ARE ULTRA-FAINT GALAXIES AT z = 6–8 RESPONSIBLE FOR COSMIC REIONIZATION? COMBINED CONSTRAINTS FROM THE HUBBLE FRONTIER FIELDS CLUSTERS AND PARALLELS^*

We constructed the photometric catalogs in each field using the SExtractor software (Bertin & Arnouts 1996). We first matched all the images to the same point-spread function (PSF) using a model based on the largest PSF derived with TinyTim (Krist et al. 2011). In order to increase the sensitivity to faint sources, we created deep images by using inverse variance (IVM) weight maps to combine all IR frames for z ∼ 7 sources and F125W, F140W, and F160W for z ∼ 8 sources, respectively. This deep image is used for source detection in the SExtractor dual-image mode, while individual images are used for photometry, weighted by the individual IVM images.

One important limitation for the detection of the faintest sources in the cluster fields is the contamination from the intracluster light (ICL) in the central region of the cluster. This diffuse light, concentrated primarily in the central region of the cluster, is due to the brightest cluster galaxy (BCG) or other bright cluster members and the tidal stripping of stars from interacting galaxies during the merging history of the cluster (e.g., Montes & Trujillo 2014). In order to mitigate the contamination of sources close to the cluster center, we subtract a median-filtered image from the detection one with a filter size of ∼2'' × 2'', while the photometry is performed on the original image. The adopted filter size is a trade-off between the removal of extended bright emission and the appearance of artifacts close to the bright galaxies of the cluster core. We note that the median-filtered detection image allows us to detect five more sources on average in cluster fields compared to the original images. This is also important for the visual inspection of galaxy candidates as the background flux is much lower in these corrected images.

In order to estimate the total flux errors, we ran simulations of galaxies with different sizes and profiles (see the completeness simulations in Section 5.1) and compared the recovered fluxes to the input values. We find that the median-filtering approach achieves an uncertainty of 0.5 mag for the faintest sources (H₁₄₀ ∼ 28–29 mag), by using a local background estimate with back_size = 6 in SExtractor for photometry. In addition, the following extraction parameters were set to improve the detection of the faintest sources in the field: detect_minarea = 2 and detect_thresh = 1.5 for the detection and deblend_nthresh = 16 for source deblending. Two types of photometry are used throughout this work. The isophotal magnitude (ISO) is used to compute the colors and ensure that the same aperture is used across the filter set. The total flux is measured within the Kron radius using the AUTO magnitude, which hereafter is used as the total magnitude. We modified the magnitude errors to account for pixel-to-pixel noise correlations in the drizzled images following Casertano et al. (2000). Finally, the individual catalogs were matched into a master photometric catalog and cleaned from spurious sources.

We adopted the Lyman break selection technique (Steidel et al. 1996; Giavalisco 2002) to detect high-redshift galaxy candidates. The selection is based on color–color criteria to sample the UV continuum dropout of the IGM absorption blueward of Lyα caused by the intervening hydrogen along the line of sight and minimize contamination by low-redshift red objects at the same time. Following Atek et al. (2015), we use the following criteria to select z = 6–7 galaxies:

$$\begin{eqnarray}({I}_{814}-{Y}_{105}) & \gt & 1.0\\ ({I}_{814}-{Y}_{105}) & \gt & 0.6+2.0({Y}_{105}-{J}_{125})\\ ({Y}_{105}-{J}_{125}) & \lt & 0.8.\end{eqnarray} \tag{ 1 }$$

In addition, we require all sources to be detected in the deep IR image and in at least two IR bands with 4σ significance or higher. We also reject any galaxy that shows up at a significant (at 1.5σ) level in the deep optical combination of B₄₃₅ + V₆₀₆ images. To preserve the Lyman break criterion in the case of nondetection in the I₈₁₄ image, we assign a 2σ limiting magnitude to this band. Therefore, we select only galaxies with Y₁₀₅ at least 1 mag brighter than the I₈₁₄ depth. Similarly, we select z ∼ 8 galaxies that satisfy

$$\begin{eqnarray}({Y}_{105}-{J}_{125}) & \gt & 0.5\\ ({Y}_{105}-{J}_{125}) & \gt & 0.3+1.6({J}_{125}-{H}_{140})\\ ({J}_{125}-{H}_{140}) & \lt & 0.5.\end{eqnarray} \tag{ 2 }$$

We require a 4σ detection in a deep J₁₂₅ + H₁₄₀ + H₁₆₀ image and the detection in the stacked deep optical image (four ACS filters) to be less than 1.5σ. The deep optical image is about one magnitude deeper than the faintest sources (detected in the IR) accepted in our sample. In Figure 2 we show the result of our selection procedure. The green circles show the location of all high-redshift galaxies identified in this work in the color–color diagram. The dotted and solid lines represent the color evolution of low-redshift elliptical galaxies and high-redshift starbursts, respectively, constructed from Coleman et al. (1980) and Kinney et al. (1996) templates. An attenuation of A_V = 1, 2, 3 is applied to the blue, orange, and red curves, respectively. The shaded region represents our adopted selection window, which was chosen to minimize contamination from low-redshift interlopers and red objects such as cool stars represented by magenta points. Our final sample, combining cluster and parallel fields, contains 227 galaxies at z ∼ 6–7, according to the selection based on Equation (1), and 25 galaxies at z ∼ 8 based on the selection of Equation (2) (see Table 3). We find roughly the same number of candidates in the cluster and the parallel fields. While the survey area is smaller in the lensed field, the magnification bias balances the number density, allowing the detection of much fainter galaxies than in the parallel fields. The redshift distribution of the selected candidates and the redshift selection function at z ∼ 7 and z ∼ 8 are shown in Figure 3.

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We now discuss the main sources of contamination for our high-redshift sample of galaxies. A first possibility is spurious sources produced by detector artifacts, diffraction features, or photometric errors scattering into the color selection space. We have visually inspected all of our candidates to identify such contaminants. Most of the spurious sources were already cleaned using the weight maps that exclude the frame edges and the IR blobs identified by STScI calibrations. We find that the remaining artifacts are mostly diffraction spikes of bright stars and few very bright cluster galaxies in the field. Fake sources due to photometric noise are also minimal since we require the detection in at least two different bands.

The second potential source of contamination are low-redshift galaxies that show similar colors to high-redshift candidates. According to our stringent spectral break criteria, such sources need to show an extremely red continuum or a large Balmer/4000 Å break. Dust-obscured galaxies would be excluded by our selection because they would exhibit relatively red colors redward of the break. The remaining galaxies that can enter the selection need to have a large Balmer break and relatively blue continuum at longer wavelengths. The existence of these peculiar objects has been discussed in Hayes et al. (2012), where a spectral energy distribution (SED) of a young burst superimposed on an old stellar population with an extreme 4000 Å break can mimic the Lyman break colors. Such objects should be very rare and represent only a minor contamination. Moreover, in the case of a significant contamination by these interlopers, we expect to detect the blue continuum by stacking the optical images of our candidates, which is not the case.

Alternatively, the Lyman break colors can also be mimicked by extremely strong emission lines in z = 1–3 star-forming galaxies (e.g., Atek et al. 2011, 2014a; van der Wel et al. 2011). In this class of galaxies the contribution of the emission-line flux to the total broadband flux is about 25% on average and can reach 85% (Atek et al. 2011) and can have important implications, not only for the high-redshift galaxy selection but also for the age and stellar mass derived from SED fitting (Schaerer & de Barros 2009; Wilkins et al. 2013; Schenker et al. 2014; Huang et al. 2015; Pénin et al. 2015). In our case, the contamination of one band can lead to an artificial Lyman break, because the faint continuum remains undetected blueward of the break. Atek et al. (2011) estimate that the optical data should be about 1 mag deeper than the detection band to be able to rule out such interlopers. Our criteria impose a minimum break of 0.8 mag between the object flux and the limiting magnitude of the optical band. Moreover, such a contamination should be even smaller because our stacked candidate images, which are at least 1.3 mag deeper than the candidate's flux, show no significant detection in the optical bands shortward of the break.

In general, observationally, estimating the contamination rate of such sources proves very difficult at z > 6 because it hinges on large spectroscopic follow-up programs that aim at detecting the redshifted Lyα emission line in these galaxies. In addition to the large amount of telescope time needed to reach the required depth, the absence of Lyα emission does not exclude the high-redshift nature of the associated objects. Indeed, the increasing neutral hydrogen fraction at z > 6 easily absorbs and diffuses Lyα photons (Atek et al. 2009; Stark et al. 2010; Caruana et al. 2014; Schenker et al. 2014). Therefore, one must rely on simulated colors based on galaxy spectral templates to estimate the contamination rate of low-redshift galaxies, which thus has been found to be less than 10% in most studies (e.g., Oesch et al. 2010; Bouwens et al. 2015b).

Another source of contamination to consider are low-mass stars. As we can see in Figure 2, a significant fraction of these stars (shown in magenta) can have similar colors to high-redshift galaxies. However, we have excluded any source that has a SExtractor stellarity parameter greater than 0.8 to minimize point-like objects in our sample. Also, the number density of cool stars ranges from 0.02 to 0.05 arcmin² derived from observations with similar or better depths (Bouwens et al. 2015b). This translates to about one contaminant in the entire z ∼ 7 and z ∼ 8 galaxy samples. We also consider transient events as possible contaminants. Because observations are taken at two different epochs (see Table 4), a supernova explosion may appear in IR images and not in the optical ones and could be selected as a dropout candidate. Similar colors can also be obtained in the case where the IR data were taken first and the supernova faded until the optical images. Again, different reasons point toward a negligible contamination level from transient sources. Such objects would show point-like profiles that would be excluded by the stellarity criterion explained above and our additional visual check for unresolved sources. The detection rate of supernovae is also very small, and so far none of the supernova detections in the dedicated search program of the HFF (e.g., Rodney et al. 2015) have been inadvertently selected as high-z galaxies in the different HFF studies (Atek et al. 2014b, 2015; Finkelstein et al. 2014; Ishigaki et al. 2015a).

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In addition to flux magnification, strong lensing produces multiple images of the same background galaxy. Therefore, we need to identify multiple images to be removed from the galaxy number counts before computing the UV LF. For each galaxy, we predict the position of potential counterimages by using the mass model and Lenstool to project its position into the source plane before lensing back the source into the image plane, where Lenstool predicts the position of all the multiple images. In the vicinity of these positions, we look for dropout sources that show similar colors and photometric redshifts. In the case of well-resolved sources, we also verify that they have similar morphological and geometrical symmetries constrained by the lensing model. In A2744 we find three systems at z ∼ 7, with a total of nine multiple images, which were discussed in Atek et al. (2014b). In MACS 0416, we identify seven systems at z ∼ 7.

In the case of MACS 0717, the multiple image region extends beyond the WFC3 field of view. Therefore, we expect each of the galaxy candidates to have counterimages with similar flux/magnification ratios given the lensing geometry of this cluster. The uncertainty on the image position predicted from the lensing model of MACS 0717 is about rms = 1.9 arcsec, much larger than in the two other clusters (see Limousin et al. 2015). Moreover, the shape of the critical line is not as well constrained, which makes it harder to identify multiple-image systems. From the Lenstool model, we estimate the multiplicity in MACS 0717 to be three on average in the WFC3 field of view. Therefore, we divide the number of galaxy candidates by this multiplicity to obtain the final number counts used for the LF calculation.

Following Atek et al. (2015), we run extensive Monte Carlo simulations to assess the completeness level as a function of the intrinsic magnitude. A total of 10,000 galaxies were simulated for each of the six fields. We take the galaxy profile into account by creating two samples of exponential disks and de Vaucouleur shapes (Ferguson et al. 2004; Hathi et al. 2008). These galaxy profiles are then distorted by gravitational lensing according to our mass model. As for galaxy sizes, we adopt a lognormal distribution with a mean half-light radius of 015 and sigma = 007. For consistency with previous results (Bouwens et al. 2004; Ferguson et al. 2004; Hathi et al. 2008; Oesch et al. 2010, 2014; Grazian et al. 2011, 2012; Huang et al. 2013), the distribution is based on the sizes derived from spectroscopically confirmed LBG samples at z ∼ 4 (Vanzella et al. 2009), while accounting for a redshift evolution of the intrinsic physical size of galaxies with a factor of (1 + z)⁻¹. HST observations of dropout galaxies at z > 6 redshifts also reveal small sizes of less than 03 (Mosleh et al. 2012; Ono et al. 2013), and smaller for galaxies fainter than M_UV − 21 mag. More recently, Kawamata et al. (2015) measured the size of lensed dropout galaxies in the HFF cluster A2744 and reported similar results. Small sizes around 01 have also been observed in lensed galaxies by Coe et al. (2013) and Zitrin et al. (2014). In addition, based on the results of Huang et al. (2013), we adopt a size–luminosity relation r ∝ L^β, with β = 0.25, for our simulations (see also Mosleh et al. 2012; Kawamata et al. 2015).

After assigning random redshifts in the range [5.5, 7.5], we simulate galaxy magnitudes in each HST band using star-forming SED templates from Kinney et al. (1996). In this step, we also assign random intrinsic absolute magnitude (in the rest-frame UV) in the range M_UV = [−14, −24] mag. We then include 10 simulated galaxies in the actual images of each band for a total 1000 images. This is where the cluster and parallel fields are treated differently in the simulations. In the cluster fields, galaxies are not included directly in the images but are simulated in the source plane. They are lensed into the image plane using the corresponding mass model. This way we ensure that all the lensing effects, including magnification, shape distortion, and position relative to the critical line, are fully taken into account. Finally, for all the images, we run the same procedure used to select high-z galaxies and determine the completeness function, which represents the fraction of the original galaxies recovered in our selection as a function of the parameters described above. This completeness function is in turn incorporated in the computation of the effective volume in each magnitude bin following the equation

$$\begin{eqnarray}&&{V}_{\mathrm{eff}}={\displaystyle \int }_{0}^{\infty }{\displaystyle \int }_{\mu \gt {\mu }_{\mathrm{min}}}\displaystyle \frac{{{dV}}_{\mathrm{com}}}{{dz}}f(z,m,\mu )d{\rm{\Omega }}(\mu ,z){dz},\end{eqnarray} \tag{ 3 }$$

where μ_min is the minimum amplification factor μ_min required to detect a galaxy with a given apparent magnitude m and V_com is the comoving volume; f(z, m, μ) is the completeness function that depends on the redshift z, apparent magnitude m, and amplification factor μ, and dΩ(μ) is the area element in the source plane, which is a function of magnification and redshift.

Figure 6 presents the results of our effective volume estimates in each field, marginalized over the intrinsic absolute UV magnitude. The extent of each filled region represents the 68% confidence intervals. We can clearly see the importance of gravitational lensing in extending the survey depth to fainter galaxies. While the blank-field completeness drops abruptly before M_UV = −18 mag, it becomes shallower in cluster fields and extends down to M_UV = −15 mag, although at a level of 10% or less.

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Using the derived effective volume as a function of absolute magnitude, we compute the UV LF following the equation

$$\begin{eqnarray}&&\phi (M){dM}=\displaystyle \frac{{N}_{i}}{{V}_{\mathrm{eff}}({M}_{i})},\end{eqnarray} \tag{ 4 }$$

where N_i and M_i are the number of galaxies and the absolute magnitude, respectively, in each magnitude bin. Following most of the studies in the literature, we choose a bin size of 0.5 mag, whereas the magnitude varies from one field to another. The individual LF determinations in each field are presented in Figure 7. The top panels show the results in the cluster fields, while the bottom panels are for parallel fields. The LF extends to M_UV = −18.25 in blank fields, whereas it reaches a magnitude of M_UV = −15.25 in cluster fields thanks to the lensing magnification. This gain can already be seen in the completeness function results (see Figure 5), reaching fainter magnitudes in cluster fields. Figure 6 also shows the distribution of the amplification factor for the dropout samples selected behind the three lensing clusters. The flux amplification is essentially in the range μ ∼ 1.25–75, with a median value of 5.2, 3.9, and 4.9 in A2744, MACS 0416, and MACS 0717, respectively.

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In addition to the sample contamination discussed in Section 3.3, several sources contribute to the uncertainties of the LF data points. The mass model errors, affecting the magnification and the survey volume (or the source-plane area Ω), are propagated into the LF determination in the case of cluster fields. We also include Poisson errors and the cosmic variance estimate based on the recent results of Robertson et al. (2015) for both cluster and parallel fields. Finally, uncertainties from incompleteness simulations, as seen in Figure 5, are incorporated in the final LF. The bright end is dominated by cosmic variance errors and small number counts, while the faint-end error bars reflect mostly the large incompleteness uncertainties at these faint magnitudes and small statistics.

We determine the shape of the rest-frame UV LF by fitting a Schechter function (Schechter 1976) to our data, which has been extensively used to describe the galaxy UV LF across a wide redshift range (e.g., Bunker et al. 2004; Beckwith et al. 2006; Bouwens et al. 2006; McLure et al. 2009; Ouchi et al. 2009; Reddy & Steidel 2009; Wilkins et al. 2010; Oesch et al. 2012; Willott et al. 2013). The Schechter function can be expressed in terms of absolute magnitudes as

$$\begin{eqnarray}&&\phi (M)=\displaystyle \frac{{\rm{ln}}(10)}{2.5}{\phi }^{\star }{10}^{0.4(\alpha +1)({M}^{\star }-M)}\mathrm{exp}({-10}^{0.4({M}^{\star }-M)}).\end{eqnarray} \tag{ 5 }$$

We perform a Schechter fit to the LF in each field and find a faint-end slope α between −2.0 and −2.07 (see Equation (5)). The best-fit Schechter parameters are shown in Table 4. We include in the fit the data points from Bouwens et al. (2015b, black squares) to constrain the bright end of the LF. The faintest bin is reached in A2744 at M_UV = −15.25. There is a hint of a shallower slope at those magnitudes that could be the result of large uncertainties in the completeness estimate, which is typically less than 10% in this bin. As a matter of fact, a similar decline is observed in MACS 0416 around M_UV = −16.25, whereas the slope is constantly steep at these magnitudes in A2744. It is clear that the constraints on the LF in MACS 0717 are not as good as in the other cluster fields. This is likely the result of larger uncertainties on the lensing model due to the complex structure of the galaxy cluster. For instance, the model prediction for image position has an rms error of ∼1.9 arcsec, while it is is about 0.7–0.8 arcsec in MACS 0416 and A2744. These kinds of deviations in the LF data points can also be observed in A2744 when using an old model based on pre-HFF observations that similarly yielded large uncertainties. Nonetheless, the overall shape of the LF remains consistent with the other clusters' results.

We now combine all the LF constraints from the lensed and parallel fields to compute the most robust UV LF at z ∼ 7. The result is shown in Figure 8. Together with our data points, we show the most recent results from the literature from the blank fields as described in the legend. We ran MCMC simulations with 10⁶ realizations to find the best fit to the LF and estimate the uncertainties on the Schechter parameters. We find that the UV LF at z ∼ 7 has a faint-end slope of $\alpha =-{2.04}_{-0.17}^{+0.13},$ a characteristic ${M}^{\star }=-{20.89}_{-0.72}^{+0.60}$, and log(ϕ^⋆) = $-{3.54}_{-0.45}^{+0.48}.$ This is in excellent agreement with earlier results presented in Atek et al. (2015), where we computed the UV LF in the HFF cluster A2744. In Figure 9, we show the likelihood analysis of the Schechter parameters at z ∼ 7, marginalized over two parameters at a time. Our results are in good agreement with the most recent results reported from the blank fields (see Table 5). In particular, the faint-end slope is close to the determination of Finkelstein et al. (2014) with $\alpha =-{2.03}_{-20}^{+21}$ and Bouwens et al. (2015b) with α = −2.03 ± 0.14. Our results show only a slightly steeper faint-end slope than the values reported in the Hubble extreme deep field (McLure et al. 2013; Schenker et al. 2013a) with $\alpha ={1.90}_{-0.15}^{+0.14}$ and $\alpha ={1.90}_{-0.15}^{+0.14},$ respectively, and agree within the reported uncertainties. Also using the gravitational lensing of the first HFF cluster A2744, Ishigaki et al. (2015a) find a slightly shallower slope of $\alpha =-{1.94}_{-0.10}^{+0.09},$ which is still in agreement with our value within the errors. We also performed a Schechter fit while excluding data points from the MACS 0717 cluster, which yields very similar parameters: α = −2.03, a characteristic M^⋆ = −20.86, and log(ϕ^⋆) = −3.52. Importantly, we note that the uncertainties on the faint-end slope decrease to σ_α ∼ 0.1.

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Table 5.  Comparison of the Best-fit z ∼ 7 Schechter Parameters

Reference	${M}_{\mathrm{UV}}^{\star }$	α	${\mathrm{log}}_{10}{\phi }^{\star }$
	(AB mag)		(Mpc−3)
This work	$-{20.89}_{-0.72}^{+0.60}$	$-{2.04}_{-0.13}^{+0.17}$	$-{3.54}_{-0.45}^{+0.48}$
Atek et al. (2015)a	$-{20.90}_{-0.73}^{+0.90}$	$-{2.01}_{-0.28}^{+0.20}$	$-{3.55}_{-0.57}^{+0.57}$
Ishigaki et al. (2015a)a	$-{20.45}_{-0.2}^{+0.1}$	$-{1.94}_{-0.10}^{+0.09}$	$-{3.30}_{-0.20}^{+0.10}$
Bouwens et al. (2015b)	−21.04 ± 0.26	−2.06 ± 0.12	$-{3.65}_{-0.17}^{+0.27}$
Finkelstein et al. (2014)	$-{21.03}_{-0.50}^{+0.37}$	$-{2.03}_{-0.20}^{+0.21}$	$-{3.80}_{-0.26}^{+0.41}$
McLure et al. (2013)	$-{19.90}_{-0.28}^{+0.23}$	$-{1.90}_{-0.15}^{+0.14}$	$-{3.35}_{-0.45}^{+0.28}$

Note.

^aUsing the first HFF cluster A2744.

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Several theoretical models and cosmological simulations produce predictions for the UV LF at high redshift. For instance, our LF results at z ∼ 7 are in good agreement with the hydrodynamical simulations of Jaacks et al. (2012) with M^⋆ = −20.82 and log(ϕ^⋆) = −3.74, although they predict a steeper faint-end slope of α = −2.30 down to a similar lower magnitude limit of M_UV = −15. Theoretical models by Mason et al. (2015) find a closer slope of α = −1.95 ± 0.17 down to a magnitude limit of M_UV = −12, corresponding to a halo mass of 10⁹ M_⊙. Similarly, Kimm & Cen (2014) find a theoretical faint magnitude limit of M_UV = −13 with a faint-end slope of α = −1.9. Semianalytical models of Dayal et al. (2014) also find a steep faint-end slope of α ∼ −2.02 at z ∼ 7, in good agreement with our observations.

Regarding the redshift z ∼ 8 LF, we followed the same procedure used for the z ∼ 7 LF. However, in lensing clusters, the survey volume at z ∼ 8 is much more significantly reduced than at z ∼ 7. In the extreme case of MACS 0717, the total survey volume is about 460 Mpc³, whereas it reaches 3600 Mpc³ in A2744. Therefore, we expect lower galaxy number counts at z ∼ 8 for high magnification values. In total, we detect only two galaxies with intrinsic magnitudes fainter than M_UV = −18, where the uncertainties on the LF estimate are very large (see Figure 10). Unlike the z ∼ 7 LF, we do not have strong constraints on the faint end of the LF at z ∼ 8. At brighter magnitudes the LF is better constrained thanks to the addition of the parallel fields and appears in agreement with previous results in the literature. As discussed in Atek et al. (2015), the redshift 8 galaxy selection in A2744 clearly shows an overdensity (see also Zheng et al. 2014; Ishigaki et al. 2015a), which translates into a large excess in the UV LF. Here we decided not to exclude the entire A2744 field in the combined LF to avoid introducing a well-known bias due to cosmic variance (see also Ishigaki et al. 2015b).

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In this study, we reliably extend the UV LF to unprecedented depth and put strong constraints on the faint-end slope down to M_UV = −15.25. The most important result is that the faint-end slope remains very steep down to a luminosity of 0.005 L^⋆, the characteristic UV luminosity at z ∼ 7. Also, thanks to the combination of six fields, we have significantly reduced the uncertainties on the faint-end slope to about 5%. With these strong constraints in hand, we can now integrate the UV LF to derive the UV luminosity density at z ∼ 7. The main advantage of these observations is the ability to set the integration lower limit to M_UV = −15. Unlike previous results that extrapolate the UV LF to lower magnitude, we use an observational constraint to estimate the ultraviolet photon budget from galaxies. For instance, based on the UV LF results in blank fields, Bouwens et al. (2015b) report a total UV luminosity density of log(ρ_UV) =25.98 ± 0.06 erg s⁻¹ Hz⁻¹ Mpc⁻³ and Finkelstein et al. (2014) a value of log(ρ_UV) =25.77 ± 0.06 erg s⁻¹ Hz⁻¹ Mpc⁻³ at z ∼ 7. Both values are computed down to M_UV = −17 AB, which is the limiting magnitude of their observations. Here we compute the UV luminosity density down to M_UV = −15 and find log(ρ_UV) = 26.2 ± 0.13 erg s⁻¹ Hz⁻¹ Mpc⁻³.

In order to determine whether the UV luminosity produced by galaxies is sufficient to reionize the IGM, one needs to estimate additional parameters, for which observational constraints remain challenging. First, the conversion factor from the UV luminosity to ionizing radiation ξ_ion (erg s⁻¹ Hz) depends on the star formation history of galaxies. The value of ξ_ion is generally constrained using stellar population models of early galaxies and the observed UV slope β of z > 6 galaxies (Bolton & Haehnelt 2007; Kuhlen & Faucher-Giguère 2012; Robertson et al. 2015). Once the ionizing photon production is determined, we need to estimate its escape fraction f_esc from galaxies to ionize the IGM. Direct observational constraints of f_esc are difficult, especially at z > 6 because of the high opacity of the intervening hydrogen residuals on the line of sight. Many studies and deep surveys were dedicated to the search of ionizing continuum (Lyman continuum) escape from z < 4 galaxies. Very few detections were reported, however, and they show very low escape fractions relative to the UV radiation, of the order of a few percent (Shapley et al. 2006; Iwata et al. 2009; Siana et al. 2010; Nestor et al. 2013). More recently, de Barros et al. (2015) reported a spectroscopic detection of Lyman continuum emission in a z ∼ 3.2 galaxy with a relative escape fraction¹⁶ of f_esc ∼ 65%.

In Figure 11, we show our determination of the UV luminosity density together with the most recent results in the literature as a function of redshift, including Bouwens et al. (2015b) and Finkelstein et al. (2014) at z = 4−8, Bouwens et al. (2015b) at z = 10, and McLeod et al. (2015) and Oesch et al. (2014) at z ∼ 9. While their values are based on the integration of the UV LF down to a magnitude limit between M_UV = −18 and M_UV = −17, our integration limit is two magnitudes fainter at M_UV = −15. There is a significant difference between the results of Bouwens et al. (2015b) and Finkelstein et al. (2014) owing to the fact that the UV LF in the former study extends one magnitude deeper than the latter. Finkelstein et al. (2014) did not make use of the full IR data available in the HUDF, which also explains the larger uncertainties in their faint-end slope constraints. The UV luminosity density of galaxies at z ∼ 7 determined in the present work is clearly larger than previous determinations, owing to a steep faint-end slope and a very faint integration limit. We can now assess whether this UV production is sufficient to ionize the IGM. We use the photon emission rate per unit cosmological comoving volume required to maintain reionization at a given redshift determined in Madau et al. (1999):

$$\begin{eqnarray}&&\dot{N}(z)=({10}^{51.2}{{\rm{s}}}^{-1}\;{\mathrm{Mpc}}^{-3}){C}_{30}{\left(\displaystyle \frac{1+z}{6}\right)}^{3}{\left(\displaystyle \frac{{{\rm{\Omega }}}_{b}{h}^{2}}{0.02}\right)}^{2}\end{eqnarray} \tag{ 6 }$$

where C₃₀ is the clumping factor ${C}_{{\rm{H}}\;{\rm{II}}}=\langle {n}_{{\rm{H}}\;{\rm{II}}}^{2}\rangle /{\langle {n}_{{\rm{H}}\;{\rm{II}}}\rangle }^{2}$ normalized to ${C}_{{\rm{H}}\;{\rm{II}}}=30,$ and ${n}_{{\rm{H}}\;{\rm{II}}}$ is the mean comoving hydrogen density in the universe. This is the minimum value for which the ionizing emission balances the recombination rate. We show in Figure 11 this limit, converted to UV luminosity density (see Madau et al. 1999; Bolton & Haehnelt 2007) assuming an escape fraction of the ionizing radiation of f_esc = 20% and three different values for the clumping factor. Assuming a standard value of ${C}_{{\rm{H}}\;{\rm{II}}}=3$ for the clumping factor of the IGM (Pawlik et al. 2009; Finlator et al. 2012), our determination of galaxy UV luminosity density at z ∼ 7 is sufficient to maintain reionization. We also show that an escape fraction as low as f_esc = 10%–15% (green hatched region) is already sufficient to ionize the IGM at z ∼ 7. At the same redshift, the ionizing emissivity constraints of Bouwens et al. (2015a) are close to our UV density constraints.

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With current observations we are not able to put better constraints on the faint end of the UV LF at z ∼ 8 and hence on the ionizing emissivity of galaxies at this redshift. The conclusions from the deep blank fields are still affected by large uncertainties that prevent any strong claims regarding the contribution of galaxies to the ionizing budget at z ∼ 8 (Finkelstein et al. 2014; Bouwens et al. 2015b). Future HST observations of the remaining HFF clusters might add better constrains on the UV luminosity density at z ∼ 8 with additional highly magnified faint galaxies.