THE REST-FRAME UV-TO-OPTICAL COLORS AND SPECTRAL ENERGY DISTRIBUTIONS OF z ∼ 4–7 GALAXIES

As a result of the installation of the WFC3/IR camera on the Hubble Space Telescope (HST), it is now possible to obtain extremely deep, high resolution observations in the near-infrared. These observations match the exquisite optical data provided by the Advanced Camera for Surveys (ACS) over deep and ultra-deep fields like the GOODS and the HUDF (Giavalisco et al. 2004; Bouwens et al. 2007). The upgrade has enabled several teams to extend their searches for Lyman break galaxies (LBGs) to very high redshifts (e.g., Bouwens et al. 2010; Oesch et al. 2010, 2012; McLure et al. 2010; Yan et al. 2010; Bunker et al. 2010; Finkelstein et al. 2010). In combination, these two cameras have allowed for high signal-to-noise (S/N) measurements of the rest-frame UV light of high-redshift galaxies over a wide wavelength baseline.

As a result of these new observations, the UV luminosity functions at z ≳ 4 are known to high accuracy. Another direct result from these observations is the determination of the UV slope of the spectral energy distributions (SEDs), generally characterized by the parameter β (f_λ∝λ^β, e.g., Meurer et al. 1999; Bouwens et al. 2009). This slope has been shown to become steeper (bluer) both with decreasing luminosity and with increasing redshift (Bouwens et al. 2009, 2011a; Wilkins et al. 2011; but see Dunlop et al. 2012; Finkelstein et al. 2011). For an intermediate aged (100  Myr) stellar population, this slope generally depends most strongly on the dust reddening so that this has been interpreted as an increase in the dust content of galaxies with cosmic time and as galaxies increase in luminosity (Bouwens et al. 2011a; Finkelstein et al. 2011).

Since the rest-frame UV light primarily probes young short-lived stellar populations (mostly O and B stars), it is interesting to extend these observations to longer wavelengths and study the relative importance of more evolved stellar populations. This is very challenging though and is now only possible thanks to the incredible sensitivity of the IRAC camera on the Spitzer Space Telescope. Some of the first observations of rest-frame optical light from z ≳ 4 galaxies showed quite sizeable UV-to-optical breaks (Eyles et al. 2005; Yan et al. 2005). Under the usual assumption of smooth, exponentially declining star formation histories (SFHs), these colors were interpreted as indicative of an evolved stellar population (ages ≳ 100 Myr) in combination with the younger populations probed by the UV light. Follow-up work on z ∼ 4–7 galaxies continued to reveal systems with moderate size UV-to-optical breaks (e.g., Eyles et al. 2007; Yan et al. 2006; Labbé et al. 2006; Stark et al. 2009; González et al. 2010), even possibly to z ∼ 8 (Labbé et al. 2010a). However interesting, these studies are only possible for the brightest z > 4 galaxies due to the extreme depths required.

Some alternative explanations have been proposed for the red UV-to-optical colors observed in z > 6 galaxies. For example, for young star-forming galaxies, one might expect strong line emission. At specific redshifts, these lines could contaminate the 3.6 and 4.5 μm IRAC fluxes, resulting in red UV-to-optical colors similar to those produced by the Balmer break (Schaerer & de Barros 2009, 2010). For emission lines to be strong enough to dominate the rest-frame optical fluxes, extremely young ages (∼6 Myr) are required. Such models have ages shorter than the dynamical times of these high-z sources and are also somewhat uncertain. It would be surprising if the majority of these galaxies, which are selected over a redshift range that spans ≳ 200 Myr, had such young ages. Even if rest-frame optical emission nebular emission lines do not dominate the measured IRAC fluxes, it is expected that they will contribute some of the flux measured in the mid-IR, but the exact contribution is difficult to establish at these high redshifts.

It has been routine, then, to compare the colors of these high-redshift galaxies with synthetic stellar population (SSP) models of relatively evolved galaxies with smooth SFHs to derive physical properties from the observations. By studying LBG samples at different redshifts in the aforementioned way, one intriguing result has emerged. At a given intrinsic luminosity, the specific star formation rate (SFR) of galaxies seems to remain remarkably constant with redshift (Stark et al. 2009; González et al. 2010, 2011; McLure et al. 2011) though accounting for the latest dust corrections by Bouwens et al. (2011a) would modify this somewhat. This result has called the attention of theorists and has proved very hard to reproduce in simulations (e.g., Weinmann et al. 2011; Khochfar & Silk 2011). The assumptions used to derive these results vary somewhat from group to group. In this work, we present the basic observations that lead to such a result, namely the observed SEDs of galaxies at z ∼ 4–7.

In the present work, we study the observational properties of the typical high-redshift galaxy. We do this by splitting our large sample in both redshift and UV-luminosity bins and constructing mean SEDs. The large number of galaxies allows us to study the typical colors at high S/N but also extend our measurements to faint limits that are currently inaccessible on an individual basis with the current data. Although the scatter about the typical properties is also highly interesting, we defer their study to a future work which relies on even deeper Spitzer observations. In Section 2, we present the data and in Section 3 the sample selection and photometry. Section 4 describes the stacking procedure and we discuss the stacked SEDs and colors in Section 5. A summary is presented in Section 6.

Throughout, we use a ($H_0,\,\Omega _M,\,\Omega _\Lambda$) = (70 km s⁻¹, 0.3, 0.7) cosmology when necessary and we quote all magnitudes in the AB system (Oke & Gunn 1983).

In this paper, we make use of the large number of z ≳ 4 galaxies found in the ultra-deep HUDF data and the wide-area Early Release Science (ERS) data to construct median SEDs for star-forming galaxies at z ∼ 4–7. The deep optical, near-IR, and deep IRAC coverage over these fields allows us to create SEDs extending from the rest-frame UV to the rest-frame optical down to very faint fluxes.

2.1. HST ACS and WFC3/IR

2.2. Spitzer/IRAC

The criteria used to identify high-redshift star-forming galaxies have already been presented in numerous previous works. For details on the selection procedure and discussion of sample contamination please see Bouwens et al. (2007, 2011b). In short, the selection criteria used to find the sources presented here are as follows:

z ∼ 4 B-dropouts:

$$\begin{eqnarray*} \quad\quad (B_{435}-V_{606}>1.1) &\wedge & [B_{435}-V_{606}>(V_{606}-z_{850})+1.1]\nonumber\\ &\wedge & (V_{606}-z_{850}<1.6) \end{eqnarray*}$$

z ∼ 5 V-dropouts:

$$\begin{eqnarray*} &&\quad\;\; \lbrace [V_{606}-i_{775}>0.9(i_{775}-z_{850})+1.9] \vee (V_{606}-i_{775}>2)\rbrace \nonumber\\ && \quad\quad\quad\quad\quad \wedge (V_{606}-i_{775}>1.2) \wedge (i_{775}-z_{850}<1.3) \end{eqnarray*}$$

z ∼ 6 i-dropouts:

$$(i_{775}-z_{850}>1.3) \wedge (z_{850}-J_{125}<0.8).$$

The combined samples contain a total of 729 sources at z ∼ 4, 178 at z ∼ 5, and 83 at z ∼ 6 (see Table 1).

We complement the z ∼ 4, 5, and 6 samples with the sample of 36 z ∼ 7 sources presented by Labbé et al. (2010a). We have adopted the z ∼ 7 stacks presented in that work.

At these depths, the Spitzer/IRAC images are fairly crowded due to the size and shape of its point spread function (PSF). As a consequence, standard aperture photometry of the sources generally results in fluxes that are contaminated by flux from nearby sources. We are able to de-blend the fluxes from the different sources by making use of the higher resolution information available through the HST images. Our method has been explained in previous works by our group (e.g., Labbé et al. 2006, 2010b; González et al. 2010, 2011) but we give a short description here. We start by registering the IRAC images to the higher resolution HST image that will be used as a light profile template. In this case, we use the WFC3/IR H₁₆₀-band image as our template because it is the closest in wavelength and has high S/N. We use the SExtractor software (Bertin & Arnouts 1996) to create segmentation maps. We isolate all the sources in a small area around each galaxy in our sample using these segmentation maps. We then convolve them with a kernel derived from the PSFs of the HST and the IRAC images. We fit for the normalization fluxes of all sources (including the source we are trying to clean) simultaneously. Finally, we remove the flux from the unrelated sources to obtain a clean image of the galaxies in our sample. Later, we use these cleaned images to produce median stacks.

The procedure described above is not always successful in subtracting flux from neighboring sources at a satisfactory level such that reliable flux measurements are possible. The reasons why it can fail vary but the most common is the presence of a neighboring source that is too bright, extended, and close to our region of interest. In these cases, the amount of flux subtracted off our source of interest is large and more uncertain and in most cases results in large residuals. We have carefully inspected the residual images (all sources subtracted, including the one in our sample) and the cleaned images (only unrelated neighbors subtracted) of each of the sources in the original sample and come up with a sub-sample of sources with clean IRAC photometry. This "by eye" inspection criterion generally results in good agreement with a criterion that selects only the images with the lowest χ² residuals but allows us to also remove sources that, despite having χ² values, present mild-to-strong residuals located very close to the source. Overall, this reduces the size of our samples to 60% of their original size (see Table 1). Since the criterion adopted here depends on the complexity of neighboring foreground sources, it is not expected that it should introduce any biases that would be relevant in the determination of the mean rest-frame optical colors (see Figure 1).

It has been shown that in star-forming galaxies, the total SFR appears to correlate with stellar mass, the so-called main sequence of star-forming galaxies (Noeske et al. 2007). This sequence has been observed at high redshifts (z ≳ 4) but contrary to what has been observed at z < 2, the normalization of the relation at fixed stellar mass does not seem to evolve over 2 < z < 7 (Stark et al. 2009; González et al. 2011). The lack of deeper rest-frame optical from Spitzer/IRAC for these sources is one of the big limitations to study this sequence to fainter magnitudes. In terms of the bulk of the population, however, progress can be made by stacking large numbers of sources to study their mean properties. In this section, we seek to construct the median SEDs of galaxies at z ≳ 4.

Due to the nature of the dropout search and the filters available, our full sample is naturally divided into redshift bins centered at 〈z〉 = 3.8, 5.0, 5.9 plus the 〈z〉 = 6.9 sample from Labbé et al. (2010a). In this section, we further split each redshift sub-sample based on their observed rest-frame UV luminosity. The filters used as reference UV luminosity are the i₇₇₅ filter for the z ∼ 4 sources; the z₈₅₀ filter for the z ∼ 5 sources; the Y₀₉₈ filter for the z ∼ 6 sources in the ERS and the Y₁₀₅ filter for the z ∼ 6 sources in the HUDF; and finally, the J₁₂₅ filter for the z ∼ 7 sources. These filters were chosen to be close to rest frame 1500 Å at the different redshifts and make the splitting criterion fairly uniform across redshifts. These bins are presented in Figure 1.

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In the case of the HST ACS and WFC3 imaging, the fluxes utilized correspond to the MAG_AUTO values determined using the SExtractor code plus an additional correction to account for the flux outside the MAG_AUTO aperture. These corrections are estimated assuming a point-source profile and are generally in the range 0.1–0.3 mag. The corrections are larger for the fainter sources (because they generally have smaller apertures). In each UV-luminosity bin, the median flux corresponds to the median of the individual measurements. Only sources with reliable IRAC fluxes were included in the median. The uncertainty in the median was estimated through bootstrap resampling simulations performed as follows. These simulations involved creating a large number of realizations of the sample, by drawing, with replacement, N_bin fluxes (from the total N_bin values available). The fluxes are perturbed within their individual uncertainties before estimating the median of the realization. The uncertainties on individual sources are generally quite small, given the very high S/N of the images. There are, however, systematic uncertainties in the absolute calibration of the different bands and instruments across the SED. These uncertainties are typically no smaller than 5%, so we adopt this value as our minimum allowed uncertainty for any given flux.

In the case of the IRAC imaging, most sources are too faint to be individually detected even in these deep ∼ 23.3 hr integration images. Instead of using individual fluxes, we first median combine (pixel by pixel) the cleaned stamps of the sources within a bin that have clean residuals from our IRAC cleaning procedure. The pixel by pixel median also removes any sizeable residuals that we may have overlooked in inspecting the individual fits. We perform standard aperture photometry on the stacked images using a circular aperture of 25 diameter and correct the fluxes to the total assuming PSF profiles. This amounts to a factor of 1.8 correction to the fluxes in both the [3.6] and the [4.5] IRAC filters. The local background is estimated from the stacks, in an annulus between 6'' and 10'' diameters around the stamp center, where the source is expected to be, and then subtracted off the image.

It is important to note that this procedure is very different from the way the HST stacking is done. We have checked that this does not impose significant biases in our measurement by applying the same procedure as described for the IRAC stacks to the H₁₆₀-band stacks. We first masked out the neighboring sources and then convolved the H₁₆₀ image with a kernel to degrade it to the resolution of the IRAC images. We have median combined these images and performed simple aperture photometry in the same way as we did for the IRAC bands, using 25 diameter apertures and correcting to the total fluxes assuming stellar profiles (factor 1.8). We find that the H₁₆₀ −IRAC colors measured with the two methods are in excellent agreement (agreeing to within 0.05 mag), indicating that we are not introducing any significant bias in the estimates of the UV-to-optical colors.

To estimate the uncertainty in the IRAC stacks, we also create bootstrap realizations. We treat the two epochs of IRAC data over the HUDF as independent stamps in the stack, thereby effectively weighting with exposure time, i.e., N_bin = N_ERS + 2N_HUDF. In each bootstrap draw then, we draw with replacement N_ERS + 2N_HUDF such stamps and estimate fluxes as described above. The image noise in each stack is dominated by the background noise (shot noise from the sources will contribute less than 2% even for the brightest sources in the sample). This image noise is expected to decrease with the total equivalent exposure time approximately as $1/\sqrt{t_{{\rm exp,eq}}}$ (t_{exp, eq} = (N_ERS + 2N_HUDF) × 23.3 hr). The actual photometric uncertainties that we derive are always greater than this because they also include the intrinsic scatter in the fluxes of the sources being stacked together (see the Appendix). Stamps for all the IRAC median stacks along with the derived magnitudes and uncertainties are presented in Figures 2–4. Table 2 is a compilation of all the stacked photometry including the Labbé et al. (2010a) stacks and information on the number of sources that go in each stack. It can be seen in the figures that even for sources as faint as 27 mag, the stacks show good detections in both IRAC bands.

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The observed colors of galaxies can give us important information about the stellar populations that compose them. Usually, this is accomplished by comparing their colors with those of Synthetic Stellar Population (SSP) models. In this work, we chiefly explore the observed UV-to-optical colors and what can be learned from them and from their dependence on luminosity and redshift. When models are invoked, we use the Bruzual & Charlot (2003, BC03) models and we assume a Salpeter (1955) IMF, constant SFH, and 0.2 Z_☉ metallicity, as these quantities cannot be constrained from our data. To derive best fits, we use the SED fitting code FAST (Kriek et al. 2009).

The rest-frame UV-to-optical color is of particular interest at high redshifts. Several studies have detected significant rest-frame UV-to-optical colors (≳ 0.5 mag) in z ≳ 4 galaxies (Eyles et al. 2005, 2007; Yan et al. 2005; Stark et al. 2009; González et al. 2010, 2011; Labbé et al. 2006, 2010a; McLure et al. 2011). The usual interpretation is that these colors derive from large Balmer breaks which are associated with evolved stellar populations with ages ≳ 200 Myr. This is surprising given how young the universe is at the time these galaxies are being observed. The main limitation for field studies is the depth of the Spitzer/IRAC imaging available, which constrains these studies to the brightest LBGs. Searches behind clusters provide an alternative to probe the fainter populations (see, e.g., Ellis et al. 2001; Bradley et al. 2008; Richard et al. 2008; Laporte et al. 2011, and the recent tentative determination of a 1.5 mag Balmer break in a z ∼ 6 galaxy by Richard et al. 2011), but the number of sources amenable to such studies remains low. We work around this limitation by stacking large numbers of sources which allows us to estimate the typical rest-frame UV-to-optical colors of faint z ≳ 4 sources.

We start by presenting the results found at z ∼ 4, where the similar and complementary work of Lee et al. (2011) allows us to study these colors over an unprecedentedly large range of UV luminosities.

5.1. The UV-to-optical Colors at z ∼ 4

Our sample of B-dropouts has a mean redshift of 〈z〉 = 3.8 ± 0.3. We divide this sample based on their i₇₇₅ luminosity (which approximately corresponds to rest frame 1500 Å) in four bins of Δi₇₇₅ = 1 mag. These are the same bins as shown in the histogram in Figure 1. The bins at i₇₇₅ > 28 mag are too faint to be detected in Spitzer/IRAC and will not be included in the analysis. Assuming the mean redshift of the sample, these bins correspond approximately to M₁₅₀₀ = −21, −20, −19, and −18, which covers the moderately bright to faint end of the population (M*_{1600, z = 4} = −20.24; Bouwens et al. 2007).

In a recent study, Lee et al. (2011) focus on the median SEDs of the brightest z ∼ 4 galaxies found in the ground-based NOAO Deep Wide-Field Survey. Their sample has a mean redshift 〈z〉 = 3.7 ± 0.4, and their SEDs also sample the rest-frame UV and optical using a combination of optical filters: B_W, R, I (Mosaic Camera), near-IR filters: J, H, K_s (NEWFIRM Camera), and the Spitzer/IRAC mid-IR channels 1 through 4⁴. Similar to the present work, they divide their sample according to the I-band luminosity, although with uneven bins. Their sources are intrinsically brighter than in this work, corresponding to L > L*_{z = 4} sources roughly covering the range −23 ≲ M₁₅₀₀ ≲ −21.

The combination of the Lee et al. (2011) sample with our data spans the UV-luminosity range −23 ≲ M₁₅₀₀ ≲ −17.5. This represents an unprecedented data set to study the SEDs, and especially the UV-to-optical colors, of z ∼ 4 galaxies over a large range of luminosities. The SEDs from both works are presented in Figure 5. In this figure, the H₁₆₀-band flux measurements are shown with open symbols since it is likely biased and should be ignored as is explained in detail later. An overall trend to bluer colors (both in the rest-frame UV and the rest-frame UV-to-optical colors) toward fainter luminosities is already apparent in this figure.

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We quantify the UV-to-optical colors by estimating the interpolated rest-frame (U_n − V_n) colors for the median-stacked SEDs in both sets. Figure 6 shows a systematic trend of redder (U_n − V_n)_rest colors as a function of increasing UV luminosity.

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The interpolated (U_n − V_n) colors were determined from the best fits to the full observed SED, where the fits correspond to a linear combination of a set of template SEDs. These SEDs correspond to the default template set from the photometric code EAzY (Brammer et al. 2008). This template set was constructed and calibrated empirically to determine accurate photometric redshifts of galaxies of various types from very blue starbursts to red ellipticals and has been shown to work well up to z ∼ 5–6 (Brammer et al. 2008). For the U_n and V_n filters, we have assumed narrow ideal filters that correspond to step functions of width of 100 Å, centered at 3500 Å and 5500 Å for the U_n and V_n filters, respectively. The colors were calculated from the best-fit combination of templates using the filters described above. To estimate the uncertainty in the (U_n − V_n)_rest estimates, we perturbed the photometry and the redshift of each median-stacked SED within the allowed uncertainty, and a new fit was obtained. A new set of colors was measured from this best fit and the procedure was repeated a large number of times to derive the confidence intervals. A similar procedure was used to derive rest-frame M₁₅₀₀ magnitudes for an ideal filter centered at 1500 Å and with a width of 100 Å.

For the data point at M₁₅₀₀ ∼ −19, only an upper limit can be obtained due to the limitations of the template set used here. The EAzY default template set only includes SEDs with (U_n − V_n)_rest ≳ 0.3. The SED at M₁₅₀₀ ∼ −19 is likely to have a (U_n − V_n)_rest color of ∼0.3 mag, so no reliable lower limit can be obtained. We choose to show a 2σ upper limit. Other more sophisticated algorithms to determine interpolated rest-frame colors for an observed SED yield very similar results (e.g., the InterRest code, Taylor et al. 2009, which implements the algorithm described in Rudnick et al. 2003). However, such algorithms also depend on the template set resulting in similar limitations.

It is important to note that, when deriving this color from best fits, we have ignored the H₁₆₀ band in our stacks and the H and K_s bands in the Lee et al. (2011) stacks. Given the redshift distribution of the sample, it is expected that for some fraction of the sources (the ones at the lowest redshifts) the H-band fluxes measured will include some rest-frame optical light. As a result, the estimated median rest-frame UV flux will be biased toward larger values. To attempt a correction for this would require us knowing the exact redshift distribution of the sample, but even then a correction would be highly uncertain, so we opt to remove these photometric points from all fits.

In recent works, Bouwens et al. (2009, 2011a) accurately determine the UV slope of LBGs at z > 3 as a function of UV luminosity and redshift. For a star-forming stellar population, the UV slope, parameterized by β (f_λ∝λ^β), is most sensitive to the dust content of the galaxy. In consequence, the authors argue that the dependence of β on UV luminosity can be fully explained by an increase in the amount of dust that these galaxies contain as they become brighter. If this is the case, then a trend of redder (U_n − V_n)_rest colors for UV-brighter sources like the one observed here is also expected, since this color is also affected by dust extinction. The bottom panel of Figure 6 shows the (U_n − V_n)_rest colors corrected for dust extinction. These were derived as in Bouwens et al. (2009) from the mean β versus UV-luminosity trend and the classic Meurer et al. (1999) relation that relates the dust content with the UV-slope β according to

$$\begin{equation} \centering A_{1600} = 4.43 + 1.99\times \beta , \end{equation} \tag{ 1 }$$

where A₁₆₀₀ is the extinction in magnitudes at 1600 Å. A Calzetti et al. (2000) extinction curve is used to estimate the extinction at other wavelengths.

As can be seen from the figure, the dust-corrected (U_n − V_n) color is essentially independent of the UV luminosity. This again suggests that the main origin for the correlation of β with the UV luminosity is an increasing dust content at brighter magnitudes. Otherwise, we would expect some residual trend in the dust-corrected color. This would be the case, for example, if a strong age trend existed with UV luminosity. As will be shown later, a similar flattening of the corrected colors is observed at all redshifts in the −21 < M₁₅₀₀ < −18 range.

5.2. The UV-to-optical Colors at Higher Redshift

We now extend our determination of the SED of high-z galaxies to z ∼ 5 and z ∼ 6, and combine our determinations with the stacked SEDs of sources at z ∼ 7 recently presented in Labbé et al. (2010a). Figure 7 shows the SEDs at 4 ≲ z ≲ 7. The expected mean redshifts of these samples correspond to 〈z〉 = 3.8, 〈z〉 = 5.0, 〈z〉 = 5.9, and 〈z〉 = 6.9, with typical spread in redshift Δz of ± 0.3. The samples at each redshift have been split into bins of 1 mag, using as reference the observed magnitude in the band closest to 1500 Å (Table 2 contains the SEDs and information about the samples in each bin). Best-fit BC03 models with constant star formation (CSF) and 0.2 Z_☉ metallicity are overlaid for reference. As explained in the previous section, we have excluded from the fitting the bands that are potentially biased (marked by the open symbols). As can be seen in this figure, all these SEDs are remarkably similar and show sizable UV-to-optical colors.

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The similarity of the SEDs can also be appreciated in Figure 8, where the SEDs from the different redshift samples have been grouped according to their approximate M₁₅₀₀ luminosities. The SEDs in the three M₁₅₀₀ bins have been re-normalized according to their M₁₅₀₀ luminosity and combined to produce oversampled SEDs, which take advantage of the fact that the different filters probe different rest-frame wavelengths at the different redshifts. The combined SEDs show the typical flat UV slopes, but also rather flat colors in the rest-frame optical, albeit with a relatively large scatter. This scatter can in part be a consequence of the normalization which is done in the far UV, which effectively acts as the pivot point. Different emission lines that sometimes contribute flux in the IRAC bands, depending on the redshift, can also be contributing to this scatter.

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5.2.1. Emission Lines in the Rest-frame Optical

We first consider the implications if the sizable red J₁₂₅ − [3.6] colors that we observe are assumed to be exclusively measuring the stellar continuum in these high-redshift galaxies. The red color would arise from large Balmer breaks and would be indicative of evolved stellar populations. As can be seen in Figure 9(a), the J₁₂₅ − [3.6] colors characteristic of these sources would then require fairly large ages of ∼1 Gyr if no dust is allowed in the models (the model tracks in the figure are CSF models). Allowing some reddening by dust (using in this case a Calzetti et al. 2000 law) reduces their ages considerably (Figure 9(c)). The amount of dust reddening is constrained however. Based on the UV continuum slopes typically observed in these galaxies (Bouwens et al. 2009), and using the z = 0 Meurer et al. (1999) relation between this slope and the dust content, it has been shown that the reddening at z ≳ 4 is typically A_V ≲ 0.7 mag. The reddening is likely to be even smaller at higher redshifts (Bouwens et al. 2009, 2011a). With this added constraint, the ages derived from SED fitting are generally estimated to be 300–400 Myr (e.g., Yan et al. 2005; Eyles et al. 2005; Stark et al. 2009; González et al. 2010; Labbé et al. 2010a).

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In our SEDs at z ≳ 5, we also find that the ([3.6]–[4.5]) color is consistently blue, with typical values of ∼ − 0.3 mag (the only exception is the faintest z ∼ 6 bin but this color is very uncertain). This color is very hard to reproduce with a model with any SFH that is based only on the stellar continuum. The addition of dust only makes the comparison worse (Figures 9(c) and (d)). It should be noted, however, that the uncertainties in this color are considerable and that in most cases the observed color is formally consistent with the stellar continuum only models.

It has been claimed (Schaerer & de Barros 2009, 2010) that at some of these redshifts, particularly z ∼ 6 and 7, the SEDs could be better fitted by very young stellar population models (≲ 10 Myr old) with moderate dust content and very strong nebular emission lines. These lines would dominate the rest-frame optical fluxes. As the galaxies are forming stars, it is likely that they have nebular emission lines, and so we have assessed whether emission lines could be influencing our fluxes and fits. The observed position of the most prominent optical nebular emission lines at each redshift is marked in Figure 7 by the dashed vertical lines (assuming the mean redshift of each sample). It can be seen that at the different redshifts involved, some of the rest-frame optical emission lines would lie within the IRAC [3.6] and [4.5] filters.

Atek et al. (2011) showed recently that at z < 2.8, there are sources that show emission lines with large enough equivalent widths to dominate the broadband fluxes in the optical. However, even for their sample of high equivalent width selected sources, such objects are not very common. For the more typical cases, the lines that they find in their sample would have moderate contributions to the IRAC broadbands, usually making them 0.2–0.3 mag brighter. At higher redshifts, 3.8 ≲ z ≲ 5, the work of Shim et al. (2011), based on spectroscopic redshifts and IRAC broadband photometry, finds similar results. They find that the sources in this redshift range show an excess of flux in [3.6] over [4.5], which the authors think can be explained by Hα emission. The majority of the sources in their sample have ([3.6]–[4.5]) colors that are consistent with an Hα contribution of 0.2–0.3 mag to the [3.6] filter, indicating moderate contributions from emission lines.

We consider the effects of a similar (moderate) contribution of emission lines to the colors of a 280 Myr old CSF model. For the purpose of this exercise, we assume an Hα rest-frame equivalent width ${\rm EW_{{\rm rest}}}=300$ Å. At z ∼ 6, this would increase the luminosity in the [4.5] filter by 0.23 mag. We only consider the strongest lines in the optical and assume the strength ratios presented by Anders & Fritze-v. Alvensleben (2003) for a 0.2 Z_☉ metallicity system. This corresponds to ${\rm EW_{{\rm rest}}({\rm O\,\mathsc{ii}}, H\beta , {\rm O\,\mathsc{iii}}) = (189, 105, 670)\,}$Å, respectively. The open squares in Figures 9(a) and (b) correspond to the median colors for a model like the one described (the median takes into account the expected redshift distribution of each sample).

As can be seen in Figure 9(a), the main effect of the contribution from the emission lines is that it allows for significantly younger ages to reproduce the J₁₂₅ − [3.6] colors (by a factor of two or more). Since this implies lower stellar continuum fluxes than previously assumed, this would also result in lower best-fit stellar masses. Typical masses (log (M/M_☉) ∼ 8.7–10; González et al. 2011) will decrease by a factor ≳ 2. Simultaneously, given the line ratios and the redshift distributions expected for these samples, a model like this can also help in reproducing the blue [3.6]–[4.5] colors of the SEDs at z ≳ 5 (Figure 9(b)). While formally models with just stellar continua can fit the data, given the current large uncertainties, such colors are hard to obtain with stellar continuum only models. It is more likely that some degree of contribution of emission lines provides a better solution.

The assessment presented here is necessarily very simplistic, given the current uncertainties, and is only meant to show the possible effects of emission lines on the colors of these galaxies. Better estimates of the contribution of these lines and its effects on the properties derived from SED fitting will depend on the actual strengths and ratios of the lines. Moderate improvement can be achieved if more precise redshifts are known for these sources; such data do not exist at this time for such faint high-redshift galaxies and so this remains an open question until improved spectroscopic capability becomes available.

5.2.2. UV-to-optical Color versus Luminosity

Regarding the trend of redder UV-to-optical colors for brighter UV luminosities presented in Figure 6 for the z ∼ 4 sample, it can also be observed for the other samples. In fact, within the uncertainties in the color determination, the J₁₂₅ − [3.6] versus M₁₅₀₀ trend is roughly the same at z ∼ 5 and 6 (Figure 10, top). This is particularly remarkable in view of the fact that this color is an observed color, not a rest-frame color, and in consequence is probing different wavelengths for the different samples. This shows again how similar and flat these SEDs are. If all the SEDs are considered simultaneously, then a trend of J₁₂₅ − [3.6] = −0.17(± 0.07) × M_{1500, AB} − 2.80(± 2.43) is found. For simple CSF models, this trend implies that the M/L ratio depends on the UV luminosity. González et al. (2011) find that at z ∼ 4, the M/L ratio changes by a factor ∼ × 5 between M₁₅₀₀ = −18 and M₁₅₀₀ = −21. So, despite the steep UV-luminosity functions characteristic at z ≳ 4, the contribution of the faintest sources to the total stellar mass density is more modest than their contribution to the SFR density.

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Similar to the analysis performed at z ∼ 4, we have derived rest-frame (U_n − V_n) colors for the median SEDs at all redshifts. The computed colors are summarized in Table 3, and shown in Figure 10. The trend with UV luminosity has large scatter and low significance but is systematic in the sense that brighter sources are redder in (U_n − V_n)_rest. A fit to the rest-frame colors as a function of M₁₅₀₀ using our results at all redshifts yields (U_n − V_n) = −0.030(± 0.027) × M₁₅₀₀ − 0.156(± 0.536), shown as the brown dashed line in Figure 10 (center panel). The z ∼ 4 sample has already been shown to have this trend in Section 5.1. We check that this trend in fact exists for the rest of the sample. A simultaneous fit to the rest of the sample excluding the z ∼ 4 points results in a slightly flatter but consistent relation (U_n − V_n) = −0.024(± 0.039) × M₁₅₀₀ − 0.039(± 0.783). The slope derived for the full sample is in very good agreement with the −0.04 slope found for the z ∼ 4 data only, also plotted for reference as the black dashed line in Figure 10. The latter trend included the bright sample of Lee et al. (2011) and is consistent within the uncertainties with the fit to all the points.

Table 3. Rest-frame Magnitude and Colors

M1500	J125 − [3.6]	(U − V)rest	(U − V)dust-corr
z ∼ 4 B-dropouts
−20.84 ± 0.22	0.62 ± 0.12	0.48 ± 0.08	0.29
−19.91 ± 0.17	0.50 ± 0.07	0.38 ± 0.05	0.25
−18.84 ± 0.16	0.25 ± 0.09	>0.32	>0.24
−17.97 ± 0.15	0.46 ± 0.15	0.36 ± 0.05	0.33
z ∼ 5 V-dropouts
−21.14 ± 0.13	0.84 ± 0.13	0.48 ± 0.06	0.29
−20.21 ± 0.14	0.77 ± 0.12	0.46 ± 0.06	0.33
−19.46 ± 0.13	0.38 ± 0.17	0.31 ± 0.03	0.22
−18.39 ± 0.16	0.55 ± 0.44	0.42 ± 0.12	0.39
z ∼ 6 i-dropouts
−20.42 ± 0.19	0.78 ± 0.30	0.43 ± 0.12	0.37
−19.68 ± 0.13	0.69 ± 0.22	0.46 ± 0.10	0.43
−18.59 ± 0.14	−0.02 ± 0.46	0.40 ± 0.12	0.42
z ∼ 7 z-dropouts
−20.71 ± 0.20	0.76 ± 0.18	0.48 ± 0.11	0.35
−19.89 ± 0.12	0.54 ± 0.18	0.45 ± 0.12	0.40
−19.00 ± 0.12	0.46 ± 0.24	0.48 ± 0.16	0.53

Notes. Rest-frame M₁₅₀₀ estimated from the best-fit power law to the rest-frame UV photometry. Possibly contaminated bands were ignored in the fit (see open points in Figure 7).

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In the bottom panel of Figure 10, we present an estimate of the reddening corrected (U − V) colors. The reddening corrections are derived assuming a Calzetti et al. (2000) extinction curve and using the local Meurer et al. (1999) relation between dust reddening and the UV-slope β (Equation (1)). The values of β are extracted from the best-fit trends measured by Bouwens et al. (2011a) at the corresponding luminosities. These corrected colors show large scatter around (U − V)_{rest, corrected} ∼ 0.3, but there is no indication of a residual trend with UV luminosity except for the z ∼ 7 sample (black symbols). This may indicate again that at 4 ≲ z ≲ 6, the evolution can be fully explained by a change in dust content and there is no strong evolution in the ages of these sources as a function of UV luminosity. This is consistent with the report by Stark et al. (2009) based on stellar population modeling of slightly brighter LBGs in this redshift range. It is also consistent with the predictions from the hydrodynamical simulations of Finlator et al. (2011), which find no trend of age with UV luminosity.

At z ∼ 7, there seems to be a residual trend in (U_n − V_n)_{rest, corrected} ∼ 0.4 versus UV luminosity in the sense that brighter sources have systematically bluer intrinsic (U_n − V_n) colors. In principle, this could indicate that the brighter sources are actually younger than the fainter sources, which would be difficult to imagine. Alternatively, it is possible that simple dust corrections (calibrated at z = 0) are not adequate at these high redshifts, due to, for example, changes in the IMF, metallicity, or escape fraction, all of which could alter the UV-slope β for a given dust content. It should also be noted that the β versus UV luminosity at z ∼ 7 is slightly steeper than at the other redshifts (Bouwens et al. 2011a) and so the corrections to the (U_n − V_n)_rest versus UV-luminosity trend are more extreme. Nevertheless, the uncertainties are sufficiently large that the z ∼ 7 trend is also fully consistent with being constant.

Determining the rest-frame UV-to-optical colors of individual UV-faint galaxies at z ≳ 4 is challenging. At such redshifts, the rest-frame optical lies at λ > 2.5 μm in the mid-IR and so it is hard to measure at the extremely faint magnitudes typical of galaxies in the first 1.5 Gyr. To gain insight into the typical spectral properties of z ∼ 4–6 galaxies, we have taken advantage of the large samples of z ∼ 4–6 sources found in the deep HST ACS and WFC3/IR images of the ERS and HUDF fields. The HST data give us rest-frame UV fluxes. We then use Spitzer/IRAC [3.6] and [4.5] μm data from the deep GOODS survey of these fields to measure rest-frame optical fluxes by stacking the IRAC images and determining median flux values. This allows us to determine the SEDs of these galaxies covering both the rest-frame UV and the optical. These SEDs represent a first comprehensive study of the rest-frame UV-to-optical properties of z ≳ 4 galaxies as a function of both redshift and UV luminosity down to very faint limits.

At z ≳ 4, we have also combined our faint SEDs with the L > L* stacks presented in Lee et al. (2011). This allows us to examine the colors of z ≳ 4 sources over an unprecedentedly large range of luminosities. Our main findings are as follows.

• 1.  
  At z ≳ 4, the (U_n − V_n) rest-frame color (interpolated from the data using a fitted SED from a set of templates) is (U_n − V_n) ∼ 0.4 mag. There is a shallow but systematic trend of redder colors for brighter UV luminosities over the range −23 ≲ M_{1500, AB} ≲ −17.5 (Figure 6, Section 5.1). A linear fit to this trend is (U_n − V_n)_rest = −0.04 × M₁₅₀₀ − 0.38
• 2.  
  The SEDs of star-forming galaxies at 4 ≲ z ≲ 7 are remarkably similar at all luminosities from −23 ≲ M_{1500, AB} ≲ −17.5, showing fairly flat rest-frame UV and rest-frame optical colors (Section 5.2 and Figures 7, 8 and 10). At a given redshift, there are weak indications of a subtle trend for redder colors for brighter sources. A simple fit to the data at all redshifts results in a (U_n − V_n)_rest = −0.03 × M₁₅₀₀ − 0.16 relation (Figure 10, center, Section 5.2).
• 3.  
  The UV-to-optical color, as measured by the observed J₁₂₅ − [3.6] color, remains fairly constant with redshift, despite the Spitzer/IRAC bands probing different wavelength regions of the SED (Figure 10, top). This suggests that the optical colors are fairly flat at all redshifts z ∼ 4–7, although there is significant scatter, which can be caused by optical emission-line contamination to the IRAC filters.
• 4.  
  The z ≳ 5 SEDs show consistently blue [3.6]–[4.5] ∼ −0.3 colors. This is hard to reproduce with models that only include stellar continuum, although it is still formally possible given the current uncertainties. Nonetheless, it can be more naturally explained with moderate flux contributions from optical nebular emission lines in the two IRAC bands (of the order of 0.2–0.3 mag). Including such a contribution from emission lines leads to lower best-fit ages and lower stellar masses than previously estimated for galaxies at these redshifts by about a factor of two for both ages and masses. We caution though that detailed assessments are not yet possible with the current data.
• 5.  
  We derive dust-corrected (U − V) colors using a simple dust correction based on the median UV-slope β versus UV-luminosity relation from Bouwens et al. (2009, 2011a) and the Meurer et al. (1999) relation (Figure 10, bottom). The dust-corrected UV-to-optical colors at 4 ≲ z ≲ 6 are (U − V) ∼ 0.3 mag. The corrected colors do not appear to depend on UV luminosity. This may suggest that moderate changes in the dust content of galaxies can explain the color dependency observed both in the UV slopes and the UV-to-optical colors. In particular, it seems that no age evolution is required to match this color dependency.

The recent deep and ultra-deep HST ACS and WFC3/IR imaging programs over the GOODS-S field have resulted in large samples of z ∼ 4 galaxies. Taking advantage of these large samples, along with a careful stacking analysis, we present a first comprehensive study of the typical SEDs over the rest-frame UV and the rest-frame optical for faint star-forming galaxies in the 4 ≲ z ≲ 7 redshift range. The stacked SEDs allow us to study the UV-to-optical colors of high-z star-forming galaxies down to very low luminosities. We find a mild trend to bluer color at fainter luminosities. Interestingly, these stacked SEDs also show a remarkable similarity across redshift in a period of considerable stellar mass growth from about 0.8 Gyr to 1.5 Gyr, suggesting a smooth self-similar mode of evolution from z ∼ 7 to z ∼ 4.

We acknowledge support from NASA grants HST-GO-11563 and HST-GO-11144. We also acknowledge funding from ERC grant HIGHZ No. 227749. This work is based on observations made with the Hubble Space Telescope and with the Spitzer Space Telescope. Support for this work was provided by NASA through an award issued by JPL/Caltech. P.O. acknowledges support provided by NASA through Hubble Fellowship grant HF-51278.01 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555.

To quantify the rest-frame optical properties of very faint high-redshift galaxies, we stack the IRAC images for a large number of faint galaxies, after removing the flux contribution from nearby neighbors (Section 4). While we do not expect large systematics in the photometry of individual sources from our de-blending procedure to remove neighboring sources, it is possible that modest systematics could arise when stacking a large number of sources. The role of this appendix is to determine how large such systematics might be. Fortunately, we are able to demonstrate that the fluxes that we measure in the stacked IRAC images are unbiased and that their significance is properly determined.

We started by selecting 200 empty areas in the HUDF field. We select them based on the segmentation maps derived from the high-resolution HST images. We processed each of the selected empty areas as if they were the position of one of the real sources in our catalog, i.e., we ran them through the de-blending code to remove the flux from nearby unassociated sources. To determine the rms for a given N_stacked number of stacked stamps, we randomly draw (with replacement) N_stacked stamps from the 200 empty areas, median combine them, and perform aperture photometry on the median stack in the same fashion as for our real stacks. We repeat the drawing 300 times and measure the rms of these 300 trials. This determination of the noise only considers the sky background noise. This is in fact the dominant source of noise in the image; the contribution of shot noise from the faint sources considered here is less than 2%. As can be seen in the upper panel of Figure 11, the limiting flux decreases as $\propto 1/\sqrt{N_{{\rm stacked}}}$, as expected for background-limited noise. In the case of the stacks that contain real sources, the rms is larger than the image noise because it is also affected by the intrinsic variation in the distribution of fluxes that are being stacked.

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As can be seen in the lower panel, the flux of the median stacks is very close to the expected zero flux.