THE MOST LUMINOUS z ∼ 9–10 GALAXY CANDIDATES YET FOUND: THE LUMINOSITY FUNCTION, COSMIC STAR-FORMATION RATE, AND THE FIRST MASS DENSITY ESTIMATE AT 500 Myr^*

We base this paper on the entire WFC3/IR and I₈₁₄ Advanced Camera for Surveys (ACS) data over the GOODS-N field from the completed CANDELS survey. The last data were taken on 2013 August 10. For details on the survey layout we refer to the CANDELS team papers (Grogin et al. 2011; Koekemoer et al. 2011). Briefly, the CANDELS GOODS-N field is part of the CANDELS-Deep survey, for which additional Y₁₀₅ imaging was obtained. The Y₁₀₅ imaging is not available in the general CANDELS-Wide component.

The central ∼65 arcmin² of the GOODS-N field was covered by ∼5 orbits of WFC3/IR imaging data in J₁₂₅ and H₁₆₀ reaching to 27.8 mag (5σ) and by ∼3 orbits of Y₁₀₅ imaging reaching 27.6 mag. Furthermore, two flanking fields totaling ∼70 arcmin² of the CANDELS-Wide program completed the WFC3/IR coverage of the GOODS-N field with roughly one orbit in each of the three filters, Y₁₀₅, J₁₂₅, and H₁₆₀, which results in a depth of 27.0–27.2 mag in all three filters. We also include all the JH₁₄₀ imaging data available over GOODS-N. These are very shallow exposures, mostly being used as pre-imaging for the GOODS-N grism program (GO:11600, PI: Wiener) with an exposure time of 800s, in addition to a few supernova follow-up observations from the CANDELS survey. Nevertheless, these can be useful for spectral energy distribution (SED) analyses of brighter sources.

We downloaded all the individual WFC3/IR data from the Barbara A. Mikulski Archive for Space Telescopes (MAST) and the Canadian Astronomy Data Centre (CADC) and reduced the data using standard procedures, as described in detail in Illingworth et al. (2013). We used the persistence masks provided by the Space Telescope Science Institute (STScI) to mask all pixels significantly affected by persistence from previous exposures. We registered all WFC3/IR frames to the official v2 GOODS-N ACS z₈₅₀-band data before drizzling to a mosaic with final pixel size of 006 and a tangent-plane projection aligned to the GOODS-N ACS data. The RMS maps produced by multidrizzle were rescaled to match the actual fluctuations present in the data as measured through circular apertures of 035 diameter randomly placed on empty sky positions in the images.

The ACS data used here are a somewhat deeper reduction than the publicly released v2 GOODS-N imaging. We included the additional data from supernova follow-up programs (see Bouwens et al. 2007). Furthermore, we reduced the new I₈₁₄-filter data obtained as part of parallel imaging from the CANDELS program. The reduction includes corrections for charge transfer inefficiency and was performed analogously to the eXtreme Deep Field (XDF) data reduction (Illingworth et al. 2013). The depth of these I₈₁₄ images surpasses all other GOODS ACS images, reaching a 5σ limit of I₈₁₄ = 28.2–28.9 mag.

The angular width of the point-spread function (PSF) of the data used here is ∼009 and ∼016 for the ACS and WFC3/IR imaging, respectively, as measured from unsaturated stars in the field.

From previous z > 8 analyses it became clear that longer-wavelength constraints from Spitzer/IRAC are essential in order to remove contamination from dusty, intermediate redshift sources (e.g., Oesch et al. 2012a). Furthermore, IRAC samples the rest-frame visible at z > 4, which is crucial for stellar mass constraints. We therefore include all the IRAC data that are available over the GOODS-N region as part of several programs. In particular, we analyzed the 3.6 μm and 4.5 μm channel IRAC reductions from the Spitzer Extended Deep Survey (SEDS) and S-CANDELS team (PI: Fazio; see also Ashby et al. 2013).

The Spitzer S-CANDELS program (P.I. G. Fazio) is a Cycle 8 Spitzer Exploration Science project to map ∼0.2 deg² in the five CANDELS fields to 50 hr depth with IRAC, thereby reaching magnitude ∼26.8 at 3.6 and 4.5 μm. Data in GOODS-N were obtained in two epochs in 2012 and combined with pre-existing IRAC data from SEDS (Ashby et al. 2013) and the original GOODS program (Dickinson et al. 2003). The corrected, basic calibrated data (cBCD) frames from the Spitzer archive were combined into calibrated mosaics following the same procedures as for SEDS (Ashby et al. 2013). The achieved depth at the positions of the z ∼ 9 candidates (Section 3) is ∼50 hr in both IRAC bands except that the 4.5 μm observation of GN-z10-1 has ∼72 hr. In blank sky areas the average IRAC 5σ depths are 27.0 and 26.7 mag (within 1'' radius apertures) in the two IRAC channels. Further analysis of these mosaics, including catalog creation and completeness estimates, is ongoing and will be reported elsewhere (M. L. N. Ashby et al., in preparation).

A significant challenge of the IRAC data is the poor angular resolution, FWHM = 17 (Fazio et al. 2004), leading to source confusion. This can be largely overcome, however, through neighbor subtraction based on the high-resolution HST data. This is particularly important for the faint sources that we study here. We used an approach outlined in several previous papers (see, e.g., Labbé et al. 2006; Grazian et al. 2006; Laidler et al. 2007) that models a region around a source of interest using its HST H₁₆₀ image convolved to IRAC resolution and subtracts all neighbors to give a "cleaned" source. Subsequently we measured fluxes in 1'' radius circular apertures and multiplied by a factor 2.4–2.6 to correct for light outside the aperture. The variation in the aperture correction is due to variations in the position dependent IRAC PSF as measured from nearby stars in the field.

While subtraction of the flux from the neighboring sources does not always work if a candidate is too close to a very bright foreground source, it is very effective in the majority of cases. The modeling and subtraction approach has been refined extensively and now allows us to perform clean IRAC photometry for ∼75%–80% of sources in the field, a factor ∼2 × larger than without neighbor subtraction.

In order to bridge the gap in wavelength range between the 1.6 μm probed by HST and the 3.6 μm covered by IRAC, we also made use of a deep K-band stack over GOODS-N from the multi-object infrared camera and spectrograph for Subaru (MOIRCS Kajisawa et al. 2006; Bouwens et al. 2008). These data were reduced using the standard MOIRCS pipeline procedures. The average seeing measured from the final stack of the data is 055. Over the region of interest, this stack varies in depth between 25.0 and 26.6 mag AB, as measured in small circular apertures of 06 diameter. Total magnitudes were derived using aperture corrections computed from the profiles of a few bright, non-saturated stars in the field.

In the last section of this paper, we will derive new constraints on the UV luminosity function (LF) and the cosmic SFRD at z ∼ 10 based on the largest possible data set. We will therefore combine the GOODS-N CANDELS data set with an identical analysis over previous deep HST imaging fields. In particular, we directly include the z ∼ 10 search and analysis from the HUDF09/12/XDF and GOODS-S field from our previous paper (Oesch et al. 2013a). However, motivated by the bright galaxies in GOODS-N, we re-analyzed the GOODS-S data set with detection criteria that are better matched to those used in GOODS-N. The result of this is presented in the Appendix. The combined WFC3/IR+ACS data set spans an area of ∼300 arcmin² and ranges in depth from H₁₆₀ = 27.5–30.0 mag AB (5σ).

The identification of LBGs in the epoch of reionization makes use of the almost complete absorption of UV photons shortward of the redshifted Lyα line due to a high neutral hydrogen fraction in the inter-galactic medium. At z > 9 the Lyα absorption shifts into the J₁₂₅ band, which renders star-forming galaxies red in their J₁₂₅ − H₁₆₀ colors. Our initial selection criterion is therefore to search for galaxies with J₁₂₅ − H₁₆₀ > 0.5 and non-detections in the shorter wavelength data. In the second part of this paper, we will restrict the sample to a more conservative criterion with J₁₂₅ − H₁₆₀ > 1.2, which includes only galaxies at z ≳ 9.5. This selection J₁₂₅ − H₁₆₀ > 1.2 also matches our previous GOODS-S analysis and allows us to use a larger sample for the subsequent analysis.

Source catalogs were obtained with SExtractor (Bertin & Arnouts 1996), which was run in dual image mode with the H₁₆₀-band as the detection image. All images were convolved to the H₁₆₀ PSF when performing photometry, and colors were measured in small Kron apertures (Kron factor 1.2), typically 02 radius. Total magnitudes were derived from larger elliptical apertures using the standard Kron factor of 2.5, typically 04 radius, with an additional correction to total fluxes based on the encircled flux measurements of stars in the H₁₆₀ band. This last correction was typically ∼0.2 mag but depended on the actual Kron aperture size of individual galaxies.

Based on these catalogs, the following HST selection criteria were applied:

$$\begin{equation} (J_{125}-H_{160})>0.5 \end{equation} \tag{ 1 }$$

$$\begin{equation*} {\rm S}/{\rm N}(B_{435} \mathrm{\ to\ } Y_{105})<2\quad \wedge \quad \chi ^2_{{\rm opt}+Y}<3.2 \end{equation*}$$

in addition to at least 5σ detections in H₁₆₀ (see Figure 1). The $\chi _{{\rm opt}+Y} ^2$ for each candidate source was computed as $\chi _{{\rm opt}+Y} ^2 = \Sigma _{i}\; {\rm SGN}(f_{i}) (f_{i}/\sigma _{i})^2$ (Bouwens et al. 2011b) where f_i is the flux in band i in a consistent aperture, σ_i is the uncertainty in this flux, and SGN(f_i) is equal to 1 if f_i > 0 and −1 if f_i < 0, and the summation is over the B₄₃₅, V₆₀₆, i₇₇₅, I₈₁₄, z₈₅₀, and Y₁₀₅ bands. The limit of $\chi ^2_{{\rm opt}+Y}=3.2$ was chosen to result only in a small reduction in the selection volume of real z > 9 sources (20% based on Gaussian statistics), while efficiently excluding lower redshift contamination (see the right panel of Figure 1). This reduction in the selection volume is accounted for in our calculations of the UV LF in Section 4.

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These HST selection criteria resulted in a total of six potential candidates in the full GOODS-N WFC3/IR data set. However, two of these sources are extremely bright in the Spitzer/IRAC bands with H₁₆₀ − [4.5] > 3.2. As shown in the left panel of Figure 1, this is much redder than expected for a real high-redshift galaxy. However, it is consistent with similarly red sources with photometric redshifts z ∼ 2–4 that we identified as contaminants in our GOODS-S high-redshift search (Oesch et al. 2012a, 2013a). Such sources are very interesting for z ∼ 2–4 studies (see, e.g., Huang et al. 2011; Caputi et al. 2012), but will not be discussed further here. We exclude these two sources from our analysis and proceed with only four potential z > 9 galaxy candidates.

While three out of the four remaining sources show negative values of $\chi ^2_{{\rm opt}+Y}$, the brightest candidate (GN-z10-1) lies very close to the selection limit (see right panel of Figure 1). This is mostly driven by a 1.5σ positive flux measurement in the z₈₅₀-band. From a visual inspection of that image, however, it appears that this is due to a feature in the background and is not associated with real flux from the source. If we remove this band, the $\chi ^2_{{\rm opt}+Y}$ drops to 0.7. Nevertheless, the $\chi ^2_{{\rm opt}+Y}$ near the selection limit indicates that this source could be a potential contaminant. Based on SED fitting, however, we will show later in Section 3 that no low redshift galaxy SED or stellar SED that we know of can reproduce the very red J₁₂₅ − H₁₆₀ color break of this source together with its flat continuum longward of 1.6 μm. Taken together, these results suggest that the most likely interpretation is that GN-z10-1 is at high redshift.

Stamps of the four viable high-redshift candidates are presented in Figure 2, and their positions and photometry are listed in Tables 2 and 3. As is evident from Figure 2, the four sources are all detected at ⩾7σ in the H₁₆₀ band. The brightest source is 15σ. Furthermore, all sources are seen in observations at other wavelengths, albeit at lower significance. With the exception of GN-z10-1, all show weak detections in J₁₂₅, and two are even seen weakly in the very shallow JH₁₄₀ data. Furthermore, the brightest source is detected at 2σ in the ground-based K-band data.

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Neighbor-subtraction was applied to the IRAC data of all four z ≳ 9 galaxy candidates. The resulting cleaned IRAC images are shown in the two right-hand columns of Figure 2. As can be seen, three of these sources are detected in at least one IRAC band. For source GN-z10-2, the residuals of the bright foreground neighbor are still visible, and its IRAC flux measurements are therefore highly uncertain. In order to provide some photometric constraints for this source from IRAC, we use conservative upper limits based on the RMS fluctuations in the residual image at the position of the bright foreground source. All flux measurements for these sources, together with the uncertainties are listed in Table 3.

Figure 3 shows the SED fits to the fluxes of the four high-redshift galaxy candidates. These are derived with the photometric redshift code ZEBRA (Feldmann et al. 2006; Oesch et al. 2010b) using a large library of stellar population synthesis template models based on the library of Bruzual & Charlot (2003). Additionally, we added nebular line and continuum emission to these template SEDs in a self-consistent manner, i.e., by converting ionizing photons to H and He recombination lines (see also, e.g., Schaerer & de Barros 2009). Emission lines of other elements were added based on line ratios relative to Hβ tabulated by Anders & Fritze-v. Alvensleben (2003). The template library adopted for the SED analysis is based on both constant and exponentially declining star-formation histories of varying star-formation timescales (τ = 10⁸ to 10¹⁰ yr). All models assume a Chabrier initial mass function and a metallicity of 0.5 Z_☉, and the ages range from t = 10 Myr to 13 Gyr. However, only SEDs with ages less than the age of the universe at a given redshift are allowed in the fit. Dust extinction is modeled following Calzetti et al. (2000).

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As is evident in Figure 3, all candidates have a best-fit photometric redshift at z ⩾ 9 with uncertainties of σ_z = 0.3–0.4 (1σ). These uncertainties could be reduced with deeper JH₁₄₀ imaging data in the future. However, the high redshift nature of these sources is quite secure given the current photometry. The right panels of Figure 3 show the redshift likelihood function. The integrated probability for z < 5 solutions is strikingly small for each of these sources. GN-z10-3 has the highest low-redshift likelihood with only 0.2%. In this case, the best-fit low redshift SED is a combination of high dust extinction and extreme emission lines, which line up to boost the fluxes in the H₁₆₀ and IRAC 4.5 μm bands. It is unclear how likely the occurrence of such an SED really is. However, deeper Y₁₀₅ data or spectroscopic observations could rule out such an SED. Some first spectroscopic constraints are already available from shallow WFC3 grism observations (see Section 3.3.2).

As a cross-check, we also tested and confirmed the high-redshift solutions with the photo-z code EAZY (Brammer et al. 2008). In particular, we fit photometric redshifts with templates that include emission lines as included in the v1.1 distribution of the code.¹² The best-fit EAZY redshifts are all within 0.1 of the ZEBRA values listed in Table 2.

As we will show in Section 4.1, the detection of such bright z ∼ 9–10 galaxy candidates in the GOODS-N data set is surprising given previous constraints on UV LFs at z > 8. A detailed analysis of possible contamination is therefore particularly important. We discuss several possible sources of contamination in the next sections.

3.3.1. Emission Line Galaxies

3.3.2. Constraints from HST Grism Data

Quantitative constraints on pure emission line sources can be obtained from the WFC3/G141 grism observations over GOODS-N from HST program 11600 (PI: Wiener). These spectra cover ∼1.05–1.70 μm at low resolution, reaching a 5σ emission line flux limit for compact sources of ∼2–5 × 10⁻¹⁷ erg s⁻¹ cm⁻² (see Brammer et al. 2012). If the H₁₆₀-band flux originated from a single emission line, the observed magnitudes of our sources (H₁₆₀ = 26.0–26.8 mag) would correspond to line fluxes of 2.5–5.5 × 10⁻¹⁷ erg s⁻¹ cm⁻². These lines should thus be detectable as ∼5σ features. We have therefore analyzed the grism spectra using reductions developed by the 3D-HST team. Three sources (excluding GN-z10-3) were covered with such data.

The grism spectra were reduced using a newly developed pipeline by the 3D-HST team (G. B. Brammer et al., in preparation). The spectrum of GN-z10-1 was heavily affected by a varying sky background during the exposures, and it was necessary to manually exclude some of the affected readouts, which effectively reduced the total exposure time by less than 25%.

The final 2D spectra of the three covered sources are shown in Figure 4. For sources GN-z10-1 and GN-z9-1, the spectra are blank, showing no significant features. For source GN-z10-2, the spectrum is partially contaminated by the trace of a nearby bright source. Two extremely faint features may be visible at low significance (∼2σ) at ∼1.38 μm and 1.50 μm. However, given the foreground contamination, the data are currently inconclusive regarding these faint features.

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The spectra of these three sources provide very useful constraints on contamination by pure emission line sources. Figure 4 also shows simulated spectra of sources for which a single line could explain the whole flux in the H₁₆₀ filter, with lines at five different wavelengths. The simulated lines were computed based on the actually observed H₁₆₀-band profile of these sources in the spatial direction and assuming a Gaussian emission line with FWHM = 100 Å in the dispersion direction. As can be seen, such a line would be significantly detectable even in the contaminated spectrum of GN-z10-2.

The grism data therefore rule out the contamination of a pure, single emission line source for these three candidates. However, based on the current data, we cannot rule out contamination by lower redshift sources with less extreme emission lines. Deeper data would be required to do so. As we shall see, while any one constraint is not definitive, the grism emission line limits, the constraints on low-redshift contamination based on SED fitting, and those from photometric scatter discussed in Sections 3.2 and 3.3.4 indicate that the sources identified here are highly likely to be at high redshift.

3.3.3. Stellar Contamination?

3.3.4. Photometric Scatter Simulations

As pointed out earlier, the GOODS-N z ∼ 10 galaxy candidates are very compact and very bright. This raises the possibility that some of these sources host an active galactic nucleus (AGN), which contributes or even dominates the observed fluxes in the H₁₆₀-band. While it would be surprising (though very interesting) to see significant AGN activity just a few hundred million years after the formation of the first stars, without spectroscopic observations, it is of course nearly impossible to reliably assess such a contribution. However, our imaging data can provide some first constraints.

At least the two brighter sources in our sample appear to be resolved. However, as is usually the case for compact high redshift sources, the current data do not exclude a point source in the center of a more extended star forming region. For such objects, probably the most stringent constraint on an AGN contribution can be obtained from a variability analysis. AGN flux variations are seen over essentially all timescales and would be a clear indicator for nuclear accretion activity (for a review see, e.g., Ulrich et al. 1997).

Given that the GOODS-N CANDELS data were acquired over almost a two-year timescale, we can directly test for variability. We have therefore split the data into five separate subsplits, sorted by acquisition time, and have reduced these frames separately. This was done for the H₁₆₀-band images of each of our candidates. We then remeasured the magnitudes of these sources via the dual image mode of SExtractor with the full stack as the detection image. The resulting flux variation is shown in Figure 5.

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For two of our sources, we do not detect a significant signal (>2σ) at a couple of epochs. This results from the low exposure times in those stacks when the source falls on masked regions of the WFC3/IR detector. Thus the lack of data in those epochs is not indicative of real variation.

Evaluation of the measurements for each source shows that none of the sources displays a statistically significant variation. This provides some indicative evidence against AGN contributions in these candidates. Due to the limited depth of the data, however, smaller amplitude flux variability (of the order of a couple of tenths of a magnitude) cannot be ruled out.

Given the brightness of our candidates, it is interesting to ask whether any of these could be significantly magnified by a foreground source. Even though none of the candidates appears to be highly magnified (none have the significant elongation which would be a clear sign for very high magnification), smaller values of magnification are possible. Wyithe et al. (2011) estimated that very high-redshift luminosity functions could be significantly distorted due to a magnification bias once the characteristic magnitude lies ∼2 mag below the survey limit. This could indeed be the case with our GOODS-N data.

We therefore examined the neighbors of all four candidates. The two lowest-redshift ones do not show a very bright source nearby and are therefore unlikely to be affected by lensing. However, the two highest-redshift sources do show neighbors within 29 and 12 (see the top two rows in Figure 2). To see if magnification was contributing to their unusual brightness, we estimated their possible magnification bias based on the simplified assumption of a Singular Isothermal Sphere (SIS) lens (see, e.g., Schneider et al. 2006).

• 1.  
  GN-z10-1. Our highest-redshift candidate shows a neighbor with H₁₆₀ = 24.7 mag and half-light radius r_1/2 =02 at a distance of 12. Our photometric redshift analysis of this source indicates that it likely lies at z_phot = 1.8, and has a stellar mass of log₁₀M = 9.1 M_☉. While we do not have any information on the velocity dispersion σ_v of this galaxy, we can obtain a rough estimate based on the virial theorem. Assuming that all the mass is contained within 2r_1/2, we estimate σ_v = 27 km s⁻¹. This seems low and so we took a more conservative assumption of a SIS with σ_v = 50 km s⁻¹. Even for this dispersion this source has an Einstein radius for lensing a z ∼ 10 source of <004, resulting in a magnification of <4% at the separation of the candidate.
• 2.  
  GN-z10-2. This candidate lies 29 from a bright galaxy at a spectroscopic redshift z_spec = 1.02 (Barger et al. 2008). The foreground source has log₁₀M = 10.8 M_☉ and half-light radius of r_1/2 = 05, resulting in an estimate of σ_v ∼ 125 km s⁻¹. A SIS model with these parameters has an Einstein radius of 03 for lensing a z ∼ 10 galaxy resulting in a possible magnification of 11% for this source.

From the above considerations, we conclude that lensing magnification is most likely not significant for our sample, amounting to at most 0.1 mag. Given the small magnifications and the uncertainties in the above estimates, we do not correct for any possible magnification.

In order to compute the expected number of sources for a given UV LF, we use extensive simulations of artificial galaxies inserted in the real data to estimate the selection volume. The artificial sources were detected and re-selected in the same manner as the original sources, from which we estimate the completeness C(m) and selection probabilities S(z, m) as a function of H₁₆₀ magnitude m and redshift z. These simulations allow us to statistically correct for the fact that our catalogs are missing a fraction of real high-redshift sources due to blending with foreground galaxies which amounts to a typical incompleteness of ∼20% across these HST fields. For more information on the simulation setup, see Oesch et al. (2013a).

Given the selection function and the completeness, we can compute the number of expected sources in bins of magnitude for a given LF ϕ(M):

$$\begin{equation} N^\mathrm{exp}(m) = \int _{\Delta m} dm \int dz \frac{dV}{dz} S(m,z)C(m)\phi (M[m,z]). \end{equation} \tag{ 2 }$$

Figure 6 shows the results of this calculation for several assumed LFs. Most importantly, for the best-fit z ∼ 10 LF from the GOODS-S+HUDF09/12 (Oesch et al. 2013a) not a single z ∼ 10 galaxy candidate was expected to be seen in GOODS-N.

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Additionally, we tested the expected number of sources based on a simple extrapolation of lower redshift LF trends to z ∼ 10. This extrapolation is based on the parameterization of Bouwens et al. (2011b), who measured the UV LF evolution across z ∼ 4 to z ∼ 8 and found: ϕ* = 1.14 × 10⁻³ Mpc⁻³ mag⁻¹ = const, α = −1.73 = const and M*(z) = −20.29 + 0.33 × (z − 6). This extrapolation results in an assumed M*(z = 10) = −18.97, and predicts 1.6 sources overall in GOODS-N, but only 0.14 at H₁₆₀ < 27 mag.

Very similar numbers are predicted by the theoretical z ∼ 10 UV LF model of Tacchella et al. (2013), from which one would have expected to see 1.9 sources overall in GOODS-N, of which only 0.5 were expected at H₁₆₀ < 27 mag. Even for other test LFs, such as the z ∼ 9 UV LF estimates from Oesch et al. (2013a) and Bouwens et al. (2012a), only ∼2 sources were expected to be seen in GOODS-N. However, they are expected to be fainter with H₁₆₀ > 27 mag. The detection of three bright sources at H₁₆₀ < 27 mag is therefore quite unexpected, given our previous constraints on the UV LFs from multiple surveys. The three GOODS-N z ∼ 10 candidates should therefore have interesting implications for the LF at early times and also for the cosmic SFRD evolution at z > 8.

It is instructive to see what must be done with current UV LFs to get as many as three bright z ∼ 9–10 galaxies. For example, 3.4 bright (H₁₆₀ < 26.8 mag) z ∼ 9–10 candidates are predicted in the GOODS-N data only if the UV LF at z ∼ 9–10 was the same as at z ∼ 8 (using, e.g., the results of McLure et al. 2013). However, using the same, unchanged z ∼ 8, LF predicts a total of 11 z ∼ 10 candidates in the GOODS-N data including fainter sources, and it predicts 42 sources in the whole combined search field (see Section 4.3). This clearly is not the case and is securely ruled out.

As we outlined in previous sections, we find no reason that the GOODS-N sample is heavily contaminated by lower redshift sources. However, the detection of three bright candidates at H₁₆₀ < 27 mag was quite unexpected based on previous analyses of the GOODS-S data set. The question arises how this finding could be affected by cosmic variance.

We used the publicly available cosmic variance calculator¹³ of Trenti & Stiavelli (2008) to estimate the likely impact of this on z ∼ 10 galaxy searches (see also Robertson 2010). Based on a simple halo abundance matching, one expects a cosmic variance of 40%–45% per 4.7 arcmin² WFC3/IR pointing, depending on the assumptions about the halo occupation fraction. For the field layout of the ∼150 arcmin² GOODS-N or GOODS-S WFC3/IR data, the expected cosmic variance ranges between 15 to 20%.

Given the very low number of expected sources in each survey, the variance is completely dominated by Poissonian statistics. For instance, the chance of finding three or more z ∼ 10 galaxy candidates in the GOODS-N field when 1.6 sources are expected is 22%, independent of whether one assumes a 20% cosmic variance or not, on top of Poissonian statistics.

What the analysis of the GOODS-N data shows, is that larger data sets have to be analyzed for reliable measurements of the UV LFs at very high redshifts in order to overcome the limitations of Poissonian statistics. It will therefore be interesting to explore the upcoming HST Frontier Fields, which will add another 8 to 12 deep field pointings in which one would expect ∼0.5–1 sources each for a (hopefully) much more reliable sampling of the UV LF, particularly at intermediate magnitudes.

In order to constrain the cosmic SFRD evolution at z > 8, we combine our analysis of GOODS-N with previous z ∼ 10 galaxy searches. In particular, we directly use the results from Oesch et al. (2012b) and Oesch et al. (2013a), who analyzed all three ultra-deep HUDF09 fields (including the new HUDF12 data in the XDF reduction) as well as the complete CANDELS GOODS-S data. In these fields, only one viable z ∼ 10 candidate was previously identified satisfying J₁₂₅ − H₁₆₀ > 1.2. This source (XDFj-38126243) is extremely faint with H₁₆₀ = 29.8. It was found in the deepest WFC3/IR imaging available in the HUDF/XDF field.

We have re-analyzed the CANDELS GOODS-S data and found one additional bright z ∼ 10 galaxy candidate. This source, GS-z10-1, together with a slightly lower redshift candidate, is discussed in detail in the Appendix.

The total z ∼ 10 galaxy sample with J₁₂₅ − H₁₆₀ > 1.2 that is used in the reminder of this paper thus comprises three bright sources in GOODS-N, one bright candidate from GOODS-S, and one faint source from the XDF data. The most striking feature of this sample is that no sources are found at intermediate magnitudes at H₁₆₀ = 27–29 (see, e.g., Figure 7). This, along with the very small sample size, will make it very challenging to derive a reliable LF (see the next section).

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The selection functions and completeness curves for the GOODS-S and HUDF09 fields have previously been computed by Oesch et al. (2012a, 2013a). The use of an identical approach to the GOODS-N analysis in this paper allows us to directly combine all search fields for a total measurement of the galaxy number density at z ∼ 10.

The dearth of z ∼ 10 candidate sources in the intermediate magnitude range H₁₆₀ = 27–29 mag (see Figure 7), makes it challenging to provide a meaningful Schechter LF fit (Schechter 1976) to the observed sources. A simple power-law might provide a better description of the UV LF at such high redshifts. However, the widespread use of Schechter LF fits at lower redshifts z ∼ 4–8 and in previous papers at z ∼ 9–10 suggests that use of the same formalism at z ∼ 10 is useful for comparative purposes. Furthermore, theoretical models and simulations still point toward a Schechter-like function (e.g., Trenti et al. 2010; Lacey et al. 2011; Tacchella et al. 2013). We thus update our previous estimates of the Schechter function parameters based on the combined data set of GOODS-N/S+HUDF09/HUDF12/XDF.

In our previous analysis we assumed the characteristic luminosity, M_*, to be the main parameter of the Schechter function to evolve to higher redshift. This was motivated by previous z ∼ 4–8 measurements of the UV LF. However, this assumption is called into question with the three detections in GOODS-N and the one bright source in GOODS-S, because, as we shall see below, an M_*-only evolution results in a substantial over-prediction of the total number of candidates in our search fields.

In order to show this, we first determine our baseline lower redshift UV LF model, relative to which we will measure the evolutionary trends. Over the last few years, several z ∼ 8 UV LF determinations have been published by several teams based on WFC3/IR data sets (e.g., Bouwens et al. 2010b, 2011b; Yan et al. 2011; Bradley et al. 2012; Oesch et al. 2012b; Lorenzoni et al. 2013; Schenker et al. 2013; McLure et al. 2013). The most recent determinations among these that use several search fields are all in good agreement with each other, and returned consistent estimates of the z ∼ 8 UV LF Schechter function parameters. As a baseline model we adopt the values from McLure et al. (2013) which represents the widest area study to date and its UV LF parameters represent a good average of recent results from several teams (see, e.g., Table 6 of Schenker et al. 2013).

Hence, for the z ∼ 8 baseline, we adopt log₁₀ϕ_*(z = 8) = −3.35 Mpc⁻³ mag⁻¹, M_*(z = 8) = −20.12 mag, and α(z = 8) = −2.02 (McLure et al. 2013). We then estimate the z ∼ 10 UV LF parameters relative to this baseline model by varying one parameter at a time. In particular, we test for M_*- and ϕ_*-evolution.

The best-fit parameters were determined by minimizing the Poissonian likelihood of observing N_obs sources in a given magnitude bin when N_exp are expected from the LF: $\cal {L} = \prod _{j} \prod _i P(N^{\rm obs}_{j,i},N^{\rm exp}_{j,i})$, where j runs over all fields, i runs over the magnitude bins of width 0.5 mag, and P is the Poissonian probability.

Doing so for M_*-only evolution relative to the baseline model results in a best-fit estimate of M_*(z = 10) = −19.36 ± 0.15. The expected magnitude distribution of z ∼ 10 candidates for this LF is shown in the lower panel of Figure 7, and the LF itself is shown as the dashed line in Figure 8. This determination lies significantly above the upper limits at intermediate magnitudes. With 9.4$^{+4.2}_{-3.0}$, the total expected number of z ∼ 10 galaxy candidates from this LF is also larger than the five observed sources, though the difference is not very significant. A larger disagreement arises since these nine sources would all be expected at magnitudes fainter than H₁₆₀ ∼ 27 mag in the different search fields (Figure 7). Yet these are not seen.

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A somewhat more consistent result is achieved from a fit with ϕ_* evolution. Assuming again the baseline z ∼ 8 LF parameters and varying only ϕ_*, we find a best-fit log₁₀ϕ_* = −4.27 ± 0.21 Mpc⁻³ mag⁻¹, almost an order of magnitude lower than the z ∼ 8 normalization. This LF is shown in Figure 8. As can be seen, it represents a better compromise between the detections at the bright and faint end and the upper limits at intermediate luminosities. The total expected number of sources for this model is $5.0^{+3.4}_{-2.2}$, consistent with the observed number of sources, but again with a magnitude distribution which peaks at H₁₆₀ = 27–29 mag, where we do not detect any candidates (see Figure 7). These best-fit UV LF parameters and the corresponding total number of expected sources are summarized in Table 4, and the stepwise z ∼ 10 UV LF constraints are tabulated in Table 5.

Table 4. Summary of z ∼ 10 UV LF and SFRD Estimates

	log10ϕ*	MUVa	α	$N_{{\rm exp}}^{{\rm tot}}$a	$\log _{10}\dot{\rho }_{*}$b
	(Mpc−3 mag−1)	(mag)			(M☉ yr−1 Mpc−3)
This Work (from candidates)	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	−3.25 ± 0.35
This Work (ϕ* evolution)	−4.27 ± 0.21	−20.12 (fixed)	−2.02 (fixed)	$5.0^{+3.4}_{-2.2}$	−3.22 ± 0.21
This Work (M* evolution)	−3.35 (fixed)	−19.36 ± 0.15	−2.02 (fixed)	$9.4^{+4.2}_{-3.0}$	−2.80 ± 0.11
Oesch et al. (2013a)	−2.94 (fixed)	−17.7 ± 0.7	−1.73 (fixed)	$0.6^{+2.5}_{-0.5}$	$-3.7^{+0.7}_{-0.9}$

Notes. ^aTotal number of z ∼ 10 candidates with J₁₂₅ − H₁₆₀ > 1.2 expected to be seen in all the search fields of this paper. These include GOODS-North, GOODS-South, the HUDF09 parallel fields as well as the HUDF12/XDF field, in which we identified a total of five candidate galaxies. ^bThe SFRD measurement is limited at M_UV < −17.7, the luminosity limit of the HUDF12/XDF data.

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Table 5. Stepwise z ∼ 10 UV LF Based on the Full Data Set

MUV	ϕ*
(mag)	(10−3 Mpc−3 mag−1)
−21.28	$0.0027^{+0.0027}_{-0.0023}$
−20.78	$0.010^{+0.006}_{-0.005}$
−20.28	<0.0078
−19.78	<0.020
−19.28	<0.089
−18.78	<0.25
−18.28	<0.68
−17.78	$1.3^{+1.3}_{-1.1}$

Note. Limits are 1σ for a non-detection.

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While previous results in the literature suggested the main evolving parameter of the UV LF at z ∼ 4–8 to be predominantly the characteristic luminosity L*, evolution that is dominantly ϕ* is consistent within the uncertainties. In fact, evolution in the normalization of the UV LF may be more easily accommodated by current theoretical models. As discussed in Section 5.5 of Bouwens et al. (2008), one challenge with L* evolution being the dominant form of evolution in the LF is that it requires some physical mechanism to impose a cut-off at a specific luminosity (and likely mass) in the UV LF and for that luminosity to depend on redshift. Since it is not clear what physical process would cause the cut-off to depend on redshift, simulators often find very little evolution in L* (e.g., Jaacks et al. 2012a).

Our concern, however, is that even the best-fit UV LFs we find here do not really reproduce well the high number of bright galaxy candidates we found in the data. Even for the best-fit LF from ϕ_*-evolution, we only expect to see 0.4 sources brighter than H₁₆₀ = 27 mag in GOODS-N, and 0.9 in all fields combined. Detecting three such bright sources in the GOODS-N alone is quite unlikely, with a probability that is only 0.8% from Poissonian statistics (i.e., it is a 2.4σ event).

Given our somewhat-improbable mix of z ∼ 10 detections and limits, i.e., with our z ∼ 10 candidate galaxies only being found at the extrema of the luminosity range probed (see Figure 8), one other possibility we have to consider is a non-Schechter-like form for the LF at z > 6, as has already been speculated elsewhere (e.g., Bouwens et al. 2011b; Bowler et al. 2012). It may be that this could be caused by very bursty and highly biased star-formation events at very high redshift with low duty cycle (see, e.g., Jaacks et al. 2012b; Wyithe et al. 2013).

The most recent WFC3/IR data sets from several independent surveys have enabled determinations of the cosmic SFRD at redshifts z ∼ 9 and z ∼ 10 that were thought to be largely inaccessible for quantitative constraints on LFs or the SFRD. Estimates of the SFRD have been performed independently from a small sample of sources from the CLASH program (Bouwens et al. 2012a; Zheng et al. 2012; Coe et al. 2013) and from the HUDF09 and HUDF12 surveys (Bouwens et al. 2011b; Oesch et al. 2012a, 2013a; Ellis et al. 2013; McLure et al. 2013). While the conclusions from these separate analyses disagree on the SFRD evolutionary trends, Oesch et al. (2013a) have shown that combining all the results from the literature, the SFRD appears to increase by an order of magnitude in just 170 Myr from z ∼ 10 to z ∼ 8, down to the current detection limits of the HUDF09/12/XDF data set.

Here we extend our previous analysis from the CANDELS GOODS-S and HUDF09/12/XDF for an updated estimate of the cosmic SFRD at z ∼ 10 with the inclusion of the new sources found in the GOODS-N field, and in the GOODS-S. Figure 9 shows the new results plus other measurements at z > 8 from the literature and the cosmic SFRD evolution constrained by these data.

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The SFRD was computed directly from the observed UV luminosity density (LD) of the three GOODS-N, the single bright GOODS-S, and the one XDF z ∼ 10 galaxy candidates. The LDs were converted to a SFRD using the conversion factor of Madau et al. (1998), assuming a Salpeter initial mass function.¹⁴ Since the HUDF12/XDF data reaches down to M_UV = −17.7 mag, the derived SFRD is limited at SFR > 0.7 M_☉ yr⁻¹. For the z > 8 points, we did not perform any dust correction, because it is expected to be negligible based on the evolution of the UV continuum slope distribution at lower redshift (e.g., Bouwens et al. 2012c, 2013b; Dunlop et al. 2013; Finkelstein et al. 2012; Wilkins et al. 2011).

The direct SFRD from the five observed candidates is $\log _{10}\dot{\rho }_{*} = -3.25\pm 0.35$ M_☉ yr⁻¹ Mpc⁻³. As can be seen from the summary in Table 4, this is a factor 0.45 dex higher compared to our previous estimate using only the one HUDF12/XDF candidate. However, it remains quite consistent with our previous estimate that a very large change occurs in the SFRD in the 170 Myr from z ∼ 10 to z ∼ 8. With the new data, the build-up remains strong at 1.05 ± 0.38 dex from z ∼ 10 to z ∼ 8, i.e., by an order of magnitude.

Together with the direct SFRD as measured from the five detected sources in the XDF and GOODS-N+S, Figure 9 also shows the SFR densities of the two best-fit UV LFs we derived in the previous section (for a summary see also Table 4). In particular, the best-fit M_* evolution results in a significantly higher SFRD, essentially equal to the current z ∼ 9 estimates. However, we stress again that M_* evolution should have resulted in nine detected z ∼ 10 candidates in our search fields and should therefore be considered an upper limit.

Combining our updated SFRD estimate with previous analyses from different data sets in the literature at z > 9 (Bouwens et al. 2012a; Coe et al. 2013; Zheng et al. 2012), the new best-fit evolution of the cosmic SFRD at z ⩾ 8 is $\log \dot{\rho }_* \propto (1+z)^{10.9\pm 2.5}$, which is almost unchanged from our previous determination without the new luminous sources in GOODS-N and GOODS-S ((1 + z)^{11.4 ± 3.1}; Oesch et al. 2013b). The small change is mostly due to the fact that our new, combined SFRD measurement from all the CANDELS-Deep and HUDF09/XDF data almost exactly falls on the previously estimated trend and that the LF is so steep that the integrated flux is dominated still by the lower luminosity sources.

As we show in Figure 10, the rapid decline at z > 8 is not completely unexpected. It seems to be a very generic prediction of a wide range of theoretical models, which reproduce the UV LF evolution across z ∼ 4–7. These models include semi-empirical estimates of the SFRD evolution (Trenti et al. 2010; Tacchella et al. 2013), semi-analytical models (Lacey et al. 2011), as well as hydrodynamic simulations (Finlator et al. 2011; Salvaterra et al. 2011; Dayal et al. 2013; Jaacks et al. 2013). Given that these models all use very different prescriptions and techniques, it is likely that this rapid decline is mostly driven by the underlying evolution of the dark matter halo mass function, which is also evolving very rapidly at z > 8.

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