SILVERRUSH. XII. Intensity Mapping for Lyα Emission Extending over 100–1000 Comoving Kpc around z ∼ 2−7 LAEs with Subaru HSC-SSP and CHORUS Data

We use NB and broadband (BB) imaging data that were obtained in two Subaru/HSC surveys, HSC-SSP and CHORUS. The HSC-SSP and CHORUS data were obtained in 2014 March–2018 January and 2017 January–2018 December, respectively. We specifically use the internal data of the S18A release. The HSC-SSP survey is a combination of three layers: Wide, Deep, and UltraDeep (UD). We use the UD layer images in the fields of the Cosmological Evolution Survey (UD-COSMOS; Scoville et al. 2007) and Subaru/XMM Deep Survey (UD-SXDS; Sekiguchi et al. 2005) because the wide survey areas (∼2 deg² for each field) and deep imaging (the 5σ limiting magnitudes are ∼26 mag in a 2'' diameter aperture) in these fields are advantageous for the detection of very diffuse Lyα emission. The CHORUS data were obtained over the UD-COSMOS field. The HSC-SSP and CHORUS data were reduced with the HSC pipeline v6.7 (Bosch et al. 2018).

The HSC-SSP provides the data of two NB (NB816 and NB921) filters in the UD-COSMOS and UD-SXDS fields, while the CHORUS images are offered in four NB (NB387, NB527, NB718, and NB973) filters in the UD-COSMOS field. In this work, we present the results in the NB387, NB527, NB816, and NB921 filters. The NB718 and NB973 filters are not used in the following sections because the number of LAEs and the image depths are not sufficient to detect diffuse Lyα emission. The NB387, NB527, NB816, and NB921 filters are centered at 3863, 5260, 8177, and 9215 Å with the full widths at half maximum (FWHMs) of 55, 79, 113, and 135 Å, respectively, which cover the observed wavelengths of Lyα emission from z = 2.178 ± 0.023, 3.327 ± 0.032, 5.726 ±0.046, and 6.580 ± 0.056, respectively. Five BB (g-, r2-, i2-, z-, and y-band) filters are also available in both HSC-SSP and CHORUS. Figure 1 shows the NB and BB filter throughputs, and Table 1 summarizes the images and filters.

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Bright sources in the NB and BB images must be masked, since they contaminate diffuse emission. We thus mask pixels flagged with either DETECT or BRIGHT_OBJECT using the masks provided by the HSC pipeline (termed original masks). A pixel is flagged with DETECT or BRIGHT_OBJECT when the pixel is covered by a detected (≥5σ) object or affected by nearby bright sources, respectively. However, because some bright sources are missed in the original masks due to bad photometry, the HSC-SSP team offered new masks that mitigated this problem (hereafter termed revised masks). ¹⁸ The revised mask is defined based on the bright stars cataloged in the Gaia Data Release 2 (Gaia Collaboration et al. 2018). We find that the stars brighter than ∼18 mag are masked. We adopt the revised masks in addition to the original masks to flag BRIGHT_OBJECT. We use the revised g-, r2-, z-, and y-band masks for the NB387, NB527, NB816, and NB921 images, respectively, because the revised masks are offered only in the BB filters. For the BB images, we use the revised masks defined for each BB filter. We visually confirm that these criteria successfully cover bright sources and contaminants in the images.

We use the LAE catalog of Ono et al. (2021). They selected LAE candidates based on color and removed contaminants by a convolutional neural network (CNN) and visual inspection. Their final catalog includes (542, 959, 395, 150) LAEs at z = (2.2, 3.3, 5.7, 6.6) in the UD-COSMOS field and (560, 75) LAEs at z = (5.7, 6.6) in the UD-SXDS field.

The NB images of the UD-COSMOS and UD-SXDS fields are deepest at the center and become shallower toward the edges (Hayashi et al. 2020; Inoue et al. 2020). We thus exclude LAEs outside of the boundaries shown with the black dashed circles in Figures 2 and 3. The boundaries are defined such that the limiting magnitudes outside are shallower than those at the center by ∼0.2 mag.

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We estimate the Lyα line luminosities (L_Lyα ) following Shibuya et al. (2018; see also Itoh et al. 2018). First, we measure the NB (BB) magnitudes m_NB (m_BB) of the LAEs at z = 2.2, 3.3, 5.7, and 6.6 in the NB387 (g-band), NB527 (r2-band), NB816 (z-band), and NB921 (y-band) filters, respectively. The magnitudes are measured with a 2'' diameter aperture because it efficiently covers the point-spread function (PSF), whose FWHM is 08–11 (Ono et al. 2021). The NB387 magnitudes are corrected for the systematic zero-point offset by 0.45 mag, following the recommendation by the HSC-SSP team. ¹⁹ Next, we follow Shibuya et al. (2018) to derive the Lyα line fluxes (f_Lyα ) from m_NB and m_BB, assuming a flat UV continuum and the IGM attenuation model of Inoue et al. (2014). Lastly, the values of L_Lyα are derived via L_Lyα = 4πd_L(z_LAE)²f_Lyα , where d_L(z_LAE) denotes the luminosity distance to the LAE at redshift z_LAE.

Although the completeness of the LAEs is as high as ≳90% at m_NB ≲ 24.5 in the CNN of Ono et al. (2021), faint LAEs may be missed in the observations and selection. To ensure completeness, we use only LAEs whose L_Lyα values are larger than the modes (peaks) of the L_Lyα histograms, which are represented as L_Lyα ^min in Table 2. This sample, termed the all sample, consists of (289, 762, 210, 56) LAEs at z = (2.2, 3.3, 5.7, 6.6) and (199, 24) LAEs at z = (5.7, 6.6) in the UD-COSMOS and UD-SXDS fields, respectively. To accurately compare the LAEs of different redshifts at similar L_Lyα values, we further exclude faint LAEs from the all sample such that the mean L_Lyα values are equal to 10^42.9 erg s⁻¹ at each redshift. This selection results in (37, 123, 125) LAEs at z = (2.2, 3.3, 5.7) and 88 LAEs at z = 5.7 in the UD-COSMOS and UD-SXDS fields, respectively, which we hereafter refer to as the bright subsample. At z = 6.6, since the mean L_Lyα values of the all sample are 10^43.0 erg s⁻¹ in both the UD-COSMOS and UD-SXDS fields, we also use the all sample as the bright subsample. In summary, we use a total of 1540 and 453 LAEs in the UD-COSMOS+UD-SXDS fields as the all sample and the bright subsample, respectively. The L_Lyα values and sample sizes are summarized in Table 2. The sky distributions of the LAEs in the UD-COSMOS and UD-SXDS fields are presented in Figures 2 and 3, respectively.

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Table 2. Summary of the Sample

	UD-COSMOS				UD-SXDS
zLAE	log LLyα min	$\mathrm{log}{L}_{\mathrm{Ly}\alpha }^{\mathrm{mean}}$	NLAE		$\mathrm{log}{L}_{\mathrm{Ly}\alpha }^{\min }$	log LLyα mean	NLAE		NLAE,total
	(erg s−1)	(erg s−1)			(erg s−1)	(erg s−1)
(1)	(2)	(3)	(4)		(5)	(6)	(7)		(8)
All Sample
2.2	42.2	42.5	289		⋯	⋯	⋯		289
3.3	42.1	42.5	762		⋯	⋯	⋯		762
5.7	42.6	42.8	210		42.2	42.8	199		409
6.6	42.8	43.0	56		42.9	43.0	24		80
NLAE,total			1317				223		1540
Bright Subsample
2.2	42.6	42.9	37		⋯	⋯	⋯		37
3.3	42.6	42.9	123		⋯	⋯	⋯		123
5.7	42.7	42.9	125		42.7	42.9	88		213
6.6 a	42.8	43.0	56		42.9	43.0	24		80
NLAE,total			341				112		453

Notes. Columns: (1) Redshift. (2) and (3) Minimum and mean Lyα luminosity of the all sample (top) and bright subsample (bottom) in the UD-COSMOS field, measured with a 2'' diameter aperture. (4) Number of LAEs. The total number of LAEs over z = 2.2–6.6 is shown in the bottom row. (5)–(7) Same as columns (2)–(4) but for the UD-SXDS field. (8) Total number of LAEs at each z.

^a At z = 6.6, we also treat the all sample as the bright subsample in each field (see Section 2.2).

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A major update of our data compared to Kakuma et al. (2021) is that we add 1051 new LAEs at z = 2.2 and 3.3 using the CHORUS data. The catalog of z = 5.7 and 6.6 LAEs is also updated in that we use the latest catalog constructed by Ono et al. (2021) based on HSC-SSP S18A images, while Kakuma et al. (2021) used the S16A catalog taken from Shibuya et al. (2018). The number of LAEs of Ono et al. (2021; a total of 1180 for the UD-COSMOS and UD-SXDS fields) increases from that of Kakuma et al. (2021; a total of 630) because the limiting magnitudes are improved by ∼0.5 mag. However, we exclude the LAEs that are faint or close to the field boundaries from the sample of Ono et al. (2021), which results in the number of LAEs (=489) and the minimum NB magnitudes (∼25–25.5 mag) comparable to those of Kakuma et al. (2021). We use the same images as Kakuma et al. (2021; i.e., those taken from the HSC-SSP S18A release) in NB816 and NB921, while our masking prescription may be slightly different.

Although the intensity mapping technique can remove spurious signals from low-redshift interlopers, other systematics, such as the sky background and PSF, may still contaminate LAE signals. To estimate the contribution from these systematics, we use foreground sources, which we hereafter term "NonLAEs." Because NonLAEs should correlate only with the systematics, but not with Lyα emission from LAEs, we estimate these systematics by applying the intensity mapping technique to NonLAEs.

We construct NonLAE samples as follows. First, we detect sources in the NB images using SExtractor (Bertin & Arnouts 1996). Second, we select only sources that are sufficiently bright (≲26 mag) in the g, r2, and i2 bands to remove spurious sources and artifacts. Third, we randomly select the sources such that they have the same sky, FWHM–magnitude distributions in NB (FWHM_NB–m_NB) as those of the LAEs in each field at each redshift. In this way, ∼10³ sources are selected, which we define as NonLAEs. We present the FWHM_NB–m_NB distributions of the LAEs and corresponding NonLAEs in Figures 4 and 5.

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To test whether our NonLAE selection biases the measurement of the systematics, we first estimate the fraction of low-redshift line emitters that mimic Lyα emission (for example, the Hα line emitted from a galaxy at z = 0.237–0.254 contaminates the Lyα flux measured with the NB816 image). Based on the colors of low-redshift line emitters given by Hayashi et al. (2020), we find that the fraction of low-redshift line emitters included in the NonLAEs is no more than ∼5%. Second, we estimate the redshifts of the NonLAEs by cross-matching them with the MIZUKI photometric redshift catalog (Tanaka 2015) and the SDSS spectroscopic source catalog (Blanton et al. 2017). As a result, only up to ∼3% of the cross-matched NonLAEs are at the redshifts that might contaminate the Lyα flux (for example, z = 0.237–0.254 for the NB816 case). These results suggest that such low-line emitters have only a negligible impact on the measurement of the systematics. Indeed, the measurement remains unchanged within the 1σ uncertainties even when we exclude such potential line emitters from the NonLAE sample. Furthermore, we also confirm that using blank locations as the NonLAEs produces the measurement consistent with the above within the 1σ uncertainties at ≳100 ckpc. To summarize these results, our NonLAE selection is very unlikely to bias the measurement of the systematics.

We compute SB as a cross-correlation function between intensities of emission in a given band (XB) and given objects (OBJs), SB_XB×OBJ, ²⁰ via

$$\begin{eqnarray}&&{\mathrm{SB}}_{\mathrm{XB}\times \mathrm{OBJ},\nu }(r)=\displaystyle \frac{1}{{N}_{r,\mathrm{OBJ}}}\sum _{i=1}^{{N}_{r,\mathrm{OBJ}}}{\mu }_{\nu ,i}^{(\mathrm{XB})}\end{eqnarray} \tag{ 1 }$$

and

$$\begin{eqnarray}&&{\mathrm{SB}}_{\mathrm{XB}\times \mathrm{OBJ}}(r)={\mathrm{SB}}_{\mathrm{XB}\times \mathrm{OBJ},\nu }(r)\times {\mathrm{FWHM}}_{\mathrm{XB}}.\end{eqnarray} \tag{ 2 }$$

The pixel of the ith pixel–OBJ pair has a pixel value of ${\mu }_{\nu ,i}^{(\mathrm{XB})}$ in the XB image in units of erg s⁻¹ cm⁻² Hz⁻¹ arcsec⁻². In NB387, we multiply ${\mu }_{\nu ,i}^{(\mathrm{NB}387)}$ by 1.5 to correct for the zero-point offset of 0.45 mag (see Section 2.2). The summation runs over the N_r,OBJ pixel–OBJ pairs that are separated by a spatial distance r. We use pixels at distances of between 15 and 40'' from each OBJ (corresponding to the outer part of the CGM and outside), which are then divided into six radial bins. A total of ∼(1–2) × 10⁹ pixels are used for the calculation at each redshift. Here FWHM_XB represents the XB filter width (in units of Hz) corrected for IGM attenuation, derived via

$$\begin{eqnarray}&&{\mathrm{FWHM}}_{\mathrm{XB}}=\displaystyle \frac{{\int }_{0}^{\infty }{e}^{-{\tau }_{\mathrm{eff}}(\nu )}{T}_{\mathrm{XB}}(\nu )d\nu /\nu }{{T}_{\mathrm{XB}}({\nu }_{\alpha })/{\nu }_{\alpha }},\end{eqnarray} \tag{ 3 }$$

where T_XB(ν) denotes the transmittance of the XB filter, and ν_α is the observed Lyα line frequency. We adopt the IGM optical depth τ_eff(ν) from Inoue et al. (2014).

The statistical uncertainty of SB_XB×OBJ is estimated by the bootstrap method. We randomly resample objects while keeping the sample size and calculated SB_XB×OBJ. We then repeat the resampling 10⁴ times, adopting the 1σ standard deviation of the SB_XB×OBJ values as the 1σ statistical uncertainty of the original SB_XB×OBJ. At z = 2.2 and 3.3, the UD-SXDS field is not observed in CHORUS, which prevents the estimation of the field variance between the UD-COSMOS and UD-SXDS fields. Therefore, we alternatively divide the LAEs at z = 3.3 into four equal regions and derive SB_NB×LAE in each region. We find that the deviation of SB_NB×LAE among the four regions is ∼10%–20% of the averaged values. We add this deviation in quadrature to the statistical uncertainties of SB_NB×LAE.

We estimate the SB of Lyα emission (SB_Lyα ) around the LAEs as follows. First, we subtract the systematics (SB_NB×NonLAE) from the emission from the LAEs (SB_NB×LAE) via

$$\begin{eqnarray}&&{\mathrm{SB}}_{\mathrm{NB}}={\mathrm{SB}}_{\mathrm{NB}\times \mathrm{LAE}}-{\mathrm{SB}}_{\mathrm{NB}\times \mathrm{NonLAE}}.\end{eqnarray} \tag{ 4 }$$

Uncertainties in SB_NB propagate from those of SB_NB×LAE and SB_NB×NonLAE. We present the radial profiles of the SB_NB×LAE, SB_NB×NonLAE, and SB_NB of the all sample and bright subsample in Figures 6 and 7, respectively.

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We use Fisher's method (Fisher & Aylmer 1970) to estimate the S/Ns of SB_NB over all of the radial bins, following Kakuma et al. (2021). Generally, a p-value is expressed as

$$\begin{eqnarray}&&p={\int }_{{\rm{S}}/{\rm{N}}}^{\infty }{ \mathcal N }(x;\mu =0,\sigma =1){dx},\end{eqnarray} \tag{ 5 }$$

where ${ \mathcal N }(x;\mu =0,\sigma =1)$ is a Gaussian distribution with an expected value μ = 0 and a variance σ² = 1. We thus use this equation to convert the S/N in the ith radial bin (S/N_i ) into the p-value in that bin (_pi ). The χ² value over all of the radial bins (1 ≤ i ≤ N), ${\hat{\chi }}^{2}$, is then calculated as ${\hat{\chi }}^{2}=-2{\sum }_{i=1}^{N}\mathrm{ln}({p}_{i})$. Since ${\hat{\chi }}^{2}$ follows a ${\chi }_{2N}^{2}$ distribution with 2N degrees of freedom, χ²(x; dof = 2N), the p-value over all of the radial bins, $\hat{p}$, is derived as

$$\begin{eqnarray}&&\hat{p}={\int }_{{\hat{\chi }}^{2}}^{\infty }{\chi }^{2}(x;\mathrm{dof}=2N){dx}.\end{eqnarray} \tag{ 6 }$$

We convert this to the S/N over all of the radial bins by solving Equation (5) for S/N.

The black vertical dashed lines in Figures 6 and 7 indicate R_vir. Following the observational results by Ouchi et al. (2010) and Kusakabe et al. (2018), we assume that the DMHs hosting LAEs have halo masses (M_halo) of 10¹¹ M_⊙ at all redshifts, which corresponds to an R_vir value of ∼150 ckpc.

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For the all sample (Figure 6), we unfortunately see no clear (<1σ) detection at z = 2.2. On the contrary, at z = 3.3, SB_NB is significantly positive over wide scales from ∼10² to 10³ ckpc with S/N = 3.2. At z = 5.7, SB_NB is significantly positive at ∼80–10³ ckpc in the UD-COSMOS field with S/N = 4.7, while the signal in the UD-SXDS field is weak (a similar trend is reported in Kakuma et al. 2021). To investigate the averaged signal between the two fields, we mean SB_NB in both fields with weights of the inverse of the SB_NB uncertainties and add the uncertainties in quadrature. As a result, we identify positive signals with S/N = 3.7. At z = 6.6, SB_NB is positive at ∼80–200 ckpc in both fields. Averaging SB_NB over the two fields, we tentatively identify a positive signal with S/N = 2.0. The values of SB_NB at z = 3.3–6.6 are as diffuse as ∼10⁻²⁰–10⁻¹⁹ erg s⁻¹ cm⁻² arcsec⁻².

For the bright subsample (Figure 7), the signals at z = 2.2 and 3.3 are not significant. Meanwhile, we find the positive signal with S/N = 2.0 when averaging SB_NB over the UD-COSMOS and UD-SXDS fields at z = 5.7.

The UV continuum emission might contribute to the SB_NB in addition to the Lyα line emission. We thus estimate the SB of the UV continuum emission, SB_cont,ν , using

$$\begin{eqnarray}&&{\mathrm{SB}}_{\mathrm{cont},\nu }\lt {\mathrm{SB}}_{\mathrm{BB},\nu }\equiv {\mathrm{SB}}_{\mathrm{BB}\times \mathrm{LAE},\nu }-{\mathrm{SB}}_{\mathrm{BB}\times \mathrm{random},\nu },\end{eqnarray} \tag{ 7 }$$

where SB_BB×LAE,ν (SB_{BB×random,ν} ) represents the SB value that is derived from the cross-correlation function between the BB images and LAEs (random sources) in units of erg s⁻¹ cm⁻² Hz⁻¹ arcsec⁻². To estimate the sky background, we use random sources, not NonLAEs, since it is difficult to match the FWHM_NB–m_NB distributions of the NonLAEs with those of the LAEs due to the faintness of the LAEs in the BB. Since SB_{BB×random,ν} neglects signals from the PSF, SB_BB,ν should be treated as the upper limit of SB_cont,ν . As shown in Figure 8 as an example, the values of SB_cont,ν at z = 2.2–6.6 are consistent with null detection within ∼(1–2)σ uncertainties. Additionally, we confirm that the UV continuum emission contributing to SB_NB, i.e., SB_cont,ν × FWHM_NB, is negligible compared to SB_NB. Therefore, we hereafter assume that SB_NB is equivalent to the Lyα SB (SB_Lyα ).

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In summary, we identify very diffuse (∼10⁻²⁰–10⁻¹⁹ erg s⁻¹ cm⁻² arcsec⁻²) Lyα signals beyond R_vir around the all sample LAEs clearly at z = 3.3 and 5.7 with S/N ∼ 3–4 and tentatively at z = 6.6 with S/N ∼ 2. These results imply the potential existence of very diffuse and extended Lyα emission around z = 3.3–6.6 LAEs. The significant detections at z = 3.3 and 5.7 are presumably due to the large number of LAEs (762 and 409, respectively) and the good image sensitivities (∼2 × 10⁻²⁰ erg s⁻¹ cm⁻² arcsec⁻²).

Again, a major update compared to Kakuma et al. (2021) is that we newly apply the intensity mapping technique to the CHORUS data to investigate extended Lyα emission at z = 2.2–3.3. In particular, we identify extended Lyα emission around the z = 3.3 LAEs with S/N levels comparable to or higher than those at z = 5.7 and 6.6. Our results at z = 5.7 and 6.6 are consistent with those obtained in Kakuma et al. (2021), which is as expected from similar properties of the LAEs of Kakuma et al. (2021) and our all sample, such as N_LAE, the L_Lya ranges, and the sky distributions (Section 2.2). In the next section, we compare our results with previous work, including Kakuma et al. (2021), in more detail.

We find that the values of SB_NB do not agree between the UD-COSMOS and UD-SXDS fields at z = 5.7 and 6.6. The cause of this deviation remains unclear; one possibility is that the deviation is attributed to the large variation in the IGM neutral fraction at high redshifts (e.g., Becker et al. 2015, 2018; Bosman et al. 2018; Kulkarni et al. 2019). Nonetheless, we cannot rule out that the deviation is caused by other systematics. Although we cannot find any systematics to bias our results (see the various tests in Section 2.3), we may still need to examine any other unknown systematics in an independent study.

We compare our SB_Lyα radial profiles with those of previous studies at z ∼ 2.2, 3.3, 5.7, and 6.6 (Figure 9). We compile the data taken from Momose et al. (2014, 2016), Leclercq et al. (2017), Wisotzki et al. (2018), Wu et al. (2020), and Kakuma et al. (2021), which are summarized in Table 3. Because SB is affected by the cosmological dimming effect, all of the SB_Lyα profiles, including ours, are scaled by (1 + z)⁻⁴ to z = 2.2, 3.3, 5.7, and 6.6 in each panel. We also shift the radii of the SB_Lyα profiles in units of cpkc by (1 + z), while fixing the radii in pkpc. For our results at z = 5.7 and 6.6, we hereafter present SB_Lyα averaged at each redshift over the UD-COSMOS and UD-SXDS fields with weights of the inverse of the SB_NB uncertainties. The uncertainties of SB_NB in the two fields are added in quadrature.

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Although the SB_Lyα profiles are measured under different seeing sizes, the typical image PSF FWHMs are as small as ≲15, corresponding to ≲40–60 ckpc at z = 2–7 (e.g., Momose et al. 2014; Ono et al. 2021). Since we focus on SB_Lyα profiles at larger scales of ≳100 ckpc, PSF differences are unlikely to affect the following discussion.

Momose et al. (2016) found that SB_Lyα profiles depend on the L_Lyα of the galaxy. To avoid this dependency, we take the data from Momose et al. (2014, 2016) and Kakuma et al. (2021) because their LAEs have L_Lyα values similar to those of our all samples in the same 2'' diameter aperture size. We additionally take the data from Leclercq et al. (2017), Wisotzki et al. (2018), and Wu et al. (2020), but these samples have different L_Lyα values measured in different aperture sizes. Therefore, for precise comparisons, we normalize the SB_Lyα profiles of these samples such that SB_Lyα integrated over a central 2'' diameter aperture ($=4\pi {d}_{{\rm{L}}}^{2}{\int }_{0^{\prime\prime} }^{1^{\prime\prime} }{\mathrm{SB}}_{\mathrm{Ly}\alpha }(r)\cdot 2\pi {rdr}$) becomes equal to the L_Lyα of our all sample at each redshift.

The top left panel in Figure 9 presents SB_Lyα radial profiles at z = 2.2. We compare the results of Momose et al. (2016; L_Lyα = 10^42.6 erg s⁻¹ subsample) against our all sample. We find that the SB_Lyα profile of Momose et al. (2016) is in good agreement with that of our all sample at r ∼ 100 ckpc.

In the top right panel of Figure 9, we show the SB_Lyα profiles at z = 3.3. We compare the results of Momose et al. (2014; z = 3.1 LAEs), Leclercq et al. (2017; an individual LAE MUSE#106), Wisotzki et al. (2018; L_Lyα > 10⁴² erg s⁻¹ subsample at z = 3–4), and our all sample. The SB_Lyα profiles from the literature approximately agree with that of our all sample even at r ∼ R_vir. We additionally show the results from a subsample of Matsuda et al. (2012) with continuum magnitudes BV ≡ (2B + V)/3 of 26 < BV < 27 (typical values for LAEs), where B and V are Subaru/SC B- and V-band magnitudes. The SB_Lyα profile of Matsuda et al. (2012) also agrees with that of our all sample around r ∼ R_vir. We note that, although the results of Leclercq et al. (2017) are represented by their individual LAE MUSE#6905, their LAEs have similar SB_Lyα profiles when the amplitudes are normalized to match the L_Lyα values at r ≤ 1''.

The SB_Lyα profiles at z = 5.7 are displayed in the bottom left panel of Figure 9. We compare the results of Momose et al. (2014; z = 5.7 LAEs), Leclercq et al. (2017; an individual LAE MUSE#547), Wisotzki et al. (2018; L_Lyα > 10⁴² erg s⁻¹ subsample at z = 5–6), Wu et al. (2020; z = 5.7 LAEs), Kakuma et al. (2021; z = 5.7 LAEs), and our all sample. The SB_Lyα profile of our all sample agrees well with those of Momose et al. (2014), Leclercq et al. (2017), Wisotzki et al. (2018), and Wu et al. (2020) at r ∼ 80–200 ckpc and that of Kakuma et al. (2021) up to r ∼ 10³ ckpc.

The bottom right panel of Figure 9 shows SB_Lyα profiles at z = 6.6 taken from Momose et al. (2014; z = 6.6 LAEs), Kakuma et al. (2021; z = 6.6 LAEs), and our all sample. The SB_Lyα profile of our all sample is consistent with those of Momose et al. (2014) and Kakuma et al. (2021) up to scales of r ∼ 100 ckpc and 10³ ckpc, respectively.

In summary, our SB_Lyα profiles are in good agreement with those of the previous studies at each redshift, provided that the LAEs have similar L_Lyα values at r ≤ 1''. Our SB_Lyα profiles (r ≳ 80 ckpc) are smoothly connected with the inner (r ≲ 100 ckpc) profiles taken from the literature at ∼100 ckpc and extend to much larger scales.

In Figure 10, we compare the SB_cont,ν radial profiles between Momose et al. (2014, 2016) and our all sample at z = 2.2, 3.3, and 5.7 (the data of Momose et al. 2014, 2016 are of the same LAEs as used in Figure 9). We find that the SB_cont,ν profiles roughly agree at r ≲ 400 ckpc, although the uncertainties are large. The SB_cont,ν profiles are much less extended than the SB_Lyα profiles, which was also suggested by Momose et al. (2014, 2016) and Wu et al. (2020). We note that the profiles at z = 6.6 are not compared here because our sample is ∼0.3 dex brighter than that of Momose et al. (2014).

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In this section, we investigate the redshift evolution of SB_Lyα profiles of extended Lyα emission. In Figure 11, we compare the SB_Lyα profiles of our bright subsample at z = 2.2–6.6 as a function of radius in units of ckpc. We also present the results taken from Momose et al. (2014; z = 5.7 and 6.6 LAEs) and Wisotzki et al. (2018; L_Lyα > 10⁴² erg s⁻¹ subsample at z = 3–4). Because our bright subsamples have uniform L_Lyα values (∼10^42.9–10^43.0 erg s⁻¹) over z = 2.2–6.6, the L_Lyα differences between the redshifts are unlikely to influence the following discussion.

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The top panel of Figure 11 shows the observed SB_Lyα profiles. We identify no significant difference among the SB_Lyα profiles beyond the 1σ uncertainties at r ∼ 10²–10³ ckpc over z = 2.2–6.6, while the uncertainties are large. This finding is consistent with that of Kakuma et al. (2021) at z = 5.5–6.6. There is also no significant difference in the profiles at r < 100 ckpc, which was also suggested by MUSE observations (Leclercq et al. 2017; see also Figure 11 of Byrohl et al. 2021) at 3 < z < 6.

The observed SB_Lyα profiles are affected by the cosmological dimming effect. To correct this effect, we shift the observed SB_Lyα profiles vertically by (1 + z)⁴/(1 + 3.3)⁴ and horizontally by (1 + 3.3)/(1 + z), which are hereafter termed as the intrinsic profiles (we match the profiles to z = 3.3 just for visibility). The intrinsic profiles are presented in the bottom panel of Figure 11. There is a tentative increasing trend in the intrinsic profiles toward z = 6.6, although those at z = 2.2 and 3.3 remain comparable due to the large uncertainties.

To quantitatively investigate the evolution, we derive the SB_Lyα intrinsic profile amplitudes at r = 200 ckpc (SB_Lyα,intr) as a function of redshift. We fit the relation with SB_Lyα,intr ∝ (1 + z)^b , where b is a constant, weighting by the inverse of the uncertainties of SB_Lyα,intr. We find that the best-fit value is b = 2.4 ± 1.4, which is consistent with the increase of the intrinsic SB_Lyα profile amplitudes toward high redshifts by (1 + z)³ at a given radius in units of ckpc. This trend might correspond to the increasing density of hydrogen gas toward high redshifts due to the evolution of the cosmic volume. Nevertheless, it is still difficult to draw a conclusion due to large uncertainties. We cannot rule out other possibilities, such as higher Lyα escape fractions toward high redshifts (e.g., Hayes et al. 2011; Konno et al. 2016). We also need to investigate the potential impact of the cosmic reionization on the neutral hydrogen density at r ∼ 10²–10³ ckpc around LAEs. Deeper observations in the future will help to elucidate the evolution and its physical interpretation.

In this section, we compare the observational results obtained in Section 3 with theoretical models taken from the literature to investigate the mechanism of extended Lyα emission production. We investigate extended Lyα emission focusing on (1) where Lyα photons originate, (2) which processes produce Lyα photons, and (3) how these photons transfer in the surrounding materials.

(1) First, we distinguish Lyα emission according to where it originates from:

• 1.  
  the ISM of the targeted galaxy (central galaxy),
• 2.  
  the CGM surrounding the central galaxy,
• 3.  
  satellite galaxies, or
• 4.  
  other halos, which refer to halos distinct from that hosting the central galaxy.

(2) We consider that Lyα photons are produced in the processes of recombination and/or collisional excitation (cooling radiation), as stated in the Introduction.

(3) Lastly, Lyα photons subsequently transfer through surrounding hydrogen gas while being resonantly scattered, which affects the observed SB profiles. Hence, we should be conscious of whether the models take into account the scattering process or not (see Byrohl et al. 2021 for the impact of scattering on SB_Lyα profiles).

In Figure 12, we compare the SB_Lyα profiles that are observed (Section 3.2) and those predicted by theoretical work. The observational results are taken from Momose et al. (2016; L_Lyα = 10^42.6 erg s⁻¹ subsample at z = 2.2), Wisotzki et al. (2018; L_Lyα > 10⁴² erg s⁻¹ subsample at z = 3–4), Momose et al. (2014; z = 5.7 and 6.6 LAEs), and our all samples (z = 2.2–6.6). Predicted profiles are taken from Zheng et al. (2011), Dijkstra & Kramer (2012), Lake et al. (2015), Mas-Ribas et al. (2017b), Kakiichi & Dijkstra (2018), and Byrohl et al. (2021) and are summarized in Table 4. We plot these observational and theoretical results at the nearest redshifts among z = 2.2, 3.3, 5.7, and 6.6, except that the model of Mas-Ribas et al. (2017b) is presented at all redshifts, with the correction for the cosmological dimming effect. We normalize all of the profiles such that they match at r = 1'' in amplitude for precise comparison under the same Lyα luminosity of the central galaxy (the models of Zheng et al. 2011, Lake et al. 2015, and Byrohl et al. 2021 are normalized in each total profile summing up different origins). We compare these observational and theoretical results in the context of the Lyα photon origins in the following subsections.

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4.2.1. Central Galaxy

4.2.2. CGM

4.2.3. Satellite Galaxies

4.2.4. Other Halos

4.2.5. Overall Interpretation