A High Space Density of Luminous Lyα Emitters at $z\sim 6.5$

Using AstroDrizzle (Gonzaga et al. 2012), we drizzle the IR direct images onto the UVIS pixel scale ($0\buildrel{\prime\prime}\over{.} 04$). We choose $0\buildrel{\prime\prime}\over{.} 04$ because drizzling all images onto the lower-resolution IR pixel scale ($0\buildrel{\prime\prime}\over{.} 13$) reduces the depth in the UVIS images, especially for small compact objects. This choice only affects the final drizzled images used for photometry. All other data reduction and cosmic-ray rejection is done on the original pixel scales.

Source detection and photometry are performed with Source Extractor in dual image mode using a combined detection image made from all HST images of the field. In detail, we first convolve the UVIS images with Gaussian kernels to match the resolution of the ${H}_{160}$ images. We then construct the detection image as the weighted average of the images in all four filters:

$$\begin{eqnarray}&&\displaystyle \frac{1}{n}\displaystyle \sum _{i}\displaystyle \frac{{I}_{i}}{\sqrt{{w}_{i}}}.\end{eqnarray} \tag{ 1 }$$

Combining the ${J}_{110}$ and ${H}_{160}$ images produces a deeper image than either individual filter and enables the detection of additional objects that would be missed by using a single filter for detection. The UVIS images are included in our detection image to ensure that there is adequate coverage of all pixels. As we cannot dither the telescope, we do not have sufficient exposures to cover all IR pixels at the $0\buildrel{\prime\prime}\over{.} 04$ pixel scale. As a result, the IR images drizzled to the UVIS pixel scale contain "bad" pixels that lack the information to have a reliable flux. These pixels have weights of zero, and we have confirmed that they do not affect the photometry.

We run Source Extractor twice for each UVIS filter: once on the original, unconvolved image, and once on the image convolved to match the resolution of ${H}_{160}$. The unconvolved UVIS images (at the original resolution) are deeper than those that have been convolved. The photometry calculated on the unconvolved images is therefore used to determine which sources are undetected in the UVIS filters. The photometry from the convolved images is used in calculating galaxy colors. We use circular aperture magnitudes with $r=0\buildrel{\prime\prime}\over{.} 3=7.5$ pixels to measure galaxy colors. All other analysis is done with Source Extractor's AUTO elliptical apertures.

Emission line candidates are identified using an automatic algorithm that selects groups of contiguous pixels above the continuum. Every candidate is then carefully inspected by two reviewers. This visual inspection is necessary to reject cosmic rays, hot pixels, and other artifacts and sources of contamination that could not be removed during image reduction due to the lack of dithering. In total, 2180 emission line galaxies have been identified in these 48 WISP fields. See Colbert et al. (2013) and Ross et al. (2016) for a detailed description of the WISP line-finding process.

While the WISP Survey is optimized to detect Hα and [O iii] emitters at $0.3\lt z\lt 2.4$, it is also well suited for the search for LAEs at $z\gt 6$. In the WISP emission line catalog, all single emission lines with no visible asymmetry are assumed to be Hα. However, there is the possibility that some of the faintest single-line emitters are actually LAEs at $z\geqslant 6$. Most of the exposure time in the longer WISP parallel opportunities is devoted to G₁₀₂ observations, enabling the grism images to reach the sensitivities necessary for detecting $z\gt 6$ emission lines. The observed equivalent width (EW) limit of the WISP Survey (40 Å, Colbert et al. 2013) corresponds to a low limit of ${\mathrm{EW}}_{0}=5.3\,$Å in the rest frame of a galaxy at z = 6.5. In Section 3, we describe how we select LAE candidates from the single-line emitters in the WISP emission line catalog.

The selection criteria, which we present in Section 3.2, aim to select single-line emitters with colors indicative of a Lyman break. We choose the criteria after minimizing the number of lower-z contaminants that enter the LAE sample. To do so, we create a large library of simulated spectral templates based on the models of Bruzual & Charlot (2003). From this library we generate a catalog of colors in the WISP bands for galaxies over $0.1\leqslant z\leqslant 8.5$. The synthetic catalog is described in Appendix A. We then use the synthetic catalog to determine the effect of varying three parameters: (1) the range of observed emission line wavelengths we consider, (2) the level of flux allowed in ${I}_{814}$, and (3) the location of the selection window in color space. In the following sections, we discuss each of these three parameters and their effect on the sample contamination. We define ${f}_{\mathrm{low} \mbox{-} z}$ as the number of lower-z galaxies selected by our criteria divided by the total number of selected galaxies: ${f}_{\mathrm{low} \mbox{-} z}={N}_{\mathrm{low} \mbox{-} z}/({N}_{\mathrm{high} \mbox{-} z}+{N}_{\mathrm{low} \mbox{-} z})$, where ${N}_{\mathrm{high} \mbox{-} z}$ is the number of galaxies at $6.00\leqslant z\leqslant 7.63$. Only lower-z galaxies in very specific redshift ranges can enter the sample and contribute to ${N}_{\mathrm{low} \mbox{-} z}$ (see Section 4 for details). The contamination fraction we expect for the WISP sample, denoted ${f}_{\mathrm{contam}}$, is much lower than ${f}_{\mathrm{low} \mbox{-} z}$ because we can use the broad wavelength coverage and typical emission line ratios from the WISP catalog to exclude lower-redshift interlopers. We discuss ${f}_{\mathrm{contam}}$ in Section 4. Likewise, the recovery fraction, ${f}_{\mathrm{recover}}$, is defined as the number of high-z galaxies selected by our criteria divided by the total number of high-z galaxies in the full synthetic catalog. The maximum ${f}_{\mathrm{recover}}$ achieved over the full parameter space is 0.9. We choose values for the three parameters that minimize ${f}_{\mathrm{low} \mbox{-} z}$ while keeping ${f}_{\mathrm{recover}}$ within 10% of this maximum.

3.1.1. Wavelength of Emission

3.1.2. Flux in ${I}_{814}$

3.1.3. Selection Window

Figure 1 shows the color–color plot used to identify $z\gt 6$ dropout galaxies. In choosing the selection criteria, we vary the shape and size of the color selection window, covering the range indicated by the dashed lines in Figure 1. The red limit in (${J}_{110}-{H}_{160}$) has the largest effect on both ${f}_{\mathrm{recover}}$ and ${f}_{\mathrm{low} \mbox{-} z}$. We consider windows as red as $({J}_{110}-{H}_{160})=1.3$ and choose 0.5 with ${f}_{\mathrm{recover}}=0.8$ and ${f}_{\mathrm{low} \mbox{-} z}=0.22$. Only 1% of the $z\lt 6$, UVIS-undetected galaxies in the selection window come from the lower right corner of our selection region. For simplicity, we therefore use a rectangular selection region rather than the more complicated windows used by, for example, Oesch et al. (2010) and Bouwens et al. (2015). The requirement for emission line detection in our sample removes any concern over contamination from this region.

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A WISP single-line emitter is identified as a $z\gt 6$ LAE candidate if and only if it

• 1.  
  has a single emission line at ${\lambda }_{\mathrm{obs}}\leqslant 1.05\,\mu {\rm{m}}$;
• 2.  
  is detected with a signal-to-noise (S/N) ratio in ${J}_{110}$ of ${({\rm{S}}/{\rm{N}})}_{{J}_{110}}\geqslant 5;$
• 3.  
  has colors consistent with those of a $z\geqslant 6$ galaxy:

  $$\begin{eqnarray}({I}_{814}-{J}_{110}) & \geqslant & 0.5,\\ ({J}_{110}-{H}_{160}) & \leqslant & 0.5;\end{eqnarray} \tag{ 2 }$$
• 4.  
  is undetected at the $1\sigma$ level in all available UVIS filters ("UVIS dropouts").

We derive the color selection criteria in Appendix A and identify it by the shaded region in Figure 1. These color criteria are comparable to those used in similar searches for $z\sim 6\mbox{--}7$ galaxies, such as Oesch et al. (2010), Schenker et al. (2013), and Bouwens et al. (2015), who employ color cuts of $(I-J)\gt 0.7-1$ and $(J-H)\lt 0.4-1$ in the same or similar filters as those used here.

We adopt the $1\sigma$ limiting magnitudes for all galaxies that are $1\sigma$ nondetections¹⁵ and plot them in Figure 1 as limits. Each LAE candidate is then inspected by eye to confirm the emission lines are real and the galaxy is truly undetected in the UVIS filters.

In the case that the Lyα emission line has been misidentified, it would likely be either Hα, [O iii], or [O ii] from lower-z galaxies. It is difficult to rule out Hα emitters based on the candidates' spectra because there are few emission lines detected redward of Hα in WISP spectra. From our synthetic catalog, however, we find that all galaxies in the redshift range in which Hα can enter our sample are detected in the UVIS images (see Figure 2). Therefore, we conclude that contamination from Hα is negligible.

For the remaining likely contaminants, [O iii] and [O ii] emitters, we look to the full WISP emission line catalog for information on the expected line ratios of galaxies at $z\lesssim 2$. The [O iii] doublet is blended at the resolution of the WFC3 grisms, so we use [O iii] to refer to [O iii] $\lambda \lambda 4959,5007$ in what follows. Similarly, Hα fluxes are not corrected for [N ii]. Figure 4 shows the Hα/[O iii] (left panel) and [O iii]/[O ii] (right panel) line ratios for sources in the WISP catalog. Here we consider all sources for which the bluer of the two emission lines lies in our wavelength selection range ($0.85\lesssim {\lambda }_{\mathrm{obs}}\leqslant 1.05\,\mu {\rm{m}}$). For example, if an emission line at ${\lambda }_{\mathrm{obs}}=0.9\,\mu {\rm{m}}$ is [O iii] instead of Lyα, then we would expect to detect Hα at ${\lambda }_{\mathrm{obs}}=1.18\,\mu {\rm{m}}$. The shaded areas in Figure 4 show the approximate regions of lower limits in the case where Hα (left) or [O iii] (right) are undetected in the WISP spectra. For both cases we adopt 2 × 10⁻¹⁷ erg s⁻¹ cm⁻² as the limiting line flux, which is the average line flux limit in the deep WISP fields.¹⁷ The line ratios for the z = 0.8 and z = 1.4 spectra plotted in Figure 3 are indicated in Figure 4 by orange and red squares, respectively, and are meant as illustrative examples for reference only.

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The median line flux ratios in the WISP catalog are Hα/[O iii] ∼ 1 and [O iii]/[O ii] ∼ 2.5, consistent with previous results from both individual galaxies (Mehta et al. 2015) and stacked WISP spectra (Domínguez et al. 2013; Henry et al. 2013). If the LAE candidates are lower-z contaminants, their line ratios would have to be extreme: Hα/[O iii] or [O iii]/[O ii] $\,\lesssim \,0.2$ for fluxes of ∼1 × 10⁻¹⁶ erg s⁻¹ cm⁻². In other words, if the single detected emission line is actually [O iii] ([O ii]), then Hα ([O iii]) must be a factor of $\gtrsim 5$ fainter to fall below our sensitivity.

As can be seen from the right panel of Figure 4, [O ii] emitters will not contaminate the LAE sample. At line fluxes of $f=1\times {10}^{-16}$ erg s⁻¹ cm⁻², virtually no galaxies have [O iii]/[O ii]$\,\lt \,0.2$. Because [O iii] is so much stronger than [O ii], we are guaranteed not to mistake [O ii] for Lyα. On the other hand, 2% of galaxies with $7\times {10}^{-17}\leqslant {f}_{[{\rm{O}}{\rm{III}}]}\,\leqslant 2\times {10}^{-16}$ erg s⁻¹ cm⁻² have Hα/[O iii]$\,\lt \,0.25$. Hence, contamination from [O iii] emitters is very rare but still a possibility.

There is always the possibility that hot pixels, cosmic rays, and other artifacts are masquerading as emission lines, although we expect only an ∼8.5% contamination rate due to false emission lines (Colbert et al. 2013). Due to the different dispersion solutions, the spectra do not fall on exactly the same pixels in G₁₀₂ and G₁₄₁. By comparing the full dispersed images in each grism, we performed a check for hot pixels, detector artifacts, and persistence that could have been incorrectly identified as emission lines. We also inspected each individual grism exposure to ensure that we are not detecting cosmic rays. Finally, we have checked that the emission lines in our sample are not zeroth orders from nearby objects. All galaxies in our sample lie sufficiently far from the right edge of the detector, so zero-order images are easily identified for their spectra.

Considering contamination from both lower-z and false emission lines, we expect the contamination fraction in the LAE sample to be no higher than ${f}_{\mathrm{contam}}\sim 2 \% \mbox{--}8 \%$.

We find two robust candidates according to the selection criteria described in Section 3: WISP368 at z = 6.38 and WISP302 at z = 6.44. Table 2 summarizes the spectroscopic and photometric properties. For both sources, a large fraction of the flux density in ${J}_{110}$ is due to the emission line, and we include this fraction, ${f}_{J110}^{\mathrm{neb}}/{f}_{J110}^{\mathrm{total}}$, in Table 2. We calculate the rest-frame EW of Lyα using the ${H}_{160}$ magnitudes for the continuum measurement, as the ${H}_{160}$ magnitudes are not contaminated by Lyα emission. In the case of WISP368, we adopt the $3\sigma$ ${H}_{160}$ magnitude limit. We also present the UV absolute magnitudes calculated at rest-frame wavelengths of 1500 Å and 2000 Å, corresponding to ${J}_{110}$ and ${H}_{160}$, respectively. The parameter M₁₅₀₀ is calculated using the ${J}_{110}$ magnitude corrected for the emission line flux. Still, M₁₅₀₀ is uncertain, so we do not calculate the UV slope β. Finally, we measure $3\sigma$ upper limits for He ii $\lambda 1640$ and C iii] $\lambda 1909$ fluxes.

Table 2.  Lyman Alpha Emitters

ID	R.A.	Decl.	${z}_{\mathrm{Ly}\alpha }$	${f}_{\mathrm{Ly}\alpha }$	EW0	${L}_{\mathrm{Ly}\alpha }$	${f}_{\mathrm{HeII}}$ a	${f}_{{\rm{C}}{\rm{III}}]}$ a
	(J2000)	(J2000)		$({10}^{-17}$ erg s−1 cm−2)	(Å)	(1043 erg s−1)	$({10}^{-17}$ erg s−1 cm−2)	$({10}^{-17}$ erg s−1 cm−2)
WISP302	02:44:54.72	−30:02:23.3	6.44	9.9 ± 5.8	798 ± 531	4.67	$\lt 6.0$	$\lt 4.3$
WISP368	23:22:32.26	−34:51:03.7	6.38	10.2 ± 3.9	$\lt 1172$	4.71	$\lt 3.9$	$\lt 2.8$
ID	${V}_{606}$ b	${I}_{814}$ b	${J}_{110}$ b	${f}_{J110}^{\mathrm{neb}}/{f}_{J110}^{\mathrm{total}}$	${H}_{160}$ b	M1500c	M2000
	(mag)	(mag)	(mag)		(mag)	(mag)	(mag)
WISP302	$\gt 27.86$	$\gt 27.49$	26.0 ± 0.11	0.67	26.1 ± 0.35	−19.6	−20.7
WISP368	⋯	$\gt 27.78$	26.3 ± 0.20	0.96	$\gt 27.67$	−17.0	$\gt -19.1$

Notes.

^aFlux limits are $3\sigma$. ^bTotal magnitudes as measured by Source Extractor's AUTO elliptical apertures. ^cM₁₅₀₀ is calculated using the ${J}_{110}$ magnitude corrected for the emission line flux.

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We present images of each candidate in Figure 5. The stamps are 3'' on a side and are each smoothed with a Gaussian kernel with $\sigma =1$ pixel. The candidates have dropped out of the UVIS filters: ${V}_{606}$ and ${I}_{814}$ for WISP302 and ${I}_{814}$ for WISP368.

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Figure 6 shows the one- and two-dimensional G₁₀₂ and G₁₄₁ spectra for each candidate. The Lyα emission lines are circled in white. Additional "emission features," identified in black in Figure 6, are present in the dispersed images of both objects. After careful examination of the images, we conclude that these features belong to nearby sources. The wavelengths of He ii $\lambda 1640$ and C iii] $\lambda 1909$ are also labeled.

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We use a Monte Carlo process to measure the line fluxes: we fit the line with a Gaussian, allow the flux at each wavelength step to vary within the uncertainties, and refit. The flux uncertainties in Table 2 are the $1\sigma$ dispersion in the distribution of measured fluxes.

There are three additional sources (black squares in Figure 1) that are too red to fall in our selection window yet meet all other criteria. As single-line emitters that drop out of the UVIS filters, these sources are worth further consideration. These three galaxies are small and compact and lie in the region of color space that contains a higher fraction of the dusty, red, lower-z galaxies in our synthetic library. Such galaxies may belong to a population of galaxies at $z\sim 1.5\mbox{--}1.8$ that are either very dusty or have strong 4000 Å breaks, causing them to mimic the broadband colors of the Lyman break. The emission line is most likely [O ii]. According to Maiolino et al. (2008), the observed limit of [O iii]/[O ii] ([O iii]/[O ii] ≲ 0.2–0.25) would imply high metallicities at these redshifts. Understanding the nature of these sources is very important but beyond the scope of this paper. We do not consider these three sources in our analysis and instead present their spectra and direct image stamps in Appendix B.

Given the two LAEs presented above, we calculate the number density as

$$\begin{eqnarray}&&{n}_{\mathrm{LAE}}=\sum _{i}\ {C}_{i}\ \displaystyle \frac{1}{{V}_{i}},\end{eqnarray} \tag{ 4 }$$

where C_i is an emission-line-dependent completeness correction, and V_i is the volume within which the emission line could be detected. The dominant sources of incompleteness in the WISP survey are (1) confusion from nearby objects and partially or fully overlapping spectra, and (2) the failure of the line-finding process to identify emission lines. Colbert et al. (2013) simulate the full emission line identification process and derive completeness corrections that depend on emission line EW and line flux S/N. We do not detect continua in the LAE spectra, so we use the completeness corrections appropriate for the highest-EW lines in the WISP catalog.

The WISP fields reach a range of depths. In determining V_i we use a modified version of the ${V}_{\mathrm{MAX}}$ method (Felten 1977) that depends on the G₁₀₂ sensitivity limit reached in each WISP field. The maximum volume within which a galaxy with the given absolute Lyα luminosity could be detected is

$$\begin{eqnarray}&&{V}_{\mathrm{MAX}}(\mathrm{LAE})=\sum _{i=1}^{{N}_{\mathrm{fields}}=48}\ {{\rm{\Omega }}}_{i}{\int }_{{z}_{L,i}}^{{z}_{U,i}}\displaystyle \frac{{dV}}{{dz}}{dz}.\end{eqnarray} \tag{ 5 }$$

Here, ${{\rm{\Omega }}}_{i}$ is the effective area of one WISP field (3.3 arcmin²); z_L is the lower redshift at which the galaxy's Lyα luminosity would fall below the G102 grism sensitivity, which cuts off steeply at the blue end; and z_U is the minimum of (1) the redshift at which the galaxy's line flux would fall below the sensitivity on the red side, and (2) the upper redshift limit set by our selection criteria, z = 7.63. The Lyα LF, however, is expected to evolve rapidly above z = 7. For the purposes of comparing our number counts with those of other studies at $z\sim 6.5$, we limit this maximum redshift to z = 7. We present an upper limit for the volume at $7.0\leqslant z\leqslant 7.63$ in Section 6.2.

The integration limits in Equation (5) are calculated for each of the 48 fields because the depth is not uniform across all fields. This corresponds to different redshift limits, z_U and z_L, and therefore different volumes probed in each field. Smaller effective volumes are probed in the shallower fields. In some cases, the emission line may not be detectable in a shallow field at any of the relevant redshifts.

Figure 7 shows a schematic representation of this process. As an example, two curves are plotted in gray showing the flux of a Lyα emission line as it would be observed if the galaxy were placed at a range of redshifts. The curves show the fluxes corresponding to ${L}_{\mathrm{Ly}\alpha }=2\times {10}^{43}$ erg s⁻¹ (dashed) and ${L}_{\mathrm{Ly}\alpha }=2.5\times {10}^{43}$ erg s⁻¹ (solid). In the first case, the emission line is too faint to be detected in this field at any redshift. In the second case, the redshifts at which the flux would drop below the grism sensitivity are marked by solid blue lines. The redshift limits in this field would be z_L = 6.31 and z_U = 7.00, where we fix z_U to calculate the effective volume at $z\sim 6.5$. For the volume calculation at $z\geqslant 7$, z_L = 7 and z_U = 7.63. Figure 8 shows the total effective volume calculated in all 48 WISP fields as a function of line luminosity. The total volume probed in WISP fields at the luminosity of the LAEs is $5.8\times {10}^{5}$ Mpc³ at $6\lesssim z\leqslant 7$. For comparison, the volumes covered by the $z\simeq 6.5$ ground-based narrowband surveys we consider in this paper are $1.5\times {10}^{6}$ Mpc³ (Hu et al. 2010), 8 × 10⁵ Mpc³ (Ouchi et al. 2010), $2.17\ \times {10}^{5}$ Mpc³ (Kashikawa et al. 2011), and $42.6\times {10}^{5}$ Mpc³ (Matthee et al. 2015). Extending the redshift range out to z = 7.63 would add another $\sim 2.2\times {10}^{5}$ Mpc³ to the WISP volume.

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We compare the number density of $z\sim 6.5$ LAEs in the WISP survey to measurements of the Lyα cumulative LF in Figure 9. The completeness-corrected number density calculated according to Equation (5) is plotted as the solid red circle. The observed number density—calculated without the completeness correction—is plotted as the smaller, open red circle. The uncertainty on n is plotted as the Poissonian error for small-number statistics and is taken from Gehrels (1986). The uncertainty on $\mathrm{log}({L}_{\mathrm{Ly}\alpha })$ is dominated by the large flux uncertainty of WISP302.

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The WISP LAEs are among the brightest discovered at these redshifts. Recently, a handful of comparably bright LAEs have been detected and spectroscopically confirmed in the COSMOS field. The two brightest, CR7 (Matthee et al. 2015; Sobral et al. 2015) and COLA1 (Hu et al. 2016), are plotted here in blue. The number density for CR7 is calculated using the full volume that Matthee et al. (2015) probe in the UDS, COSMOS, and SA22 fields, $42.6\times {10}^{5}$ Mpc³. Hu et al. (2016) cover an additional ∼2 deg² in COSMOS, which we roughly convert to a volume using the width of the narrowband filter NB921 the authors used to discover the bright LAEs. COLA1 was discovered in this additional area, which probed a combined volume of $\sim 58.6\times {10}^{5}$ Mpc³. In each luminosity bin, the open blue circles show the observed number densities. The closed blue circles are the number densities corrected for the shape of the NB921 filter profile using the luminosity-dependent correction factors presented in Matthee et al. (2015).

We plot the $z\sim 6.5$ cumulative LFs of Hu et al. (2010), Ouchi et al. (2010), Kashikawa et al. (2011), and Matthee et al. (2015) in Figure 9 and discuss this comparison in Section 6.1.

LAEs are expected to have extended Lyα emission. Lyα photons created in star-forming regions are resonantly scattered outward, creating large diffuse halos of extended Lyα emission (Zheng et al. 2010). At $z\geqslant 6$, where the surrounding IGM is partially neutral, the Lyα halo could extend as far as 1 Mpc from the galaxy (Zheng et al. 2011). Evidence for extended Lyα halos has been detected around galaxies at $z\sim 0$ (Hayes et al. 2014), $z\sim 2\mbox{--}3$ (e.g., Steidel et al. 2011; Matsuda et al. 2012), and $z=3\mbox{--}6$ (Wisotzki et al. 2016). At $z\geqslant 6$, these analyses are incredibly difficult to perform on individual galaxies, and narrowband images are almost always stacked (Momose et al. 2014).

In the two-dimensional WISP spectra extracted from the full grism images, spatial information is preserved along the cross-dispersion axis. We can therefore measure the spatial extent of Lyα emission around the LAEs in our sample. We create stamps of the 2D spectra around the emission line of each LAE. There are no continua detected in the spectra, but to be sure we fit the background row by row on either side of the emission line and subtract it out of the spectral stamp.

In each stamp, four columns of pixels (∼100 Å) centered on the emission line are collapsed along the wavelength direction. This results in a one-dimensional profile of the Lyα emission along the spatial axis, as shown in blue in Figure 10. In the same way we collapse the continuum image of the galaxy in ${J}_{110}$ and ${H}_{160}$ along the same axis and plot these profiles as solid and dashed lines, respectively. As WISP368 is not detected in ${H}_{160}$, we plot only the ${J}_{110}$ profile for this LAE. All profiles are normalized to the peak values for easy comparison of the profile shapes.

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We measure Lyα and continuum emission that are both equally compact, with FWHM of $\sim 0\buildrel{\prime\prime}\over{.} 4$. This corresponds to ∼2.2 kpc at these redshifts. Unfortunately, our measurements are limited by the depth of the WISP spectra. Extended Lyα emission may be present below our surface brightness limit. We discuss this possibility in Section 6.3.

The WISP survey is probing the most luminous LAEs at $z\geqslant 6$, a population that can provide important information about the state of the IGM at these redshifts. It is expected that the observed number density of LAEs decreases as the volume-averaged neutral hydrogen fraction of the IGM, ${x}_{\mathrm{HI}}$, increases. Upon encountering neutral hydrogen, photons at the Lyα resonance are scattered out of the line of sight. Drops in the observed number densities of LAEs from $z\sim 5.5\,\mathrm{to}\,7$ (e.g., Hu et al. 2010; Ouchi et al. 2010; Kashikawa et al. 2011) are often interpreted as evidence of an increasingly neutral IGM and indirect measurements of the end of reionization.

Lyα photons can escape from the surroundings of a galaxy during the epoch of reionization if the galaxy lies in an ionized bubble large enough to allow the photons to redshift out of resonance before encountering the neutral IGM at the edge of the H ii region. We can expect, then, to preferentially observe the most luminous LAEs—those capable of ionizing the largest bubbles—at earlier times during reionization (e.g., Matthee et al. 2015; Hu et al. 2016). As ${x}_{\mathrm{HI}}$ increases with redshift, Lyα emission from fainter galaxies—those that cannot create bubbles out to sufficiently large radii—will be increasingly suppressed. The more luminous galaxies are already surrounded by ionized media and so are less affected.

Recent studies have indicated that the observed number density of bright LAEs is relatively unchanged from $z\sim 6.5$ to z = 5.7 compared with that of the fainter LAEs (Matthee et al. 2015; Santos et al. 2016). This effect can be seen as a flattening of the Lyα LF at the bright end. Matthee et al. (2015) find that the bright end of the z = 6.6 Lyα LF is best fit by a power law, indicating that there are more bright LAEs than expected for a Schechter-like LF. In a continuation of the same survey, Santos et al. (2016) find that while there is a drop in the number densities of faint LAEs from z = 5.7 to z = 6.6, there is almost no evolution at the bright end. This result could indicate that the brightest galaxies already reside in ionized bubbles by $z\sim 6.5$. Remarkably, our results are consistent with the measurements of Matthee et al. (2015) and Santos et al. (2016).

Other studies show the opposite effect. Kashikawa et al. (2011) find a deficit of bright LAEs at z = 6.5 as compared with z = 5.7. Additionally, at z = 6.5, the number densities of bright LAEs measured by Hu et al. (2010), Ouchi et al. (2010), and Kashikawa et al. (2011) are all far below those of the WISP fields (see Figure 9). For example, Kashikawa et al. (2011) find only one LAE with ${L}_{\mathrm{Ly}\alpha }\gt {10}^{43}$ erg s⁻¹. This result, however, may be heavily influenced by cosmic variance. While Kashikawa et al. (2011) survey a much larger area (∼900 arcmin²) than that presented here (∼160 arcmin²), they cover only a single pointing in a narrow redshift range. Meanwhile, the 48 pure-parallel WISP fields presented in this paper are completely uncorrelated. We estimate that the cosmic variance in the WISP sample is $\lt 1$% (Trenti & Stiavelli 2008), compared with the ∼30% of Kashikawa et al. (2011). The 24%–34% decrease Kashikawa et al. (2011) find in the number density of LAEs from z = 5.7 to z = 6.5 may be due in part to cosmic variance. However, at log $({L}_{\mathrm{Ly}\alpha })\sim 43.5$, Matthee et al. (2015) observe a number density that is ∼100 times higher than that of Kashikawa et al. (2011), a difference that cannot be explained by cosmic variance alone. Enhanced clustering of LAEs introduced by reionization (e.g., McQuinn et al. 2007) could explain some of this observed difference.

We note that the surveys presented in Figure 9 have different EW limits, a situation that can affect the measured LFs (see, for example, the SED models presented by Konno et al. 2016). However, Ouchi et al. (2008) show through Monte Carlo simulations that when they consider all LAEs down to a rest-frame EW of ${\mathrm{EW}}_{0}=0$ Å, the normalization of the Schechter LF, ${\phi }^{* }$, increases by $\lesssim 10$% compared with that for EW limits of ${\mathrm{EW}}_{0}\sim 30\mbox{--}60$ Å. This exercise indicates that the $\sim 5\mbox{--}10$ Å difference between the EW limits of the WISP Survey and those of, for example, Ouchi et al. (2010) and Kashikawa et al. (2011) will have at most a minor effect on the number density of LAEs we observe. Additionally, given their fluxes and EWs, the WISP LAEs and those discovered by Matthee et al. (2015) at the bright end would have been easily detected in the narrowband surveys of Ouchi et al. (2010) and Kashikawa et al. (2011).

In Figures 9 and 12, we also compare our results to predictions from mock light cones based on the model of Garel et al. (2015) and adapted for the area and redshift range covered by the WISP fields. Garel et al. (2015) combine the GALICS semianalytic model with numerical simulations of Lyα radiation transfer through spherical, expanding shells of neutral gas and dust (Verhamme et al. 2006) to predict the emission of Lyα photons in high-redshift galaxies and their transfer in galactic outflows, ignoring the effect of IGM attenuation. GALICS describes the formation and evolution of galaxies within dark-matter halos extracted from a large cosmological simulation box (${L}_{\mathrm{box}}=100\,{h}^{-1}$ comoving Mpc). For each model galaxy, Garel et al. (2015) use scaling relations to connect the expansion velocity, column density, and dust opacity of the shell to the galaxy properties output by GALICS (see Garel et al. 2012 for more details). The Lyα line profiles and escape fractions are then estimated using the library of Lyα transfer models in shells presented in Schaerer et al. (2011).

The shaded regions in Figure 9 are the $1\sigma$ dispersion of the LF measured over 100 realizations of the mock light cones. The gray region, labeled ${f}_{\mathrm{esc}}^{\mathrm{Ly}\alpha }{L}_{\mathrm{Ly}\alpha ,\mathrm{intr}}$, shows the LF dispersion for mock light cones in which ${f}_{\mathrm{esc}}^{\mathrm{Ly}\alpha }$ is calculated as described above. We see that this model is in better agreement with the data of Hu et al. (2010), Ouchi et al. (2010), and Kashikawa et al. (2011), but it cannot reproduce the high number density of bright LAEs (log $({L}_{\mathrm{Ly}\alpha })\gtrsim 43.5$) found in the WISP survey or by Matthee et al. (2015).

We see from Figure 9 that the dispersion of the LFs estimated from the mock light cones is significant at the bright end, which provides hints to the cosmic variance expected in our survey. However, the $1\sigma$ dispersion from the mock light cones cannot be reconciled with our data point even within the error bars, so it seems unlikely that field-to-field variation is responsible for the difference between our LF measurement and the LF estimated from the mock light cones or from the other surveys. Nevertheless, we note that cosmic variance is underestimated in the mock light cones of Garel et al. (2015) because of the finite volume of the simulation box they use, which misses the fluctuations on the very large scales.

Another interpretation of the difference between our measurements and the predictions from Garel et al. (2015) could arise from the fact that they do not account for the growth of the HII bubbles during the epoch of reionization when dealing with the Lyα transfer. Instead, for all model galaxies, Lyα photons need to travel through outflows of neutral gas and dust (as described above), which unavoidably reduce their observed luminosities. Interestingly, we find that our observed number density lies close to the mean LF of the Garel et al. (2015) models in which ${f}_{\mathrm{esc}}^{\mathrm{Ly}\alpha }=1$ (the blue region, labeled ${L}_{\mathrm{Ly}\alpha ,\mathrm{intr}}$, in Figure 9). This might suggest that most Lyα photons can easily escape the bright WISP LAEs and that there is very little neutral hydrogen in their surrounding medium (see also Section 6.4).

The observed number density of the WISP LAEs is consistent with the density of the brightest LAEs detected to date at similar redshifts, CR7 and COLA1. The WISP number density is also consistent with that of model galaxies in a completely ionized IGM with ${f}_{\mathrm{esc}}^{\mathrm{Ly}\alpha }=1$. We expect the WISP LAEs, like CR7 and COLA1, to reside in highly ionized bubbles. Such bubbles would enhance the field-to-field variations in the observed number counts of LAEs and may also partially explain the differences at the bright end between the LFs in Figure 9. We discuss these bubbles in Section 6.4.

If the ionized bubbles are large enough that emission blueward of the Lyα line center is not suppressed by the damping wings of the neutral IGM, we may expect the WISP LAE Lyα line profiles to have blue wings. Line profiles with both blue and red emission peaks are predicted for galaxies with low neutral hydrogen column densities (e.g., Verhamme et al. 2015). Double-peaked emission is common among "green pea" galaxies (Henry et al. 2015) and has been tentatively detected in the spectra of COLA1 (Hu et al. 2016). The detection of blue wings is beyond the resolution of WISP spectra and is one goal of planned follow-up observations.

As Konno et al. (2016) point out, at z = 2.2 all LAEs with log $({L}_{\mathrm{Ly}\alpha })\gtrsim 43.4$ may be active galactic nuclei (AGNs). High-ionization emission lines such as C iv $\lambda 1549$, He ii $\lambda 1640$, and C iii $\lambda 1909$ can be useful in identifying AGNs. However, these strong UV nebular emission lines may also indicate galaxies with young, metal-poor stellar populations and large ionization parameters (Panagia 2005; Stark et al. 2014, 2015, 2016). At the redshifts of the WISP LAEs, C iv $\lambda 1549$ falls on the overlap region between G₁₀₂ and G₁₄₁, where the sensitivity in the WISP spectra decreases significantly. We instead measure upper limits for He ii $\lambda 1640$ and C iii] $\lambda 1909$ fluxes (see Table 2). The limits we measure on the line ratios with respect to Lyα are too uncertain to allow us to determine the dominant source of photoionization, and we cannot distinguish between AGNs, metal-poor galaxies, and normal star-forming galaxies (Schaerer 2003; Stark et al. 2014). The emission lines we detect are unresolved, and therefore the FWHM is less than ∼1500 km s⁻¹. Although we can rule out broad-line AGNs, this limit does not allow us to distinguish between narrow-line AGNs and star-forming galaxies. We also notice that the Lyα rest-frame EW for the WISP LAEs is many times larger than what Konno et al. (2016) observe for AGNs of similar UV magnitudes. Finally, neither Sobral et al. (2015) nor Hu et al. (2016) find strong evidence of AGN emission in the CR7 and COLA1 spectra, although the possibility of an AGN contribution remains. We cannot draw specific conclusions about the physical characteristics of the LAEs from the present WISP data.

Moving to higher redshifts, Konno et al. (2014) find a deficit at all luminosities at z = 7.3 compared to that at z = 6.6. This evolution of the Lyα LF may be the result of an increasing fraction of neutral hydrogen in the IGM during reionization. The authors also suggest that it could be due to the selective absorption of Lyα photons by neutral clumps in otherwise ionized bubbles. On the other hand, there have been several bright LAEs spectroscopically confirmed at $z\geqslant 7$ (e.g., Iye et al. 2006; Vanzella et al. 2011; Shibuya et al. 2012). Roberts-Borsani et al. (2016) recently discovered four galaxies at $z\sim 7\mbox{--}9$, all of which are emitting Lyα (Stark et al. 2016). With fluxes ${f}_{\mathrm{Ly}\alpha }\sim (0.7\mbox{--}2.5)\times {10}^{-17}$ erg s⁻¹ cm⁻², these $z\gt 7$ galaxies are all fainter than or on par with our detection limits.

We find no LAEs in the redshift range $7.0\lt z\lt 7.63$ in the volume covered by the WISP fields, $2.17\times {10}^{5}$ Mpc³. Assuming the Lyα LF does not evolve from z = 6.5 to z = 7, how many would we expect to observe? We calculate the expected number of LAEs at $7.00\leqslant z\leqslant 7.63$ given the four $z\sim 6.5$ LFs in Figure 9 and the volumes probed by the 48 WISP fields in this redshift range. In Equation (5), we limit the redshift range so that ${z}_{L,i}\geqslant 7$ and ${z}_{U,i}\leqslant 7.63$, covering a volume of $2.17\times {10}^{5}$ Mpc³. The results are plotted in Figure 11. The shaded region shows the luminosity range to which the WISP fields are sensitive. The edge of the region is plotted at the $3\sigma$ flux limit of the deepest field.

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At the median $3\sigma$ depth of the WISP fields (dashed black line), we would expect to detect 3.4 LAEs at $7\leqslant z\leqslant 7.63$ based on the Matthee et al. (2015) Schechter function LF (blue solid line). Given our nondetection at $z\geqslant 7$, we find that the probability that this z = 6.6 LF also applies at $z\geqslant 7$ is 3.3%. If we consider the authors' power-law fit to the bright end (dashed blue line), the expected number of $z\geqslant 7$ LAEs increases to 7.9, and the probability decreases to 0.037%. If either LF from Matthee et al. (2015) is representative at $z\sim 6.5$, we detect evolution in the Lyα LF from $z\sim 6.5$ to $z\gt 7$. However, given the LFs of Ouchi et al. (2010), Hu et al. (2010), and Kashikawa et al. (2011), we would expect to detect only 0.1–0.5 $z\geqslant 7$ LAEs. Our observations are inconclusive if these three LFs are more indicative of galaxy number densities at $z\sim 6.5$.

We next use the volume probed at $7\leqslant z\leqslant 7.63$ to place a limit on the observable yet undetected number density of LAEs over this redshift range. This limit is shown as a red arrow in Figure 12 and is calculated at the median 3σ depth of the WISP fields presented in this paper, $f=3.6\times {10}^{-17}$ erg s⁻¹ cm⁻². At z = 7.25, this corresponds to ${L}_{\mathrm{Ly}\alpha }=2.2\times {10}^{43}$ erg s⁻¹.

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The highly uncertain cumulative LF at z = 7.3 from Konno et al. (2014) is plotted in black. The gray symbols show the number densities of LAEs at $z\gtrsim 7$, including Iye et al. (2006) at $z=6.96$, Ota et al. (2010) at z = 7, Vanzella et al. (2011) at z = 7.008 and 7.109, and Shibuya et al. (2012) at z = 7.215. These number densities are as presented by Faisst et al. (2014), where the authors have accounted for the different cosmologies and corrections used in the individual surveys. The black circles show the weighted median that Faisst et al. (2014) calculate for these $z\geqslant 7$ surveys.

The WISP limit is consistent with the other $z\sim 7$ measurements. Comparing this upper limit with the number density of the WISP $z\sim 6.4$ LAEs and the z = 6.6 Matthee et al. (2015) LF, we again find evidence for a decrease in the number density of LAEs from $z\sim 6.5$ to $z\gtrsim 7$. This drop could be due to a higher neutral hydrogen fraction in the IGM. However, it could also at least in part be due to an evolution in the intrinsic properties of galaxies at these redshifts, such as in the escape fraction of Lyα photons (e.g., Dijkstra et al. 2014).

As in Figure 9, the shaded regions in Figure 12 show the $1\sigma$ dispersions of the Lyα LFs measured from 100 realizations of mock light cones. While still within the region corresponding to galaxies with ${f}_{\mathrm{esc}}^{\mathrm{Ly}\alpha }=1$, the WISP point is of course an upper limit.

The detection, or lack thereof, of extended Lyα emission around a galaxy can provide important information about the presence and properties of its surrounding neutral hydrogen. Lyα photons may escape from a galaxy if they have been redshifted out of resonance by scattering through a shell of expanding material (e.g., Verhamme et al. 2006). The scattering process acts to diffuse the Lyα photons outward from their point of origin. The extent of the resulting Lyα halo is an indirect probe of the fraction of neutral hydrogen present around the galaxy. Extended emission is expected to be common around galaxies surrounded by partially or mostly neutral hydrogen, while more compact emission is expected when the surrounding hydrogen is ionized (and therefore scattering is minimized). Extended Lyα emission has been detected at redshifts in the range $z\sim 0.03\mbox{--}6$. The 14 well-studied galaxies in the Lyα Reference Sample (LARS; Hayes et al. 2013, 2014; Östlin et al. 2014) have Lyα emission that is ∼3 times more extended than either their Hα or FUV emission. At z = 2.2, Momose et al. (2016) find scale lengths of Lyα halos ranging from $7\,\mathrm{to}\,16\,\mathrm{kpc}$, while Steidel et al. (2011) find evidence for Lyα halos extending out as far as 80 kpc at z = 2.6. At $z\sim 3.1$, Matsuda et al. (2012) detect Lyα halos out to $\geqslant 60\,\mathrm{kpc}$. Wisotzki et al. (2016) study a sample of galaxies at $3\leqslant z\leqslant 6$ and find the Lyα emission is more extended than the UV by a factor of 5–10. On the other hand, compact Lyα emission has been observed at both intermediate and high redshifts: $z\simeq 2.1$, 3.1 (Feldmeier et al. 2013); and $z\simeq 5.7$, 6.5 (Jiang et al. 2013). The observed compact emission could indicate that the galaxies at these redshifts are surrounded by highly ionized hydrogen, even at the end of reionization at $z\sim 6.5$.

It is likely, however, that measurements of compact Lyα emission such as those of Feldmeier et al. (2013) and Jiang et al. (2013) reflect the surface brightness limits of the observations (e.g., Steidel et al. 2011; Schmidt et al. 2016; Wisotzki et al. 2016) rather then the physical environments surrounding the galaxies. Guaita et al. (2015) redshift LARS galaxies to simulate observations of these galaxies at $z\sim 2$ and $z\sim 5.7$. By z = 5.7, the extended Lyα emission is only detected in stacked narrowband images, and the stacked Lyα profile drops below the surface brightness limit at ∼5 kpc. Repeating this process for galaxies at z = 7.2 for the Grism Lens-Amplified Survey from Space (GLASS), Schmidt et al. (2016) find that the surface brightness of the extended Lyα emission in LARS galaxies is too faint to be detected in their stacked spectra.

Both LARS and GLASS reach depths comparable to or slightly deeper than WISP: 3 × 10⁻¹⁸ erg s⁻¹ cm⁻² in the z = 5.7 simulated LARS spectra and $(3.5-5)\times {10}^{-18}$ erg s⁻¹ cm⁻² (observed, uncorrected for magnification) in the GLASS spectra. The WISP spectra are therefore only sensitive to the central, high-surface-brightness core of the Lyα emission. Indeed, the $1\sigma$ G₁₀₂ depths reached in the two WISP fields are $5.5\times {10}^{-17}$ erg s⁻¹ cm⁻² arcsec⁻², a factor of 550 times brighter than that reached by Wisotzki et al. (2016). We therefore do not draw conclusions from the compact Lyα profiles we measure. Instead, we suggest that the LAEs presented here are good candidates for targeted, deep follow-up observations aimed at exploring the extent of the Lyα halo at $z\sim 6.5$.

It is instructive to compare the observed Lyα luminosities with the intrinsic one, computed with basic assumptions on the stellar population of the WISP LAEs. We consider a range of parameters, including both Chabrier (2003) and Salpeter (1955) IMFs, metallicities of $Z/{Z}_{\odot }=0.005,0.02$ and 0.2, and ages from 10 Myr to 1 Gyr. Assuming Case B recombination, n_e = 100 cm⁻³, and ${T}_{e}={10}^{4}\,{\rm{K}}$, the intrinsic Lyα luminosity of a galaxy can be estimated from the production rate of ionizing photons as (e.g., Schaerer 2003)

$$\begin{eqnarray}&&{L}_{\mathrm{Ly}\alpha ,\mathrm{intr}}=C\ (1-{f}_{\mathrm{esc}})\ N\gamma ,\end{eqnarray} \tag{ 6 }$$

where $C=1.04\times {10}^{-11}$ erg, and ${f}_{\mathrm{esc}}$ is the escape fraction of ionizing photons. Note that $N\gamma$ can be computed by scaling the stellar population model to the observed ${H}_{160}$ magnitude (rest-frame 2000 Å, not contaminated by the Lyα emission). For reference, we adopt ${f}_{\mathrm{esc}}=0$ and perform this calculation for WISP302 only, since WISP368 is undetected in the ${H}_{160}$ continuum.

According to this model, and assuming the lowest metallicity covered by the BC03 models ($Z=0.005{Z}_{\odot }$) and an age of 10 Myr, WISP302 can produce $5.1\times {10}^{54}$ ionizing photons per second. The ratio of observed to intrinsic Lyα emission is therefore ∼0.9, implying that we are detecting almost all of the Lyα photons produced by this galaxy. More moderate parameter values result in an observed ${L}_{\mathrm{Ly}\alpha ,\mathrm{obs}}$ that is greater than the intrinsic ${L}_{\mathrm{Ly}\alpha ,\mathrm{intr}}$. Only models with a very young age and low metallicity produce a ratio ${L}_{\mathrm{Ly}\alpha ,\mathrm{obs}}/{L}_{\mathrm{Ly}\alpha ,\mathrm{intr}}\lt 1$.

This exercise suggests that these photons are not only able to escape from the galaxy's interstellar medium (ISM), but they are also not substantially attenuated by the surrounding IGM. In fact, local (i.e., where the IGM is not affecting the Lyα profile) analogs to high-z galaxies with large escape fractions of Lyα radiation are characterized by an emission line profile showing substantial flux blueward and close to the systemic velocity (Henry et al. 2015; Verhamme et al. 2015). The neutral IGM at $z\sim 6.5$ would attenuate this blue emission considerably, causing ${L}_{\mathrm{Ly}\alpha ,\mathrm{obs}}\ /{L}_{\mathrm{Ly}\alpha ,\mathrm{intr}}\lesssim 0.5$. Hence, we conclude that a sizable neutral fraction in the presence of this galaxy is unlikely. This conclusion is also supported by the agreement between the LF calculated from the intrinsic Lyα emission (Garel et al. 2015) and the high number density of WISP LAEs (see Figure 9).

It is possible that the stellar population of WISP302 is more extreme than our simple assumption. Both Pop III stars and models that include binaries have effectively harder spectra than typical Pop II stars and can produce a factor of up to ∼3 more ionizing photons than the spectral template discussed above (Schaerer 2002; Eldridge et al. 2008). A larger ${L}_{\mathrm{Ly}\alpha ,\mathrm{intr}}$ would imply a much lower ${L}_{\mathrm{Ly}\alpha ,\mathrm{obs}}/{L}_{\mathrm{Ly}\alpha ,\mathrm{intr}}$ ratio, removing the need for a fully ionized IGM around this object. We can search for evidence of extreme stellar populations in WISP302 by looking for the He ii $\lambda 1640$ Å emission line (Panagia 2005; Stanway et al. 2016) as well as other UV nebular emission lines (e.g., Stark et al. 2014).

The presence of dust could also reduce the ${L}_{\mathrm{Ly}\alpha ,\mathrm{obs}}/{L}_{\mathrm{Ly}\alpha ,\mathrm{intr}}$ ratio. If dust were present, ${L}_{\mathrm{Ly}\alpha ,\mathrm{intr}}$ would be higher than what we estimate from our simple dust-free model. At the absolute magnitude of WISP302, however, Bouwens et al. (2016) show that the correction for dust extinction is negligible ($\lt 0.2$ magnitude). As we cannot reliably measure the UV slope β, we rely on this estimate of dust extinction.

If extreme stars are not important, then the high ${L}_{\mathrm{Ly}\alpha ,\mathrm{obs}}/{L}_{\mathrm{Ly}\alpha ,\mathrm{intr}}$ ratio indicates that the IGM is mostly ionized around this galaxy. The current measurement of the Thomson optical depth from the cosmic microwave background radiation would allow for an end of the reionization process by as early as $z\sim 6.5$ (Robertson et al. 2015; Planck Collaboration et al. 2016a). However, if this were the case, we would expect bright galaxies such as the WISP LAEs to be more common. Therefore, it is more likely that objects like WISP302 reside in rare, localized bubbles of ionized gas.

We now investigate the sources that are needed to create a sufficiently large ionized bubble for the Lyα emission to escape the effects of the IGM damping wing. Lyα photons will be transmitted through the IGM if the optical depth they experience is ${\tau }_{\mathrm{IGM}}\lt 1$. Miralda-Escudé (1998) shows that the minimum radius required is ${R}_{\min }\sim 1.216$ proper Mpc. Following Cen & Haiman (2000), we can define ${R}_{\max },$ the maximum radius ionized over the course of WISP302's lifetime, as

$$\begin{eqnarray}&&{R}_{\max }={\left(\displaystyle \frac{3{N}_{\mathrm{ion}}}{4\pi \langle {n}_{{\rm{H}}}\rangle }\right)}^{1/3}.\end{eqnarray} \tag{ 7 }$$

Here, $\langle {n}_{{\rm{H}}}\rangle$ is the mean hydrogen density within ${R}_{\max }$, and ${N}_{\mathrm{ion}}$ is the total number of ionizing photons emitted. Note that ${N}_{\mathrm{ion}}$ can be expressed as the product of the rate of ionizing photons produced by the galaxy, the fraction of these that escape, and the galaxy's lifetime: ${N}_{\mathrm{ion}}={N}_{\gamma }\ {f}_{\mathrm{esc}}\ t$. We assume the same stellar population as above, but we consider a longer star formation episode (i.e., t = 100 Myr). This age will provide us with a conservative upper limit on the radius of the ionized region.

Following Stiavelli (2009), we calculate the hydrogen number density from the mean density of a virialized halo, ${\rho }_{\mathrm{vir}}$:

$$\begin{eqnarray}{\rho }_{\mathrm{vir}} & = & \xi \ {{\rm{\Omega }}}_{M}\ {\rho }_{0}\ {(1+z)}^{3}\\ {n}_{{\rm{H}}} & = & \displaystyle \frac{{\rho }_{\mathrm{vir}}\ {{\rm{\Omega }}}_{b}}{\mu \ {m}_{{\rm{p}}}\ {{\rm{\Omega }}}_{M}},\end{eqnarray} \tag{ 8 }$$

where $\xi \simeq 178$ is the ratio between the density of a virialized system and the matter density of the universe, $\mu \simeq 1.35$ is the mean gas mass per hydrogen atom and accounts for the contribution of helium, ${m}_{{\rm{p}}}$ is the mass of a proton, and we adopt ${{\rm{\Omega }}}_{b}{h}^{2}=0.0223$ (Planck Collaboration et al. 2016b). We find ${R}_{\max }\simeq 0.45{({f}_{\mathrm{esc}})}^{1/3}$ Mpc. Even if all of the ionizing photons escaped the galaxy's ISM (${f}_{\mathrm{esc}}=1$), the size would still be less than half of the minimum required radius, ${R}_{\min }.$

Clearly, WISP302 is not capable of ionizing a large enough bubble on its own. We consider two alternative sources for the needed ionizing photons: a population of faint galaxies, as in Vanzella et al. (2011) and Castellano et al. (2016), or a bright quasar close to the studied LAE but outside the WISP field of view.

We begin with the first possibility. From Equation (7) we find that at least $1.45\times {10}^{57}$ photons s⁻¹ are required to create a sufficiently large ionized bubble, where we have assumed an escape fraction of ${f}_{\mathrm{esc}}=0.1$. We next determine how many galaxies are needed to produce the required number of photons. To do so, we find the Lyα luminosity density by integrating

$$\begin{eqnarray}&&\int \ L\ \phi (L)\ {dL},\end{eqnarray} \tag{ 9 }$$

where $\phi (L){dL}$ is the LF, and we normalize by the observed number density of WISP LAEs. We then convert the Lyα luminosity density to a density of ionizing photons using Equation (6). Faint galaxies are the dominant source of ionizing photons, so we assume a simple power law LF and begin by considering a slope of $\alpha =-1.5$, matching the slopes plotted in Figure 9. In order to reach the requisite 10⁵⁷ photons s⁻¹, we must integrate Equation (9) down to ${L}_{\mathrm{Ly}\alpha }\sim 0.001{L}_{\mathrm{Ly}\alpha }^{* }$. This luminosity limit is on par with the minimum UV luminosities adopted by, for example, Robertson et al. (2015) and Rutkowski et al. (2016) in evaluating the contribution of star-forming galaxies to reionization. If we allow for a steeper faint-end slope such as $-2.3\lt \alpha \lt -2.0$ (e.g., Dressler et al. 2015), we need only integrate down to ${L}_{\mathrm{Ly}\alpha }\sim 0.04-0.1{L}_{\mathrm{Ly}\alpha }^{* }$. A substantial, but not unreasonable, number of faint galaxies is required to produce 10⁵⁷ ionizing photons in the volume. Alternatively, in the presence of an overdensity, an increase in the LF normalization could further relax the need for faint galaxies. These calculations strongly depend on the escape fraction of Lyman continuum photons in these high-z galaxies (e.g., Rutkowski et al. 2016; Smith et al. 2016; Vanzella et al. 2016).

We now consider the second possibility that WISP302 resides in a bubble ionized by a nearby quasar. For the same UV luminosity, quasars produce approximately an order of magnitude more ionizing photons than do star-forming galaxies. Moreover, the escape fraction of ionizing radiation is likely close to 100% (e.g., Loeb & Barkana 2001; Cristiani et al. 2016). For a single QSO to produce the required number of ionizing photons, it would need to be as bright as ${H}_{160}\sim 22$, not unreasonable given the luminosities of $z\gt 6$ QSOs observed by Fan et al. (2006). This object would be easily identified in the WISP survey, although none is detected in the region observed around WISP302. At z = 6.4, however, 1 Mpc corresponds to $\sim 3^{\prime}$. Thus, it is possible that the quasar falls outside the WFC3 field. At this redshift, the average baryonic density of the universe is such that the recombination time is of the order of the age of the universe and shorter than typical QSO lifetimes (Trainor & Steidel 2013). Once ionized, the bubble could then remain ionized after the QSO has turned off. Imaging and spectroscopy over a wider area around WISP302 are needed to investigate these possibilities.