BRIGHT STRONGLY LENSED GALAXIES AT REDSHIFT z ∼ 6–7 BEHIND THE CLUSTERS ABELL 1703 AND CL0024+16^*

Deep observations and surveys with the Hubble Space Telescope (HST), such as GOODS (Giavalisco et al. 2004; Dickinson et al. 2004), the HUDF (Beckwith et al. 2006), the HUDF05 (Oesch et al. 2007), and the HUDF parallel observations (Bouwens et al. 2004a), have greatly enriched our knowledge of the distant universe, enabling the discovery of more than 600 i₇₇₅-band dropouts (i-dropout; Bouwens et al. 2006, 2007), and eight z₈₅₀-band dropouts (z-dropout; Bouwens et al. 2008) which are believed to be galaxies at z ∼ 6 and 7, respectively. An L* galaxy of M = −20.3 at z ∼ 6 exhibits an apparent magnitude ∼26.8 (AB, and hereafter); consequently, the majority of z > 5.5 galaxies are fainter than AB = 26.

Bright high-redshift galaxies are rare. Ten i-dropouts brighter than AB = 25.5 were found in ∼400 arcmin² of GOODS, HUDF, and HUDF parallel fields (Bouwens et al. 2006, 2007). Two of them have been confirmed to be high-redshift objects spectroscopically (Bunker et al. 2003; Stanway et al. 2004). In a survey of the Subaru Deep Field of 767 arcmin² (Shimasaku et al. 2005; Taniguchi et al. 2005), 18 i-dropout galaxies were spectroscopically confirmed to be at z ∼ 5.7, and nine at z ∼ 6.6, but the brightest among them is only at magnitude of 25.4. In a recent survey that covers 1 deg² in the field of the Subaru/XMM-Newton Deep Survey (Ouchi et al. 2008b), 17 Lyα emitters (LAEs) at z ∼ 5.7 were found, of which only one is brighter than AB = 25.5 in the z band. At least one bright LAE has been found at z ∼ 6.6 (z-band magnitude 25.4, narrow band (921nm) magnitude 23.5; Ouchi et al. 2008a). Combining the results of these three surveys, the brightest z ∼ 6 candidate over 5000 arcmin² is at AB = 24.5 (in broad bands–LAEs are intrinsically brighter in a narrow band).

Gravitational lensing by massive galaxy clusters enables the detection of high-redshift galaxies that are fainter than can be found even in very deep surveys. In addition, lensed galaxies can be resolved spatially and, if bright enough, can be candidates for spectroscopy (Hu et al. 2002; Kneib et al. 2004; Pelló et al. 2004; Schaerer & Pelló 2005; Richard et al. 2006; Frye et al. 2008; Bradley et al. 2008; Bouwens et al. 2009; Richard et al. 2008). The number of z ≳ 6 candidates reported, however, has varied considerably depending on how aggressive the selection criteria are (and consequently how reliable the detected sources are: see, e.g., discussions in Bouwens et al. 2009). The HST images of clusters are the best in terms of spatial resolution and photometric accuracy, thus permitting the most reliable selections of high-redshift galaxies. One salient example is the three i-dropout arclets in Abell 2218 found by Kneib et al. (2004). These arclets represent different views (multiple images) of the same source at z = 6.75 ± 0.1. Bouwens et al. (2003) found an i-dropout object in the field of cluster RDS1252 − 29 as bright as AB = 24.2, and follow-up spectroscopy (Dow-Hygelund et al. 2005) confirmed it as a Lyman-break galaxy at z = 5.515 and revealed stellar absorption lines in the continuum. Recently, Bradley et al. (2008) discovered a galaxy candidate at z ∼ 7.6 in the field of Abell 1689 that is spatially resolved and has an observed H-band magnitude of 24.7. The cluster lensing magnifies this galaxy (A1689-zD1) by a factor of ∼10.

Taking advantage of the NICMOS data of 21 arcmin² over 11 galaxy clusters (including Abell 1689), Bouwens et al. (2009) searched for strongly lensed z-dropout galaxies at z ≳ 7 and found that A1689-zD1 is the only robust candidate in these fields. This suggests that bright high-redshift galaxies may be rare in cluster fields, even given the smaller field size of cluster regions. Since the amount of NICMOS data available over cluster fields is still very limited, there is reason to look at the surface density of such objects over larger areas and at somewhat lower redshifts, in order to overcome the effect of small number statistics.

The purpose of this paper is to report on the results of a search for bright (H-band magnitude ⩽25.6), highly magnified i- and z-dropout galaxies over a larger area than was used by Bouwens et al. (2009). Such sources provide us with a unique opportunity to examine the properties of lower-luminosity galaxies in detail. The lower-luminosity galaxy population is of great interest because it appears to dominate the UV luminosity density, SFR density, and production of ionizing (λ₀ ≲ 912 Å) photons (Yan & Windhorst 2004; Yoshida et al. 2006; Beckwith et al. 2006; Bouwens et al. 2006, 2007; Oesch et al. 2007; Reddy et al. 2008; Frye et al. 2008; Chen et al. 2009). In particular, we consider ∼4 arcmin² of additional search area over CL0024+16 and CL1056 − 03 obtained in a recent NICMOS program HST-GO10874 (PI: W. Zheng). These areas were not included in the z-dropout search of Bouwens et al. (2009).

The plan for this paper is as follows. In Section 2, we describe the observational data. In Section 3, we outline our search criteria and summarize the results of our search for bright z ∼ 6–7 galaxies. In Section 4, we use stellar-population modeling and the available lensing models to remark on the physical properties of the high-redshift galaxy candidates we are examining, and in Section 5, we summarize our results.

A summary of the HST ACS, WFPC2, and NICMOS imaging observations used here to search for z ∼ 6–7 i- or z-dropout galaxies is given in Table 1. Of particular interest are new NICMOS observations acquired over CL0024+16 (two NICMOS NIC3 pointings) and CL1056 − 03 (three NICMOS NIC3 pointings) from the program HST-GO10874. These observations were taken to better quantify the volume density of faint galaxies at z ∼ 7. Each NICMOS image is only 52'' × 52'' in size and covers just a portion of the total area with deep ACS data over these two clusters.

The NICMOS/NIC3 images of CL0024+16 were obtained in 2007 July, with exposures of 9.4 ks in both the F110W and F160W band. The NICMOS/NIC3 images of CL1056 − 03 were obtained in 2007 January and December, and 2008 January, with exposures of 6.6–8 ks in both the F110W and F160W bands. We used a custom pipeline written at the University of California Santa Cruz to process the NICMOS images ("nicred;" Magee et al. 2007) into a final mosaic. The 5σ limiting magnitudes for these data are approximately 26.7.

CL0024+16 was observed in 2004 November in six broad optical bands: F435W, F475W, F555W, F625W, F775W, and F850LP, including 16.3 ks in the z band and 10.1 ks in the i band. CL1056 − 03 was observed in 2004 March in the F606W, F775W, and F850LP bands, including 17.7 ks in the z band and 17.3 ks in the i band. All the ACS science images over these fields were processed with our pipeline APSIS (Blakeslee et al. 2003) and registered with the available NICMOS data.

We retrieved archival Spitzer/IRAC images of the field of Abell 1703 and CL0024+16, observed in 2007 January and 2003 December, respectively. The mosaic images are in the form of Post-BCD (Basic Calibrated Data), produced by the Spitzer pipeline calibration MOPEX. For Abell 1703, the exposure times were 6.2 ks for both the 3.6 and 4.5 μm bands, reaching a 5σ limiting magnitude of ∼24.7. For CL0024+16, the exposure times were 2.7 ks in the 3.6 μm band and 4 ks in the 4.5 μm band, reaching a 5σ limiting magnitude of ∼24.5.

We also searched for bright z ∼ 6 i-dropouts in the cluster data considered by Bouwens et al. (2009), who had used these data to search for z- and J-band dropouts at z ⩾ 7 and include NICMOS observations over 11 high-redshift clusters (Abell 1689, Abell 1703, Abell 1835, Abell 2218, Abell 2219, Abell 2390, Abell 2667, AC114, CL0024+16, 1E0657 − 56, and MS1358+61). Most of these clusters have deep ACS and WFPC2 optical data to ensure that the candidates we select at z ∼ 6 as i-dropouts are not detected in the optical to very faint limits. We refer to Bouwens et al. (2009) for more details on the reductions and processing of those data. Since we will be reporting on a bright z ∼ 6 candidate behind Abell 1703, we will summarize its ACS + NICMOS observations as well. NICMOS/NIC3 images of Abell 1703 were obtained in 2007 July, with exposures of 2.6 ks in both the F110W and F160W band. The cluster was observed at three other positions in the F110W band (see Figure 1).

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Independently as part of another program to search for high-redshift galaxies, we have acquired deep IR images of these cluster fields using a wide variety of different ground-based telescopes (Gemini-North/NIRI, Magellan/PANIC, and the VLT/ISAAC). Abell 1703 was observed with the Gemini-N/NIRI on 2003 June 11, with a total exposure time of 7.6 ks in the J band, and a 5σ limiting magnitude of 23.3. The Magellan/PANIC observations of CL0024+16 were made in 2003 October 3 and 5: the J-band observations took 17.8 ks, and the image reaches a 5σ limit of AB ∼26. The infrared images were processed with the IRAF/XDIMSUM package. Images taken on each night and with the same instrument configuration were sky-subtracted, shifted by the amount determined using the positions of a bright point source in dithered images, and combined. We select dropout galaxies when they are not detected beyond 2σ level, and the color decrements are more than two magnitudes. While these ground-based observations are shallower than the NICMOS data, they were used to tentatively identify the i-dropout galaxies. In a forthcoming paper (W. Zheng et al. 2009, in preparation) we will be presenting a few of these z-dropout galaxies from these wider-area ground-based data

Source catalogs were produced using SExtractor (Bertin & Arnouts 1996). We coadded the available NICMOS images for the clusters under study to create the detection image (Szalay et al. 1999). We then measured the fluxes on each of the ACS, WFPC2, and NICMOS images using the same scalable apertures, after PSF-correcting the higher resolution ACS and WFPC2 images to match the NICMOS images. As in Bouwens et al. (2009), we measure colors from smaller scalable apertures (Kron factor of 1.2; Kron 1980), typically ∼03. We then correct the fluxes measured in these smaller apertures to total magnitudes by comparing the light inside a larger scalable aperture (Kron factor of 2.5) of ∼06, on the detection image to that inside a smaller aperture.

Our color selection is based on the magnitudes measured in small-scalable apertures. The selection criteria for i-dropouts are similar to that of Giavalisco et al. (2004) and Bouwens et al. (2006), but with some variations:

$$\begin{eqnarray*} &&(i_{775}-z_{850}) > (1.3 + 0.9 (z_{850} - J_{110})) \end{eqnarray*}$$

or

$$\begin{eqnarray*} &&(i_{775} - z_{850}) > 2.0 \wedge (z_{850} - J_{110}) < 0.8 \end{eqnarray*}$$

where ∧ represents the logical AND symbol. In addition, we require that objects are not detected (<2σ) in all bluer bands to exclude lower-redshift interlopers. Also, selected dropout galaxies must have a star/galaxy index <0.8 and an image dimension greater than three pixels to exclude stars and artifacts.

The selection criterion for the z-dropouts (Bouwens et al. 2008) is

$$\begin{eqnarray*} &\displaystyle (z_{850} - J_{110}) > 0.8) \wedge \\ &\displaystyle (z_{850} - J_{110}) > (0.8 + 0.4 (J_{110} - H_{160})) \wedge \\ &\displaystyle (J_{110} - H_{160})) < 1.2. \end{eqnarray*}$$

Also, we require that objects are nondetected in all the bands shortward of 8500 Å.

In cases of nondetection in a shorter-wavelength band, we define the color decrement by setting the flux in that band to be zero, with an error that is equal to the 1σ detection limit. The nondetection in the r, g, V bands is important, as some sources are weakly detected in some of these bands. We found five other objects that were weakly detected in the shorter-wavelength bands. Their large i − z color decrements are probably produced by a Balmer decrement instead of a Lyα edge, and therefore the objects are at low redshift, e.g., z ∼ 1. Without deep images in the shorter-wavelength bands, these objects may be considered as "high-redshift candidates." This may explain why some other searches yield a considerable number of dropout galaxies.

Finally, we set an H-band magnitude limit of 25.6 to identify only the brightest sources in our survey. Applying the above selection criteria across our search fields, we identify three new dropout galaxies in total. One source, called A1703-iD1, is found in Abell 1703 (see also Richard et al. 2009, who also report on this source) and two other sources, CL0024-iD1 and CL0024-zD1, are found over CL0024+16. We also identified the z ∼ 6.5 i-dropout in Abell 2218 (Kneib et al. 2004) and the z ∼ 7.6 z-dropout over Abell 1689 (Bradley et al. 2008). No bright dropouts are found in CL1056 − 03 or any other clusters. Our three new galaxy candidates are given in Table 2, along with the previously known sources. The positions of these sources in Abell 1703 and CL0024+16 are shown with the red circles in Figures 1 and 2. Their cutout stamps are given in Figures 3 and 4.

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For our high-redshift candidates, we used the available Spitzer/IRAC data to measure fluxes at 3.6 and 4.5 μm. Since these data have a considerably larger PSF than the ACS/NICMOS data, this poses a challenge for accurate photometry. First, the IRAC PSF (∼16 at 3.6 μm) is considerably larger than the apertures used in the HST images (typically ≲ 05 in radius). We used an aperture size of 25 diameter, and then applied corrections of 0.56 and 0.6 mag for the 3.6 μm and 4.5 μm band, respectively, to account for flux outside of the aperture. These corrections were derived for stellar profiles (see, e.g., Bradley et al. 2008). In the field of A1703-iD1, there are two nearby sources of comparable brightness approximately 2'' away (Figure 3). We ran the task Galfit (Peng et al. 2002) to deblend the source fluxes with fixed source positions and a standard PSF profile of FWHM = 16. The derived magnitudes are presented in Table 2.

A1703-iD1 is a prominent i-dropout object, with a z-band magnitude AB = 24.2. As shown in Figure 3, it is well detected in the ACS z-band and NICMOS J and H bands, but not in the i-band and the other bands at shorter wavelengths. The object is detected in the Gemini-N image in the J band, with a magnitude of 24.2 ± 0.4. Our confidence that this source is a galaxy at z ∼ 6 rather than a lower-redshift object (Stanway et al. 2005) is largely motivated by the source's large color decrement of >2.6, which is twice the threshold in a normal selection (1.3–1.5). The possibility that this source is a dusty galaxy at lower redshift is ruled out as the source is roughly equally bright in the z- and J-bands, and entirely undetected in the r₆₀₆- (r) and i-bands, which is clearly a sign of a break in the spectral energy distribution (SED) instead of a gradual decrease toward bluer wavelengths. The source is resolved into two components (magnitudes 24.3 and 24.9; Figure 3) separated by ∼045. The only other objects with such colors are T-dwarfs, which can be ruled out by the fact that the source is extended. The FWHM for each component is ∼04, which is four times the ACS resolution. This source is detected at low significance (<2σ) in the F435W band (magnitude 27.7 ± 0.5), but not in an overlapping band F475W (>28.5) and F555W and F625W. This weak detection is probably just an upward statistical fluctuation and does not affect the SED fitting results noticeably.

The two sources in CL0024 pose an interesting question. These sources, CL0024-zD1 and CL0024-iD1, are separated by only 25. As we shall see below they have very similar redshifts and SEDs, and this small separation corresponds to just 2 kpc in the source plane. Thus they are likely to be spatially associated. This will be discussed further below, but for now we discuss their individual properties.

The source CL0024-iD1 is resolved in both the J- and H-band images. Its NICMOS J-band magnitude is 25.1 (Table 2). An independent check comes from our Magellan/PANIC image data which gives 25.8 ± 1.1, which is consistent with the NICMOS measurement. The source CL0024-zD1 appears to be marginally resolved into two components in the J₁₁₀ band image (Figure 4), but not in the H₁₆₀ band. In the Magellan images, its magnitude is 26.3 ± 1.3, which again is consistent with the NICMOS data. The detection in the 4.5 μm band is marginal, and appears to be consistent with background fluctuations.

It is interesting to note that A1689-zD1 (z ∼ 7.6; Bradley et al. 2008) also consists of two components separated by ∼1 kpc in the source plane. The apparent frequency of high-redshift galaxies with two bright components is perhaps not surprising, in that we expect to see bright star-bursting galaxies imbedded in massive halos that are merging at this very early epoch.

Because of the long time baseline of our ACS, NICMOS, IRAC, and ground-based observations, none of these sources are likely to be supernova outbursts or transiting objects. In addition, because the sources are detected in multiple bands, it is highly unlikely that they are spurious detections.

Current studies of the UV luminosity function (LF) at z ∼ 2–6 suggest that lower-luminosity galaxies provide the dominant contribution to the overall luminosity density in the UV, the stellar mass density, the ionizing photon budget necessary for reionization, and the build-up of metals (Yan & Windhorst 2004; Yoshida et al. 2006; Beckwith et al. 2006; Bouwens et al. 2006, 2007; Reddy et al. 2008; Chen et al. 2009). As such, clearly it is important to quantify the properties of this faint population. Unfortunately, this can be difficult to do in the field, due to the integration times required and due to crowding issues in deep IRAC images. This makes the present sample of highly magnified galaxy candidates at z ∼ 6–7 very useful for investigating the properties of lower-luminosity galaxies at high redshifts.

4.1. Intrinsic Luminosity

4.2. Spectral Energy Distribution and Photometric Redshift

We performed fits to the multiband photometry of these three sources by using the stellar-population models of Bruzual & Charlot (2003). For all of the models, we assume a simple stellar population (single-burst; SSP) with a Salpeter (1955) initial mass function with mass cutoffs of 0.1 and 100 M_☉. We explored models with both solar (Z = 0.02) and subsolar (Z = 0.0004 = Z_☉/50) metallicities. The models use the obscuration law of Calzetti et al. (2000) and are corrected for Lyman-series line-blanketing and photoelectric absorption following the procedure of Madau (1995). In the stellar-population model fits, we constrain the stellar age to be less than the age of the universe at the fit redshift (e.g., 0.8 Gyr at z = 6.5).

The best-fit stellar-population models are shown in Figures 5–7 and the parameters are given in Table 3. While the nondetections are shown in these figures as 2 σ upper limits, we used the measured fluxes, not the limits, to fit the SEDs. For both solar and subsolar metallicities, we found acceptable fits for the models. IRAC photometry places important constraints on the stellar-population models as it provides the rest-frame optical magnitudes for high-redshift galaxies (Labbé et al. 2006). Using the ratio of UV-optical luminosity one can estimate the galaxy age with considerable accuracy. Considering the uncertainties associated with the mass models themselves and in potential reddening factors, the real errors are likely somewhat higher than those listed in Table 3.

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Table 3. Best-fit Stellar-Population Model Results

Object	zphot	zforma	Massb (109 M☉)	Agec (Myr)	AV	χ2ν
High Redshift, Solar Metallicity (Z = 0.02)
A1703-iD1	5.9 ± 0.1	6.2	9.2 ± 3.2	55+17−27	0.0 ± 0.2	1.2
A1703-iD1	5.827	6.2	12 ± 0.6	64+10−9	0.0 ± 0.1	1.1
CL0024-iD1	6.4 ± 0.1	6.7	1.5 ± 0.1	43+15−17	0.0 ± 0.1	0.7
CL0024-zD1	6.5 ± 0.3	7.1	2.0 ± 0.4	81+41−72	0.0 ± 0.1	0.1
High Redshift, Subsolar Metallicity (Z = 0.0004)
A1703-iD1	6.0 ± 0.1	6.5	12 ± 4.6	64+41−44	0.2 ± 0.2	1.1
A1703-iD1	5.827	5.9	13 ± 3.4	13+12−2.5	1.2 ± 0.1	1.7
CL0024-iD1	6.5 ± 0.1	7.0	2.1 ± 0.8	72+24−44	0.0 ± 0.2	0.5
CL0024-zD1	6.7 ± 0.4	7.4	2.5 ± 0.2	90+101−77	0.2 ± 0.4	0.1
Low Redshift, Solar Metallicity (Z = 0.02)
A1703-iD1	1.2 ± 0.1	1.4	2.4 ± 0.4	454+117−49	0.8 ± 0.3	9.3
CL0024-iD1	1.3 ± 0.2	1.5	0.4 ± 0.1	571+235−156	0.3 ± 0.4	2.8
CL0024-zD1	1.4 ± 0.5	1.5	0.4 ± 0.2	571+444−315	0.7 ± 0.9	0.6
Low Redshift, Subsolar Metallicity (Z = 0.0004)
A1703-iD1	1.2 ± 0.2	1.4	4.2 ± 0.9	454+140−22	1.8 ± 0.3	11.4
CL0024-iD1	1.3 ± 0.2	1.5	0.7 ± 0.2	454+187−167	1.4 ± 0.4	4.2
CL0024-zD1	1.4 ± 0.6	1.6	0.6 ± 0.4	404+402−290	1.8 ± 1.0	0.9

Notes. ^aFormation redshift calculated from the fitted redshift and SSP stellar age. ^bBest-fit stellar mass, corrected for the cluster magnification. ^cAge of the single-burst stellar population (SSP model).

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For A1703-iD1 (Figure 5), the best-fit redshifts are z = 5.9–6.0 with an 1σ error of 0.1. The best-fit results, with χ²_ν = 1.1, suggest a high-redshift galaxy with a mass of 0.9–1.2 × 10¹⁰ M_☉ and age of 55–64 Myr. Richard et al. (2009) measure a redshift of z = 5.827 from Keck spectroscopy, which is broadly consistent with our fitting results. We also ran the fits to photometry with the redshift fixed to z = 5.827, and the results are presented in Table 3 and Figure 5. Using the spectroscopic redshift removes one of the degrees of freedom, but the modeling results still do show some dependence on the unknown metallicity: The fit with solar metallicity produces a satisfactory result, with χ²_ν = 1.1, but that with a low metallicity does not fit as well, with χ²_ν = 1.7, suggesting that the metallicity may well be high in this very luminous (3 L*) galaxy, or, if the metallicity is low, that the low-metallicity models may not match the SED very well in these high-redshift galaxies. The low-redshift solutions are inconsistent (χ²_ν ∼ 10) with the observed photometry.

For CL0024-iD1 (Figure 6), again we find that the high-redshift solutions (χ²_ν = 0.5–0.7) provide a better fit to the data than the low-redshift solutions (χ²_ν = 2.8–4.2). Of note, the low-redshift SED models are inconsistent with the observed r- and i-band 1 σ upper limits and the z- and J₁₁₀-band photometry. The best-fit redshifts are z = 6.4–6.5 with an 1 σ error of 0.1. The stellar masses are 1.5–2.1 × 10⁹ M_☉ with ages of 43–72 Myr. The reddenings derived from the fits to both the solar and subsolar models were A_V = 0.0.

For CL0024-zD1 (Figure 7), we find the high-redshift solutions (χ²_ν ∼ 0.1) are only modestly better than the low-redshift solutions (χ²_ν = 0.6–0.9). With the exception of the z-band photometry, which has large uncertainty, the low-redshift SED models can also reproduce the measured fluxes blueward of the break in the SED. We still favor the high-redshift solutions (z = 6.5–6.6 ± 0.4) over the low-redshift models (z = 1.4 ± 0.6). The stellar masses are ∼2–2.5 × 10⁹ M_☉ and the ages ∼85 Myr. The solar and subsolar models have fit reddenings of A_V = 0.0 and 0.2, respectively.

4.3. Are CL0024-iD1 and Cl0024-zD1 Physically Related?

4.4. Surface Density of Bright High-Redshift Candidates

We compare our sample (Figure 8) with the distribution of known galaxy candidates at z ∼ 6, based on the LF of Bouwens et al. (2006) and scaled to a search area of 25 arcmin². To a limiting magnitude of 25.6, a survey in an unlensed field is anticipated to find ∼1.4 candidates at z ∼ 6. We, however, find 4–5 such bright z ∼ 6–7 candidates behind lensing clusters. This effectively illustrates how lensing from foreground clusters can help us identify high-redshift galaxies at relatively bright magnitudes–which is helpful for numerous follow-up studies, including spectroscopy. The observed enhancement is expected because of the steep slope of the LF expected at higher luminosities (i.e., −d(log dΦ)/dlog L > 1: e.g., Broadhurst et al. (1995)). Such steep slopes are seen brighter than L* where there is an exponential cut-off, but not fainter than L*. For A1703-iD1, its intrinsic z-band magnitude is approximately 25 after correcting for the 3× model magnification factor (see Table 4). According to the z ∼ 6 LF, one would expect to require 40–250 arcmin² to find one such bright candidate. Since the discovery of A1703-iD1 was made over an area of approximately 7 arcmin² (after correcting for the 3× dilution factor), it would seem to be a rather serendipitous discovery. For the four other dropout candidates listed in Table 4, if we assume a nominal magnification factor of 9 in the cluster field, their intrinsic magnitudes are AB 27–28. Over 2 arcmin² in the source plane, the z ∼ 6 LF predicts approximately 2–5 such galaxies. The four such galaxies found are therefore consistent, within the uncertainties, with the known distribution of high-redshift galaxies.

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4.5. Rest-frame Optical Fluxes of the Lower-Luminosity Galaxy Population

Perhaps the most interesting property to examine in our small sample of highly magnified galaxy candidates is their stellar mass. The stellar masses tell us about the past star formation rate in a galaxy and therefore its likely contribution to the reionization of the universe as well as the production of metals. The stellar masses estimated in the previous section are useful for assessing the contribution of individual galaxies to the reionization of the universe. However, what we really want to know about the galaxy population at z ∼ 6–7 is their stellar mass density–since we can use this to constrain the SFR history at z > 7. It is difficult to determine this directly from the above measurements since we only have five high-redshift galaxy candidates from which to derive a mass function (and also the masses we derive will be sensitive to uncertainties in the model magnification factors: see, e.g., R. J. Bouwens et al. 2009, in preparation).

A better way of estimating the total stellar mass density is to start with determinations of the UV LF at z ∼ 6–7 and then use the measurements of UV-to-optical colors of z ∼ 6–7 galaxy candidates to estimate the stellar mass function of the galaxies (given the link between rest-frame optical colors and our estimates of stellar mass). Such colors have been available for the more UV luminous galaxy candidates at z ∼ 6–7 (Eyles et al. 2005; Yan et al. 2006; Stark et al. 2007), but until the present have been lacking for the less UV luminous galaxy candidates at z ∼ 6–7. This is where our sample of highly magnified galaxy candidates at z ∼ 6–7 is useful since they provide a luminosity-to-mass calibration for the less luminous galaxies that have previously lacked colors.

For the sake of uniformity, we will use the H − 3.6 μm colors of our sample of high-redshift galaxy candidates to represent the rest-frame UV-to-optical colors. We plot this color distribution for the four strongly lensed galaxy candidates in our sample with IRAC fluxes in Figure 9. We compare this distribution with the colors of more luminous galaxy candidates at z ∼ 6–7 identified in the HUDF (Yan et al. 2005; Labbé et al. 2006). No significant differences are observed between the H − 3.6 μm colors of our sample and the more luminous galaxy candidates Labbé et al. (2006) examined in the HUDF. A t-test yields a significance of 51%, suggesting no large differences between the ages (and mass-to-light ratios) of the lower-luminosity galaxy population at high redshift and that at higher luminosities. This has obvious implications for the total stellar mass density at z ∼ 6–7 and therefore the total star formation rate density at z ≳ 7 (Chary 2008), since it allows us to estimate the fraction of the total stellar mass density at z ∼ 6–7 that come from high- and low-luminosity systems. Our result does not suggest that lower luminosity galaxies have substantially different M/L ratios than at higher luminosities, and therefore provide no indication that lower luminosity galaxies contribute anything significantly different from what we might expect based upon their contribution to the luminosity density. It is also consistent with the hypothesis that more massive galaxies are unresolved aggregates of lower-luminosity galaxies.

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4.6. Morphology of High-Redshift Galaxies

We have found three bright, strongly lensed i- and z-dropouts in the fields of the massive clusters Abell 1703 (see also Richard et al. 2009) and CL0024+16. Their large color decrements make the selection of these high-redshift galaxy candidates robust (with the exception of CL0024-zD1 for which the evidence is a little weaker), and detailed cluster mass models enable us to derive the intrinsic properties of the high-redshift galaxies. The similar redshifts, SEDs, and luminosities, and the quite small separation in projection, of the two sources in CL0024+16 suggest that they may be spatially associated with a separation of ∼2 kpc. Using stellar-population models to fit the rest-frame UV and optical fluxes, we derive best-fit stellar masses on the order of 10^9–10 M_☉. Even after correcting for the lensing magnification (a factor of 3), A1703-iD1 remains intrinsically luminous. The three galaxy candidates are extended, with intrinsic sizes between 0.2 and 2 kpc, and resolved into a pair of nuclei. They, along with A1689-zD1 (Bradley et al. 2008), which is also double with component separation of ∼1 kpc in the source plane, suggest that merger driven growth and star formation may be a defining characteristic of high-redshift galaxies. Bright resolved galaxies such as these will be important targets for spectroscopy with the largest ground based telescopes and future large-aperture space telescopes like the James Webb Space Telescope.

The ACS was developed under NASA contract NAS 5-32865, and this research has been supported by NASA grant NAG5-7697. Infrared observations were made using the Gemini-North Telescope during the quarter GN-2003B-Q-28. We acknowledge the support of HST grants AR10310 and GO10874, and Spitzer grant GO20749. V.M. acknowledges the support by FONDECYT grant 1071008. Archival HST data were provided by the Multimission Archive at the Space Telescope Science Institute (MAST). We thank the anonymous referee for many thoughtful and detailed comments, which enabled us to improve the quality of this paper considerably.