SPECTROSCOPIC OBSERVATION OF Lyα EMITTERS AT z ∼ 7.7 AND IMPLICATIONS ON RE-IONIZATION

Understanding when and how the universe re-ionized is fundamental to our understanding of how galaxies and large-scale structures form and evolve and is sensitive to global cosmological parameters. In particular, the fraction of neutral hydrogen, x_H i, in the intergalactic medium (IGM) is closely tied to early galaxy formation because it is related to the gas accretion rate onto galaxies. From current measurements, it is still unclear when re-ionization occurred and what the sources of re-ionizing radiation are.

The best of such current measurements come from cosmic microwave background (CMB) experiments and high-redshift quasar studies, with additional constraints from Lyman break galaxy (LBG) and Lyα-emitting galaxy studies. The Wilkinson Microwave Anisotropy Probe (Larson et al. 2011) and Planck (Tauber et al. 2010) place a ∼2σ–3σ constraint on when re-ionization occurred, based on the optical depth to the CMB due to Thompson scattering of electrons. These data are usually fit by a quick re-ionization at z ∼ 10.5 but are also fully consistent with a more gradual re-ionization with a tail ending at z ∼ 6–7 (Komatsu et al. 2011; Planck Collaboration et al. 2013). Direct measurements of the optical depth from quasars indicate that the universe is neutral up to z ∼ 7.1, based on the highest redshift quasars known today (Fan et al. 2006; McGreer et al. 2011; Mortlock et al. 2011). Furthermore, ultraviolet (UV)-continuum measurements of LBGs between z ∼ 7–10 (Bouwens et al. 2011; Bradley et al. 2012; Schenker et al. 2013; McLure et al. 2013) suggest that galaxies have a difficult time re-ionizing the universe until later times, unless the luminosity function (LF) is unusually steep at the faint end or the continuum escape fraction is high (Robertson et al. 2013).

The fraction of strong Lyα emitters (LAEs) within LBG samples should give us a more direct, complementary, and unique measurement of x_H i and, therefore, how quickly and when the universe is re-ionizing.

Fundamentally, Lyα photons are scattered in areas where the IGM contains more neutral hydrogen, so the escape fraction of Lyα photons is proportional to the volume of re-ionized hydrogen around the young galaxies. Hence, the fraction of galaxies with strong Lyα emission is related to the neutral fraction of the IGM (Haiman & Spaans 1999; Malhotra & Rhoads 2004, 2006; Dijkstra et al. 2007; Dijkstra & Wyithe 2010). However, it is important to note that this probe is also sensitive to the evolution of the interstellar medium (ISM) inside galaxies (like dust; see Bouwens et al. 2012; Finkelstein et al. 2012; Mallery et al. 2012), so one must understand the effects of galaxy evolution to probe the IGM.

The Lyα emission of LBG galaxies (selected using broad bands) is indicative of re-ionization ending at z ∼ 6–7 and a neutral hydrogen fraction of ∼50% at z ∼ 7 (Fontana et al. 2010; Stark et al. 2010; Pentericci et al. 2011; Ono et al. 2012; Schenker et al. 2012; Caruana et al. 2013). In particular, the fraction of strong LAEs in LBG samples is found to rapidly drop beyond z > 6.5 over a range of Δz ≳ 1, a timescale of only ∼200 Myr (Stark et al. 2011; Curtis-Lake et al. 2012; Schenker et al. 2012).

An alternative to LBG selection is the use of narrow-band (NB) filters to directly detect LAEs at specific redshifts (e.g., Malhotra et al. 2001; Hu et al. 2004, and references therein). This method allows one to directly map the Lyα LFs as a function of redshift, which can then be compared to the LBG UV-continuum LFs to estimate the neutral IGM fraction.

An overall change in the Lyα LFs between 5.7 < z < 6.6 has been firmly established by large samples of spectroscopically confirmed LAEs (Ouchi et al. 2008, 2010; Hu et al. 2010; Kashikawa et al. 2011; Malhotra & Rhoads 2004). But the source of this change could be either an evolution in the IGM or a change in the internal ISM of the galaxies.

The evolution of the Lyα LF based on LAEs beyond z > 7 is far less clear. Apart from a few spectroscopically confirmed LAEs at z ∼ 7 (one spectroscopically confirmed out of two at z = 6.96 (Ota et al. 2008) and one spectroscopically confirmed out of three at z = 7.22 (Shibuya et al. 2012a)), there are no confirmed LAEs at higher redshifts. A total sample of ∼15 candidate LAEs at z = 7.7 is known (Hibon et al. 2010; Tilvi et al. 2010; Krug et al. 2012). Tilvi et al. (2010) and Krug et al. (2012) favor a non-evolution of the Lyα LF between 5.7 < z < 7.7 (see also Hibon et al. 2011), which is in tension with other NB searches for LAEs at z > 7 that only place limits on the number counts of LAEs (Sobral et al. 2009; Clément et al. 2012; Ota & Iye 2012; Matthee et al. 2014). The reason for this tension may be low-redshift interlopers and false detections in the LAE samples. At z < 7, both of these are estimated to contribute less than 10%–20% (see, e.g., Ouchi et al. 2010); at higher redshifts, these contribution are not known yet, but are probably much higher (see Matthee et al. 2014 and this work). Spectroscopic follow-up observations of high-redshift candidate LAEs are therefore necessary to resolve the tensions between the LAE and LBG results at z > 7 and to constrain the process of re-ionization at higher redshifts.

In this work,⁵ we present Keck-I Multi-Object Spectrometer for Infra-Red Exploration (MOSFIRE) spectroscopic follow-up of two z ∼ 7.7 LAE candidates (Section 2) originally found by Krug et al. (2012). We then go on to compare these results to existing data at lower redshift (Section 3) and to an empirical model derived from the LBG UV-continuum LF and observed equivalent width (EW) distribution (Sections 4.1 and 4.2). This allows us to place limits on the neutral fraction of the IGM at z ∼ 8 (Section 4.3) and enables us to predict the LAE LF at z ∼ 8–9 (Section 5).

2.1. Candidate Selection by Krug et al. (2012)

2.2. MOSFIRE Observations and Data Reduction

We observed the two LAE candidates (α = 10^h00^m4694, δ = +02°08'4884 and α = 10^h00^m2052, δ = +02°18'5004) with the MOSFIRE (McLean et al. 2012) spectrograph on the Keck-I Telescope on the nights of 2013 January 15 and 16. Each candidate was observed with a separate mask created using the MOSFIRE Automatic graphical-user-interface-based Mask Application (MAGMA,⁶ version 1.1) and aligned using bright Two Micron All Sky Survey (2MASS) stars. The conditions were photometric on both nights, with an average seeing around 10. The observations were carried out in Y-band (9710–11250 Å) using the YJ grating and a 07 slit width, resulting in a resolution of R ∼ 3270. We used 180 s exposures with 16 multiple correlated double samples. The telescope was nodded by ±125 with respect to the mask center position between exposures. The total integration times were 46 × 180 s = 8280 s = 2.3h for LAE1 and 40 × 180 s = 7200 s = 2.0h for LAE2.

Before creating the mask, we verified that the 2MASS, COSMOS, and NEWFIRM astrometric systems agreed to within measurable errors (∼01). During the observations, we make sure that the masks were properly aligned by using either alignment stars and/or bright filler targets. In addition, several bright sources with known fluxes and morphologies from the zCOSMOS-bright spectroscopic survey (Lilly et al. 2009) were placed on the mask to verify slit losses (estimated to be 40%–50%). We observed 12 and 4 of these galaxies in the LAE1 and LAE2 masks, respectively. The comparison of the expected spatial position from MAGMA to the final spatial position on the reduced two-dimensional (2D) spectra indicates that the alignment was better than 02 during the observations.

We used the public MOSFIRE python data reduction pipeline⁷ for sky subtraction, wavelength calibration, and co-addition of the single exposures. The pipeline performs an A–B/B–A subtraction and co-adds the single exposures using a sigma-clipped noise weighted mean after shifting them to a common pixel frame and masking bad pixels. The atmospheric OH sky lines are used for wavelength calibration. The final 2D spectra have a spatial resolution of 018 pixel⁻¹ and a spectral resolution of 1.09 Å pixel⁻¹. Figure 1 shows the final 2D spectra (degraded to R ∼ 1500) together with the slit positions on sky. We measured an rms noise of 5–10 × 10⁻¹⁹ erg s⁻¹ cm⁻² (4.4 Å resolution element) in the 10545–10565 Å wavelength region, in good agreement with the estimated noise from the MOSFIRE exposure time calculator,⁸ corrected for our estimated slit losses. Absolute flux was measured using the white dwarf spectrophotometric standard star GD71. The standard star was observed during the same nights with identical settings and reduced in the same way as the science exposures. We present the sensitivity curve for the MOSFIRE Y-band in Figure 2, together with the line fluxes of the two targets derived from UNB filters. This shows that we would have clearly detected the two LAEs as is further discussed below.

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2.3. Tests and Simulations: Establishing Our Detection Limits

2.4. No Detection of Lyα in LAE1 and LAE2

A large number of studies have looked at the Lyα LF at z < 7. A summary of the surveys at z ∼ 3–5 is given in Table 1, and the mean data points adopted for this redshift range are shown in Figure 3 panel (A). It can be seen that the LAE LF changes only slightly in this redshift range. Schechter functions fitted to the data as a function of redshift result in less than 15% change in L* and ϕ*, respectively (Ouchi et al. 2008). Note that in this and the following comparisons of LFs, we account for eventual differences in the cosmologies assumed by the authors. Furthermore, some authors apply a correction to their Lyα luminosities to account for absorption of the Lyα forest. This correction is debated, as it was recently shown that the Lyα line profile is asymmetric at z ∼ 0, where IGM absorption is negligible. This suggests that Lyα is already redshifted when escaping the galaxy and most probably makes the above correction factor superfluous and result in an overestimation of the LAE luminosity (Scarlata et al. 2014). The LFs presented in this paper are not corrected by this factor.

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At 5 < z < 7, there are several major studies (Taniguchi et al. 2005; Shimasaku et al. 2006; Murayama et al. 2007; Ouchi et al. 2008, 2010; Hu et al. 2010; Kashikawa et al. 2011). All of these use the Subaru/Suprime-Cam camera with the NB812/NB921 filters. Additional constraints come from Malhotra & Rhoads (2004) compiling a large sample of LAE surveys. The above studies are summarized in Table 2. These large studies have significant disagreements in the derived LFs, with the various studies citing contamination rates, selection functions, and spectroscopic incompleteness as possible sources of disagreement. The Hu et al. (2010) study uses several widely spaced fields to rule out cosmic variance as the source of the discrepancy. In Figure 3, we combine the various studies and find that, while the fits to the LAE LFs done by the different authors disagree, the data are consistent within errors, indicating that counting statistics and fitting methods are the likely source of the discrepancy. We adopt weighted averages of the data points for the redshifts 3.1 < z < 4.9, z ∼ 5.7, and z ∼ 6.6, as indicated by the colored symbols in Figure 3 panels (A) through (C). In panel (D), we also show LAE detections by Iye et al. (2006), Ota et al. (2010), Vanzella et al. (2011),⁹ and Shibuya et al. (2012b) at z ∼ 7 with their weighted averages. We note that there are differences in the normalization of the above studies, which are likely linked to sample incompleteness and contamination (estimated to be less than 20% for these studies). These uncertainties are captured in the individual error bars, which we take into account in the final error bars of the weighted averages. At z ∼ 7.7, we combine the candidate detections from Hibon et al. (2010) and Tilvi et al. (2010) with the two remaining candidates from Krug et al. (2012) by adding up the comoving volumes of the studies. The new limits at z ∼ 7.7 are shown in Figure 3 panel (E). The single points are shown in Figure 3 panel (D), together with the limit from Clément et al. (2012) shown by the gray line. Finally, in Figure 3 panel (E), we show our combined LFs over the redshift range 3.1 < z < 7.7.

Table 2. LAE Surveys at z ∼ 5.7, 6.6, 7.7, and 8.8

Redshift	Phot. Cand.	Spec. Conf./Observed	Spectr. Fractiona	Limits [AB]	Type of Limit and Aperture	Areab	References
5.7	89	46/66 + 8c	55%	26.0 (NB816)	5σ, 2'' aperture	1 × 0.25	Kashikawa et al. (2011)
5.7	∼140	87/140d	100%	25.3 (NB816)	5σ, 3'' aperture	7 × 0.2	Hu et al. (2010)
5.7	401	17/29	4%	26.0 (NB816)	5σ, 2'' aperture	5 × 0.2	Ouchi et al. (2008)
5.7	119	⋅⋅⋅	0%	25.1 (NB816)	5σ, 2'' aperture	1 × 1.95	Murayama et al. (2007)
5.7	89	28/39 + 6/24	36%	26.6 (NB816)	3σ, 2'' aperture	1 × 0.2	Shimasaku et al. (2006)
5.7	56e	30/35	55%	⋅⋅⋅		∼0.76	Malhotra & Rhoads (2004)
6.6	207 (+58)e	16/24 (+ 16.22 + 1)e	13%	26.2 (NB921)	3σ, 2'' aperture	5 × 0.2	Ouchi et al. (2010)
6.6	58	42/52 + 3f	74%	26.0 (NB921)	5σ, 2'' aperture	1 × 0.25	Kashikawa et al. (2011)
6.6	∼70	30/70	100%	25.2 (NB912)	5σ, 3'' aperture	7 × 0.2	Hu et al. (2010)
6.6	61g	12/23	20%	⋅⋅⋅		∼0.82	Malhotra & Rhoads (2004)
7.7	4	0/2	0%	22.4 (UNB1056)	50% compl., auto aper.	1 × 0.2	Krug et al. (2012)
7.7	0	⋅⋅⋅	⋅⋅⋅	26.0 (NB1060)	5σ, ∼1''aperture	3 × 0.02	Clément et al. (2012)
7.7	7	0/5	0%	25.2 (NB1060)	4σ, 15 apert. (= 50% compl.)	1 × 0.1	Hibon et al. (2010)
7.7	4	⋅⋅⋅	0%	22.5 (UNB1063)	50% completenes	1 × 0.2	Tilvi et al. (2010)
8.8	13h	0/5h	0%	22.2 (NBJ)	5σ, 2'' aperture	∼10	Matthee et al. (2014)i

Notes. ^aFraction of spectroscopically confirmed galaxies used in the analysis. ^bGiven in deg². ^cTwenty in addition to Shimasaku et al. (2006). ^dPart of this sample is based on Hu et al. (2004). ^eBased on Kashikawa et al. (2006). ^f28 in addition to Kashikawa et al. (2006) and Taniguchi et al. (2005). ^gThis sample is combined from different studies. Corrections for false detections are applied to the LFs; see Malhotra & Rhoads (2004) for more information. ^hIncluding two with J and K detections. ⁱSee also Sobral et al. (2009, 2013).

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This clearly shows a rapid evolution in the number density of bright LAEs at 6 < z < 8. However, it is unclear whether this evolution is driven by changes in the IGM opacity or evolution in the density of the underlying galaxy population. We will disentangle these two effects in the following section.

Lyα emission is produced in young galaxies with a substantial amount of on-going star formation. It is therefore the amount of UV radiation and the ISM of a galaxy which constrains the amount of Lyα emission. As the Lyα photons escape from the galaxy, they get scattered in areas of dense neutral hydrogen in the IGM. The amount of neutral hydrogen around galaxies sets the amount of Lyα emission that can be measured by our telescopes. As soon as galaxies are formed, they start to re-ionize larger and larger bubbles of neutral hydrogen around themselves, and the transparency for Lyα photons is increased. By recording the amount of Lyα emission, i.e., the rest-frame EW (EW₀) distribution, as a function of redshift, it is therefore possible to estimate the change in the volume fraction of neutral hydrogen, x_H i, and therefore map the re-ionization process.

However, the change in the fraction of Lyα-emitting galaxies also depends on the density of the underlying galaxy population as well as on internal (ISM) properties of the galaxies, like star formation rate and dust content. Studies of the Lyα emission properties of UV-continuum selected LBGs suggest that the Lyα emission is rising with redshift in galaxies at z = 4–6 (Stark et al. 2010; Mallery et al. 2012; Schenker et al. 2013), where the universe is thought to be fully re-ionized. In particular, Zheng et al. (2014) note that the EW distribution in this redshift range (4 < z < 6) is skewed to larger rest-frame EW values for higher redshifts. This suggests evolution of the internal properties of galaxies (e.g., dust; Bouwens et al. 2012; Finkelstein et al. 2012; Mallery et al. 2012), enhancing the amount of Lyα emission with increasing redshift (e.g., Treu et al. 2012).

In order to constrain the fraction of neutral hydrogen at z ∼ 8, we have to separate these effects from the IGM. We therefore first model the intrinsic (i.e., without IGM absorption) Lyα LF (Section 4.1). Later, we will compare this intrinsic LF to the observed LFs at different redshifts (Section 4.2) and, combined with two possible implementations of the re-ionization process, constrain x_H i (Section 4.3).

4.1. A Model of the LAE Galaxy Population

To separate ISM from IGM effects on the Lyα LF (see also Dijkstra & Wyithe 2012), we first create an empirical model of the LAE LF based on the UV LF and the Lyα rest-frame EW (EW₀) distribution at z < 6, where the IGM is fully re-ionized. In brief, we assume the z = 4–9 UV-continuum LFs of LBGs derived by Bouwens et al. (2007, 2011) and Oesch et al. (2013). These LFs can be well explained by assuming that the luminosity and stellar mass of a galaxy is directly related to its dark-matter halo assembly and gas infall rate (Tacchella et al. 2013). Especially the LF at z > 7 are therefore put on more solid ground. We then convolve these UV LFs with two observed Lyα EW₀ distributions of Mallery et al. (2012) (4 < z < 6) and Stark et al. (2010) (3 < z < 7) by using a Monte Carlo sampling method to estimate an LAE LF.

We first draw random galaxies from the UV-continuum LFs. The number of galaxies is defined by the integral of the UV LF at the different redshifts. On the bright end, we integrate to M_UV = −30.0, above which the contribution of galaxies becomes negligible. On the faint end, we set the integration limit to M_UV = −15.0. We note that this is ∼2 mag below the Lyα luminosity, which is observed at all redshifts. Changing M_UV above this limit does not change the output of our model. This faint M_UV limit however means extrapolating the observed UV-continuum LFs used from the literature (usually going down to M_UV = −18.0). So we also verified that the implications of our model are insensitive to changes of the faint end slopes of the UV-continuum LFs and other LF parameters between different studies (Bradley et al. 2012; McLure et al. 2013; Schenker et al. 2013). For each of the galaxies drawn from the UV-continuum LF, we then pick a random rest-frame EW from the input distributions and compute the cumulative Lyα LFs. We assume no correlation between EW₀ and UV luminosity for simplicity, although there are hints of less luminous galaxies reaching larger EW₀ compared to more luminous ones (Schaerer et al. 2011 but see Nilsson et al. 2009 and Zheng et al. 2014 for a contradictory study). We also assume that every galaxy is emitting Lyα (which is then absorbed in the IGM and the EW distribution captures the ISM physics), i.e., the fraction of Lyα emission (X_Lyα) is 100% for our model.

Our models are shown as shaded regions in Figure 4, panels (A) through (E). The points show the same weighted averages as in Figure 3, and we find that our model is very sensitive to the assumed EW₀ distribution. This is illustrated by the broad swath of the shaded region, indicating the range of values obtained by the Mallery et al. (2012) and Stark et al. (2010) EW₀ distributions. This is not surprising, as from the comparison of the two EW₀ distributions it can be seen that Mallery et al. (2012) is missing high EW₀ compared to Stark et al. (2010), which results in a much lower Lyα LF estimate. In the following, we will assume the Stark et al. (2010) EW₀ distribution as the basis because it samples fainter galaxies, which contribute to the majority of objects in our sample while Mallery et al. (2012) is restricted to UV-continuum redshifts and therefore brighter galaxies. To illustrate the dependence on EW₀ further, the dotted, dashed, and dash-dotted lines in Figure 4 show constant input rest-frame EWs with EW₀ = 20, 30, 50 Å.

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4.2. Interpreting the Evolution of LAEs

4.3. Constraint on x_H i and Lyα Optical Depth at z ∼ 7.7

Turning to a more qualitative analysis, we use our model to constrain the change in the neutral hydrogen fraction in the IGM at z > 6.

For this, we consider two different possibilities of how we think Lyα photons get absorbed in the IGM. The two different approaches lead to different imprints of re-ionization in the Lyα LFs. We consider (1) a "black and white" process where Lyα emission of a galaxy is either absorbed or not ("patchy/absorption model") and (2) a smooth process where the Lyα emission is attenuated by a certain degree ("smooth/attenuation model").

The former process will decrease the number of Lyα-emitting galaxies irrespective of their emission strength. It will lead to a "global" shift of the LAE LF. The latter process will lower the Lyα emission in all of the galaxies, preferentially removing galaxies with high Lyα rest-frame EW. It will lead to a change in normalization and shape of the LAE LF.

For both of these models, we can constrain x_H i independently. We estimate x_H i for the former by using the simulations by McQuinn et al. (2007), and for the latter, we apply the models by Dijkstra et al. (2011).

We note that, with the current data, it is not possible to (dis)prove one or the other approach. But we will see that both approaches will lead to consistent results.

4.3.1. A Patchy Model of Re-ionization

In this case, Lyα is blocked by the neutral IGM, which results in a decrease of the Lyα LF for all luminosities. We tune our model LF to fit the observed LAE LFs at z ∼ 5.7, 6.6, and 7.7 by adjusting X_Lyα (the total fraction of galaxies for which Lyα is not absorbed), which is (at first) independent of magnitude (see Figure 5 panels (A) through (C), dotted curves). We find that X_Lyα is almost undistinguishable between 5.7 < z < 6.6 but drops by a factor of four beyond z = 7, as shown in Figure 5, panel (D) by the filled squares. Furthermore, we follow the approach of Schenker et al. (2012) and introduce two different values, $X_{{\rm Ly}\alpha }^{{\rm bright}}$ and $X_{{\rm Ly}\alpha }^{{\rm faint}}$, for simulated galaxies with M_UV < −20.25 AB and M_UV > −20.25 AB in order to compare the fraction of LAEs from our empirical model to real observations at z < 7. This is shown in Figure 5 panels (A) and (B) by the dashed line (we do not apply this split at z ∼ 7.7 because of the sparse data). The values for $X_{{\rm Ly}\alpha }^{{\rm bright}}$ and $X_{{\rm Ly}\alpha }^{{\rm faint}}$ for EW₀ > 25 Å are shown in panel (D) (filled and open circles, respectively). The error bars are estimated by changing the M_UV cut in a range of M_UV = −20.25 ± 2. Also shown are the observations by Schenker et al. (2012; light gray), Treu et al. (2012; black), and Curtis-Lake et al. (2012; dark gray) for galaxies with EW₀ > 25 Å and the same magnitude cut.

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In general, we find a good agreement of X_Lyα(z) with the values observed in UV-continuum selected LBGs at z < 7. We find a significant drop of a factor of 4 ± 1 in the fraction of LAEs at z ∼ 7.7 compared to z = 6. Note that the Curtis-Lake et al. (2012) estimate of X_Lyα for bright galaxies is a factor of ∼2 higher than the estimates from the other studies. Different selection and sample variance are a very likely cause for this discrepancy. Nonetheless, their results support a strong drop of X_Lyα above z = 7.

This change in LF can be converted into a neutral hydrogen fraction (x_H i) by using the results from the 186 Mpc radiative transfer simulations by McQuinn et al. (2007) as follows: their Figure 4 shows the relative change of the Lyα LF as a function of neutral hydrogen fraction at z = 6.6 assuming full re-ionization at z = 6. For example, x_H i= 0.18, 0.38, 0.53, 0.67, and 0.80 result in a rescaling of the LF with factors of 0.76, 0.50, 0.33, 0.20, and 0.05, respectively. We then assume that this rescaling of the LF is directly proportional to the change in the fraction of LAEs, i.e., X_{Lyα, z = 7.7}/X_{Lyα, z = 6} ∼ 4 (see Figure 5, panel (D), blue and red squares). Assuming the dust extinction properties at z ∼ 7.7 are the same as at z = 6, we conclude that the drop in X_Lyα implies a neutral hydrogen fraction of at least x_H i = 0.60 ± 0.07 at z ∼ 7.7. Assuming the dust content of galaxies above z = 6 is further decreasing and therefore extrapolating X_Lyα(z) from the values at 4 < z < 6 (see Stark et al. 2010) implies even higher limits (x_H i = 0.71 ± 0.04). Note that the small change in X_Lyα between z ∼ 5.7 and z ∼ 6.6 is indicative of little neutral hydrogen. This is in line with the results by McQuinn et al. (2007), who suggest that the universe is fully ionized at these redshifts.

Note that we can estimate x_H i without applying our model by directly taking the ratio of the LAE LFs at z ∼ 5.7 and ∼7.7 and again applying the simulations by (McQuinn et al. 2007). This approach leads to consistent results.

Having established a lower limit on x_H i, we can use the patchy model to further constrain the Lyα optical depth. Assuming the change in X_Lyα above z = 6 is due to the IGM, it can be associated with the average change of Lyα optical depth $\langle e^{-\Delta \tau _{{\rm Ly}\alpha }}\rangle$ under the assumption that re-ionization is completed at z ∼ 6 (i.e., τ_{Lyα, z = 5.7} = 0 and Δτ_Lyα(z) = τ_Lyα(z) − τ_{Lyα, z = 5.7}). Note that this approach is identical to Treu et al. (2012), and we can set X_Lyα(z)/X_{Lyα, z = 5.7} ≡ _p(z), where _p is defined as in Treu et al. (2012) and _{p, z = 6} = 1 by construction. From Figure 5 panel (D), we find _p = 0.8 ± 0.2 for z ∼ 6.6 (blue and green squares) and _p = 0.25 ± 0.05 for z ∼ 7.7 (blue and red squares), respectively. Our z ∼ 6.6 (z ∼ 7.7) value is consistent with the z ∼ 7 (z ∼ 8) value of 0.66  ±  0.16 (<0.28) found by Treu et al. (2012) (Treu et al. 2013) within errors. We then compute the Lyα optical depth by equating $\epsilon _{p}(z) = \langle e^{-\Delta \tau _{{\rm Ly}\alpha }(z)} \rangle$. The final result of Δτ_Lyα(z) w.r.t. z ∼ 6 is shown in Figure 6. Our limit at z ∼ 7.7 is important to constrain Δτ_Lyα(z) as the values at z ∼ 6 and 7 are almost indistinguishable. The overall change in optical depth as a function of redshift can be expressed by Δτ_Lyα(z)∝(1 + z)^α with α = 2.2 ± 0.5. Note that this exponent is a lower limit because of the upper limit in the LAE LF at z ∼ 7.7. We find an increase in optical depth of at least 1.3 between z = 6 and z ∼ 8. Our best fit model is fully consistent with the Gunn–Peterson optical depth measurements in quasars (Goto et al. 2011; Fan et al. 2006); however, the functional forms of the estimates lead to different exponents (see Figure 6).

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4.3.2. A Smooth Model of Re-ionization

In this case, there is no global scaling of the LF as before; however, a steepening of the LF may occur because the EW₀ distribution gets skewed to lower EW₀ as the redshift increases beyond z = 6 (see also Zheng et al. 2014). We represent the Stark et al. (2010) EW distribution in the same manner as Treu et al. (2012) by using a Gaussian truncated at negative values. In contrast to the case outlined before, we now change the width of the EW₀ distribution (similar to the "smooth model" in Treu et al. 2012). As in the case above, we have to take the difference in evolution between z = 6 and z = 7.7 (assuming the IGM is fully re-ionized at z = 6). We therefore start directly with the z = 6 EW₀ distribution (see Figure 5, panel (A), dotted curve) and tune it to fit the z ∼ 7.7 limits by changing its width (dashed-dotted line in Figure 5, panel (C)). From the final EW₀ distribution at z ∼ 7.7, we compute the cumulative fraction P(> EW₀), which has now changed w.r.t. z = 6 as we have adjusted the width of the EW₀ distribution. These fractions can be converted into x_H i by using the models by Dijkstra et al. (2011; using semi-numerical simulations by Mesinger et al. 2011), combining galactic outflow models and large-scale semi-numeric simulations of reionization. From our final EW₀ distribution fitting the limits at z ∼ 7.7, we find P(> 100 Å) = 0.02 ± 0.01, P(> 75 Å) = 0.07 ± 0.02, and P(> 50 Å) = 0.20 ± 0.05, which translates, by adopting Figure 5 in Pentericci et al. (2011), into upper limit neutral hydrogen fractions of x_H i = 0.7  ±  0.1, 0.6  ±  0.1, and 0.5  ±  0.2, respectively. Note that x_H i is more difficult to estimate for smaller EW₀ cuts as P(> EW₀) approaches unity for all x_H i by construction (Pentericci et al. 2011). Taking this into account, the limits we find with our second approach are consistent with the results above.

4.3.3. Summary of Our Findings

In summary, we have looked at two different ways how re-ionization can be imprinted in the change of Lyα LF. We have considered an absorption model resulting in a global shift of the Lyα LF and an attenuation model resulting in a skewing of the EW₀ distribution and therefore, a steepening of the Lyα LF. Note that both approaches can fit the observed LAE LFs within its uncertainty, and we are not able to judge which of the models is right. However, a skewing of the EW distribution is likely, as it seems from the observational data at z ∼ 5.7 and z ∼ 6.6 that the evolution of the bright end is stronger than at the faint end of the LAE LF. In either way, we are able to constrain x_H i using both approaches, resulting in lower limits for the neutral hydrogen fraction between x_H i = 0.53 and x_H i = 0.70 at z ∼ 7.7.

Finally, we stress that our results are based on the assumption that all changes in X_Lyα and the EW₀ distribution are caused by a change in the ionization state of the IGM at z > 6. However, an alternative explanation involves an increase of the escape fraction of ionizing photons and would lead to a drop in X_Lyα and thus an overestimation of x_H i (Dijkstra et al. 2014). Without a changing ionization state of the IGM, the escape fraction needed to explain the observations is at odds with other studies (Wyithe et al. 2010; Kuhlen & Faucher-Giguère 2012; Robertson et al. 2013; Dijkstra et al. 2014). However, a mixture of changing x_H i (∼0.2) and f_esc (∼0.2–0.3) would be consistent with our results and direct escape fraction measurements.

Given these results at z ∼ 7.7, it is important to push to higher redshifts to better constrain the evolution of the LAE LF. Assuming that the LAE LF continues to trace the LBG LF at z > 8, we can put upper limits on the number of LAEs that should be found in planned surveys. The final UltraVISTA NB118 survey (McCracken et al. 2012; Milvang-Jensen et al. 2013) is able to search for potential LAE candidates at z ∼ 8.8 on 0.9 deg² on sky down to 1.5 × 10⁻¹⁷erg s⁻¹ cm⁻². Assuming this as limiting the Lyα line flux and combined with our model from the LBG UV LF (optimistically assuming X_Lyα(z = 8.8) = 1), it is unlikely that this survey will find LAEs at this redshift (expected counts are 0.6 ± 0.3). Likewise, with the same assumptions, Euclid (Laureijs et al. 2011) is not expected to find LAEs at z > 8 with its spectroscopic configuration (1.1 μm–2 μm, 3 × 10⁻¹⁶ erg s⁻¹ cm⁻² on 20,000 deg²). On its proposed deep area (40 deg²), a flux limit of at least 3 × 10⁻¹⁷ erg s⁻¹ cm⁻² must be reached to find one LAE at z > 8. Other space-based spectroscopic surveys, like WISPs (Atek et al. 2010) or 3D-HST (Brammer et al. 2012) using the Hubble Space Telescope (HST) grism G141, current flux limits around 5 × 10⁻¹⁷ erg s⁻¹ cm⁻², and area of 600–800 arcmin², need to be substantially (roughly five times) deeper to find LAEs at z ∼ 8.8. Very deep small area blind imaging surveys with instruments on 8–10 m telescopes, such as HAWK-I (75 × 75) or MOSFIRE (61 × 61), must reach flux limits of 5 × 10⁻¹⁸ erg s⁻¹ cm⁻² in NB118 to pick up one LAE at z ∼ 8.8 on a total of ∼10 pointings.

We have presented follow-up observations on two bright LAE candidates at z ∼ 7.7 using MOSFIRE. We rule out any line emission at a level of several σ for both objects. The limits inferred from these non-detections suggest a strong evolution of the LAE LF between 6 < z < 8, consistent with what is seen in LBG samples. We create an empirical model using the observed LBG UV-continuum LFs and Lyα rest-frame EW distributions to understand the interplay between LAE and UV-continuum selected galaxies. We find that our model and the observed LAE LF follow each other but note a secondary effect, which is due to a change in the EW₀ distribution of the galaxies as a function of redshift. From this differential evolution and assuming two different models on Lyα absorption, we find consistent lower limits on the neutral hydrogen fraction at z ∼ 7.7 of 50%–70%. Furthermore, we find a strong evolution in the Lyα optical depth at z > 6, which can be characterized by (1 + z)^{2.2 ± 0.5}. All in all, our results are indicative of a continuation of strong evolution in the IGM beyond z = 7.

We would like to acknowledge the support of the Keck Observatory staff who made these observations possible as well as B. Trakhtenbrot and W. Hartley for valuable discussions. We also thank Nick Konidaris for providing and supporting the MOSFIRE reduction pipeline and Gwen Rudie for providing the MOSFIRE exposure time calculator. A.F. acknowledges support from the Swiss National Science Foundation. A.F. also thanks Caltech for hospitality while working on this article. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.

Facility: Keck:I (MOSFIRE) - KECK I Telescope