THE HUBBLE SPACE TELESCOPE WIDE FIELD CAMERA 3 EARLY RELEASE SCIENCE DATA: PANCHROMATIC FAINT OBJECT COUNTS FOR 0.2–2 μm WAVELENGTH^*

In the current ERS program, the unique panchromatic capabilities of WFC3 are used to survey the structure and evolution of galaxies at the peak of the galaxy assembly epoch at z≃ 1–3. Deep ultraviolet and near-IR imaging, and slitless near-IR spectroscopy of existing deep multi-color GOODS-S/ACS fields are used to gauge star formation and the growth of stellar mass as a function of galaxy morphology, structure and surrounding density in this critical cosmic epoch at redshifts 1 ≲ z ≲ 3.

The total HST filter set provided by the WFC3 ERS imaging of the GOODS-South field is shown in Figure 1(a), and its properties are summarized in Tables 1 and 2. WFC3 adds the F225W, F275W, and F336W filters in the WFC3 UVIS channel, and the F098M, F125W, and F160W filters (hereafter Y_sJH) in the WFC3 IR channel. Together with the existing GOODS ACS F435W, F606W, F775W, and F850LP images (Giavalisco et al. 2004), the new WFC3 UVIS and IR filters provide a total of 10 HST filters that span the wavelength range λ ≃ 0.2–1.7 μm nearly contiguously. We refer to this entire 10-band survey hereafter as the "ERS," to these 10 filters as the "ERS filters," and to the seven reddest ERS filters as the "BVizY_sJH" filters throughout. Details of the GOODS survey can be found in Giavalisco et al. (2004) and references therein. The top panel of Figure 1(a) compares the ERS filters to the spectral energy distribution (SED) of two single burst model galaxies (middle and bottom panels of Figure 1(a)) with ages of 0.1 and 1 Gyr at redshifts of z = 0, 2, 4, 6, and 8, respectively.

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The ERS images in the WFC3 UVIS filters F225W, F275W, and F336W are used to identify galaxies at redshifts z ≳ 1.5 from their UV continuum breaks, which between the F225W and F275W filters is sampled at redshifts as low as z≃ 1.5–1.7 (see Figure 1). These filters provide star formation indicators tied directly to both local and z ≳ 3 galaxy populations, which are the ones best observed through their Lyman breaks from the ground at λ ≳ 350 nm. The critical new data that the WFC3 UVIS channel can provide are thus very high resolution, deep images for 0.2 μm ≲ λ ≲ 0.36 μm, as illustrated in Figure 1(a).

The ERS images in the WFC3 near-IR filters F098M, F125W, and F160W are used to probe the Balmer and 4000 Å breaks and stellar mass function well below 10⁹ M_☉ for mass-complete samples in the critical redshift range of z≃ 1–3. The unique new data that the WFC3 IR channel can provide are high-resolution, very sensitive near-IR photometry over fields larger than those possible with HST NICMOS, or over wide fields with adaptive optics from the ground (e.g., Steinbring et al. 2004; Melbourne et al. 2005).

In addition to these broadband ERS filters, we used the WFC3 near-IR grisms G102 and G141 to obtain slitless spectroscopy of hundreds of faint galaxies at a spectral resolution of R≃ 210–130, respectively. The WFC3 near-IR grism data can trace the primary indicators of star formation—the Lyα and H-α emission-lines—in principle over the redshift range for z≃ 5–13 and z≃ 0.2–1.7, respectively. WFC3 can also trace the Lyman break and the rest-frame UV continuum slope, as well as the Balmer and 4000 Å breaks over the redshift range z≃ 1–9 and z≃ 0–2.5, respectively. The ERS grism program thus at least covers the peak of the cosmic star formation history at redshifts 1 ≲ z ≲ 2, using some of the most important star formation and post-starburst indicators, while also providing some metallicity-independent reddening indicators. Both IR grism dispersers provide capabilities that cannot be reproduced from the ground: slitless spectroscopy of very faint objects (AB ≃ 25–26 mag) over a contiguous wide spectral range in the near-IR, that is not affected by atmospheric night-sky lines. The ERS grism observations are two orbits in depth each, covering a single WFC3 field, which was also covered in a previous ACS G800L grism survey (Straughn et al. 2009). An example of the ERS G141 and G102 grism spectra is shown in the figures of Appendix B.2. Further details of the ERS grism data reduction and the analysis of the faint emission line galaxies are given in Appendix B.2 and by Straughn et al. (2011).

WFC3 UVIS G280 UV-prism observations were not made as part of the 104 orbit intermediate-redshift ERS program, because of its much lower throughput and the significant overlap of its many spectral orders (Bond & Kim Quijano 2007; Wong et al. 2010). Currently, one Cycle 17 GO program (11594; PI: J. O'Meara) is using the WFC3 G280 prism to carry out a spectroscopic survey of Lyman limit absorbers at redshifts 1.8 ≲ z ≲ 2.5. Readers interested in the WFC3 G280 prism performance should follow the results from that program.

In the context of the WFC UVIS and IR channel performance for intermediate- to high-redshift early- and late-type galaxies, it is useful to briefly summarize here the possible effects of UVIS channel filter red-leaks and IR channel filter blue-leaks on the measured fluxes of these objects. UVIS red-leaks are defined as the fraction of flux longward of 400 nm of an SED of given effective temperature T_eff that makes it erroneously into the UV filter. The IR blue-leaks are defined as the fraction of flux shortward of 830 nm of an SED of given effective temperature T_eff that makes it erroneously into the IR filter or grism (for details, see Wong et al. 2010).

The WFC3 UVIS filters were designed with great attention to minimize their red-leaks, which were much larger in the earlier generation WFPC2 UV filters. Similarly, the WFC3 IR filters and grisms were designed to minimize the blue-leaks. For both sets of WFC3 filters, lower out-of-band transmission usually goes at the expense of lower in-band transmission, and vice versa. Hence, both the WFC3 and IR filters were designed and fabricated such that the in-band transmission was optimized as much as possible, while keeping the out-of-band transmission to acceptable or correctable levels for all SEDs expected in the relevant astrophysical situations.

The resulting WFC3 UVIS red-leaks are acceptably small (≲10%) for all zero-redshift SEDs with T_eff ≳ 5000 K for the F225W filter, T_eff≳ 4000 K for the F275W filter, and T_eff ≳ 2000 K for the F336W filter, respectively (Wong et al. 2010). For cooler (T_eff ≲ 2000–5000 K) zero-redshift SEDs, some red-leak correction thus has to be applied to the observed F336W, F275, and F225W fluxes, respectively. However, for objects at substantial redshifts (z ≳ 0.75–1), the SED will shift out of the UVIS sensitivity regime quickly enough to significantly reduce the red-leak. Hence, the WFC3 UVIS red-leaks in general only need to be corrected for the reddest (T_eff ≲ 5000 K), lower-redshift (z ≲ 0.75) SEDs observed in the bluest UVIS filters (F225W). Further details are given in Rutkowski et al. (2011).

The WFC3 IR blue-leaks are very small (≲0.01%) for all zero-redshift SEDs with T_eff ≲ 10,000 K for the F098M, F105W, F125W, and F160W filters, and remains very small (≲0.1%) even for the bluest zero-redshift SEDs with T_eff ≃ 30,000–50,000 K (Wong et al. 2010). For higher-redshift SEDs (z ≳ 1) of any T_eff, the redshift further reduces the IR blue-leak. Similarly, the G141 grism was made on a glass substrate with no transmission below 750 nm, and is well blocked by its coatings shortward of 1050 nm and long-ward of 1700 nm (Baggett et al. 2007). Hence, it also has acceptably an small blue-leak. The same is true for the higher-resolution G102 grism.

The WFC3 UV-blue optimized CCDs were chosen specifically to complement those of ACS. They were made by E2V in the UK, and are thinned, backside illuminated, CCD detectors with 2k × 4k 15 μm (00395) pixels, covering the wavelength range 200–1000 nm with Quantum Efficiency QE ≳ 50% throughout (Wong et al. 2010; Kimble et al. 2010). The total WFC3 UVIS field of view with these two CCDs is 162'' × 162''.

The WFC3 near-IR detectors were Teledyne HgCdTe infrared detectors (molecular beam epitaxy-grown and substrate removed) with Si CMOS Hawaii-1R multiplexers and have 1k × 1k 18 μm (0130) pixels, covering the wavelength range 800–1730 nm with QE ≳ 77% throughout (Wong et al. 2010; Kimble et al. 2010). The total WFC3 IR field of view is 123'' × 136''. Further specifications of the WFC3 detectors are listed where relevant below.

Table 1 summarizes the resulting WFC3 sensitivities from our relatively short ERS exposures. The table lists the number of orbits per filter and the 5σ depths in AB magnitudes and F_ν units. A net exposure time of 2600–2700 s was available in each HST orbit for on-source ERS observations. In Figure 1(b), the equivalent depths are plotted in physical terms, by comparing with the spectral synthesis models of Bruzual & Charlot (2003) at the three fiducial redshifts, following Ryan et al. (2007, 2008, 2011). Simple stellar populations models with single bursts or exponentially declining star formation rates with an e-folding time of 1 Gyr are plotted. Figure 1(b) shows the predicted SEDs for models with ages ranging from 10 Myr to 3 Gyr, along with the 5σ depths of the WFC3 ERS program. The three panels represent redshifts z = 1.0, 1.5, and 2.0, and models with stellar masses of M = 10⁹, 4 × 10⁹, and 10¹⁰ M_☉, respectively. These SED tracks illustrate the intended SED and mass sensitivity of the WFC3 ERS observations as a function of cosmic epoch. Galaxies with ongoing star formation, even with fairly large ages, are easily detected in the WFC3 UV observations. At z ≃ 2, a maximally old τ ≃ 1 model with a mass of ∼0.3 M* is detectable above the WFC3 detection threshold in the F336W filter, while at z≃ 1, the WFC3 ERS can detect young star-forming galaxies with masses as low as a few × 10⁷ M_☉, or about a M ∼0.01 M* galaxy in that filter.

Table 2 summarizes the HST instrument modes and the ERS filters used, the filter central wavelength λ, its width, and the point-spread function (PSF) FWHM as a function of wavelength, the AB magnitude zero points for all 10 filters for a count rate of 1.0 e⁻ s⁻¹, as well as the zodiacal sky background measured in each ERS filter. The GOODS sky-background values in the F435W, F606W, F775W, and F850LP filters (hereafter BViz) are from Hathi et al. (2008).

Figure 2 shows that on average, the on-orbit WFC3 UVIS sensitivity is 6%–18% higher than the predicted pre-launch sensitivity from the ground-based thermal vacuum test (left panel), and the on-orbit WFC3 IR sensitivity is 9%–18% higher (right panel). The red lines are best fits to the in-flight/pre-launch sensitivity ratio. For the UVIS data, this is just a parabolic fit, as the in-flight/pre-launch excess does not seem to follow the CCD sensitivity curve (Kalirai et al. 2009a). For the IR data, a polynomial fit was folded with the IR detector sensitivity curve, since the in-flight/pre-launch does somewhat resemble the IR detector sensitivity curve (Kalirai et al. 2009b). The true cause of this beneficial, but significant discrepancy is unknown. It possibly results from uncertainties in the absolute calibration procedure of the optical stimulus used in the thermal vacuum tests of WFC3 (Kimble et al. 2010), and/or perhaps from slow temporal changes in the HST Optical Telescope Assembly (OTA) itself (Kalirai et al. 2009a, 2009b). The cause of this discrepancy is currently being investigated, and lessons learned will be applied to the upcoming ground-based calibrations of the James Webb Space Telescope (JWST) thermal vacuum absolute throughput measurements.

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4.1.1. WFC3 UVIS

4.1.2. WFC3 IR

4.2.1. WFC3 UVIS Astrometry

4.2.2. The WFC3 UVIS MultiDrizzle Procedure

These first-pass aligned images were then run through a full combination with MultiDrizzle (Koekemoer et al. 2002), which produced a mask of cosmic rays for each exposure, together with a cleaned image of the field. The cosmic ray mask was used to create a cleaner version of each exposure, by substituting pixels from the clean, combined image. These were then rerun through the cross-correlation routine to refine the relative shifts between the exposures, achieving an ultimate relative alignment between exposures with an accuracy of ≲2–5 mas. This process was limited primarily by the on-orbit cosmic ray density, and the available flux in the faint UV objects visible in each individual UVIS exposure. In the end, about 3 independent input pixels from four exposures contributed to one MultiDrizzle UVIS output pixel. Of these, typically ≲1%–2% were rejected in the cosmic ray rejection, leaving on average three independent UVIS measurements contributing to one MultiDrizzle output pixel in both the F225W and F275W filters. In F336W, about 2.3 independent input pixels from the three F336W exposures contributed to one output pixel during the MultiDrizzle process.

After this relative alignment between exposures was successfully achieved, each set of exposures needed to be aligned to the absolute GOODS astrometric reference frame. This was achieved by generating catalogs from the cleaned, combined images for each of the three ERS UVIS filters F225W, F275W, and F336W, and matching them to the GOODS B-band catalog (Giavalisco et al. 2004; Grogin et al. 2009). This was done by solving for linear terms (shifts and rotations) using typically ∼30–50 objects matched in each pointing, depending on the UVIS filter used. This procedure successfully removed the mean shift and rotational offsets for each visit relative to the GOODS astrometric frame. MultiDrizzle also produced "weight" maps (Koekemoer et al. 2002), which are essential for the subsequent object detection (Section 5.1), and for the computation of the effective area, which is needed for the object counts (see the figures in Sections 6 and 7).

In order to perform matched aperture photometry (see Section 5.2), our approach was to create images at all wavelengths at the same pixel scale. Since the IR data was necessarily created at 0090 per pixel (see Appendix A), we created UVIS mosaics at that same pixel size. This essentially "smoothed" over the remaining issue of the geometric distortion solution (see Appendix A), and created a sufficient data product for the purpose of producing matched aperture photometric catalogs, reliable total magnitudes in all 10 ERS filters, performing z ≃ 1–3 dropout searches, and many other "total magnitude applications." The performance of the panchromatic ERS images for photometric redshift estimates is described by Cohen et al. (2011). Further details on the remaining uncertainties from the UV geometric distortion and its corrections are given in Appendix A and in Figures 4(a) and (b).

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The current 0090 per pixel UVIS image mosaic is referred to as "ERS version v0.7." In the future, when the UV GDC is well measured, and better on-orbit WFC3 flat fields or sky flats become available, we will make higher-resolution images (0030 per pixel) for applications such as high-resolution faint-galaxy morphology, structure, half-light radii, and other high-precision small-scale measurements of faint galaxies, and make these end-products available to the community.

4.2.3. IR Astrometry and MultiDrizzle Procedure

4.3.1. The Panchromatic 10-band ERS Mosaics

Figure 5(a) shows the panchromatic 10-band color image of the entire ERS mosaic in the GOODS-South field. All 10 ERS filters in Figures 5, 6, 13, and 14 are shown at the 0090 pixel sampling discussed in Section 4. All RGB color images of the 10-band ERS data were made as follows. First, the mosaics in all 10 filters were registered to the common WCS of the ACS GOODS v2.0 reference frame to well within one pixel. Second, all images were rescaled to F_ν units of Jy per pixel using the AB zero points of Table 2. Next, the blue gun of the RGB images was assigned to a weighted version of the UVIS images in the F225W, F275W, and F336W filters and the ACS F435W filter. The green gun was assigned to a weighted version of the ACS F606W and F775W images, which had the highest S/N of all available images. The red gun was assigned to a weighted version of the ACS z-band (F850LP) and WFC3 IR F098M, F125W, and F160W images. All weighting was done with the typical image sky S/N, sometimes adjusted so as to not overemphasize the deepest multi-epoch GOODS v2.0 images in the V and i filters. This procedure thus also rebalanced the different sensitivities per unit time in these filters, as shown in Figures 1(a) and (b), and corrected for the fact that some filters have their central FWHM-range overlap somewhat in wavelength, so they are not completely independent (see Table 2). This is especially noticeable for the ACS z-band filter F850LP—which at the long wavelength side is cutoff by the sharp decline in the QE-curve of silicon—and the IR F098M filter, which does not have this problem at its blue side, but overlaps with F850LP for about 40% of its OTA × T × QE integral, where OTA is the net OTA reflectivity, T in the product of the WFC3 optics reflectivities and filter + window transmissions, and QE is the detector Quantum Efficiency as a function of wavelength. (When the QE of the HgCdTe detectors produced by Teledyne increased from ∼10%–20% in 2001 to ≳80% after 2005, the F098M filter thus became almost a replacement of the ACS z band).

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In Figures 5(a) and (b), we used a log(log) stretch to optimally display the enormous dynamic range of the full resolution ERS color TIFF images. Figure 5(a) only displays the overlap between the 4 × 2 ERS UVIS mosaics, the GOODS v2.0 ACS BViz mosaics, and the 5 × 2 ERS IR mosaics. Each of the ERS mosaics are 8079 × 5540 pixels in total, but only about 6500 × 3000 pixels or 975 × 45 or 43.875 arcmin² is in common between the UVIS and IR mosaics and shown in Figures 5(a) and (b). The area of the individual UVIS mosaics used in each of the UV–optical galaxy counts of Section 7 is substantially larger than this, but the total usable area of the IR mosaics is comparable to the area shown in Figure 5(a).

Figure 5(b) (see Appendix B.1) shows a zoom of the 10-band ERS color image, illustrating the high resolution available over a factor of 10 in wavelength, the very large dynamic range in color, and the significant sensitivity of these few orbit panchromatic images. Further noteworthy objects in the images are discussed in Appendix B.1 below.

4.3.2. Astrometric Quality of the ERS Mosaics

4.3.3. The Panchromatic ERS PSFs

Figure 6(a) shows a full color reproduction of a stellar image in the 10-band ERS color images in the GOODS-South field, and Figure 6(b) shows a "double" star. These images give a qualitative impression of the significant dynamic range in both intensity and wavelength that is present in the ERS images. Figure 7(a) shows images in all 10 ERS filters of an isolated bright star that was unsaturated in all filters, and Figure 7(b) shows its 10-band stellar light profiles. Table 2 lists the stellar PSF FWHM values in the 10 ERS bands. These include the contribution form the OTA and its wavefront errors and the specific instrument pixel sampling.

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Table 2 and Figure 7(b) show the progression of the HST PSF (λ/D) with wavelength in the 10 ERS filters. Table 2 implies that the larger pixel values used in the multidrizzling of Section 4.2.2 indeed add to the effective PSF diameter. Table 2 also shows that that HST is diffraction limited in V band and longward, while shortward of V band, the PSF FWHM starts to increase again due to mirror micro-roughness in the ultraviolet. At wavelengths shorter than the V band, HST is no longer diffraction limited, resulting in wider image wings, and a somewhat larger fraction of the stellar flux visible outside the PSF core. The "red halo" at λ ≳ 0.8 μm is due to noticeable Airy rings in the stellar images in the WFC3 IR channel, and the well known red halo in the ACS z band (Maybhate et al. 2010) has an additional component from light scattered off the CCD substrate. Details of the on-orbit characterization of the WFC3 UVIS and IR PSFs are given by Hartig (2009a, 2009b).

4.3.4. The 10-band ERS Area and Depth

Table 1 summarizes the exposure times and the actual achieved depth in each of the observed ERS filters, while Table 2 also lists the effective area covered in each filter mosaic at the quoted depth.

The histograms of Figures 8(a)–(c) give the cumulative distribution of the maximum pixel area that possesses a specified fraction of total orbital exposure time. These effective areas must be quantified in order to properly do the object counts in Sections 6 and 7. After Multidrizzling the ERS mosaics in the UV and IR, these effective areas were computed from the weight maps, which include the total exposure time, and the effects from CR rejection, dithering, and drizzling. Figure 8(a) shows that about 50 arcmin² of the UV mosaics has ∼80% of the UVIS exposure time, or ∼90% of the intended UV sensitivity. For reference, one 0090 pixel could be composed of 5.2 native WFC3 UVIS pixels times the number of exposures on that portion of sky. Due to overlapping dithers (see Figure 3), some pixels have more than the total orbital exposure time contributing to their flux measurement. The histograms of Figure 8(b) give the same information as Figure 8(a), but for the six GOODS v2.0 mosaic tiles in BViz that overlap with the ERS. Figure 8(c) gives the same information as Figure 8(a), but for the ERS mosaics in the IR. About 40 arcmin² has ∼80% of the exposure time in the ERS IR mosaics, or ∼90% of the intended IR sensitivity. The overall WFC3 UVIS–IR sensitivity is 9%–18% better than predicted from the ground-based thermal vacuum tests (see Section 2.4 and Figure 2), and so in essence 100% of the intended ERS exposure time was achieved over the 50 arcmin² UVIS images and the 40 arcmin² IR images.

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All initial catalogs were generated using SExtractor version 2.5.0 (Bertin & Arnouts 1996). In general, these catalogs were generated SExtractor's single image mode for each ERS filter separately, so that the object finding could be done using the total object flux from each ERS filter independently, as is required when determining the star counts (Section 6) and the galaxy counts (Section 7). SExtractor was only used in its dual image mode to generate the additional catalogs that were used exclusively to make the color–color diagrams in Section 5.6 to confirm our star–galaxy separation procedure, using the H band as the detection image. As stated in Section 4.2.1, the ACS B-band image was used as the detection image to get an optimal object definition in the UVIS filters for reasons explained in detail here.

It was necessary to change the parameters in SExtractor to handle the UVIS images slightly differently than the ACS/WFC and WFC3/IR ones. This is due to several factors, both cosmetic and physical. The major difference is that galaxies appear much smoother in the IR and more clumpy in the UV, which occurs due to the specific distribution of their young and old stellar populations as well as their dust (see Windhorst et al. 2002 for a discussion of this effect for all Hubble types). Hence, star-forming regions in well-resolved galaxies can be deblended into separate objects by SExtractor if the deblending is overly aggressive. Fortunately, most of these intermediate-redshift galaxies are not bright in the observed UV, causing the UVIS fields to appear rather sparse, and making deblending a minor issue.

The UVIS images have a less uniform background (∼10%–15% of sky), which as discussed in Section 4.1.1 can possibly be improved, when accurate on-orbit UVIS sky flats have been accumulated over time. For these reasons, we adopted a seemingly low threshold for object detection with SExtractor, requiring 4 connected pixels that are 0.75σ above the background in the UV. Due to the clumpy nature of the ERS objects in the UV, we convolved the UVIS image with a Gaussian kernel of FWHM of 6.0 pixels for the object detection phase only. The deblending parameter, DEBLEND_MINCONT, was set to 0.1, to assure that real objects were not overdeblended. It should be emphasized that object crowding is not an issue in these medium depth UV images (e.g., Windhorst et al. 2008), so that the use of a larger SExtractor convolution filter, a lower SB-detection threshold, and less object deblending is fully justified. The 6.0 pixel Gaussian convolution kernel improves the SB sensitivity by ∼2 mag, given that the low-level UV sky gradients occur over much larger spatial scales than the typical faint galaxy sizes (see Sections 4.1 and 5.5). Together with the fact that the UVIS catalogs were made with SExtractor in dual image mode—using the much deeper ACS B-band image as the detection image, as described above—avoids excessive deblending of the very clumpy UV objects, which limits the number of spurious UV objects detected, as shown in the discussion of the ERS catalog reliability in Section 5.3.

The SExtractor input parameters for the ACS images and WFC3/IR images were the same. The detection threshold was set to 1.5σ, again requiring 4 connected pixels above the threshold for catalog inclusion. The convolution filter was a Gaussian with FWHM of 3.0 pixels, and DEBLEND_MINCONT was set to 0.06. For all 10 bands, the appropriate weight maps (see Section 4.2.2) were used in order to correctly account for image borders (Figure 3), as well as to properly characterize the photometric uncertainties and the effective areas for each mosaic (see Figures 8(a)–(c)).

Two post-processing steps were taken to clean the catalogs of residual artifacts. First, due to the relatively small number of exposures per ERS filter, there were residual cosmic rays at the borders of the dither patterns, and in the chip gaps. These were cleaned by masking out all objects in regions where the number of exposures was less than three. Therefore, the total area coverage in each filter (Table 2 and Figures 8(a)–(c)) is slightly different. Second, SExtractor will detect the diffraction spikes of bright point sources. These are removed by searching for bright objects with FWHM near the size of the PSF and searching for surrounding objects in the catalog that are both highly elongated and oriented radially outward in sets of four from that compact object. Since the number of bright stars is not large (see Section 4.3.2 and figures therein, Sections 5.5 and 6.1), this is only a minor correction to the catalog, and only a few dozen diffraction spikes were found by SExtractor and removed in this way.

Magnitudes were all measured on the AB scale using the most current zero points available on the WFC3 Web site, which are listed in Table 2. Both Petrosian (1976) magnitudes were measured using a Petrosian factor of 2.0, and Kron (1980) magnitudes were measured using a Kron factor of 2.5 (SExtractor parameter MAG_AUTO). For the galaxy counts in Section 7.2, Kron magnitudes were used, because the correction to total magnitude—preferably using a Sersic extrapolation—is less than that typically required for a Petrosian magnitude. Within the errors, the Kron and Sersic based number counts are indistinguishable (Hill et al. 2011). The total magnitude errors in the ERS as a function of total AB magnitude were determined from the SExtractor errors in each filter, which are a combination of the MultiDrizzle RMS-map errors and the image shot noise.

To test the reliability of ERS object catalogs, we performed the negative image test (cf. Yan & Windhorst 2004). In brief, all 10 ERS mosaics were multiplied by –1.0, and then SExtractor was run with exactly the same parameters as the object finding procedure in Sections 5.1 and 5.2. This test showed that our ERS catalog generation was conservative due to the combination of several factors. These include drizzled the larger mosaic pixel size of 0090, the requirement of four connected pixels above the detection threshold, and the sizes of the Gaussian filters applied in the object detection phase. The choice of the SExtractor parameters listed in Sections 5.1 and 5.2 were determined by trial and error to create the most reliable catalogs at each wavelength.

In fact, these SExtractor parameter settings yielded no plausible spurious detections when it was run on the 10 negative ERS images. In total, only six negative "objects" were found, but these were all on the image borders, and the real ERS object catalogs were similar cleaned of such border defects. If the noise in the ERS images were completely Gaussian, then at the ≳5σ detection limit we would expect that 2.9 × 10⁻⁷ of the 6500 × 3000/4 independent ERS pixels (see Figure 5(a)) would yield a bogus object, or ∼1.4 bogus object in the combined 10-band catalog (the grand union) of 22,000 ERS objects. This is consistent with no convincing bogus objects found in the 10 negative ERS images after discarding the image borders. This exercise shows that at the 5σ 50% completeness level (see also Figure 9 below), our ERS object catalogs are ≳99.97% reliable. In astrophysical data samples, a compromise always has to be sought between sample reliability and sample completeness, while ideally maximizing the sum of the two (Windhorst et al. 1984a). The reason we choose here to have essentially 100% reliable catalogs—at the expense of some catalog incompleteness below—is the existence of the deeper optical–near-IR ACS and WFC3 images in the HUDF (Beckwith et al. 2006; Bouwens et al. 2010b; Yan et al. 2011b) in the BVizY_sJH filters. These images made digging deeper into the ERS image noise unnecessary. Instead, the faint end of the galaxy counts at AB ≳ 26–27 mag in Section 7 will be derived in BVizY_sJH from these HUDF images, which is in roughly the same direction of the sky.

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Figure 9 shows the sample completeness functions of the 10-band ERS images. These were derived by Monte Carlo insertion of faint point sources into the ERS images, and plotting the object recovery ratio as a function of total magnitude. Most faint galaxies observed by HST are slightly resolved at the HST diffraction limit (e.g., Cohen et al. 2003; Hathi et al. 2008; Windhorst et al. 2008), so that for faint galaxies these limits are slightly brighter than for point sources, as discussed in Section 7.2 and shown in Figure 10(a).

In summary, the WFC3 UVIS images are ∼50% complete for point-like objects with ≳5σ detections in total flux for AB ≃ 26.3 mag in F225W, AB ≃ 26.4 mag in F275W, and AB ≃ 26.1 mag in F336W. The WFC3 IR images are ∼50% complete to AB ≃ 27.2 mag in F098M, AB ≃ 27.5 mag in F125W, and AB ≃ 27.2 mag in F160W, as listed in Table 1. The multi-year GOODS ASC/WFC v2.0 images in BViz are substantially deeper than this, and reach AB ≳ 27.5 mag in general. The actual star counts in Section 6 appear indeed complete to roughly these limits in the UV, but to slightly brighter limits in the IR due to the increasing object confusion of red stars with faint red background galaxies (see the figure in Section 5.5).

The actual UV galaxy counts in Section 7.2 turn over at a level rather close to the above UVIS point-source sensitivity limits. This is due to the generally more compact nature of the ERS objects, and the extremely faint zodiacal sky background in the UV. In the IR, the galaxy counts turn over at levels a little brighter than the 5σ point-source sensitivity limits listed in Table 2. This is due to the higher zodiacal sky-background values in the near-IR (see Table 2), combined with their somewhat larger sizes at the longer wavelengths (Section 5.5 and figures therein; see also Windhorst et al. 2002), even though faint red field galaxies selected in Y_sJH are in general still rather compact. Object confusion at these flux levels is relatively modest, especially at the HST diffraction limit, although natural confusion—which due to the intrinsic object sizes and not the instrumental PSF FWHM—becomes increasingly important at fainter fluxes (AB ≳ 25 mag; e.g., Windhorst et al. 2008).

In summary, the point-source sensitivity of our ERS catalogs is described by the simulations in Figure 9. The corresponding 50% point-source completeness limits are listed in Table 1. The actual observed panchromatic star counts (Section 6.1 and figures therein) are complete to roughly the 5σ limits of Figure 9 in the WFC3 UVIS filters, and to the 10σ limits of Figure 9 in the ACS BViz and WFC3 IR filters.

Rather than repeating the object simulations of Figure 9 to assess the actual completeness limits for the slightly extended galaxies (see Section 5.5 and figures therein), in Section 7 below we take a different and more empirical approach of determining the ERS incompleteness for faint galaxies by directly comparing the panchromatic ERS galaxy counts to AB ≲ 25.5–27 mag to the galaxy counts in the much deeper, but adjacent HUDF field. Since the effects of cosmic variance are relatively small over the 4' separation between the ERS and HUDF fields (see Section 7 and Figure 3), this comparison directly shows that the ERS catalogs are approximately ≳50% complete for samples of compact galaxies (see Section 5.5) to flux levels that are approximately 0.5–1.0 mag brighter (from the UVIS to the IR) than the ERS stellar samples in the same filters.

Stars and galaxies were separated as follows. In each filter, the stellar locus was defined as shown in the usual plot of the object FWHM versus total AB magnitude (e.g., Cohen et al. 2003). Figure 10(a) illustrates our star–galaxy separation procedure used for the 10-band ERS images. Objects with FWHM < PSF FWHM (from Table 2) are image defects, bad pixels, and some remaining CRs. Hence, objects to the left of the black vertical lines plotted at FWHM ≃ 007–015 are smaller than the PSF, and are discarded. Objects in the thin vertical filaments immediately larger than this are stars (plotted as thin reds dots in Figure 10(a)), and they in general have PSF FWHM ≲ FWHM ≲ (1+) × PSF FWHM, where 0 ≲ <1. Figure 10(a) shows that ERS stars straddle the instrumental PSF FWHM to AB ≃ 27 mag. Objects to the right of the black dashed slanted lines are galaxies, and they in general have FWHM ≳ (1+) × PSF FWHM, where "1+" is a weak function of total S/N, as shown by the two solid slanted lines in each of the panels in Figure 10(a).

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Next, all 10 independent ERS object catalogs—each with their independent star–galaxy separation and photometry—were merged by astrometric cross-matching. In order to maximize the 10-band information, we considered an object to be a star if it was classified as stellar in at least 3 out of 10 ERS filters. This provides robust stellar classifications, perhaps to fainter limits than can be done in single filter alone.

From Figure 10(a), we can see that the stars separate out well from the galaxies to about AB ≃ 25.5–26.0 mag, and somewhat fainter in the ACS BViz filters and the WFC3 IR filters. To these flux levels, the star counts follow a power law rather well, as shown in Section 6.1. The choice to require an object to be classified as a star in three filters—as opposed to all 10 filters—was made because stars can be either very red or sometimes very blue, and so stars are often not detected in all 10 ERS filters. Also, we are merging the data from three different HST instruments and detectors (WFC3 UVIS CCD, ACS/WFC CCD, and the WFC3 IR detector), so subtle PSF and sampling differences between these instruments can lead to the misclassification of a faint star in some of the 10 ERS filters, depending on its color. Since brighter stars are always seen at least in three (adjacent) ERS filters, we require all of the fainter stars to be classified as stellar in at least three of the ERS filters as well.

As shown in Section 4.3.2 and Figure 4(c), all ERS objects together—which are ≳97.8% galaxies—allowed us to bring the WFC3 UVIS and IR coordinate system on average on top of the ACS WFC WCS to within 0.4–0.5 mas in both R.A. and decl. After having done this, the 4511 ERS objects classified as galaxies show indeed no significant residual motion over 5.97 years. However, for all 103 ERS objects classified as stars, an average proper motion of 2.30–2.02 mas yr⁻¹ was detected at the 4.1σ–5.8σ level in R.A. and decl., respectively (see Section 4.3.2). For at least 32 out of the 103 ERS stars, this proper motion was discovered individually at the ⩾3σ level (see Figure 4(c)). The total average proper motion of all 103 ERS stars on the sky is 3.06 mas yr⁻¹, summed in quadrature over the R.A. and decl. proper motions. The mean error is 0.66 mas yr⁻¹, which amounts to a 4.6σ detection of the overall ERS stellar proper motion. The dispersion on this number in Figure 4(c) is 6.70 mas yr⁻¹. We will interpret these numbers in more detail below. In conclusion, while ERS proper motions alone cannot confirm that all our ERS objects classified as stellar are in fact Galactic stars, average stellar proper motion is detected at high significance level for the entire sample of 103 ERS stellar candidates, making it in retrospect likely that most of these are in fact Galactic stars.

The ERS colors in Figure 10(b) are more conclusive in supporting our ERS star–galaxy separation procedure a posteriori. Figure 10(b) shows the (i − z) versus (B − V) color–color diagram in the GOODS filters, where all ERS objects have the highest S/N (see Figure 9). ERS objects classified as galaxies as shown as black dots, and ERS objects classified as stars with green or red asterisks. Green asterisks mark ERS objects that show proper motion at the ⩾3σ level in Figure 4(c) (see Section 4.3.2). The (i − z) versus (B − V) colors are compared to the Pickles (1998) model library SEDs (blue squares), which range in spectral type from O5V–M7V, and also show giant branch models up to M7III. The observed ERS stellar colors are shown with their 1σ error bars. Only stars with combined color errors along each axis ≲0.5 mag are plotted. It is clear that within the errors, most stellar ERS objects have colors of K–M type main-sequence stars, although there are a few ERS stars with color as blue as BV–GV types.

There are about 20 ERS stars in the color range 0 ≲ (B − V) ≲ 1.4 mag with (i − z) colors ≳0.3 mag redder than the Pickles (1998) main sequence. At least eight of these also have significant proper motion at the ≳3σ level, and are thus real Galactic stars. All 20 objects significantly redder than the Pickles (1998) main sequence were inspected by eye and correlated with other data. Three have VLT redshifts: one is a Seyfert galaxy at z = 1.031 in a group with similar spectroscopic redshifts, the other a compact elliptical at z = 0.251 next to a very faint stellar object, and the third is a stellar object next to an object at z = 2.217 with a neighbor at a similar redshift. The latter two stellar objects also have significant proper motion, and are likely real Galactic stars that are very close to an extragalactic object whose VLT redshift was actually measured.

Thus at least 17—and likely 19—of these 20 ERS stars with colors significantly redder than the Pickles (1998) main sequence have either significant proper motion and/or clear stellar morphology. Many of these appear to be stars that were unavoidably saturated in the ERS images. Because both their colors are ≳0.0 mag—they have higher ADU in i band than in z band, and in V band than in B band—given the ACS/WFC QE curve. Hence, their measured (i − z) flux will be too red, and their (B − V) color slightly too blue. Since these stars are saturated in nearly every ACS exposure, more accurate colors cannot be determined with the current mosaics, and their appearance above the Pickles (1998) main sequence does thus not rule them out as stars. Some of the reddest stars well away from the Pickles (1998) main sequence could be asymptotic giant branch stars with surrounding dust shells that could considerably redden their (B − V) and (i − z) colors significantly.

We also need to address how many of the stellar objects that are within the errors consistent with the Pickles (1998) stellar main sequence could be compact background galaxies. Figure 10(b) shows that the (i − z) versus (B − V) color space of zero-redshift stellar SEDs overlaps somewhat with the colors of intermediate-redshift galaxies, which largely occupy the region (B − V) ≲ 1 mag and (i − z) ≳ 0.15 mag. This is a limitation of the current color confirmation of the stellar ERS candidates. Only multi-parameter 10-band SED fitting of all ERS objects can address this issue more fully, which we will address in a future paper (Cohen et al. 2011). However, the available VLT spectra can give us some idea.

Among the 103 objects classified as ERS stars, many would have been bright enough to have been included in the VLT redshift survey, which is complete to AB ≲ 24 mag, but covered objects as faint as AB ≲ 25 mag. Among the 103 stellar ERS objects, 11 appear to be compact extragalactic objects confirmed to have VLT redshifts z>0. One of these is a quasar with an underlying early-type galaxy at z = 0.734.

In summary, this detailed study in Figure 10(b) confirms that at least 90–92 of the 103 stellar ERS objects have either significant proper motions (Figure 4(c)), stellar colors consistent with the Pickles (1998) main sequence (Figure 10(b)), and/or are not extragalactic objects with VLT redshifts z>0. Conservatively, we can thus conclude that our ERS stellar objects are indeed Galactic stars with ≳87% reliability. This provides a posteriori confirmation that our ERS star–galaxy separation method of Section 5.5—which was based on measured effective image diameters only (Figure 10(a))—is indeed valid. This then also means that we may consider the statistical proper motions of all ERS stars in Figure 4(c), to investigate if the implied average proper motion shows us something interesting about Galactic structure of very faint stars at high Galactic latitude (the GOODS-South field has b^II = −54°). We discuss this in Section 6 in more detail.

As a final remark, ideally one would like the star–galaxy separation procedure to also include accurate fits of a library of (redshifted) SEDs to the 10-band ERS object photometry, and so help decide whether an object is most likely a zero-redshift star or a redshifted galaxy. This is beyond the scope of the current paper, and is pursued by Cohen et al. (2011) for the ERS stars and galaxies separately. This paper will also attempt to do a stellar + power-law AGN SED fits to all ERS objects, including on a pixel-to-pixel basis. This procedure will also provide better estimate of the AGN contamination of the ERS sample, rather than relying on the presence of weak point-like components in the ERS images alone. Suffice to say here that in Figure 10(b) most ERS stars have colors consistent with the stellar main sequence, so that contamination of our stellar ERS objects by weak AGN or other compact extragalactic objects is likely small. This is confirmed by the high proper motion stars in Figure 10(b), which have statistically the same color distribution as the stellar ERS objects without measurable proper motion.

Figure 11(a) shows the differential panchromatic star counts in the 10-band ERS images. The star–galaxy separation breaks down at fluxes AB ≳ 26 mag in BVizY_sJH. However, for AB ≳ 22 mag galaxies outnumber stars by a large margin, so the more uncertain star–galaxy separation for AB ≳ 26 mag will not affect the quality of the galaxy counts. The star counts, of course, become correspondingly harder to do for AB ≳ 25 mag, and so in Section 6.2 and Figure 10(b) additional criteria such as colors and proper motion were used to confirm faint stars at higher confidence.

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The solid black line in the F850LP panel of Figure 11(a) represents the spectroscopic star counts to AB ≃ 25 mag from the HST Cycle 14 ACS grism survey "PEARS" (Probing Evolution And Reionization Spectroscopically) of Pirzkal et al. (2009). Since for these objects we can use the low-resolution ACS G800L spectroscopic data as independent confirmation of their stellar nature, they have higher accuracy than the image-based star counts alone. The southern PEARS ACS grism survey was done over a similar sized area to the ERS, covering an overlapping portion of GOODS-S. Hence, it is encouraging that the Pirzkal et al. (2009) grism star counts, which are for spectral types of M0 and later, have the same slope as our direct-imaging ERS star counts in F850LP. The slightly different star count amplitude for the flux range 18 mag ≲ AB ≲ 25 mag is likely due to the fact that the spectroscopic sample was limited to later spectral types, where those grism classifications were most reliable. The good agreement in star counts between the two different survey methods confirms that—as far as faint stars are concerned—our star–galaxy separation is accurate to about AB ≃ 25 mag.

Figure 11(b) shows the ERS star count slope versus observed wavelength in the flux ranges AB ≃ 19–25.5 mag for the three UV WFC3 filters, AB ≃ 16–26 mag for the GOODS/ACS BViz filters, and AB ≃ 15–25 mag for the three WFC3 IR filters, respectively. The GALEX FUV and NUV points of Xu et al. (2005) are also plotted at 153 and 231 nm, and cover the flux range AB ≃ 17–23 mag, using primary color criteria to accomplish star–galaxy separation at the 4''–66'' FWHM GALEX resolution. The statistics of the star counts in the three bluest ERS filters (F225W, F275W, and F336W) are rather sparse (Figure 11(a)). As a consequence, our three bluest best-fit ERS power-law slope values are rather uncertain, as indicated by the larger error bars in Figure 11(b). The GALEX FUV and NUV star count points of Xu et al. (2005) are complete to somewhat brighter levels (AB ≃ 23–24 mag), but have much better statistics. As a consequence, the GALEX FUV and NUV star count slope points in Figure 11(b) have smaller error bars, and at the common wavelength of ∼230 nm they therefore carry larger weight than the ERS star count slope in the mid-UV.

Given these uncertainties, the Galactic star count slope at the faint end is remarkably flat at all wavelengths from the Balmer break to the near-IR, although it is rather poorly determined from the ERS data alone below the Balmer break. The values of the best-fit ERS power-law star count slope is in general of order 0.03–0.05 dex mag⁻¹. Including the more accurate GALEX star count slope values at 150 and 230 nm, the panchromatic faint end of the star-count slope appears to be always in the range 0.03–0.20, i.e., at all ERS wavelengths the faint star-count slope remains well below Euclidean value of 0.6 dex mag⁻¹. This shows that to a depth of AB ≃ 25–26 mag at all wavelengths in the range 0.2–2 μm, the ERS images readily penetrate through most of the thick disk of our Galaxy at these latitudes (b^II ≃ −54°) in the direction of the Galactic anti-center (l^II = 224°; Ryan et al. 2005; Beckwith et al. 2006). This trend was also seen in the red ACS imaging parallels of Ryan et al. (2005), and the red ACS GRAPES and PEARS grism observations of Pirzkal et al. (2005, 2009), respectively, each of which constrained the scale height of Galactic L and T dwarfs to about 300–400 pc.

In the bluest three WFC3 filters F225W, F275W, and F336W, the WFC3 ERS finds only 22, 18, and 27 faint stellar candidates, respectively. Most of the full sample of ERS stars have 10-band colors red enough to indicate Galactic halo K–M type stars and possibly a few L and T dwarfs, but a few of the faint stars are blue (see Section 5.6 and Figure 10(b)). The latter could be faint Galactic white dwarfs, though there were no UV detected stars that were not also seen in the ACS B band. The effective ERS UV stellar detection limit of AB ≃ 25 mag could trace a T = 2 × 10⁴ K white dwarf with an absolute magnitude in the range M_bol ≃ +15 to +10 mag (Harris et al. 2006) out to a distance of 1–10 kpc, respectively, assuming modest bolometric corrections. The faint stellar objects in the 10-band ERS data are obviously of great interest by themselves and will be studied in more detail in a future paper. An important lesson learned for UV observations of high-latitude fields is that there are so few UV bright stars, that one has to ensure that individual exposures are long enough in order to align and drizzle (or stack) them using faint galaxies. In the ERS UV images we did this using the cross-correlation technique, as explained in more detail in Appendix A.

Figure 10(b) suggests that the majority of ERS stars have red colors characteristic of faint red main-sequence stars. Their typical spectral type is in the range K0V–M5V with an average spectral type of ∼K5V. For these stars, the expected M_V ranges from +5.8 to +12.3 mag with an average of M_V ∼+8 mag. With the flat ERS star count slope of Figure 11(a), the average ERS star has an AB magnitude of ∼23 mag, while the ERS stellar detection limit is AB ≲ 26 mag. Hence, the average faint red ERS star will be at a distance of about R ≃ 10 kpc from the Sun. The direction of the GOODS-South field at R.A. = 03^h32^m39^s, decl. = −27°47'291 is in the Southern Galactic hemisphere, about 54° below the plane of the Milky Way, and in the general direction of the Galactic anti-center. Stars in this direction at ∼10 kpc distance from the Sun will thus be bulge and disk stars ∼8 kpc below the Galactic plane, i.e., well below the outer Orion arm of the Galaxy. At this distance, the above average ERS proper motion of 3.06 ± 0.66 mas yr⁻¹ amounts to an average stellar tangential velocity of ≲145 ± 31 km s⁻¹ (m.e.). These stellar velocities and their dispersion are in part due to the projected solar motion in the sky—compared to the Galactic Local Standard of Rest—and in part due to the true space velocities of ERS stars in the Galactic bulge and disk. While a detailed discussion of the proper motion of ERS stars and its implication for Galactic structure is beyond the scope of the current paper, we will here briefly discuss how our ERS proper motion results compare to previous proper motion and radial velocity observations of the Galactic bulge and disk at intermediate to high Galactic latitude.

A proper motion study to V ≲ 22.5 mag at the North Galactic Pole by Majewski (1992) shows a systemic velocity of −120 km s⁻¹ at the edge of the thick disk (z ≳ 5.5 kpc). Clarkson et al. (2008) show similar proper motion values at R∼ 5 kpc, but in Baade's window from multi-epoch HST/ACS images that are effectively complete to about I ≲ 21 mag given the more crowded images at low Galactic latitudes. Kinman et al. (2007) find that Galactic Blue Horizontal Branch stars with an average distance to the Galactic plane of z ≲ 8 kpc have zero galactic rotation and roughly isotropic velocity dispersions of 93–81 km s⁻¹ in the tangential and z directions, respectively, or ∼123 km s⁻¹ in the plane of the sky. Theoretical disk+bulge+halo models (Battaglia et al. 2005; Klypin et al. 2002) predict velocity dispersions at R∼ 5–10 kpc of 150 km s⁻¹ for the Galactic bulge+thick disk components.

These values are very similar to the 145 km s⁻¹ value implied from the average proper motion observed for our faint red ERS stars at relatively high Galactic latitude (b^II = −54°). In other words, the Galactic (thick disk+bulge) velocity dispersion implied from our faint red ERS stellar proper motions is consistent with these previous observations and theoretical model predictions. It is worth noting, however, that these previous observations are based on high-resolution radial velocities and proper motions of Galactic stars with V ≲ 16 mag, or proper motions alone for stars with V ≲ 22.5 mag. Our ERS observations push this substantially fainter for proper motions at high Galactic latitudes, to flux levels (AB ≲ 25–26 mag) where high resolution spectroscopy cannot be done with current ground based facilities. Systematic proper motion studies of very faint stars at HST resolution at high Galactic latitudes thus have the potential to sample part of Galactic structure that is otherwise not easily accessible. This topic will be studied in further detail in a subsequent paper.

Figure 11(a) also shows the differential panchromatic galaxy number counts in the 10-band ERS images. No completeness corrections—as implied by Figures 9 and 10(a)—were applied to the faint end of the panchromatic ERS galaxy counts in Figure 11(a). Instead, to be conservative, the data points are not plotted in all panels of Figure 12 at the flux level where the counts clearly start to deviate from a best-fit faint-end power law (see Figures 11(a) and (c)) by more than 50%. This in general occurs 0.5–1.0 mag brighter than the 50% point-source completeness limits listed in Table 1, as derived from Figure 9.

Figure 11(c) shows the ERS galaxy count slope versus observed wavelength in the flux ranges AB ≃ 19–25 mag for the three UV WFC3 filters, AB ≃ 18–26 mag for the GOODS/ACS BViz filters, and AB ≃ 17–25 mag for the three WFC3 IR filters, respectively. The GALEX FUV and NUV points of Xu et al. (2005) are also plotted at 153 and 231 nm, and cover AB = 17–23 mag, again using primary color criteria to accomplish star–galaxy separation at the 4''–6'' FWHM GALEX resolution. The statistics of the galaxy counts in the three bluest ERS filters (F225W, F275W and F336W) are sparse (Figure 11(a)), and at the bright-end the ERS object definition and deblending is more complex given the sizes of the brighter objects (Figure 10(a)). As a consequence, the best-fit ERS galaxy count power-law slope values become somewhat more uncertain at the bluer ERS wavelengths (Figure 11(c)). The GALEX FUV and NUV galaxy counts of Xu et al. (2005) are complete to somewhat brighter levels (AB ≃ 25 mag), but have much better statistics than the ERS. Given the much larger size of the GALEX beam (4''–6'' FWHM), they do however suffer from more uncertain star–galaxy separation, which for GALEX needed to be done by using multi-color information as well (Baldry et al. 2010). At the longer GALEX wavelength, it may be harder to separate Galactic stars from low-redshift older galaxies using colors alone. As a consequence, the GALEX NUV count slope point in Figure 11(c) has a somewhat larger error bar at the common wavelength of ∼230 nm.

Given the above uncertainties in the GALEX and ERS UV galaxy count slopes, the galaxy counts show the well known trend of a steepening of the best-fit power-law slope at the bluer wavelengths, which is caused by a combination of the more significant K-correction and the shape of the galaxy redshift distribution at the selection wavelength. The galaxy count slope changes significantly from a ≳ 0.44 dex mag⁻¹ at 0.23 μm wavelength to a ≃ 0.26 dex mag⁻¹ at 1.55 μm wavelength. Hence, the galaxy counts have a slope flatter than the Euclidean value of a ≃ 0.6 dex mag⁻¹. However, at wavelengths below 0.4 μm the UV galaxy counts are steeper than the a⩽ 0.4 dex mag⁻¹ value required for their sky brightness integral to converge to a finite value, if they were to continue with this power-law slope for AB ≳ 27 mag. That is, the UV galaxy counts will have to turn over with a slope flatter than ⩽0.4 dex mag⁻¹ for AB ≳ 27 mag. In Section 7.3 we will confirm that they indeed do so.

Figures 12(a)–(j) show the galaxy number counts in the 10-band ERS images compared to a number of other panchromatic surveys at the bright end and at the faint end. At the bright end, we added the counts from the GAMA survey (Driver et al. 2009) in NUV+ugrizYJH, which cover AB = 10–21 mag (Xu et al. 2005; Hill et al. 2010). Details on the ground-based data obtained in the GAMA survey are given by Driver et al. (2009) and Hill et al. (2010). The GAMA survey also uses matched aperture Kron magnitudes, which are comparable to our total magnitudes used for the ERS.

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The GAMA star–galaxy separation procedure is quite different than for the ERS, since there is a significant potential for contamination by stars which dominate the number counts at brighter magnitudes (Figure 11(a)). The GAMA star–galaxy separation therefore uses the (r_PSF–r_model) parameter to determine how extended an object is, and also uses the well-defined stellar locus in the (g − i) versus (J − K) color–color diagram. Details of the star–galaxy separation methods used in the GAMA survey are given by Baldry et al. (2010).

At the faint end in Figures 12(d)–(j), we added the HUDF counts in BViz from Beckwith et al. (2006), which cover AB = 24–30 mag, and the HUDF counts from the Bouwens et al. (2010b) data in the F105W, F125W, and F160W filters (hereafter YJH), as compiled by Yan et al. (2011b), which cover AB = 24–30 mag. In the UV, we added the William Herschel Telescope (WHT) U-band counts and the HDF-North and South F300W counts as compiled by Metcalfe et al. (2001), the deep Large Binocular Telescope (LBT) U-band counts of Grazian et al. (2009), as well as the deep HST STIS UV counts of Gardner et al. (2000).

We note that the filter systems in the comparisons in each of Figures 12(a)–(j) are not quite identical, although they were chosen in every case to be as close as possible in wavelength (typically to within 0.1 dex). Hence where necessary, small but appropriate AB-mag offsets or color transformations were made between the filters and models used in each plot, following Metcalfe et al. (2001) or Windhorst et al. (1991). These corrections generally contain some color dependence. When applying them as a single AB-flux scale correction to a given survey can introduce uncertainties of order 0.1 mag in the flux scale used. Over the entire AB = 10–30 mag range shown in Figures 12(a)–(j), such ∼0.1 mag offsets would not be noticeable. However, for a detailed set of modeling in subsequent work, more subtle flux and color dependent corrections may need to be applied. This will be the subject of a future paper.

The error bars in each of the counts in Figures 12(a)–(j) are Poisson, and therefore do not include effects from cosmic variance. To increase the statistics where necessary at the bright end of each survey, bins were combined logarithmically using the local slope of the galaxy counts, following the prescription of Windhorst et al. (1984b). At the faint end, the counts are not plotted in Figures 12(a)–(j) fainter than the flux level where these are deemed complete. Based on Figures 9 and 11(a), this occurs in general where the counts turn over significantly within the statistical error bars. Hence, in principle, the panchromatic counts of Figures 12(a)–(j) should be comparable over the entire flux range AB ≃ 10–30 mag, except for the effects of cosmic variance. The latter is small for the panchromatic ∼116 deg² GAMA survey, but it could be important for the other panchromatic survey areas plotted, such as the ERS and the HUDF which are both (disjoint) parts of GOODS-S, as well as the HDF-North (in GOODS-North) plus the HDF-South and various other ground-based surveys in the U band.

In the flux range where the panchromatic GAMA and HUDF counts in Figures 12(a)–(j) overlap with the panchromatic ERS counts, the agreement is in general quite good, except at the bright end of the ERS, which suffers from cosmic variance, and from the fact that the GOODS/ERS field was chosen to be devoid of objects much brighter than AB = 18 mag. As a consequence, the bright end of the ERS galaxy counts also suffers somewhat from incompleteness. The same is true for the bright end of the HUDF, which suffers similarly from cosmic variance and the avoidance of objects much brighter than AB ∼ 21–22 mag when that field was selected in early 2003 for the ultradeep HST survey. The HUDF is adjacent to, but does not overlap with the ERS area (see Figure 3). The HUDF galaxy counts in BVizY_sJH are in good agreement with the ERS galaxy counts to the flux levels where the panchromatic ERS counts are considered complete (AB ≃ 26–27 mag in Figure 11(a)).

The good agreement between these various surveys also implies that the flux scales of the panchromatic ERS counts are approximately correct. Had one of the ERS filter zero points been off significantly (e.g., by more than 0.1–0.2 mag), we would have noticed this as a significant offset between the counts. Note this argument only holds for the counts at AB ≳ 20 mag, as these cover the same general area of sky in the GOODS-South field. Hence, cosmic variance likely affects these counts similarly over such scales (≲ 30%; Somerville et al. 2004).

Figures 12(a)–(j) overplot simple galaxy evolution models by Driver et al. (1995, 1998), which have been updated for the current comparison with the ERS. Driver et al. (1995, 1998) and Cohen et al. (2003) provide further details of these models. In short, they use the best available local LF as a function of galaxy type, and K-corrections from the Bruzual & Charlot (2003) spectral evolution models, also as a function of galaxy type. The local galaxy LF then gets integrated with the WMAP year 7 (Komatsu et al. 2011) cosmological volume element to predict the number density of galaxies observed to the total-flux limit in each ERS filter. These models also include internal reddening as a function of galaxy type.

These models have been updated with the best available local panchromatic LFs in ugrizYJHK from the Millennium Galaxy Catalog survey by Hill et al. (2011), and in the UV they use the GALEX LFs of Robotham & Driver (2011). These LFs will be updated in future work with GAMA redshifts from the three-year Anglo-Australian Telescope survey that was concluded in 2010. Robotham et al. (2010) provide further details on the GAMA redshift survey. This GAMA data set is currently 99% redshift complete for r_Petro ≃ 19.4 mag, and provides high-fidelity, matched-volume panchromatic LFs, which are essential to interpret the higher-redshift panchromatic ERS work.

Evolution of the faint-end LF slope is not yet included in these simple models, but the panchromatic local GAMA LFs automatically includes the well-known steepening of the local LF toward shorter rest-frame wavelengths, where the local LF is dominated by the more rapidly star-forming late-type galaxies (see Driver et al. 1998; Robotham & Driver 2011; Hill et al. 2011). The epoch-dependent galaxy redshift distribution is also not an input to these models, but can instead be inferred from the local LF as a function of type (e.g., Driver et al. 1996), the total constraints provided by the panchromatic galaxy counts (Figures 12(a)–(j)), the adopted K-corrections as a function of galaxy type, and the adopted evolutionary model parameters. These simple evolution models used are either a pure luminosity evolution (PLE) model with e(z) = 2.5 log[(1+z)^β] and PLE exponent β, or a number density evolution (NDE) model with n(z) = n_o [(1 + z)^γ] and NDE exponent γ, or a combination thereof.

Based on the currently available, best panchromatic local GAMA LFs, Figures 12(a)–(j) show for AB = 10–30 mag the PLE model prediction with PLE exponent β = 1 (dotted lines), the NDE model prediction with NDE exponent γ = 1 (short-dashed lines), or a combination of both models indicated by both parameters β = γ = 1 (long-dashed lines). The solid lines show in all cases the non-evolving model (β = γ = 0).

Over the entire flux range AB ≃ 10–30 mag, Figures 12(a)–(j) show that no single PLE model fits all the available galaxy count data, since there is not enough volume at high redshift to make any PLE model fit the high observed counts, especially in the visual to near-IR (Figures 12(d)–(j)). This means that one has to invoke NDE as well, i.e., β ≳ 1 and some modest amount of luminosity evolution for γ ≳ 0. The best models using these PLE or pure density evolution (PDE) prescriptions are either the β ≃ 1 or the γ ≃ 1 model. Figures 12(a)–(j) also shows that no single combined PLE+NDE model fits the panchromatic galaxy counts in all 10 bands simultaneously over the entire observed range AB ≃ 10–30 mag, not even with the best available panchromatic local LF from the GAMA survey (Hill et al. 2011).

In particular, Figures 12(d)–(j) show that at the faint end of the galaxy counts in YJH there exists a significant excess in observed object numbers compared to these simple models. This could be due to either an additional population of objects at high redshifts, or—more likely—due to lower luminosity objects at lower redshifts, and/or because some essential aspects are missing in these models. A detailed discussion of these possibilities is beyond the scope of the current paper, but the reader is referred to, e.g., Bouwens et al. (2010b), Yan et al. (2011b), and Wyithe et al. (2011) for a discussion of some of these possibilities.

More realistic galaxy evolution models would be ones in which the faint-end Schechter LF-slope α also evolves with redshift, as has been suggested by, e.g., Ryan et al. (2007) and Khochfar et al. (2007). In particular, the faint-end LF-slope α steepens significantly at higher redshifts, which was suggested by, e.g., Yan & Windhorst (2004), Ryan et al. (2007), Hathi et al. (2010), and Oesch et al. (2010b). One would like to compare our panchromatic ERS galaxy counts from 0.2 to 2 μm over the entire observed range AB = 10–30 mag (Figures 12(a)–(j)) to state-of-the-art hierarchical simulations that reach from z = 8 to z = 0, and properly fold star formation and stellar population evolution models with these ΛCDM simulations. Such models have been made, e.g., by Croton et al. (2006), de Lucia & Blaizot (2007), and Nagamine et al. (2005a, 2005b), and are discussed in further detail by, e.g., Kitzbichler & White (2007), Monaco et al. (2007), and Nagamine (2006). It is difficult for such models to predict reliable panchromatic galaxy counts from 0.2 to 2 μm that cover the entire observed range AB = 10–30 mag, because such simulations take a very large amount of computing time to cover the low-redshift regime (z ≲ 3), to cover the entire galaxy LF, and to let and them run all the way to z = 0. In addition, such models need to include increasingly complex physics with cosmic time, such as hierarchical merging and/or downsizing, feedback processes from SNe and AGNs, and how these processes changed the faint end and bright end of the galaxy LF, respectively, over cosmic time, as well as include the physics of dust. This will be the subject of a future paper that compares the observed panchromatic galaxy counts from 0.2 to 2 μm over the entire flux range AB = 10–30 mag to available hierarchical models.

For now, we conclude that the simple PLE+PDE models with the best available observed panchromatic local LF from GAMA can explain each of the 10-band counts for 10 mag ≲ AB ≲ 30 mag individually, but no single one of the simple PLE+NDE models can explain the counts over this entire flux range in all 10 filters simultaneously.

Given the issues related to the GDC discussed in Section 4.2.2, it was apparent that some astrometric residuals remained—at the level of ≲2–3 Multidrizzled pixels—that were a function of position across both UVIS detectors, after the shifts and rotations had been removed. A worst case is shown in the lower panel of Figure 4(a). These residuals were apparent between the three UVIS filters, as well as relative to the GOODS astrometric frame. At the time of the data reduction, the best available Instrument Distortion Coefficients (IDCtab's; file t982101i_uv_idc.fits)—which are used for the GDC—had been created using the WFC3 SMOV F606W data alone³⁰. This GDC did not yet include any wavelength-dependent distortion terms, though these will be measured during Cycle 18 or beyond³¹, and distributed to the community by the WFC3 instrument team. Since our WFC3/UVIS data are all taken at wavelengths below 3500 Å, it is likely that the remaining astrometric residuals are indicative of the absence of these color-dependent terms in the currently existing GDC tables. The wavelength-dependent terms of the GDC come from the different index of refraction of the glass optics and filters in the UVIS channel of WFC3. This is in addition to the first- to third-order geometric distortion coefficients, which results from the CCD tilt (which was necessary to minimize internal reflections), and from other reflective optics, and are therefore largely wavelength-independent.

The ultimate goal of the UVIS part of the WFC3/ERS is to create images in F225W, F275W, and F336W filters at the same pixel scale (0030 per pixel) and astrometric grid as the GOODS ACS images (Giavalisco et al. 2004) of the same portion of the GOODS-South field. As discussed in Section 2, the eight ERS UVIS pointings were designed to overlap with each other, in order to achieve the best possible astrometric precision. After the extensive astrometric work described above, it turned out that we had reached the limit of what was possible with the present wavelength-independent geometric distortion solution. We were able to align all UVIS images such that the average object was well aligned with the GOODS B-band image. However, objects near the individual UVIS field edges were not well aligned (lower panel of Figure 4(a)). Figure B.1 of the WFC3 Instrument Handbook (Wong et al. 2010) also suggests that in these locations the geometric distortion is the largest. This was most noticeable on the few stars in the overlap regions between pointings, as Figure 4(a) demonstrated.

Some of these stars also showed significant proper motion between the original 2004–2007 GOODS observations and the 2009 ERS observations, complicating their use as astrometric fiducials (see Sections 4.3.2 and 6). This is quite visible as significant color offsets in some of the ERS bright star images in the very high resolution versions of Figures 5(a) and (b) and 6(c), which are available at the URL given in the figure caption. In attempting to create a 0030 per pixel UVIS mosaic, the stars in the overlap regions of the eight UVIS pointings were somewhat elongated (Figure 4(a)), even though the exposures from the same UVIS orbit were well aligned—i.e., having round stars and astrometric residuals to a fraction of a pixel—and even though each pointing was well matched to the GOODS frame. In other words, even after correcting the WCS in the FITS headers for both the relative and the absolute position deviations, there still remained some astrometric residuals primarily at the field edges, that we suspect are likely due to the uncertain wavelength dependence of the GDC (Figure 4(b)).

Figure 4(b) shows the astrometric residuals for four of our ERS pointings in the F336W filter (visits 25, 26, 29, and 30). Each frame within a visit was registered using the MultiDrizzle scripts of Koekemoer et al. (2002), which CR-cleaned and cross-correlated the images, to revise the flat-fielded (FLT) image WCS header keywords, as described in Section 4.2.1. These images were then drizzled with PIXFRAC = 1.0 to a scale of 0030 per pixel and to a position angle of 0 deg (final_rot = 0). The PA(V3) was 111 deg. Catalogs were then created with SExtractor (Bertin & Arnouts 1996), which were in turn matched in equatorial coordinates to a similar catalog made from the GOODS-South B-band image (GOODS v2.0; Giavalisco et al. 2004; N. Grogin 2009, private communication). Note that all four visits in Figure 4(b) show similar bimodal residuals, suggesting that this is a systematic error. We suspect that this is due to the wavelength-dependent geometric distortion in the UV, since the only distortion solution available at the time of the data processing was measured in the F606W filter. Since two distinct blobs of points occur in similar locations in all four panels of Figure 4(b), the MultiDrizzle images of objects seen in only one pointing—which includes 80%–90% of the total ERS area (see Figures 3 and 8(a))—are round at 0090 pixel sampling. However, the images of the brighter objects in the overlap areas between mosaic pointings—10%–20% of the total area—are not always completely round, as shown in Figure 4(a). (Visual inspection of the F225W and F275W mosaics showed similar trends for bright stars as seen for F336W in Figures 4(a) and (b)—confirming our conjecture that this is due to the GDC only having been calibrated in the F606W filter. However, these trends are seen at lower S/N than in F336W—since faint stars are red, see Section 4.3.2 and figures therein—and so Figures 4(a) and (b) are not reproduced here for F225W and F275W.)

When Multidrizzling the four exposures of each pointing, each individual object is well aligned with itself. However, in the WFC3 field corners, an object can be offset from the GOODS WCS by ±01–02 (Figures 4(a) and (b)). In the area of field overlap, an object in the ERS image corners or at a visit's field edges can thus be misaligned with itself by ∼01–02, and so be elongated (see Figure 4(a)), but still be on average on top of the GOODS v2.0 WCS. In other words, with the current wavelength-independent GDC and MultiDrizzle, we cannot have it both ways for a given object in the image borders of the ERS mosaic, until the wavelength-dependent GDC has been fully measured in the UV, and a sufficient larger number of dither points is available to take full advantage of the full 00.0395 pixel sampling of the WFC3 UVIS images. This is at the moment not the case. Therefore, in this paper we use the total-flux measurements from the UVIS images that were Multidrizzled at 0090 pixel⁻¹, and use large enough apertures that the total flux measurements are reliable.

For the WFC3 IR Channel, the GDC has only been measured in the F160W filter³², and so the GDC in the other two ERS IR filters F098M and F125W is correspondingly more uncertain. However, because the WFC3 IR Channel GDC is much smaller to begin with (see Wong et al. 2010)—due to the IR Channel design—and because of the larger IR channel pixels, the wavelength dependence of the IR Channel GDC is much less of an issue than for the WFC3 UVIS channel. As for the WFC3 UVIS channel, the wavelength dependence of the IR Channel GDC will be measured in more detail in Cycle 17 and beyond, and will be applied to a future version of the ERS data release and discussed in subsequent ERS papers.

Figure 13 shows several panchromatic postage stamps of lower-redshift early-type galaxies in the ERS with nuclear star-forming rings, bars, or other interesting nuclear structure. Each postage stamp is displayed at a slightly different color stretch, that best brings out the UV nuclear structure. Rutkowski et al. (2011) present examples of ellipticals at z≃ 0.3–1.5 with various amounts of UV-excess flux. These galaxies are red and relatively featureless in the optical, but show considerable emission in the UV, which is not all point-like. Hathi et al. (2010) and Ryan et al. (2011) present ERS samples of faint UV-dropouts and very high redshift red galaxies, respectively. Many more such studies can be done with the ERS data.

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Figure 14 shows panchromatic postage stamps of objects with interesting morphological structure in the 10-band ERS color images of the GOODS-South field, yielding high-S/N detections of galaxies resembling the main cosmological parameters H₀, Ω, ρ_o, w, and Λ, respectively. The panchromatic galaxy morphology and structure in the ERS images is so rich that a patient investigator can find galaxies of nearly any appearance in the epoch z≃ 1–3. This is because galaxy merging was in full swing in this epoch.

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Figures 15(a)–(d) display the WFC3 G102 and G141 grism images of the same region in the GOODS-South field (green box in Figure 3), together with short finder exposures in the WFC3 grism continuum filters F098M and F140W. For a detailed discussion of the ACS G800L and WFC ERS G102 and G141 grism spectra, please see Straughn et al. (2009, 2011). All brighter object WFC3 grism spectra in Figures 15(a)–(d) show a zeroth-order image to their left, displaced by about twice the spectral image length, which should not be confused with real emission lines. When one zooms in on the full-resolution version of this image (see the caption of Figures 15(a)–(d)), many faint object spectra are visible to a continuum flux as faint as AB ∼ 25–25.5 mag in two HST orbits, including many faint emission line galaxies.

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Figures 15(e) and (f) show examples of some specific WFC3 G102 and G141 spectra for emission line galaxies in the ERS at z = 0.738 and z = 0.610. For the emission line galaxy at z = 0.610, the available lower-resolution ACS G800L grism spectrum is also shown in green. For further details, see Straughn et al. (2011). Figure 15(f) shows that WFC3 near-IR grisms G102 and G141 have a spectral resolution of R ≃ 210 and R≃ 130, respectively, while the ACS G800L has a lower resolution of R≃ 100. It is clear from Figure 15(f) that R ≳ 200 is far superior for faint emission-line (and by implication also for weak absorption feature) detection than an R ∼ 100 grism. This should be a critical consideration for the design of the JDEM/WFIRST missions that are now being planned (Blandford et al. 2010) to carry out wide-field near-infrared imaging and grism spectroscopy from space for this coming decade.

In conclusion, the WFC3 broadband IR filters and its G102 and G141 grisms provide low-resolution imaging and faint object spectroscopy over the entire 0.80–1.70 μm range, unimpeded by the ground-based OH forest. They have shown the tremendous power of the WFC3 IR grism data above Earth's atmosphere, which are now used by a number of different WFC3 GO programs in HST Cycle 17 and beyond. They also illustrate the discovery power of the new frontier that will be opened up by the near- to mid-infrared 6.5 m JWST after its launch in 2015 (Gardner et al. 2006; Windhorst et al. 2006), and by future wide-field near-infrared space missions such as JDEM/WFIRST and Euclid.