\mathrm{pix}}^{2}$ is the per-pixel variance determined from an analysis such as that in Figure 6.

The product of Equation (2) and the inverse of the curves of growth shown in Figure 4 (i.e., aperture corrections) defines an optimal photometric aperture size where this product is minimized (Whitaker et al. 2011). For our K_s-band mosaics, this optimal aperture has $D\sim 0\buildrel{\prime\prime}\over{.} 6$, just larger than the FWHM of point-source profiles. The 5σ limiting magnitudes (AB) within $0\buildrel{\prime\prime}\over{.} 6$ diameter apertures are indicated in Figure 7 and listed in Table 1. Reaching 26th magnitude (AB), the HAWK-I images presented here are among the deepest K_s-band images ever obtained and will provide an important complement to the deep HST and Spitzer imaging of the Frontier Fields.

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We conclude here with a brief comment on the "HUGS" ultra-deep HAWK-I images of the CANDELS GOODS-S and UDS survey fields. Fontana et al. (2014) report a final depth of 26.5 AB for point sources within $D=0\buildrel{\prime\prime}\over{.} 4$ apertures for their deepest field, "GOODS-D1." This field has an exposure time of 31.5 hr, similar to the deep HAWK-I fields summarized in Table 1. Fontana et al. (2014) assume ideal noise properties that likely suffer some residual correlation between adjacent pixels, such as that indicated by the red curves in Figure 6, where we found that the drizzled rms was some 40% higher than that measured in the presence of the pixel correlations for $0\buildrel{\prime\prime}\over{.} 1$ pixel mosaics. This effect (∼0.4 mag) along with the relative exposure time difference (∼0.1 mag) can account for much of the difference between the reported depths of the deepest HUGS pointings and the Hubble Frontier Fields HAWK-I images described here. The comparison must be made because any additional half magnitude increase depth is exponentially more expensive to obtain!

We compute source detection completeness curves as a function of source brightness following the techniques described by Whitaker et al. (2011) and Muzzin et al. (2013). Briefly, we insert artificial sources in blank regions of the portions of the images covering the HST "parallel" fields and compute the fraction of sources recovered with SExtractor as a function of the source magnitude. The resulting completeness curves are shown in Figure 8. As in the sensitivity analysis above, we find that the detection completeness curves are nearly identical for the deep HAWK-I fields, with 50% (90%) source completeness at ${K}_{s}\sim 25.9$ (25.7) AB. The completeness thresholds for the shallower northern MACS-1149 and MACS-0717 fields are ∼0.75 mag brighter.

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We perform this completeness analysis to provide a general characterization of the K_s-band image mosaics and to provide a point of comparison for earlier surveys, such as UltraVISTA (Muzzin et al. 2013). However, in the case of the Frontier Fields cluster and parallel fields with much deeper photometry available from HST (c.f. 28.7 AB in H₁₆₀), the K_s-band images can be more effectively exploited for most applications by detecting objects in the deeper HST images and performing forced K_s-band photometry at the positions of the HST sources. Merlin et al. (2016) present multiwavelength catalogs of the Abell 2744 and MACS-0416 fields constructed in this way, including incorporating an early version of the HAWK-I K_s-band mosaics. The generation of these catalogs is beyond the scope of the present work and will be presented in further detail by H. Shipley et al. (2016, in preparation).