Evidence for Large-scale Fluctuations in the Metagalactic Ionizing Background Near Redshift Six

We acquired deep HSC imaging of the field around J0148 from 2016 September and 2017 August, with the majority of data obtained in 2017. Imaging was performed in the r2, i2, and NB816 filters in dithered exposures centered on the quasar position. Total exposure times are listed in Table 1. The NB816 filter has a transmission-weighted mean wavelength of λ = 8177 Å, corresponding to Lyα at z = 5.726, and ≥50% peak transmission over 8122 Å < λ < 8239 Å, corresponding to 5.681 < z < 5.777.

Table 1.  Imaging Data Summary

Filter	texp	Seeinga	m5σb
	(hr)	(arcsec)	15	PSF	CModel
r2	1.5	0.62	26.5	27.5	27.4
i2	2.4	0.64	26.0	27.0	26.9
NB816	4.5	0.60	25.3	26.3	26.1

Notes.

^aMedian seeing FWHM across all source positions in the combined mosaic. ^bMagnitude at which 50% of detected sources detected have S/N ≥ 5. Values are given for fluxes within 15 circular apertures, as well as for PSF and CModel fluxes.

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The data were processed using the LSST Science Pipeline⁴ Version 13, release w_2017_28 (Axelrod et al. 2010; Jurić et al. 2015), with an implementation closely following the HSC Software Pipeline described in Bosch et al. (2018). The pipeline processes the individual CCDs and combines them into stacked mosaics. Pan-STARRS1 DR1 imaging (Chambers et al. 2016) was used for photometric and astrometric calibration. The pipeline also estimates the seeing parameters as a function of position. The median seeing in all bands was roughly 06 (Table 1).

The LSST pipeline performs a range of photometric measurements. For our analysis we used forced measurements, wherein the intrinsic spatial parameters of a source are determined from the band in which it is detected with the highest significance (typically NB816 for our sources). These parameters are then held fixed for other bands, and the model profile is convolved with the local point-spread function when measuring fluxes. This approach is useful for determining accurate colors of extended sources. Except where noted below, we adopt CModel magnitudes, which use a composite of the best-fit exponential and de Vaucouleurs profiles (Abazajian et al. 2004; Bosch et al. 2018). The median 5σ limiting CModel magnitudes are listed in Table 1. For reference, we also include 5σ limits for PSF magnitudes and for magnitudes measured within 1.5 arcsec apertures. The values in Table 1 are the magnitudes at which 50% of all detected sources have signal-to-noise ratios S/N ≥ 5. We verified that, for the circular aperture and PSF cases, these values are very similar (within 0.05 mag) to the limits directly measured at randomly placed positions within 40 arcmin of the field center that are free of sources. In all bands the sensitivity declines by  0.2 mag from the center of the field to a radius of 40 arcmin, then deteriorates rapidly at larger radii. The majority of our analysis is therefore confined to the inner 40 arcmin.

Before proceeding to the LAE selection, we note that our imaging data allow us to check the Lyα ${\tau }_{\mathrm{eff}}$ measurement along the J0148 line of sight. Here, we use PSF fluxes, since the object is known to be point-like. We measure a narrowband flux from the quasar of ${F}_{\lambda }^{{NB}816}=(1.9\pm 1.0)\times {10}^{-20},\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}\,\mathring{\rm A}$. We meanwhile measure an i2 flux from the quasar of ${F}_{\lambda }^{i2}\,=3.7\times {10}^{-18},\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}\,\mathring{\rm A}$, with negligible error. We use the i2 flux to scale the X-Shooter spectrum presented in Becker et al. (2015) by convolving the spectrum with the i2 transmission curve, and estimate an unabsorbed continuum flux at the NB816 wavelength of ${F}_{\lambda }^{\mathrm{cont}}=2.0\times {10}^{-17},\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}\,\mathring{\rm A}$. These measurements translate into an effective optical depth over the NB816 wavelength range of ${\tau }_{\mathrm{eff}}=-\mathrm{ln}({F}_{\lambda }^{{NB}816}/{F}_{\lambda }^{\mathrm{cont}})\,={6.94}_{-0.40}^{+0.68}$ (1σ), with a 2σ lower limit of τ_eff ≥ 6.26.⁵ These values are consistent with the 2σ limit of τ_eff ≥ 7.2 measured by Becker et al. (2015) for the 50 ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$ section centered at z = 5.796, which largely overlaps but is ∼70% longer than the NB816 passband.

Candidate z = 5.7 LAEs are selected to have a narrowband excess indicative of Lyα emission and an r2 − i2 color consistent with Lyα forest absorption by the IGM. Following Ouchi et al. (2008), we impose the following selection criteria:

$$\begin{eqnarray}&&\qquad \ i2-{NB}816\geqslant 1.2,\mathrm{and}\\ &&[(r2\gt 2{\sigma }_{r2})\,\mathrm{or}\,(r2\leqslant 2{\sigma }_{r2}\,\mathrm{and}\,r2-i2\geqslant 1.0)].\end{eqnarray} \tag{ 2 }$$

The narrowband excess is intended to identify line emitters, while the broadband criteria are used to avoid low-redshift interlopers. We note that we do not include an additional bluer filter (e.g., g or V), as done by Ouchi et al. (2008, 2018), Shibuya et al. (2018a), and Konno et al. (2018), that would further help to eliminate low-redshift sources. On the other hand, similar to Ouchi et al. (2008), we require all sources detected at more than 2σ in r2 to satisfy our r2−i2 cut. This is somewhat more restrictive than the 3σ threshold used by Ouchi et al. (2018), Shibuya et al. (2018a), and Konno et al. (2018). These factors may affect the contamination rate from lower-redshift interlopers. As discussed below, however, we do not expect our main findings to be significantly impacted because the contamination should be uniform across our field. Similar to Ono et al. (2018) and Shibuya et al. (2018a) we also select on a number of pipeline flags to avoid blended or contaminated sources. For a list of flags see Shibuya et al. (2018a). Sources are chosen to have NB816 ≤ 26.0 and S/N(NB816) ≥ 5, and to lie within 45' of the quasar position. Each source satisfying these criteria is visually inspected in the combined images. This check is used to reject uncorrected hot pixels and cosmic rays, rapidly moving objects that appear as trails in the combined images, noise features in the outskirts of bright objects, and other artifacts. For candidates passing this initial visual inspection, individual NB816 exposures are examined as a further check for moving or other spurious sources that appear in only one or a small subset of the exposures. In total, 806 LAE candidates pass our selection process. Their properties are summarized in Table 2. Cutout images for four of these objects, spanning a range of NB816 magnitude, are shown in Figure 2.

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Table 2.  Properties of LAE Candidates

ID	α	δ	NB816	${ \mathcal F }(r2)$	${ \mathcal F }(i2)$	${ \mathcal F }({\text{}}{NB}816)$	log LLyα
	(J2000)	(J2000)	(mag)	(mJy)	(mJy)	(mJy)	erg s−1
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
J014551+055853	01 45 51.453	+05 58 53.74	25.53	0.000 ± 0.016	0.036 ± 0.026	0.224 ± 0.035	${42.623}_{-0.073}^{0.062}$
J014553+061419	01 45 53.708	+06 14 19.60	25.00	0.031 ± 0.015	0.101 ± 0.024	0.362 ± 0.044	${42.832}_{-0.057}^{0.050}$
J014554+061920	01 45 54.792	+06 19 20.72	25.61	−0.004 ± 0.010	−0.000 ± 0.016	0.207 ± 0.030	${42.590}_{-0.067}^{0.058}$
J014556+060639	01 45 56.396	+06 06 39.90	25.89	0.012 ± 0.010	0.043 ± 0.018	0.161 ± 0.028	${42.479}_{-0.083}^{0.069}$
J014556+055250	01 45 56.989	+05 52 50.80	25.73	−0.010 ± 0.014	0.056 ± 0.017	0.186 ± 0.031	${42.542}_{-0.078}^{0.066}$
J014557+060459	01 45 57.299	+06 04 59.24	25.04	0.001 ± 0.012	0.002 ± 0.023	0.350 ± 0.039	${42.817}_{-0.052}^{0.046}$
J014557+061720	01 45 57.383	+06 17 20.58	25.48	0.008 ± 0.011	0.027 ± 0.015	0.233 ± 0.034	${42.640}_{-0.069}^{0.059}$
J014557+060324	01 45 57.545	+06 03 24.84	24.84	0.034 ± 0.011	0.096 ± 0.020	0.423 ± 0.031	${42.899}_{-0.033}^{0.031}$
J014557+060606	01 45 57.898	+06 06 06.41	24.97	0.024 ± 0.013	0.097 ± 0.020	0.373 ± 0.033	${42.844}_{-0.040}^{0.037}$
J014558+054525	01 45 58.048	+05 45 25.19	25.53	0.004 ± 0.011	0.020 ± 0.017	0.222 ± 0.035	${42.620}_{-0.075}^{0.064}$
J014558+061023	01 45 58.477	+06 10 23.17	25.24	−0.024 ± 0.010	0.011 ± 0.018	0.291 ± 0.030	${42.737}_{-0.046}^{0.042}$
J014559+054157	01 45 59.199	+05 41 57.48	25.83	−0.020 ± 0.010	−0.008 ± 0.015	0.169 ± 0.028	${42.502}_{-0.077}^{0.065}$
J014559+061720	01 45 59.492	+06 17 20.25	24.49	0.009 ± 0.014	0.046 ± 0.024	0.579 ± 0.036	${43.036}_{-0.028}^{0.026}$
J014559+054349	01 45 59.540	+05 43 49.56	25.45	0.014 ± 0.009	0.055 ± 0.013	0.241 ± 0.024	${42.655}_{-0.046}^{0.042}$
J014600+054322	01 46 00.030	+05 43 22.60	25.49	−0.009 ± 0.012	0.023 ± 0.016	0.231 ± 0.031	${42.637}_{-0.062}^{0.055}$
J014600+061908	01 46 00.132	+06 19 08.00	25.23	−0.039 ± 0.012	0.037 ± 0.021	0.295 ± 0.037	${42.743}_{-0.059}^{0.052}$
J014600+061505	01 46 00.497	+06 15 05.02	25.46	0.023 ± 0.009	0.060 ± 0.014	0.237 ± 0.026	${42.649}_{-0.051}^{0.046}$
J014600+054204	01 46 00.724	+05 42 04.68	25.70	−0.019 ± 0.012	0.016 ± 0.017	0.191 ± 0.030	${42.555}_{-0.075}^{0.064}$
J014600+060622	01 46 00.896	+06 06 22.00	25.90	0.000 ± 0.008	0.030 ± 0.015	0.158 ± 0.024	${42.472}_{-0.073}^{0.063}$
J014601+061112	01 46 01.607	+06 11 12.99	25.82	−0.011 ± 0.008	0.022 ± 0.014	0.170 ± 0.026	${42.504}_{-0.072}^{0.062}$

Note. (1) Identifier. (2) R.A. (3) decl. (4) NB816 magnitude. (5) r2 flux. (6) i2 flux. (7) NB816 flux. (8) Log Lyα luminosity. Lyα luminosities were computed by multiplying the observed NB816 flux by $4\pi {D}_{{\rm{L}}}^{2}$, where D_L is the luminosity distance at z = 5.726.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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The goal of this paper is to determine the relative density of LAEs near the quasar line of sight by self-consistently comparing this region to the outskirts of the HSC field. We therefore do not attempt to make a detailed completeness estimate that would be needed to determine a luminosity function. Nevertheless, we can compare our number counts to previous results from the literature. In Figure 3 we plot the surface density of LAE candidates in the J0148 field as a function of NB816 magnitude. Raw results are shown, along with results roughly corrected for completeness, where the completeness within each half magnitude bin is estimated as the fraction of all NB816 sources in that bin that meet our S/N ≥ 5 cut. For comparison, we plot the surface density of LAEs from the Subaru Suprime-Cam observations of Ouchi et al. (2008), and the shallower Hyper Suprime-Cam observations of Konno et al. (2018; previously described in Shibuya et al. 2018a), both corrected for completeness. Overall we find good agreement with the surface densities of these works, which gives us confidence in our selection process. We note that some level of contamination is expected in our sample. We address this in Section 3.3.

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The distribution of LAE candidates on the sky is shown in Figure 4. Symbols marking the location of LAE candidates are color-coded according to their NB816 magnitude. The dotted circles centered on the quasar position are drawn in increments of 10 ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$ projected distance. As noted above, our sensitivity is roughly constant out to Δθ ≃ 40' (R ≃ 66 ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$).

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We compute the surface density of LAEs in radial bins centered on the quasar position. We use 10 ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$ bins in all but the outermost annulus, which is truncated at 45' (74.5 ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$). Raw surface densities are corrected by a factor ${{\rm{\Sigma }}}_{{NB}816}^{\mathrm{all}}/{{\rm{\Sigma }}}_{{NB}816}^{R}$, where ${{\rm{\Sigma }}}_{{NB}816}^{R}$ is the number density of all narrowband sources (not just LAE candidates), with NB816 ≤ 26 and S/N ≥ 5 within a radial bin, and ${{\rm{\Sigma }}}_{{NB}816}^{\mathrm{all}}$ is the number density of narrowband sources meeting these criteria within Δθ ≤ 40'. These corrections, which are less than 10%, are meant to account for radial variations in sensitivity, as well as for missing areal coverage due to the presence of bright sources. Our results are summarized in Table 3, and the corrected surface density of LAE candidates is plotted as a function of radius in Figure 5. The dotted line shows the mean "background" surface density computed over 15' ≤ Δθ ≤ 40', which is 0.049 (${{\rm{h}}}^{-1}\,\mathrm{Mpc}$)⁻². The number density of LAE candidates is consistent with this value in all bins at R ≥ 20 ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$. Near the quasar position, however, the number density is significantly lower. We find only one candidate within 5 ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$ (30) of the quasar line of sight, and four within 10 ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$ (60), or roughly one-quarter of the background density.

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Table 3.  LAE Number Density

R	Δθ	NLAE	Correction	ΣLAE
(${{\rm{h}}}^{-1}\,\mathrm{Mpc}$)	(arcmin)			(${{\rm{h}}}^{-1}\,\mathrm{Mpc}$)−2
5.0 (0.0–10.0)	3.0 (0.0–6.0)	4	0.91	0.012 (0.006–0.021)
15.0 (10.0–20.0)	9.1 (6.0–12.1)	28	0.98	0.029 (0.024–0.036)
25.0 (20.0–30.0)	15.1 (12.1–18.1)	77	0.98	0.048 (0.043–0.054)
35.0 (30.0–40.0)	21.2 (18.1–24.2)	107	0.99	0.048 (0.044–0.054)
45.0 (40.0–50.0)	27.2 (24.2–30.2)	156	1.01	0.056 (0.051–0.061)
55.0 (50.0–60.0)	33.2 (30.2–36.3)	146	1.00	0.042 (0.039–0.046)
65.0 (60.0–70.0)	39.3 (36.3–42.3)	191	1.02	0.048 (0.044–0.051)
72.2 (70.0–74.5)	43.7 (42.3–45.0)	97	1.10	0.053 (0.048–0.059)

Note. Values in parentheses for R and Δθ give the range subtended by each annual bin. Surface densities are computed as Σ_LAE = Correction × N_LAE/Area. The correction factor roughly accounts for sensitivity variations and loss of areal coverage due to bright sources. Values in parentheses for Σ_LAE are corrected 68% Poisson intervals.

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We can assess the significance of the underdensity of LAE candidates around the quasar in two ways. In terms of Poisson statistics, for a background number density of 0.049 (${{\rm{h}}}^{-1}\,\mathrm{Mpc}$)⁻², the expected number of detections within 10 (20) ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$ is 15.3 (61.2), and the probability of detecting 4 (28) or fewer candidates is 7 × 10⁻⁴ (3 × 10⁻⁵). These values ignore the somewhat higher sensitivity at the center of the field, but they also ignore clustering. For randomly placed circular apertures of radius 10 (20) ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$ that fall entirely within 40' of the quasar position, the fraction containing at most 4 (32) candidates is 0.037 (0.027). The low density of LAE candidates within 20 ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$ of the line of sight toward J0148 therefore appears to be highly significant.

To better visualize the spatial distribution of LAE candidates, we create a source density map. To do this, we superimpose a regular grid of 0.4 ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$ (024) pixels onto the map of LAE candidates shown in Figure 4. At each grid point, we find the distance, d₁₀, to the tenth nearest candidate. This distance is converted into a source surface density as ${{\rm{\Sigma }}}_{\mathrm{LAE}}\propto {d}_{10}^{-2}$. The Σ_LAE values are normalized by their mean value, and the grid is smoothed using a Gaussian kernel of σ = 2.0 ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$. Finally, we truncate the map at Δθ = 40' to exclude regions with lower sensitivity. The result is shown in Figure 6. The quasar line of sight passes near the center of an elongated low-density region that extends roughly 40 ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$ north–south and 20 ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$ east–west. This is another indicator that the extreme Gunn-Peterson trough toward J0148 is associated with a region that is highly underdense in LAEs.

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We now turn to comparing our results to predictions from models for the large spread in IGM Lyα opacities near z ∼ 6. Here, we consider the UVB fluctuation model of Davies & Furlanetto (2016) and the temperature fluctuation model of D'Aloisio et al. (2015), in which deep Gunn-Peterson troughs such as the one toward J0148 arise in underdense and overdense regions, respectively. In this section, we briefly describe the implementation of these models in Davies et al. (2018) and their predictions for LAEs in the J0148 Gunn-Peterson trough. We also consider a model in which strong UVB fluctuations are driven by rare, bright sources (QSOs), as in Chardin et al. (2015, 2017).

The UVB and temperature fluctuations were computed in a volume 546 ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$ on a side, using the semi-numerical reionization code 21cmFAST (Mesinger et al. 2011) to compute the density field and dark matter halo distributions (minimum halo mass of 2 × 10⁹ M_⊙). For the galaxy UVB model, ionizing luminosities were assigned to dark matter halos via abundance matching to the Bouwens et al. (2015; non-ionizing) UV luminosity function, allowing the ratio of ionizing to non-ionizing luminosities to be a free (but uniform) parameter that is later chosen to produce a predetermined mean H i photoionization rate. The UVB was then computed on a coarse 156³ grid with a spatially fluctuating mean free path of ionizing photons following the method of Davies & Furlanetto (2016), assuming an average mean free path of 10.5 ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$. As noted above, this is roughly a factor of three smaller than would be expected from a naive extrapolation of lower-redshift values (Worseck et al. 2014), although it is possible that some of the highest-redshift (z ∼ 5) direct measurements are biased high (D'Aloisio et al. 2018).

Motivated by the possibility of a QSO-dominated UVB (Giallongo et al. 2015; Chardin et al. 2017, but see McGreer et al. 2018; Parsa et al. 2018), here we extend the modeling framework of Davies et al. (2018) to include a simple QSO model of UVB fluctuations. In this model we abundance-matched⁶ dark matter halos to QSOs from the Giallongo et al. (2015) luminosity function and assumed the Lusso et al. (2015) QSO spectrum to compute their ionizing luminosities, with zero contribution to the UVB from galaxies. We note that this is in some sense a more extreme QSO model than the one used by Chardin et al. (2017), who included a minor contribution from galaxies. We choose an average mean free path of 42 ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$, which is much longer than the one in our galaxy model, to reproduce the measured UVB strength at z ∼ 5.7 (D'Aloisio et al. 2018). As in the galaxy UVB and Chardin et al. (2017) QSO models, the mean free path varies spatially, scaling with the local H i ionization rate, Γ_{H i}, and the overdensity, ${\rm{\Delta }}=\rho /\bar{\rho }$, as ${\lambda }_{\mathrm{mfp}}\propto {{\rm{\Gamma }}}_{{\rm{H}}\,{\rm{I}}}^{2/3}{{\rm{\Delta }}}^{-1}$. Finite lifetime effects may play a large role in the structure of the radiation field (e.g., Croft 2004; Davies et al. 2017), but for computational simplicity and consistency with Chardin et al. (2017), we assumed a static QSO population. Example slices through the galaxy UVB and QSO UVB radiation fields are shown in Figure 7.

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To model temperature fluctuations, we used 21cmFAST to compute a reionization redshift field (mean z_reion = 8.8; see Figure 3 in Davies et al. 2018), and then assumed that the gas in each cell is heated to T_reion = 30,000 K at its corresponding reionization redshift. The subsequent thermal evolution of each cell, predominantly cooling via inverse Compton scattering off of CMB photons and through adiabatic expansion, was then integrated from its reionization redshift to z = 5.7 following a method similar to Upton Sanderbeck et al. (2016). The temperatures are illustrated in Figure 7.

The opacity of the Lyα forest was computed for 1,000,000 50 ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$ skewers in each model using the fluctuating Gunn-Peterson approximation (Weinberg et al. 1997) with optical depths re-scaled to reproduce the median effective optical depth of the Lyα forest on 50 ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$ scales at z = 5.7 (τ_eff ∼ 3.5). All three models, including our new QSO UVB model, generally reproduce the distribution of observed τ_eff from Becker et al. (2015) (Figure 8).

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To predict the distribution of LAEs in these simulations, we assigned Lyα equivalent widths to galaxies using the probabilistic prescription presented in Dijkstra & Wyithe (2012). Galaxies were assumed to have a fixed UV spectrum ${F}_{\lambda }\propto {\lambda }^{-2}$, a narrow Lyα emission line, and a cutoff at wavelengths shorter than rest-frame Lyα due to the onset of Lyα forest absorption. We then selected LAEs in mock narrowband observations using the same filters and color cuts as Ouchi et al. (2008). We chose a UV spectral index of β = 2 to be consistent with typical UV-selected galaxies at z ∼ 6 (Bouwens et al. 2014), but we note that LAEs may have somewhat bluer UV continua (β = −2.9 ± 1.0, Ono et al. 2010; β ∼ −2.3, Jiang et al. 2013). Due to the relatively short wavelength coverage of the i2 filter and our EW-based prescription for the Lyα line strengths, a bluer UV continuum would only change the narrowband excess of our simulated LAEs by a few percent, so we do not expect our predictions to be sensitive to this assumption.

As discussed in Dijkstra & Wyithe (2012), there is a moderate inconsistency in their approach that tends to overproduce the total number of LAEs. To adjust for this, we discard a random ∼50% of the selected LAEs, thereby matching the normalization of the Ouchi et al. (2008) LAE luminosity function. Due to the large number of LAEs in the simulation, and the large volume probed by our mock observations, our predictions for the LAE distributions are insensitive to the random seed used to discard potential LAEs.

In Figure 9 we compare the model predictions for the radial distribution of LAEs in fields with τ_eff > 7 to our observations of the J0148 field. Surface densities as a fraction of the mean are shown in order to minimize the impact of observational incompleteness and uncertainties in the model normalizations. Overall, we find excellent agreement with the predictions of the galaxy UVB model, with the observations closely following the expected decrease in surface density close to the QSO line of sight. Such a strong decrease is not generally expected for the QSO model, in which UVB and density fluctuations are less tightly coupled; however, our innermost data point still falls within the 95% expected bounds. In contrast, the temperature model appears strongly disfavored. Whereas an upturn in galaxy density is expected near the quasar line of sight, the opposite trend is observed.

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At face value, the results presented here support a picture wherein high IGM Lyα opacity near z ∼ 6 occurs in low-density regions. As discussed above, this is consistent with a model wherein large-scale opacity fluctuations are created by spatial variations in the UVB, and disfavors a scenario wherein the opacity fluctuations are due mainly to temperature variations. While this conclusion may seem straightforward, however, it is worth considering a few caveats.

Our basic observational result is that the projected surface density of LAE candidates around the quasar line of sight is significantly lower than the "background" density at larger radii. This is a self-consistent comparison and should be robust to incompleteness, provided that our selection efficiency for LAE candidates is roughly constant across the field. Given that the correction factors listed in Table 3 are close to unity at all radii, this is probably close to the truth. As in all narrowband surveys for high-redshift LAEs, our sample will be contaminated at some level by low-redshift interlopers and other spurious sources. Shibuya et al. (2018b) estimated a low (∼8%) contamination rate based on spectroscopic follow-up of z = 5.7 LAE candidates selected using criteria similar to those used here, although the spectroscopically confirmed sources are all brighter than NB816 = 25.3, 0.7 mag brighter than our faintest sources. As long as contaminants do not dominate our sample (which seems unlikely, given our broad agreement with the Ouchi et al. (2008) number densities), contamination should not significantly affect our fundamental result. If the contaminants are distributed randomly in the field, then removing the contaminants would tend to decrease the surface density of sources by the largest fraction in regions where the total source density is low. This would tend to enhance the deficit of LAEs around J0148. The contaminants are unlikely to trace the spatial distribution of genuine LAEs. Nevertheless, we can evaluate the potential impact of contaminants in this case. In trials where we randomly reject 30% of all sources as interlopers, the fraction of randomly placed 20 ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$ radius apertures that contain a number of enclosed sources less than or equal to the number of sources within 20 ${{\rm{h}}}^{-1}\,\mathrm{Mpc}$ of the quasar position is ≲7% in 95% of trials. The deficit of LAE candidates around the quasar is therefore likely to be robust to high levels of contamination, even in this unphysical scenario.

A second possible concern is how accurately LAEs trace the underlying density field on these scales. In imaging of two high-redshift quasar fields, Díaz et al. (2014) found that the spatial distribution of narrowband-selected LAEs at z = 5.7 is not well matched by the distribution of broadband-selected Lyman Break Galaxy (LBG) candidates chosen to lie near z ∼ 5.7. Ota et al. (2018) found a similar result for LAEs at z = 6.6 and z > 6 LBGs in the field of a high-redshift quasar. Without the spectroscopic redshifts of the broadband-selected objects, however, it is difficult to know how closely these populations overlap in redshift space. Our baseline assumption is that galaxies that intrinsically emit Lyα radiation trace the underlying density field on large (≳Mpc) scales. This should be true even if LAEs typically reside in lower-mass halos than UV-selected LBGs at the same redshift (e.g., Ouchi et al. 2010; Bielby et al. 2016).

Perhaps a more serious concern is whether Lyα emission from galaxies could be suppressed in the vicinity of a deep Gunn-Peterson trough. After all, we selected this region because it exhibited very strong Lyα absorption along the quasar line of sight. It is therefore worth asking whether galaxy Lyα emission could also be strongly extinguished. There is strong evidence that the fraction of star-forming galaxies with detectable Lyα emission declines at z > 6 (Fontana et al. 2010; Treu et al. 2013; Pentericci et al. 2014; Schenker et al. 2014; Tilvi et al. 2014). This decline is typically attributed to scattering by neutral gas along the line of sight, an indication of ongoing reionization (e.g., Bolton & Haehnelt 2013; Mesinger et al. 2015; Mason et al. 2018). In principle there could be remaining patches of neutral gas near z ∼ 5.7 along the J0148 line of sight. We note, however, that the quasar spectrum shows transmission in the Lyβ forest, which requires a highly ionized IGM, near the central redshift of the NB816 filter (Figure 1). An explanation for the lack of LAEs in this region that appeals to neutral gas in the IGM would also need to explain this transmission.

Alternatively, a locally low UVB could enhance the apparent deficit of sources by making LAEs more difficult to detect. If the UVB is highly suppressed, then dense circumgalactic gas may become increasingly neutral. This would tend to scatter Lyα out to larger galactic radii, decreasing its surface brightness (e.g., Sadoun et al. 2017; Weinberger et al. 2018). In this scenario, the striking deficit of LAEs around the J0148 line of sight could be due to a lower-than-average number density of galaxies combined with Lyα suppression. In principle, we can test this possibility by conducting a separate survey for continuum-selected galaxies. Such a search would need to be deep enough to detect a sufficient number of sources to probe the density field, and would need photometric redshifts (or spectroscopic redshifts from lines other than Lyα) that were sufficiently accurate to identify galaxies within the redshift range of the NB816 filter and/or the full J0148 absorption trough. As shown by Davies et al. (2018), the ability to probe the entire length of the trough means that a survey for continuum-selected galaxies could provide an even stronger test of the ${\tau }_{\mathrm{eff}}$ fluctuation models than the LAE results presented here.