A Metal-poor Damped Lyα System at Redshift 6.4

To estimate the column densities of the metals shown in Figure 4, we first need to model the quasar continuum in order to normalize the FIRE spectrum. We use the interactive task continuumfit from the linetools python package. The continuum is fit by interpolating cubic splines between knots placed along the spectrum.

We visually inspect the normalized spectrum for all potential metal absorption lines consistent with being at z = 6.43902 and select the velocity limits that are used for subsequent analysis (see Figure 4). Next, we calculate the rest-frame equivalent widths (EWs) and column densities. All these quantities are listed in Table 1. We calculate the column densities with the apparent optical depth method (AODM; Savage & Sembach 1991), using the wavelengths and oscillator strengths reported in Morton (2003).

At intermediate resolution (R ∼ 6000), saturation or blending of lines can show up as discrepant column density estimates for different transitions of the same ion. This is the case for the Si ii detection in our system: the column densities for Si ii λ1260 and Si ii λ1526 are 10^13.53 cm⁻² and 10^14.15 cm⁻², respectively (see Table 1). As discussed in Appendix B, the Si ii λ1526 line must be contaminated as its column density predicts much stronger Si ii λ1260 and λ1304 absorptions than observed (see Figure 13). We therefore do not use the Si ii λ1526 column density in the remainder of the paper. The column density of Si ii λ1260 is consistent with the marginal detection of Si ii λ 1304; however, the Si ii λ1260 column density is likely to be contaminated by a C iv λ1548 absorption line from a system at z = 5.0172. Therefore, we consider the Si ii λ1260 measurement as an upper limit. In Appendix B, we conclude that we cannot rule out the possibility of hidden saturation for O i λ1302 and Al ii λ1670. Thus, to take possible saturation effects into account, we have increased their uncertainties from 0.06 to 0.20 dex (see Table 1 and Figures 15 and 16). This highlights the need for obtaining much higher-resolution spectroscopy in systems like this one, although this is very challenging for the current generation of telescopes.

We note that the fine-structure line C ii* λ1335 is not detected in our data (dotted blue line in Figure 4). This line is ubiquitous in the spectra of GRB host galaxies (GRB-DLAs; e.g., Fynbo et al. 2009). Under some assumptions, C ii* can be used to determine the distance between quasar and absorber (we refer the reader to the discussion in Ellison et al. 2010 and references therein). The non-detection of this line supports the idea that this PDLA is not associated with the quasar host galaxy.

In Figure 4 we also show the regions around C iv λλ1548,1550, Si iv λλ1393,1402, and N v λλ1238,1242. They are not convincingly detected even though the AODM in the velocity range (−150 $\mathrm{km}\,{{\rm{s}}}^{-1}$, 150 $\mathrm{km}\,{{\rm{s}}}^{-1}$) reports that C iv λ1548, Si iv λ1393, and N v λ1242 are more than 3σ significant. The oscillator strength of N v λ1242 is weaker than that of N v λ1238, therefore the possible absorption at λ1242 is inconsistent with the non-detection of λ1238. Higher signal-to-noise ratio (S/N) data are required to confirm potential detection of high-excitation lines but in the remainder of the paper we consider these lines as non-detections and report their 3σ limits (Table 1). In Table 2 we show the element ratios relative to the solar abundances reported in Asplund et al. (2009). Solar abundances are defined using the meteoritic values for all elements other than C and O, for which we use the photospheric values given that these elements are volatile and cannot be recovered completely from meteorites (Lodders 2003).

Table 2.  Column Densities and Relative Abundances of the DLA at z = 6.40392 Toward the Quasar P183+05 at z = 6.4386

X	$\mathrm{log}\epsilon {({\rm{X}})}_{\odot }$ a	log NX	[X/H]	[X/O]	[X/Si]	[X/Fe]
H	12.00	20.68 ± 0.25	⋯	2.92 ± 0.32	>2.66	2.94 ± 0.26
C	8.43	14.30 ± 0.05	−2.81 ± 0.26	0.11 ± 0.21	>−0.15	0.13 ± 0.07
O	8.69	14.45 ± 0.20	−2.92 ± 0.32	⋯	>−0.26	0.02 ± 0.21
Mg	7.53	13.37 ±  0.03	−2.84 ± 0.25	0.09 ± 0.20	>−0.18	0.10 ± 0.06
Al	6.43	12.49 ± 0.20	−2.62 ± 0.32	0.31 ± 0.28	>0.04	0.32 ± 0.21
Sib	7.51	<13.53	<−2.66	<0.26	⋯	<0.28
Fe	7.45	13.19 ± 0.05	−2.94 ± 0.26	−0.02 ± 0.21	>−0.28	⋯

Notes. The column densities N_X are in units of cm⁻². Relative abundances do not include ionization or depletion corrections. Our assumed metallicity is based on oxygen ([O/H] = −2.92 ± 0.32) as is an undepleted element and has an ionization potential similar to H i. Element ratios are relative to the solar values, i.e., $[{\rm{X}}/{\rm{Y}}]=\mathrm{log}{({N}_{{\rm{X}}}/{N}_{{\rm{Y}}})-\mathrm{log}({N}_{{\rm{X}}}/{N}_{{\rm{Y}}})}_{\odot }$.

^a $\mathrm{log}\epsilon {({\rm{X}})}_{\odot }=12+\mathrm{log}{({N}_{{\rm{X}}}/{N}_{{\rm{H}}})}_{\odot }$. The solar abundances are taken from the meteoritic values reported in Asplund et al. (2009), except for C and O, for which we use the photospheric values. ^bHere we only used limits from Si ii λ1260, which are more stringent.

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In order to estimate the H i column density of the absorber at z = 6.40392, we first need to model the quasar's intrinsic Lyα emission. This is not straightforward given the variety of Lyα strengths observed among quasars. A further complication for P183+05 is that its C iv line is blueshifted by 5057 ± 93 $\mathrm{km}\,{{\rm{s}}}^{-1}$ with respect to the systemic [C ii] redshift. Quasar spectra with such large blueshifts are not rare among the highest-redshift quasars (Mazzucchelli et al. 2017) but they are not well represented in low-redshift quasar samples, making it challenging to reconstruct them using standard techniques (see discussions in Davies et al. 2018b and Greig et al. 2019). Here we model the quasar's emission by creating composite spectra based on spectra of the SDSS DR12 quasar catalog (Pâris et al. 2017) with comparable C iv properties to P183+05 (see Mortlock et al. 2011; Bosman & Becker 2015; Bañados et al. 2018). Our approach can be summarized in the following steps.

• 1.  
  We select quasars from the SDSS DR12 catalog flagged as non-broad absorption-line quasars in the redshift range 2.1 < z < 2.4 (i.e., quasar spectra covering the Lyα, C iv, and Mg ii lines). To preselect quasars with extreme blueshifts we require the pipeline redshift to be blueshifted by at least 1500 $\mathrm{km}\,{{\rm{s}}}^{-1}$ from the Mg ii-derived redshift. This yields 3851 quasars.
• 2.  
  We then measure the median S/N at the continuum level of the C iv region for each spectrum. We only retain objects with a median S/N > 5 in the wavelength range 1450–1500 Å. After this step, we are left with 2145 quasars.
• 3.  
  We model the C iv line wavelength region for each quasar as a power law plus a Gaussian. We estimate the C iv EWs and their velocity offsets with respect to the Mg ii redshift, which is thought to be a reliable systemic redshift estimator (Richards et al. 2002).
• 4.  
  We require the quasars to have C iv EWs consistent with that measured in P183+05 (EW = 11.8 ± 0.7 Å) at the 3σ level. Given that some z > 6 quasars have significant blueshifts between Mg ii and [C ii] lines (Venemans et al. 2016), we select SDSS quasars with a C iv blueshift (measured from the Mg ii line) consistent within 1000 $\mathrm{km}\,{{\rm{s}}}^{-1}$ of the P183+05 C iv blueshift (5057 ± 93 $\mathrm{km}\,{{\rm{s}}}^{-1}$; measured from the [C ii] line). After applying these criteria, we are left with 61 P183+05 "analogs."
• 5.  
  We fit the continua of these analogs by a slow-varying spline to remove strong absorption systems and noisy regions. We then normalize each spectrum at 1290 Å and average them. This mean composite spectrum and the ±1σ dispersion around the mean are shown as the red line and orange region in Figure 1, respectively. The dispersion at 1290 Å is zero by construction and increases at shorter and longer wavelengths. The mean spectrum (red line) matches the general features in the observed spectrum of P183+05 well and predicts a weaker Lyα line than observed in typical low-redshift quasars (Pâris et al. 2011).

Using this continuum model, we fit a Voigt profile to the damping wing with a fixed centroid at z_DLA = 6.40392, the redshift of the DLA derived from low-excitation metal lines (Section 3). A least-squares optimization yields a best-fit value of N_HI = 10^20.77 cm⁻², which reproduces the data well and is consistent with no emission spikes at the expected location of the Lyβ absorption (see Figure 2). We assume a conservative uncertainty of 0.25 dex, which represents the credible range allowed by the S/N of our spectrum. This was determined by overplotting Voigt profiles, varying the input column density to identify the range allowed by the data.¹⁰ We note that the least-squares best-fit Voigt profile (N_HI = 10^20.77 cm⁻²) seems systematically lower than the data at λ_rest > 1216 Å. Even though it is possible to find profiles that better match the data at those wavelengths by lowering N_HI, in those cases the match to the data at λ_rest < 1216 Å worsens (see, e.g., the violet dashed lines in the top panel of Figure 3).

A closer look at the top panel of Figure 3 reveals that a DLA alone cannot reproduce the sharp drop in flux around λ_rest = 1212–1215 Å (see the yellow region in the residuals panel). We attempted other DLA fits using alternative continua as intrinsic model in Appendix A.1 but were not able to find another case that could fit the data better. On the other hand, a damping wing produced by a ${\overline{x}}_{{\rm{H}}{\rm{I}}}=0.80$ IGM can reproduce the data around λ_rest = 1212–1215 Å well (see Appendix A). This indicates that the combined effects of a neutral IGM and a DLA might be the most plausible scenario. In Appendix A.2 we discuss that the joint IGM+DLA fit is degenerate (see Figures 10 and 11). We take as our preferred model the combined fit shown in the bottom panel of Figure 3, i.e., we fix a ${\overline{x}}_{{\rm{H}}{\rm{I}}}=0.10$ IGM contribution and then we find a best-fit DLA with N_HI = 10^20.68±0.25 cm⁻². This is motivated by the following two facts: (i) we see metal absorption lines (Figure 4) with low internal velocity dispersion of the gas (narrow lines) that are characteristic of very metal-poor DLAs (e.g., Cooke et al. 2015) and (ii) IGM neutral fractions ${\overline{x}}_{{\rm{H}}{\rm{I}}}\gtrsim 0.4$ have only been reported at significantly higher redshifts (z ∼ 7.5; e.g., Davies et al. 2018a; Hoag et al. 2019). We note, however, that joint fits with an IGM neutral fraction in the range ${\overline{x}}_{{\rm{H}}{\rm{I}}}=0.05\mbox{--}0.50$ produce fits to the data comparable to our assumed scenario. A different way to reproduce the data in the λ_rest = 1212–1215 Å region is to include additional saturated but weak absorbers in the proximity zone of the quasar. For example, an additional absorber with $\mathrm{log}{N}_{\mathrm{HI}}=15.51$ at z = 6.427 is consistent with the sharp drop in flux at ∼1214 Å. When including the z = 6.427 absorber, the corresponding best-fit $\mathrm{log}{N}_{{\rm{HI}}}$ for the DLA is 20.68. Thus a ${\overline{x}}_{{\rm{H}}{\rm{I}}}=0$ scenario cannot be completely ruled out with the current data. Our assumed fiducial value for the DLA column density with its conservative uncertainty of 0.25 dex, includes all the N_HI best-fitting values when considering the contribution of an IGM with a neutral fraction in the range ${\overline{x}}_{{\rm{H}}{\rm{I}}}=0-0.38$ (see Figure 11).

For systems with large column densities of hydrogen like DLAs in which nearly all of the metals are in either their neutral or first excited states (as is the case for the system of this study) the ionization corrections are negligible (Vladilo et al. 2001). However, because of the proximity of the DLA to P183+05 it is important to quantify whether the ionization radiation from the quasar would significantly affect our derived metallicities. We use the spectral synthesis code Cloudy (Ferland et al. 2017) to explore the maximum ionization corrections allowed by the observed upper limit on $\mathrm{log}{N}_{\mathrm{SiIV}}-\mathrm{log}{N}_{\mathrm{SiII}}\lt -0.53$. The simulation was made to simultaneously reproduce the observed neutral hydrogen column density $\mathrm{log}{N}_{\mathrm{HI}}=20.68$ and the observed upper limit on the Si iv/Si ii ratio. This can be achieved by placing an active galactic nucleus source of the same observed 1450 Å brightness as P183+05 at >375 physical kpc from the DLA cloud. A detection of Si iv at this level would indeed require two thirds of the hydrogen of the DLA to be ionized (N_HI/N_H > 0.33), leading to a total hydrogen column density of $\mathrm{log}{N}_{{\rm{H}}}=21.16$. Nevertheless, we find that the correction is negligible for N_OI/N_HI, which was expected because of the charge-exchange equilibrium between O i and H i. The other common low ion abundances (Si ii/H i, C ii/H i, and Mg ii/H i) are also remarkably insensitive to the neutral gas fraction (H i/H); the required correction factors for the metal abundances would be as small as $({N}_{\mathrm{SiII}}/{N}_{\mathrm{HI}})/(N(\mathrm{Si})/N({\rm{H}}))=1.16$, $({N}_{\mathrm{CII}}/{N}_{\mathrm{HI}})/({N}_{{\rm{C}}}/{N}_{{\rm{H}}})=1.09$, and $({N}_{\mathrm{MgII}}/{N}_{\mathrm{HI}})/({N}_{\mathrm{Mg}}/$ N_H) = 0.95. As Si iv is not actually detected, the actual corrections would be even smaller. Based on these results, and the fact that the observed metallicities are very similar to that based on O i/H i, we do not apply ionization corrections. In this way we are also able to directly compare our results to similar high-redshift absorption systems from the literature that do not include ionization corrections (e.g., Becker et al. 2012; D'Odorico et al. 2018).

Another factor to consider is dust depletion, which might have fundamental consequences for derived metallicities as we know that large amounts of dust exist even in some of the most distant galaxies identified to date (e.g., Venemans et al. 2018; Tamura et al. 2019). Indeed, recent studies have demonstrated that dust-depletion corrections are important for the derived metallicities of high-redshift DLAs associated with both GRBs and quasars (e.g., De Cia et al. 2018; Poudel et al. 2018; Bolmer et al. 2019) although it is also well established that the levels of depletion reduce with decreasing metallicity (Kulkarni et al. 2015). Thus, for our metallicity estimate we use the element oxygen which is very weakly affected by both dust depletion and ionization corrections.

The derived metallicity of [O/H] = −2.92 ± 0.32 makes this object one of the most metal-poor DLAs currently known. In fact, the three most metal-poor DLAs were reported recently: Cooke et al. (2016, 2017) presented two z ∼ 3 DLAs with metallicities of [O/H] = −2.804 ± 0.015 and [O/H] = −3.05 ± 0.05 while D'Odorico et al. (2018) reported a z = 5.94 DLA with metallicity [O/H] ≥ −2.9 (and [Si/H] = −2.86 ± 0.14, but not dust-corrected). Thus, the metallicity of the DLA of this paper is consistent with the current record holders, within the uncertainties. We note that the fact that this z = 6.4 DLA and the z = 5.94 DLA from D'Odorico et al. (2018) do not present evidence of high-excitation ions (e.g., C iv) departs from typical DLAs at lower redshift (z ∼ 2–3), which tend to have associated C iv (e.g., Rubin et al. 2015), but is not unexpected given the diminishing rate of incidence of high-ionization absorbers beyond z ∼ 5 (e.g., Becker et al. 2009; Codoreanu et al. 2018; Cooper et al. 2019). This is consistent with the idea that the gas causing C iv and higher ions resides in and follows the density evolution of the general IGM, while the DLA gas is more closely associated with galactic halos (Rauch et al. 1997).

In Figure 5 we show metallicity versus redshift for the DLAs compiled by De Cia et al. (2018), the metal-poor DLAs compiled by Cooke et al. (2017), the z > 4.5 absorbers reported by Poudel et al. (2018), and the z = 5.94 DLA reported by D'Odorico et al. (2018). All the metallicities are either dust-corrected or based on the undepleted element oxygen. Our new data point at z = 6.40392 (red hexagon) and the z = 5.94 DLA are in line with the general trend of decreasing metallicity with redshift.

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It is remarkable that the metallicities of the two highest-redshift DLAs still do not drop significantly below other measurements of the metallicity of overdense gas, but simply straddle the lower-metallicity envelope prescribed by the mean metallicity of the IGM (Figure 4), which is nearly constant over a long-redshift baseline ranging from z ∼ 2.5 (e.g., C iv and O vi absorbers: Rauch et al. 1997; Schaye et al. 2003; Simcoe et al. 2004) through 5 < z < 6 (e.g., O i systems; Keating et al. 2014), to the present DLA at z > 6. Modeling of what appears to be a metallicity floor in the IGM by contemporary outflows without invoking even more ancient phases of pre-enrichment has remained a challenge both at intermediate (Kawata & Rauch 2007) and high redshift (Keating et al. 2016).

This DLA is seen only ∼850 Myr after the big bang, thus there was not much time for metal enrichment. This is in line with it being one of the most metal-poor DLAs currently known, as discussed above. Therefore, this makes it an interesting system for which to ask whether its chemical abundance patterns could be explained by the yields of the first metal-free stars.

We note that, in general, the element ratios of this system are close to solar (see Table 2), which differs from the sub-solar abundances observed in typical metal-poor DLAs at z ∼ 3 (see Figure 13 in Cooke et al. 2011). Nevertheless, the solar relative abundances of this system are consistent with the patterns observed by Becker et al. (2012) and Poudel et al. (2018) in a sample of absorbers at higher redshifts (Figure 6).

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The [C/O] abundance has received significant attention over recent years as it still challenges our understanding of stellar nucleosynthesis. [C/O] increases linearly with metallicity from ∼−0.5 to ∼0.5 when [O/H] > −1. This has been explained by the yields of carbon produced by massive rotating stars, which increase with metallicity, in addition to a delayed contribution of carbon from lower-mass stars (Akerman et al. 2004). Conversely, current models of Population II nucleosynthesis predict that [C/O] should decrease or reach a plateau below a metallicity of [O/H] ∼ −1. However, both observations of metal-poor stars (Akerman et al. 2004; Fabbian et al. 2009) and metal-poor DLAs (Cooke et al. 2017) show the opposite trend, i.e., [C/O] increases to solar abundance at lower metallicities (see Figure 7). This intriguing trend has been interpreted as an enhanced production of carbon by Population III stars or by rapidly rotating Population II stars (Cooke et al. 2017). On the other hand, recent simulations show that high values of [C/O] can be due to the enrichment by asymptotic giant branch stars formed before z = 6 without including Population III stars (Sharma et al. 2018). Our new data point follows and further expands this empirical tendency (see the red hexagon in Figure 7), which is still lacking a definite explanation.

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To see what possible formation scenarios could describe the chemical composition of the DLA of this paper we refer to the discussions in Cooke et al. (2011) and Ma et al. (2017), with special attention to their Figures 14 and 5, respectively. Both studies investigate the expected abundance patterns produced by the first stars in high-redshift DLAs. The relative abundances observed in the DLA toward P183+05 do not match any of the Population III patterns expected by these studies. In particular, none reproduces the [C/O] abundance.

To investigate whether there are nucleosynthesis models of massive metal-free stars that can reproduce the observed abundances seen in the DLA of P183+05 we fit Population III supernova yields (Heger & Woosley 2010) using the tools developed¹¹ by Frebel et al. (2019; see their Section 4.4). The best fits have a very similar χ² and seem almost indistinguishable. For better visualization of the different models, in Figure 8 we show the first, 10th, 20th, and 30th best-fitting models (i.e., the model with the lowest χ², the 10th lowest χ², etc.). The best-fitting models prefer a progenitor mass in the range of $13\,{M}_{\odot }\lesssim M\lesssim 15\,{M}_{\odot }$ and a range of explosion energy. We note that these models give the yields produced by a single-progenitor supernova and it is clear that they cannot reproduce all the abundances observed in the DLA, particularly the Al abundance. This could indicate that more than one supernova was responsible for the enrichment in the DLA, which could hide any potential signature due to Population III stars (see also Maio & Tescari 2015). In addition, we do not observe the level of carbon enhancement ([C/Fe] > 0.70) seen in most of the very metal-poor stars (see e.g., Placco et al. 2014), which is thought to be a signature produced by the first stars.

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Therefore, we do not find evidence that the yields of Population III stars need to be invoked to explain the chemical enrichment of the DLA presented here.

We explore the results of using three alternative continuum models of the Lyα region as shown in Figure 9. First, we use the mean SDSS quasar spectrum from Pâris et al. (2011) as a model. The mean SDSS quasar has stronger emission lines than P183+05 (see also Figure 1) and therefore requires a higher neutral hydrogen column density than our fiducial model to match the onset of the damping wing. However, given the expected stronger N v line is not possible to find a reasonable DLA fit using this continuum model to match the data (see the dotted line and shaded gray region in Figure 9). Second, we reconstruct the Lyα region using the method presented in Davies et al. (2018b). This method is based on PCA decomposition and is specially designed to reconstruct the Lyα region of z ≳ 6 quasars. The PCA continuum model is shown as a solid blue line in Figures 1 and 9. Although the PCA continuum matches well the general characteristics of P183+05, it clearly underpredicts the observed flux near the Lyα region and it is virtually impossible to fit a Voigt profile consistent with the data using this continuum model (see the solid blue line and hatched region in Figure 9). Possible explanations are that the modest S/N of our data hinders this method and that we do not cover crucial emission lines (e.g., C iii]) that have strong predictive power (similar effects would impact other sophisticated methods that take advantage of high-S/N spectra and availability of several key emission lines, e.g., Greig et al. 2017). Third, we use a rather simplistic and unrealistic Lyα model consisting of a linear fit to the data right redward of the Lyα line (green dashed line in Figure 9). This is to showcase an extreme scenario with a very weak Lyα line. The last, unrealistic case gives a more reasonable DLA fit than the other two alternative continua but it is still far from being a good match to the data.

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Here we explore different alternatives, combining the effects of a neutral IGM and a DLA. We model the IGM damping wing following the formalism of Miralda-Escudé (1998), assuming a constant IGM neutral fraction between the quasar's proximity zone and z = 6, while being completely ionized at z < 6. The proximity zone is typically defined as the physical radius at which the transmission drops to 10%, which for P183+05 corresponds to 0.67 physical Mpc. We note that this proximity zone is much smaller than the expected ∼4.5 physical Mpc for a quasar with the luminosity and redshift of P183+05 (Eilers et al. 2017). In this particular case a small proximity zone does not come as a surprise given the existence of the proximate DLA, which is in fact one of the possible explanations for the small proximity zones found by Eilers et al. (2017).

For simplicity, in all cases here we use the SDSS-matched spectrum as the intrinsic continuum of the quasar. If we fit the data with a combined model of IGM+DLA with three free parameters (${\overline{x}}_{{\rm{H}}{\rm{I}}},{N}_{\mathrm{HI}}$, and the proximity zone), the outcome is highly degenerate. We use the differential evolution algorithm (Storn & Price 1997) to find the global minimum of the root-mean-deviation between the data and the model. This yields ${\overline{x}}_{{\rm{H}}{\rm{I}}}=0.81$, $\mathrm{log}{N}_{\mathrm{HI}}=19.55$, and a proximity zone of 0.72 physical Mpc. The global minimum is dominated by a very neutral IGM because an IGM absorption can reproduce the steep step in flux near the λ_rest = 1212–1215 Å region that the DLA alone underfits (compare the top and bottom panels in Figure 10). To reduce the dimensionality of the problem, in what follows we fix the proximity zone to the measured value (0.67 physical Mpc).¹² Even then a combined model of IGM+DLA with two free parameters is degenerate. To overcome this difficulty, we step through a number of IGM damping wing profiles using a fixed ${\overline{x}}_{{\rm{H}}{\rm{I}}}$ (blue dashed lines in Figure 10). Then we perform a least-squares regression to find the best DLA profile to match the data using as input the continuum already attenuated by the IGM. The result is that with a combined IGM+DLA model we always find a better fit to the absorption profile than using only a DLA. Because neutral IGM neutral fractions ${\overline{x}}_{{\rm{H}}{\rm{I}}}\gtrsim 0.4$ have only been reported at z ∼ 7.5 (Davies et al. 2018a; Hoag et al. 2019) we find that unlikely to be the case at z ∼ 6.4, which would also be in strong tension with constraints obtained toward other quasars and GRBs at comparable redshifts (e.g., Chornock et al. 2014; Melandri et al. 2015; Eilers et al. 2018). We assume as our fiducial scenario an IGM that is 10% neutral, in which case the best-fit DLA profile has a column density of $\mathrm{log}{N}_{\mathrm{HI}}=20.68$. Nonetheless, we note that the cases where the IGM neutral fraction ranges from 5 to 50% produce comparable good fits to the data (see Figure 10). We also note that ${\overline{x}}_{{\rm{H}}{\rm{I}}}=0$ cannot be completely ruled out as the step in flux around λ_rest ∼ 1214 Å could be reproduced if one includes a saturated but otherwise weak (e.g., $\mathrm{log}{N}_{\mathrm{HI}}\sim 15.5$) Lyα absorption in that region. Indeed, such absorption features are frequently seen in DLAs and PDLAs at lower redshifts (e.g., Prochaska et al. 2005, 2008). Our fiducial value with its conservative uncertainty, $\mathrm{log}{N}_{\mathrm{HI}}=20.68\pm 0.25$ (see Section 3.2), encompasses the best-fit N_HI values found for all cases where ${\overline{x}}_{{\rm{H}}{\rm{I}}}\lt 0.38$ (see Figure 11).

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