PANORAMIC SURVEY OF Lyα EMITTERS AT z = 3.1

Lyα emission from high-redshift galaxies is an important and useful probe in studying the star formation and structure formation history of the universe (Partridge & Peebles 1967). The sensitive narrowband imaging observations have succeeded to detect a large number of the Lyα emitters at intermediate and high redshift toward z ∼ 7 (e.g., Hu & McMahon 1996; Steidel et al. 2000; Rhoads & Malhotra 2001; Rhoads et al. 2003; Kodaira et al. 2003; Palunas et al. 2004; Hayashino et al. 2004; Matsuda et al. 2004, 2010, 2011; Taniguchi et al. 2005; Gronwall et al. 2007; Iye et al. 2006; Ouchi et al. 2008, 2010).

As the narrowband imaging can constrain the redshift of the objects to the small range, Lyα emitters are also useful in studying the spatial distribution of the star-forming galaxies at high redshift. It is known that high-redshift galaxies are strongly clustered due to the formation bias to the underlying mass distribution (Kauffmann et al. 1999; Benson et al. 2001; Weinberg et al. 2004). While it is not trivial that Lyα emitters follow the simple halo-mass bias in the hierarchical structure formation, since the origins and timescale of the Lyα emission may be diverse, the high-density region of the Lyα emitters may mark the region where galaxy formation preferentially occurs at the epoch. Typical spectral resolution δλ/λ of the narrowband imaging is 50–100, which corresponds to the comoving scale of 50–100 Mpc at z ∼ 3, and narrow enough to locate the clustered regions and voids.

More than a few high-density regions of the Lyα emitters and star-forming galaxies at high redshift have been studied (Keel et al. 1999; Steidel et al. 2000, 2005; Shimasaku et al. 2003; Palunas et al. 2004; Hayashino et al. 2004; Matsuda et al. 2004, 2009, 2010; Ouchi et al. 2005; Kajisawa et al. 2006; Miley et al. 2006; Venemans et al. 2007; Hatch et al. 2008, 2009; Overzier et al. 2008; Digby-North et al. 2010; Kuiper et al. 2010; Yang et al. 2010). Among them, the structure at z = 3.09 in the SSA22 region, specifically the area around the original selected survey area at 22^h (Cowie et al. 1990), is one of the most prominent and interesting ones. The large density excess was first discovered in the redshift distribution of the Lyman break galaxies (LBGs) by Steidel et al. (1998). The density of the region within 20 × 15 × 21 Mpc³ (in the flat ΛCDM with H₀ = 70 km s⁻¹ Mpc⁻¹) comoving volume was reported to be six times greater than that of the average. In fact, the peak has the largest density enhancement in the entire survey volume (Adelberger et al. 1998; Steidel et al. 2003) and it remains one of the largest density peaks discovered at high redshift so far. Subsequent narrowband observations (Steidel et al. 2000; Hayashino et al. 2004; Matsuda et al. 2004) found that the Lyα emitters, which have some overlap with LBGs but are clearly from a different sample in terms of the UV luminosity and the Lyα equivalent width, also show similar density enhancement. The following multiwavelength studies of the field show that the density of the active galactic nuclei (AGNs) detected in X-ray as well as the infrared or submillimeter sources is also high compared to other fields (Geach et al. 2005, 2007; Lehmer et al. 2009; Webb et al. 2009; Tamura et al. 2009).

While the region is often referred to as a "protocluster," there is still uncertainty regarding the value of the density enhancement of the Lyα emitters as a distinguished structure. First, neither LBGs nor Lyα emitters show prominent concentration on the sky and their distributions extend over the observed fields of view (FoV) of either Steidel et al. (1998) or of Steidel et al. (2000), although some local density structure is recognized (Steidel et al. 2000). Hayashino et al. (2004) revealed that the region is a part of a "belt-like" large-scale structure with the comoving scale of ∼30–50 Mpc, which also extends over the observed field of the Subaru Suprime-Cam, ≈27' × 34'. While the subsequent spectroscopic observation revealed that this large-scale high-density structure seems to consist of the filamentary structures in the redshift space and the density peak discovered by Steidel et al. (2000) located near the intersection of the filaments (Matsuda et al. 2005), further observations covering the larger area are needed to characterize the density peak in the large volume. The control sample should also be improved. When Steidel et al. (2000) evaluated the density enhancement of Lyα emitters, the compared "field" sample was comprised of those obtained earlier in a relatively small volume (Cowie & Hu 1998; Pascarelle et al. 1996, 1998). Hayashino et al. (2004) referred to the sample they obtained in a general field of area similar to SSA22-Sb1. The data were, however, shallower than that obtained at the SSA22 field and the significance of the overdensity was evaluated by using only the relatively bright objects. A single field for the control sample is also not enough to evaluate the field-to-field variation of the number density of the emitters.

In this paper, we present the results of our wide-field and deep surveys of the Lyα emitters at z = 3.1 around the dense structure in the SSA22 fields (Steidel et al. 1998, 2000; Adelberger et al. 1998; Hayashino et al. 2004) as well as the general blank deep survey fields. The survey volume is significantly enlarged to be 10 times larger than that in Hayashino et al. (2004). The goal of this paper is to characterize the high-density region of the Lyα emitters and to evaluate the significance of their density enhancement. The detection of the extended Lyα nebulae, namely Lyα blobs in the same fields, was reported in our previous paper (Matsuda et al. 2011).

2.1. Observations

We conducted the deep and wide-field imaging observations with the Subaru 8.2 m telescope equipped with the Subaru Prime Focus Camera (Suprime-Cam; Miyazaki et al. 2002). The custom narrowband filter NB497 (Hayashino et al. 2004), whose central wavelength and width are 4977 Å and 77 Å, respectively, was used to sample the Lyα emitters at z = 3.09. The width corresponds to the redshift range z = 3.062–3.125, or 59 Mpc in the comoving scale.

In order to expand the z = 3.1 Lyα emitter survey around the SSA22 region, we first observed the six adjacent Suprime-Cam FoVs around the original field, SSA22-Sb1 (Hayashino et al. 2004; Matsuda et al. 2004). The coordinates of the fields, referred to as SSA22-Sb2 to SSA22-Sb7, and the summary of the observations are shown in Table 1. Their configuration in the sky is shown in Figure 1. The boundaries of the fields used in this paper are indicated by the colors of the dots which show the positions of the detected sources (1 in 50 of the objects are plotted). Typical exposure time for the NB497, B-, and V-band filters are 5 hr, 1 hr, and 1 hr, respectively. The seeing conditions were fairly homogeneous except for some observations of the SSA22-Sb4 field where we need to apply a slight aperture correction to match the other data (see below).

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Table 1. Summary of the Observed Objects

Field	R.A.	Decl.	Filter	FWHM	5σ Limit	Exp. Time
	J2000.0	J2000.0		(arcsec)	AB mag.	(hr)
SSA22-Sb1	22:17:34.0	+00:17:01.0	NB497	1.0	26.33	7.0
			B	1.0	26.49	1.5
			V	1.0	26.69	1.5
SSA22-Sb2	22:16:36.7	+00:36:52.0	NB497	1.0	26.25	5.5
			B	1.0	26.53	1.0
			V	1.0	26.36	1.0
SSA22-Sb3	22:18:36.3	+00:36:52.0	NB497	1.0	26.30	5.5
			B	1.0	26.81	1.0
			V	1.0	26.55	1.0
SSA22-Sb4	22:19:40.0	+00:17:00.0	NB497	1.1	25.85	5.5
			B	1.1	26.31	1.0
			V	1.1	26.21	1.1
SSA22-Sb5	22:15:28.0	+00:17:00.0	NB497	1.0	26.11	5.5
			B	1.0	26.45	1.0
			V	1.0	26.37	1.0
SSA22-Sb6	22:14:30.7	+00:33:52.0	NB497	1.0	26.27	5.5
			B	1.0	26.83	1.3
			V	1.0	26.58	1.3
SSA22-Sb7	22:17:42.7	+00:56:52.0	NB497	1.0	26.15	5.5
			B	1.0	26.62	1.0
			V	1.0	26.44	1.0
SDF	13:24:39.0	+27:29:26.0	NB497	1.0	26.53	7.2
			B	1.0	27.82	9.9
			V	1.0	27.25	5.7
SXDS-N	02:18:00.0	−05:25:00.0	NB497	1.0	26.19	4.9
			B	1.0	27.56	5.5
			V	1.0	27.08	1.4
SXDS-C	02:18:00.0	−05:00:00.0	NB497	1.0	26.28	5.3
			B	1.0	27.51	5.8
			V	1.0	27.29	1.6
SXDS-S	02:18:00.0	−05:00:00.0	NB497	1.0	26.28	4.8
			Bb	1.0	27.60	5.5
			Vb	1.0	27.24	1.8
GOODS-N	12:37:23.6	+62:11:31.0	NB497	1.1	26.55	10.0
			B	1.1	26.68	2.3
			V	1.1	26.15	1.0

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For the control sample, we also obtained the similar deep narrowband data in the five general blank fields, specifically the Subaru/XMM-Newton Deep Survey (SXDS)-North, -Center, -South (Furusawa et al. 2008), the Subaru Deep Field (SDF; Kashikawa et al. 2004), and the field around the Great Observatory Optical Deep Survey North (GOODS-N; Dickinson et al. 2004) fields. We also used the broadband data of the SXDS and SDF fields taken and published by each of the other deep survey teams. As the available public broadband data of the Suprime-Cam in the GOODS-N fields are not as homogeneous as the other general fields, we must be careful when analyzing the equivalent-width distribution of the GOODS-N field. Here we simply omitted it in the discussion of the equivalent width.

Thus, in this paper, the data for the seven Suprime-Cam fields in the SSA22 region, including the original SSA22-Sb1 field as well as those of the five Suprime-Cam fields in the three separated general blank fields (SXDS-N, -C, and -S, SDF, GOODS-N), are analyzed. The total areas used in the analysis are 1.38 deg² for the SSA22 fields and 1.04 deg² for the blank fields.

2.2. Data Reduction

2.3. Photometry and the Galactic Extinction Correction

The sources were detected by using the software SExtractor 2.1.6 (Bertin & Arnouts 1996). The combined image of each field in each filter was analyzed with SExtractor and the pseudo total flux, FLUX AUTO (or MAG AUTO for magnitude), within a 2.5 × Kron radius as well as the flux within a 2'' diameter circular aperture were obtained for the detected objects. We also analyzed the broadband images together with the narrowband images by using the SExtractor double-image mode and the FLUX AUTO within the Kron aperture, as well as the fixed aperture at the position at which the narrowband-detected sources were obtained. The photometric errors are dominated by the sky background noise and the 5σ limiting magnitude for the 2'' diameter aperture in each field is shown in Table 1. Sometimes the narrowband-selected objects are too faint to be detected significantly in the continuum image. In calculating and analyzing the colors or the equivalent width of the objects, we will substitute them as the 1σ limiting magnitude for the aperture.

To obtain the appropriate continuum flux to be compared with the narrowband flux, we constructed the weighted "BV-band" images by summing the B- and V-band images by (2B + V)/3. We refer this average magnitude as BV.

The seeing of the SSA22-Sb4 images was relatively poor and we could not match them to the target image size of 10. As the seeing of the images from the other 10 fields is better, although we match all of the images to the poorest SSA22-Sb4 one, we made a small correction of 0.061, 0.065, 0.070, and 0.069 mag to the aperture magnitudes in B, NB497, V, and BV band for the sources in SSA22-Sb4, respectively. These correction values were obtained by comparing the observed and the artificially degraded images of SSA22-Sb1 and confirmed by comparing the sources in the Sb1–Sb4 overlap region. Since the broadband data of the GOODS-N field also have relatively poor image quality, we also smoothed cut all of the GOODS-N-field images to FWHM = 11 and applied the same aperture corrections as for SSA22-Sb4.

Figure 2 shows the number counts in the NB497 band of the detected sources in the SSA22 fields (filled circles and the black lines) as well as for those in the general fields (open squares with the red lines). The counts in the SSA22 fields are systematically low, which is due to the Galactic extinction as the SSA22 fields are located at a relatively low Galactic latitude, (l, b) ≈ (63°, −45°). We therefore have to correct the flux of the objects in the SSA22 fields to the Galactic extinction in order to compare the data with the general fields which are located at higher Galactic latitudes. For example, the mean extinction in the V band is 0.22 mag in SSA22 while the mean extinctions are 0.08 mag and 0.06 mag in the SXDS and SDF fields, respectively. The difference of the extinction within the seven SSA22 Suprime-Cam fields should also be carefully considered as we will discuss the inhomogeneity in the spatial distribution of the Lyα emitters over the fields. For that purpose, we refer to the most modern map of Galactic reddening over the sky based on the COBE DIRBE and the IRAS ISSA far-infrared data (Schlegel et al. 1998, hereafter SFD) shown in Figure 3 with the projected seven Suprime-Cam FoVs. The spatial resolution of the SFD map is 032. The color excess E(B−V) ranges from 0.05 to 0.09, and gradually changes from northwest to southeast.

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For all of the detected sources we applied the correction for Galactic extinction from the E(B − V) value at the position of the SFD map by using the following relations, A_V = 3.16 × E(B−V), A_B = 4.11 × E(B−V), and A_NB497 = 3.55 × E(B−V), based on the extinction curve derived by Kenyon et al. (1994). Figures 4(a) and (b) show the comparison of the source counts between the SSA22 and the general fields as well as those among the seven SSA22 fields after the Galactic extinction correction. While the SFD map smoothed out the patchy structure smaller than 032, the agreement between the average of the corrected counts in the SSA22 fields and the general fields is reasonably good. The scatter among the seven SSA22 fields also becomes small after the correction while the field-to-field variation with ∼10% in the number density remains. Note that the counts in the SSA22-Sb1 field, shown by the blue line, are the lowest among them and they would not be an artificial cause of the overdensity of the Lyα emitters in the field.

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Figure 5 shows the distribution of the BV − NB497 colors for the objects between 23 mag and 25 mag in both the bands. The vertical dashed (red) line indicates the peak (mode) value of the SSA22-Sb1 field and the dotted line in each panel shows the same for each field. The peak coincides within ∼0.02 mag, which enables us to make the uniform selection of the narrowband excess objects.

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We now describe the selection criteria for the z = 3.1 Lyα emitters. The aperture magnitude values are used for this purpose. Figures 6 and 7 show the color–magnitude diagram of the objects detected in the NB497 images in the SSA22 fields and in the general fields, respectively. The very slight additional correction for the color zero point left after the photometric calibration above was made in the Lyα emitter (LAE) identification so as to ensure more complete sample homogeneity over the fields.

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The criteria to identify the Lyα emitters at z ∼ 3.1 are as follows.

(1) NB497 < 25.73 (S/N > 6.6), and,

(2a) BV − NB497 > 1.0 and B − V_c > 0.2

            (when V_c < 26.5),

or,

(2b) BV − NB497 > 1.3

            (when V_c > 26.5).

V_c is the line-corrected V-band magnitude. The criteria are similar to those in Hayashino et al. (2004) but the color threshold was slightly relaxed based on the fact that a few contaminations by the foreground objects were found in our previous spectroscopic observations. In fact, the spectroscopic observations (Matsuda et al. 2005, 2006) show that the contamination of the foreground objects, mostly [O ii] emitters at z = 0.33, is at most 1%, or negligible. The B − V_c criteria are useful to further prevent the contamination of the z = 0.33 [O ii] emitter, although we cannot apply it to the continuum faint sources, V_c > 26.5.

For the robustness of the sample, we also apply an additional constraint that the observed BV − NB497 color must be larger than the 4σ value of the background noise in the SSA22-Sb4 field. The limit is shown by the curves in Figures 6 and 7. Only a small fraction of the objects are rejected by the last criteria.

In total, we identified the 1394 and 767 emission-line objects in the SSA22 and blank fields, respectively. The NB497 limiting magnitude corresponds to either ≈1.8 × 10⁻¹⁷ erg s⁻¹ cm⁻² or the luminosity of ≈1.5 × 10⁴² erg s⁻¹ at z = 3.09. The numbers and the area for each field (without overlapping) are summarized in Table 2. Based on the previous studies of SSA22-Sb1, including the spectroscopic observations, we emphasize that the sample is quite robust as the z = 3.1 Lyα emitters are not contaminated by the foreground objects by more than ∼1% in the fraction. This is also confirmed by the recent spectroscopic data for 100 sources in Sb1 (Yamada et al. 2012) as well as the ongoing observations for Sb2–Sb7 for a few hundred sources. We show the number counts of the NB497, B, and V bands of the Lyα emitters in Figures 8–10. The catalog of the Lyα emitters will be published in a future paper (T. Yamada et al. 2012, in preparation).

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The sky distributions of the z = 3.1 Lyα emitters are shown in Figures 11–14. The separation of 1° corresponds to 109 Mpc in the comoving scale at z = 3.1. As shown in Table 2, the surface densities averaged in each Suprime-Cam FoVs of the five blank fields range from 0.13 (SXDS-N) to 0.26 (SDF) arcmin⁻² and the whole average of the five fields is 0.204 ± 0.007 arcmin⁻², which corresponds to 1.1 × 10⁻³ Mpc⁻³.

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We also calculated the average densities and the standard deviations for the randomly placed circular areas with various different diameters between 6' and 20'. The average values are nearly constant over the diameters and distribute within the ranges of 0.23–0.26 arcmin⁻² in SDF and 0.16–0.20 arcmin⁻² for the whole SXDS and GOODS-N while the standard deviation decreases as the diameter increases; it is ≈0.1 arcmin⁻² at the diameter of 6' and ≈0.03 arcmin⁻² at 20'. In this paper, we adopted 0.20 arcmin⁻² for the nominal average number density of the Lyα emitters selected by our criteria described above. We also calculated the local smoothed number density with the Gaussian kernel with σ = 15 and the contours in Figures 11–14 show the smoothed densities of 1.5, 2.5, 3.5, 4.5, and 5.5 times the nominal average density. The large-scale inhomogeneity in the SSA22 is clearly seen in Figure 11 and the number-density excess in the SSA22-Sb1 is evident. The highest peak with ≈6 times the average is seen in the SSA22-Sb1 field at (α, δ) ≈ (33435, 03), right at the position of the local "peak" discussed in Steidel et al. (2000; northeast one in their Figure 10). There is only one small peak with ∼3.5 times the average in SDF but none in other general fields. The highest peak in the SSA22-Sb1 is thus very conspicuous.

The densities of the SSA22 Suprime-Cam fields range from 0.20 to 0.44 arcmin⁻² (Table 2) and the average is 0.28 arcmin⁻². The high surface density of the SSA22-Sb1 field is prominent and more than two times higher than the average of the general blank fields. There is also a large under dense region over ≈30 Mpc (in the comoving scale) in the eastern half of SSA22-Sb6 at around (α, δ) ≈ (3337, 06), while the surface density is high in the western half of SSA22-Sb5 at around ≈(3337, 02). The whole average of the SSA22 fields omitting SSA22-Sb1 is 0.25 arcmin⁻², which is still higher than the average but a similar value to the SDF, which is the densest among them.

We also compare our results with the previous survey of Lyα emitters at z ∼ 3. Ouchi et al. (2008) observed the z = 3.1 Lyα emitters in SXDS by the slightly different narrowband filter NB503 and detected 356 objects in 0.98 deg² brighter than NB503 = 25.3 and V − NB503 > 1.2, which yields a surface number density of 0.099 ± 0.005 arcmin⁻². While the selection criteria are slightly different, we also counted the number of our Lyα emitters with NB497 < 25.3 and BV − NB497 > 1.2. We found 309 and 530 Lyα emitters in the five general fields (1.04 deg²) and SSA22 (1.38 deg²), respectively. The surface density of our sample in the general fields is thus 0.083 ± 0.004 arcmin⁻² which is only slightly smaller than the value in Ouchi et al. (2008). On the other hand, the average surface density in the whole SSA22 field and that in SSA22-Sb1 are 0.11 arcmin⁻² and 0.18 arcmin⁻², respectively, which is similarly high even if we compare the average density of the NB503 emitters in Ouchi et al. (2008) to the magnitude and equivalent-width limit.

Gronwall et al. (2007) also searched the Lyα emitters at z = 3.1 down to the magnitude limit of ≈25.4 and the equivalent-width limit of ∼20 Å in 0.28 deg² and found 167 emitters, or 0.16 arcmin⁻². As the width of the narrowband filter is somewhat different (50 Å in Gronwall et al.), a direct comparison is rather difficult. If we apply the similar selection threshold and corrected the 1.5 times volume difference in a unit area, we found 0.16 arcmin⁻² for the general fields, and 0.24 and 0.34 arcmin⁻² in the whole SSA22 and SSA22-Sb1, respectively. Thus, our result is reasonably consistent with the previous results in terms of the number density in the general fields and the very large density excess in the SSA22 fields is robust.

The color–magnitude diagrams of Figures 6 and 7 show that the observed narrowband color excess of the emitters ranges from BV − NB497 = 1 (selection limit) to at least 3.5, which corresponds to the equivalent width of the Lyα emission between ≈190 Å to 1900 Å in the observer's frame or ≈50 Å to 500 Å in the rest frame at z = 3.09. Note that the emission line is located at the shoulder of the V band. If we correct the line flux in the V band, the BV − NB497 becomes even larger, especially for the objects with large equivalent widths. The attenuation of the Lyα emissions by the intergalactic medium (IGM) in the line of sight (≈20% at z = 3) should also be corrected.

Interestingly, there is a large fraction of objects whose uncorrected rest-frame Lyα equivalent width is larger than ∼150 Å, which corresponds to BV − NB497 = 2.3. For a constant continuous star formation model with a 0.05 solar metallicity and Salpeter initial mass function with the upper and lower mass cut of 120 and 0.1 M_☉, respectively, the expected equivalent width at an age larger than 10 Myr at the equilibrium phase is ∼150 Å without any reprocessing of the Lyα and UV flux (Malhotra & Rhoads 2002; Schaerer 2003). If the Lyα emission suffers from larger dust extinction due to the large optical path by scattering before escape, this becomes smaller. In the clumpy medium case (Finkelstein et al. 2007), on the other hand, the Lyα equivalent width may be enhanced at most by ∼50%, and it may be as large as ∼230 Å,  which corresponds to BV − NB497 = 2.7. The observed BV − NB497 distribution of our sample spreads over the value. This result suggests that the sample of Lyα emitters is powered by photoionization with hotter stars, namely, younger or metal-poor stars, or by other processes such as the collisional gas heating during the gravitational collapse or galactic superwind.

The distribution of the rest-frame equivalent width calculated from the color measured in 2'' diameter aperture is shown in Figure 15. Here we corrected for both the V-band line contamination and the attenuation by IGM. We adopted the same value for the IGM attenuation factor, 0.81, as quoted in Ouchi et al. (2008) at z = 3.1. The counts in the SSA22 fields from the objects whose BV-band flux is below the detection limit (i.e., only the lower limit of the equivalent width available) are indicated by the light magenta histogram. If we consider the whole range of the equivalent width, the distribution is not fitted very well by a single exponential law. The best-fitted decaying scale is 112.4 ± 7.2 Å for the whole SSA22 fields and 97.9 ± 8.7 Å for the whole sample of the general fields except for GOODS-N. The fraction of the objects with large equivalent widths is larger in SSA22. On the other hand, if we fit them below 200 Å, the e-folding value is 73.68 ± 30.59 Å and 63.86 ± 27.75 Å, for the SSA22 fields and the general fields, respectively. The larger error is due to the small number of bins. Figure 16 shows the same distribution of the equivalent width but in the cumulative manner. It is more clearly shown that the distribution in the SSA22 fields is more weighted to the larger equivalent-width objects, which is not due to the difference of the detection limit of the continuum bands.

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We may also compare the distribution of the equivalent width, although the different continuum depth makes the direct comparison more difficult. Gronwall et al. (2007) found the e-folding scale to be 76 + 11 − 8 Å. This is smaller than our results for the full sample of the general fields, 97.9 ± 8.7 Å, although they are not very inconsistent considering the errors.

Since the Lyα emission is typically more extended than the continuum (Hayashino et al. 2004), it may not be appropriate to calculate the equivalent width in the fixed circular aperture when we are interested in the global process in the galaxies for the origins of the Lyα emission. While the fixed aperture should be used to evaluate local processes like photoionization in the star-forming region, the whole extent of the Lyα emission should be considered if we include global scattering effects or other process like shock heating by infalling or outflowing gas. We found that the equivalent width measured in the pseudo total aperture (i.e., SExtractor FLUX AUTO using the Kron aperture) is on average ≈1.6 times larger than those measured with the 2'' diameter apertures. The equivalent-width distribution, which is already spread to the large value above 150 Å, is further stretched to show the large fraction of the large equivalent-width objects. This trend is seen more conspicuously for the emitters in the SSA22 fields.

We have constructed a robust and homogeneous sample of the Lyα emitters at z = 3.1 around the SSA22 high-density peak as well as the blank fields. The primary result is that the high-density region originally discovered by Steidel et al. (1998) is now characterized as a very significant structure. It is the most conspicuous density peak in the survey area of a total of 2.42 deg², or in the comoving volume of 1.8 × 10⁶ Mpc³. No other region shows a density larger than 3.5 times the average of the blank fields. For the number density, the SSA22 high-density region is likely to be rarer than the present-day clusters of galaxies with L_X(0.5–2 keV) ∼10⁴⁴ erg s⁻¹ (Böhringer et al. 2002), which is about half the luminosity of the Coma cluster.

From Figure 11, the extension of the density peak is ∼5 arcmin ×  10 arcmin, or ∼3 × 6 Mpc at z = 3.1 in the proper length, if we take the contour of 3.5 times the average as the boundary. The size is comparable with the extension of the X-ray gas of the rich cluster (e.g., ∼3 Mpc for Coma cluster). The overdensity, δN/N₀, of the Lyα emitter in the region is also found to be very large. The density inside the ∼5 × 10 arcmin² area is ∼1.0 arcmin⁻², which is five times the average density of the general fields, 0.20 arcmin⁻². This overdensity is ≈10 × the standard deviation of the Lyα emitters in the general field, 0.09 arcmin⁻². The structure should correspond to the extremely rare peak which must be a progenitor of the very massive structure if the clustering of the Lyα emitters obey the clustering of the dark matter halos. Thus, we can confidently call the structure a "protocluster."

We now evaluate the significance of the overdensity of the high-density region of the Lyα emitters at different scales by comparing them with the predictions for the structure formation models. The area of 700 arcmin², a Suprime-Cam FoV, corresponds to the comoving volume of 1.4 × 10⁵ Mpc³ for the depth sampled by the narrow band, 59 Mpc. The distribution of the mass or the number-density fluctuation of the galaxies is well approximated by the Gaussian distribution at z = 3.1 at this scale. The underlying mass fluctuation can be roughly estimated assuming the standard ΛCDM model with the linear approximation. Adopting the normalization of the power spectrum σ₈ = 0.81 (Komatsu et al. 2011) and the approximation for the mass variance with the top-hat window, σ(R) = σ₈(R/r₈)^−β (Mo et al. 2010) with β ≈ 0.7 (CDM shape parameter Γ = 0.2), and the linear growth rate in the non-zero cosmological constant (Carroll et al. 1992), ≈3.3 at z = 3.1, we obtain the σ(R) = 〈(δρ/ρ₀)²〉^1/2 at the corresponding comoving scale (R ≈ 32 Mpc) at z = 3.1 is ≈ 0.11. The observed density variation among the five general fields, (δN/N₀)_LAE = −0.38 (SXDS-N) to +0.21 (SDF), is comparable with the value, if we consider that the Lyα emitters trace mass distribution with the linear biasing factor b ∼ 2–6, as obtained in the previous study of Lyα emitters at z = 2–5 from the analysis of the two-point correlation functions (Shimasaku et al. 2003; Gawiser et al. 2007; Guaita et al. 2010). On the other hand, the density excess of the SSA22-Sb1 with (δN/N₀)_LAE = 1.13 ± 0.01 even at this scale is unexpectedly large, more than ≈10 × the mass fluctuation, which implies that the field is the very rare, >5σ_LAE peak with b = 2 (Gawiser et al. 2007).

In Table 3, we also compare the observed overdensity with the expected mass fluctuation for both the smaller area with 100 arcmin² that contains the local density peak of the emitters and for the entire seven fields of SSA22. Note that the average density of the general blank fields changes very little with the observed area (Section 3) and it is reasonable to assume the constant average surface density over these scales. The 100 arcmin² area centered at (α, δ) = (334.392, 0.250), which corresponds to the SSA22a in Steidel et al. (2000), contains 89 emitters, which corresponds to the overdensity of 3.36 ± 0.03 while the 1σ mass fluctuation is 0.18. We assumed that the mass fluctuation at this scale was still represented by the σ(R) evaluated as above, although the entire distribution may be deviated from the Gaussian at this scale at z = 3.1. The peak is confirmed to be very significant, 19 times the average of mass fluctuation. At the larger scale of the entire SSA22 Sb fields, the overdensity is observed to be 0.37  ±  0.01 while the expected mass fluctuation is 0.07 at this scale. With b = 2, it is the 2.6σ peak at the dimension of ≈100 Mpc scale. The SSA22 field is a very significant high-density region in the universe on the scale of the Great Wall (Geller & Huchra 1989).

Furthermore, we also compared the overdensity with the distribution of the model galaxies in the cosmological simulation. We use the public semi-analytic model galaxy catalogs at z = 3.06 from the Millennium simulation (De Lucia et al. 2006). The distribution of galaxies within the 500 h⁻¹ Mpc cube and the model parameters for the star formation rate (SFR) and the mass weighted age are available in the catalog. It is not easy to make a sample of the model galaxies that exactly represents the observed Lyα emitters since the Lyα emission may be diverse, not only by the condition of ionization and excitation of the gas, but also by dust extinction and resonance scattering. We chose a sample of star-forming galaxies that may crudely mimic the observed galaxies and investigated their general properties. We first make the samples of the model galaxies by simply dividing by their SFR in order to see how the fluctuation behaves as the SFR of the model galaxies changes. Those with SFR > 18 M_☉ yr⁻¹ are in Sample A, 10 M_☉ yr⁻¹ < SFR < 18 M_☉ yr⁻¹ are in Sample B, and 6.5 M_☉ yr⁻¹ < SFR < 10 M_☉ yr⁻¹ are in Sample C. The ranges are chosen so that the number density is the same as the observed value in the general blank fields. The observed rest-frame ultraviolet continuum flux of the Lyα emitters, V = 25–27 mag, corresponds to the SFR of a few to ≈10 M_☉ yr⁻¹ at z = 3.1 without reddening correction (Matsuda et al. 2004). Considering that the Lyα luminosity may vary both with the SFR and age, we also make a sample (Sample D) of the model galaxies that satisfy the condition log τ < A/SFR, where τ is the age and A is the constant to match their number density to the observed value. Model galaxies, either large SFR or young age, are selected by the criteria.

We then randomly put the boxes which correspond to the 700 arcmin² rectangular Suprime-Cam FoV (1000 boxes), or the 100 arcmin² square region (5000 boxes), both with a depth of 59 Mpc, into the volume of the Millennium simulation to obtain the distribution of the counts in the boxes. Each distribution is fitted by a single Gaussian function in order to evaluate the standard deviation σ_model of the model galaxies in the sample. While the distribution for the 700 arcmin² sample can be fitted by the Gaussian function very well from low to high overdensity values, the small tails of the high overdensity are seen for the 100 arcmin² samples, especially for Sample A with the large SFR, which can be better represented by the log-normal type probability distribution function. Table 4 summarizes the results. We found that the fluctuation becomes smaller for the sample of the lower SFR, which is reasonable if the objects with higher SFR galaxies are associated with more massive halos on average. This trend is small, however, and the standard deviation is not much different among the samples. Compared with these values, the observed overdensity is significantly large, 3.6–4.5 σ_model at the 700 arcmin² scale, and 8.4–9.1 σ_model at the 100 arcmin² scale.

Thus, we conclude that the high-density region of the SSA22 has a very rare density peak with 3σ–4σ significance at the scale of ≈60 Mpc (diameter), and likely to be 2σ–3σ at ≈100 Mpc. The overdensity is 8–10 times the standard deviation at the ≈30 Mpc scale. Note that there is no region with a similar overdensity of the model galaxies in the (500 h⁻¹)³ Mpc³ volume of the Millennium simulation in our realizations (1000 boxes and 5000 boxes for the larger and the smaller scales, respectively).

The SSA22 structure is thus characterized as a very important large-scale, high-density region used to study the earliest galaxy formation and evolution in the universe. There is evidence that the active phenomenon related to galaxy formation is enhanced over the large-scale structure. It is important to note that the number density of the giant Lyα blobs with sizes larger than 100 kpc is significantly high in the SSA22 area compared with the other general fields; Matsuda et al. (2010) reported the detection of 12 such giant blobs in the SSA22 fields (in 1.38 deg²) but only two objects in the general fields (1.04 deg²). Six objects are distributed in the SSA22-Sb1 field, and of them five are clustered near the density peak of the distribution of Lyα emitters, although they seem to avoid the very central region (see Figure 3 of Matsuda et al. 2010). These giant Lyα blobs are likely to be massive galaxies in their forming phase (Yamada 2009; Uchimoto et al. 2008, 2011). While the formation of the massive galaxies in the densest part might have occurred relatively earlier or faster, as the density peak of the stellar massive objects coincides with that of the Lyα emitters (Uchimoto et al. 2011), it is more active in the surrounding volume at the epoch. Tamura et al. (2009) also reported significant clustering of the bright submillimeter galaxies in the SSA22 field, and they show positive cross-correlation with the sky distribution of the Lyα emitters. Geach et al. (2005, 2007) found that more than a few Lyα blobs in Sb1 field are bright submillimeter or infrared sources. Lehmer et al. (2009) and Webb et al. (2009) also show that the fraction of AGNs is also high in the SSA22 field and several Lyα blobs are associated with AGNs. The SSA22 region can be called the Rosetta Stone because it helps us understand early galaxy formation as a function of the large-scale density of the universe.

We thank the staff of the Subaru Telescope for their assistance. This research is supported in part by the Grant-in-Aid 20450224 for the Scientific Research of the Ministry of Education, Science, Culture, and Sports in Japan. Data analysis was in part carried out on a common use data analysis computer system at the Astronomy Data Center, ADC, of the National Astronomical Observatory of Japan.