A FIRST SITE OF GALAXY CLUSTER FORMATION: COMPLETE SPECTROSCOPY OF A PROTOCLUSTER AT z = 6.01

Revealing structure formation and galaxy evolution are compelling objectives in modern astronomy. In the local universe, many studies have shown that these two topics are closely related. Star-formation activity is quenched in high-density environments, such as galaxy clusters, where red and early-type galaxies dominate. These galaxies represent the characteristic features of galaxy clusters, such as red sequences or morphology-density relation (Visvanathan & Sandage 1977; Dressler 1980). Even in modest galaxy-group environments, the star formation is known to be effectively quenched at z < 0.1 (e.g., Rasmussen et al. 2012). Especially, massive and bright elliptical galaxies in clusters have significantly different properties from their field counterparts, such as higher stellar velocity dispersion and higher α/Fe ratio. These differences suggest that elliptical galaxies in galaxy clusters contain more dark matter and involve a shorter star-formation timescale (Thomas et al. 2005; von der Linden et al. 2007). These are intuitively expected within the hierarchical structure formation scenario: halos in higher-density regions should collapse earlier and merge more rapidly, which causes earlier galaxy formation and more rapid evolution (Kauffmann et al. 1999; Benson et al. 2001; Springel et al. 2005; De Lucia et al. 2006). In this way, both observational and theoretical studies predict that galaxy evolution strongly depends on the environment. Therefore, direct observation of protoclusters, which are high density regions at high redshift, is required to clarify the relation between galaxy evolution and structure formation over cosmic time.

The fraction of star-forming galaxies in a galaxy cluster increases at higher redshift (Butcher & Oemler 1984; Haines et al. 2009; Lerchster et al. 2011), and a higher star-formation rate (SFR) is observed in higher-density environments at z ∼ 1 (e.g., Popesso et al. 2011). At z > 2, massive clusters as seen in the local universe have not yet formed; protoclusters are growing by merging and activating the star formation through accretion of material from their surroundings. Thus, protoclusters are identified as overdense regions of star-forming galaxies such as Lyman break galaxies (LBGs) and Lyα emitters (LAEs) (Malkan et al. 1996; Steidel et al. 1998; Venemans et al. 2007; Mawatari et al. 2012; Lee et al. 2014). Although star-forming and young galaxies are the majority, many red and massive galaxies certainly exist in some protoclusters, suggesting that environmental effects are actually seen at least up to z ∼ 2–3 (Kodama et al. 2007; Zirm et al. 2008; Kubo et al. 2013; Lemaux et al. 2014). Protocluster galaxies have higher stellar mass than their field counterparts (Steidel et al. 2005; Kuiper et al. 2010; Hatch et al. 2011), and exceptional objects, such as Lyα blobs, submillimeter galaxies, and active galactic nuclei, are likely to be discovered in high density environments (Digby-North et al. 2010; Tamura et al. 2010; Matsuda et al. 2011). What causes this difference between protocluster regions and field regions? In order to address this question, further observations of higher redshift protoclusters are important to probe the onset of initial environmental effects in the early universe. The findings will provide important information about the relation between the galaxy and environment during the first stage of cluster formation. Although the physical properties of protoclusters are not fully revealed at higher redshifts due to the difficulties involved in multi-wavelength imaging and the small number of spectroscopic confirmations, some studies pushed forward searching for high-redshift protoclusters. A handful of samples of protoclusters was discovered at z > 4 (Ouchi et al. 2005; Venemans et al. 2007; Overzier et al. 2009; Capak et al. 2011), and some overdense regions without spectroscopic confirmation were identified at even higher redshifts (Malhotra et al. 2005; Zheng et al. 2006; Stiavelli et al. 2005; Trenti et al. 2012).

In this paper, we extend the previous spectroscopic follow-up observations presented in Toshikawa et al. (2012). We have carried out a further spectroscopic observations of a protocluster at z = 6.01 in the Subaru Deep Field (SDF), which is the highest redshift protocluster known to date with sufficient spectroscopic confirmation.

Based on these complete spectroscopic observations, we attempt to investigate whether there are any differences between the protocluster and field galaxies at z = 6 by analyzing UV/Lyα luminosities and the three-dimensional distribution of protocluster galaxies.

The structure of this paper is as follows: we summarize the previous and new observations in Section 2 and describe the redshift identifications in Section 3. Section 4 compares the results with model predictions. We discuss the properties and the structure of the protocluster in Section 5. The conclusions are presented in Section 6. We assume the following cosmological parameters: $\Omega _\mathrm{M}=0.3, \Omega _\Lambda =0.7, H_0=70 \mathrm{\,km\,s^{-1}\,Mpc^{-1}}$, which yield an age of the universe of 910 Myr and a spatial scale of 40 kpc arcsec⁻¹ in comoving units at z = 6.01. Unless otherwise noted, we use comoving units throughout, and magnitudes are given in the AB system.

2.1. A Protocluster at z = 6.01

2.2. Complete Follow-up Spectroscopy of the Protocluster

We used the DEIMOS on the Keck II telescope in Multi-Object Spectroscopy (MOS) mode (Faber et al. 2003). The DEIMOS observation was conducted using a 830 line mm⁻¹ grating and the OG550 order blocking filter, providing a wavelength coverage of 7000–10000 Å with a pixel resolution of $0.47\,\mathrm{{\rm \mathring{\rm{A}}} \,{\rm pixel}^{-1}}$. The slit width was set to 10, giving a spectral resolution of 4.3 Å (R ∼ 2000). We targeted 34 i' dropout galaxies in/around the protocluster; 14 of these were already observed by our previous follow-up spectroscopy but no signal was detected. In addition, we allocated slits to 11 secondary targets having i' − z' > 1.0. The observation was carried out on 2013 April 8, and the sky condition was good with a seeing of ∼06. We obtained 15 exposures for a total integration time of 7.5 hr. Long slit exposures of a standard star, BD+332642, were used for the flux calibration. The data were reduced using the pipeline spec2d.⁸ Furthermore, we obtained spectra of two i' dropout galaxies through other MOS observations with Keck/DEIMOS on different projects (Kashikawa et al. 2011).

Combining our previous follow-up spectroscopic observations, we observed 53 i' dropout galaxies in/around the protocluster region. The DEIMOS pointing of this observation was set to cover both the protocluster region and a 2σ overdense region extending from the main protocluster region. The sky distribution of i' dropout galaxies and spectroscopically observed galaxies are shown in Figure 1. All of the i' dropout galaxies in the 2σ significant overdense region were completely observed with spectroscopy.

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From the observation as shown in above section, 14 emission lines are identified by careful examination of two- and one-dimensional spectra. All emission lines in our wavelength coverage are single emission lines; thus, there is almost no chance that Hβ or [O iii] emission lines contaminate our spectra because the wavelength coverage of our observation is wide enough to detect all these lines simultaneously. However, only [O iii]λ5007 emission, which is typically the strongest emission among them, may be detected if the other emissions are too faint to detect. We investigated the possibility that Hα, [O ii], and [O iii]λ5007 emission lines might have contaminated our sample, based on both imaging and spectroscopic data. Haines et al. (2008) demonstrated that ∼30% of red-sequence galaxies in the field have ongoing star-formation activity with EW(Hα) > 2 Å, but they also found that these galaxies disappear at an absolute r-band magnitude of M_r ≳ −18. Our samples are much fainter (>3 mag) than this magnitude, if they were at z ∼ 0.3 based on the photometry of our samples. Regarding [O ii] doublet emission lines, it is possible to distinguish between Lyα and [O ii] emission lines based on the line profile. The spectral resolution of our spectroscopic observation is high enough to resolve [O ii] emission lines as doublets (Δλ = 6.3 Å at z ∼ 1.3), although it would be practically difficult to resolve these in most cases due to low signal-to-noise ratio (S/N). In this case, the [O ii] emission line should be skewed to blueward, while Lyα emission lines from high redshift galaxies should be skewed to redward. We also calculated weighted skewness, S_w, which is a good indicator of the line asymmetry (Kashikawa et al. 2006). The asymmetric emission lines with S_w > 3 are evidence of Lyα emission from high redshift galaxies. Although some emission lines of this study have S_w < 3, strong sky lines and low S/N data prevent the accurate determination of skewness in these cases. The red optical color of i' − z' > 1.5 may indicate passive or dustier galaxies if they are at z ∼ 1.5 or 0.7, while [O ii] and [O iii]λ5007 emissions contradict with the prominent emission lines as the sign of high star-formation activity. Furthermore, according to Ly et al. (2007, 2012), [O ii] emitters at z ∼ 1.5 and [O iii] emitters at z ∼ 0.7 typically have i' − z' ∼ 0.2, and almost all have i' − z' < 1.0, much bluer than the selection criterion of our sample (i' − z' > 1.5). Therefore, it is unlikely that Hα, [O ii], and [O iii]λ5007 emission lines contaminate our sample, and Lyα is the most plausible interpretation for these single emission lines. We can conclude that all single emission lines detected from our i' dropout sample as Lyα emission lines at z ∼ 6.

Although the detection limit of an emission line depends on the wavelength and line width, the 1σ detection limit for emission lines is typically 6.3 × 10⁻¹⁹ erg s⁻¹ cm⁻² in this observation, which was derived from the sky fluctuations in a typical line width (∼6.3 Å). The limiting observed-frame equivalent width (EW) corresponding to the line detection limit is estimated to be 26.4 Å (5.3 Å) at $m_{z^{\prime }}=27.0\,\mathrm{mag}$ (25.0 mag).

One of the targets in this study was already detected as ID1 of Toshikawa et al. (2012), whose S/N was worse in the previous study; thus, the spectroscopic properties of ID1 are replaced with those derived in this study. Therefore, we were able to newly confirm 13 z ∼ 6 galaxies; thus, in total 28 z ∼ 6 galaxies, including the 15 in Toshikawa et al. (2012), are identified in/around the overdense region. We estimated the observed properties of the spectroscopically confirmed galaxies, such as UV absolute magnitude (M_UV), Lyα luminosity (L_Lyα), and rest-frame Lyα EW (EW_rest). Although faint continuum flux could not be detected in the observed spectra, M_UV were estimated from the z' band magnitudes by subtracting the spectroscopically measured Lyα flux and assuming flat UV continuum spectra (f_ν = constant). The spectra and observed properties of all these galaxies are provided in Figure 2 and Table 1. The redshift distribution is shown in Figure 3. It is clear that 10 galaxies are clustered in a narrow redshift range between z = 5.984 and z = 6.047 (Δz ≲ 0.06), corresponding to the radial distance of 26.1 Mpc in comoving units. The central redshift of the protocluster is estimated to be z = 6.01 using biweight (Beers et al. 1990) of 10 galaxies. This concentration is about 4.5 times higher than the number expected from a homogeneous distribution in redshift space.

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Table 1. Observed Properties of the 28 Spectroscopic Confirmed Galaxies

IDa	R.A.	Decl.	z'	i' − z'	zb	MUVc	fLyαd	LLyα	EWreste	Sw
	(J2000)	(J2000)	(mag)	(mag)		(mag)	(10−18 erg s−1 cm−2)	(1042 erg s−1)	(Å)	(Å)
1	13:24:31.8	+27:18:44.2	25.91 ± 0.04	1.48	$5.758^{+0.001}_{-0.001}$	−20.74 ± 0.04	4.39 ± 0.86	1.59 ± 0.31	7.7 ± 1.4	5.61 ± 1.36
2	13:24:18.4	+27:16:32.6	25.69 ± 0.03	1.70	$5.916^{+0.002}_{-0.002}$	−20.97 ± 0.03	12.49 ± 0.36	4.82 ± 0.14	19.0 ± 0.8	5.66 ± 1.14
3	13:24:25.2	+27:16:12.2	27.02 ± 0.09	1.89	$5.984^{+0.006}_{-0.002}$	−19.60 ± 0.10	4.95 ± 0.51	1.96 ± 0.20	29.6 ± 4.1	3.41 ± 4.03
4	13:24:30.2	+27:14:13.5	26.81 ± 0.08	1.96	$5.991^{+0.002}_{-0.002}$	−19.51 ± 0.11	15.42 ± 0.63	6.12 ± 0.25	107.5 ± 12.2	5.26 ± 1.21
5	13:24:26.0	+27:16:03.0	26.50 ± 0.06	1.71	$5.992^{+0.002}_{-0.002}$	−20.11 ± 0.10	8.16 ± 0.58	3.24 ± 0.23	31.4 ± 3.8	10.01 ± 0.93
6	13:24:21.3	+27:13:04.8	25.91 ± 0.04	2.65	$5.999^{+0.002}_{-0.006}$	−20.79 ± 0.04	7.59 ± 0.68	3.02 ± 0.27	15.3 ± 1.5	12.28 ± 1.84
7	13:24:29.0	+27:19:18.0	26.50 ± 0.06	1.60	$6.012^{+0.002}_{-0.002}$	−20.11 ± 0.07	7.87 ± 1.50	3.15 ± 0.60	30.7 ± 6.2	5.06 ± 1.84
8	13:24:28.1	+27:19:32.8	26.10 ± 0.04	1.54	$6.012^{+0.002}_{-0.002}$	−20.32 ± 0.06	21.34 ± 0.57	8.54 ± 0.23	70.8 ± 4.5	4.07 ± 0.73
9	13:24:26.5	+27:15:59.7	25.47 ± 0.03	1.91	$6.025^{+0.003}_{-0.004}$	−21.03 ± 0.05	29.94 ± 2.63	12.04 ± 1.06	50.9 ± 5.1	8.00 ± 0.21
10	13:24:31.5	+27:15:08.8	25.91 ± 0.06	1.95	$6.027^{+0.002}_{-0.002}$	−20.43 ± 0.10	27.36 ± 2.95	11.02 ± 1.19	95.7 ± 14.2	8.12 ± 0.23
11	13:24:26.1	+27:18:40.5	26.59 ± 0.06	2.32	$6.131^{+0.003}_{-0.003}$	−19.87 ± 0.11	12.38 ± 1.19	5.19 ± 0.50	67.0 ± 9.5	4.24 ± 0.35
12	13:24:31.6	+27:19:58.2	26.47 ± 0.06	2.07	$6.190^{+0.002}_{-0.002}$	−19.36 ± 0.19	24.48 ± 0.69	10.49 ± 0.29	213.1 ± 40.3	4.69 ± 0.88
13	13:24:44.3	+27:19:50.0	26.43 ± 0.06	2.49	$6.211^{+0.004}_{-0.007}$	−20.23 ± 0.09	15.01 ± 0.74	6.48 ± 0.32	58.7 ± 6.1	7.24 ± 1.24
14	13:24:20.6	+27:16:40.5	27.01 ± 0.09	1.90	$6.271^{+0.002}_{-0.005}$	−19.35 ± 0.22	14.28 ± 0.94	6.30 ± 0.42	136.4 ± 32.1	6.25 ± 0.62
15	13:24:32.6	+27:19:04.0	25.54 ± 0.03	1.47	$6.278^{+0.005}_{-0.002}$	−21.75 ± 0.03	4.00 ± 0.50	1.77 ± 0.22	2.2 ± 0.3	2.35 ± 3.20
16	13:24:44.8	+27:17:48.8	26.10 ± 0.04	1.76	$5.764^{+0.001}_{-0.001}$	−20.55 ± 0.04	7.08 ± 0.72	2.57 ± 0.26	16.0 ± 1.8	6.82 ± 0.71
17	13:24:44.5	+27:20:23.4	26.70 ± 0.07	1.09	$5.791^{+0.001}_{-0.001}$	−19.95 ± 0.07	6.18 ± 0.71	2.27 ± 0.26	26.6 ± 3.3	2.80 ± 1.39
18	13:24:27.4	+27:17:17.4	26.62 ± 0.06	1.75	$5.797^{+0.001}_{-0.001}$	−20.03 ± 0.06	5.67 ± 0.70	2.09 ± 0.26	23.3 ± 2.9	2.15 ± 0.42
19	13:24:26.6	+27:16:41.7	26.84 ± 0.08	1.74	$5.844^{+0.001}_{-0.001}$	−19.84 ± 0.08	1.26 ± 0.33	0.47 ± 0.12	6.3 ± 1.5	−0.66 ± 0.67
20	13:24:12.7	+27:16:33.3	25.99 ± 0.04	1.39	$5.914^{+0.001}_{-0.001}$	−20.67 ± 0.04	13.17 ± 0.74	5.08 ± 0.29	30.2 ± 2.2	2.51 ± 0.27
21	13:24:10.8	+27:19:04.0	26.61 ± 0.06	2.30	$6.039^{+0.001}_{-0.001}$	−19.88 ± 0.09	10.95 ± 0.99	4.43 ± 0.40	54.6 ± 8.3	6.04 ± 0.57
22	13:24:05.9	+27:18:37.7	26.87 ± 0.08	2.04	$6.047^{+0.001}_{-0.001}$	−19.84 ± 0.09	3.97 ± 0.72	1.61 ± 0.29	20.9 ± 4.5	4.53 ± 0.82
23	13:24:30.2	+27:16:10.8	26.15 ± 0.05	2.21	$6.125^{+0.001}_{-0.001}$	−20.61 ± 0.06	9.37 ± 0.60	3.92 ± 0.25	28.4 ± 2.4	0.93 ± 0.19
24	13:24:37.3	+27:20:08.5	26.00 ± 0.04	2.88	$6.224^{+0.001}_{-0.001}$	−20.93 ± 0.06	13.46 ± 1.37	5.85 ± 0.59	26.9 ± 3.9	30.20 ± 6.33
25	13:24:51.7	+27:19:55.3	26.84 ± 0.08	2.07	$6.252^{+0.001}_{-0.001}$	−19.99 ± 0.12	8.90 ± 0.57	3.90 ± 0.25	43.1 ± 6.6	0.87 ± 0.90
26	13:24:06.6	+27:16:46.4	26.81 ± 0.08	1.79	$6.267^{+0.001}_{-0.001}$	−20.28 ± 0.09	4.99 ± 0.40	2.20 ± 0.18	19.3 ± 2.5	2.00 ± 0.11
27	13:24:24.5	+27:15:56.9	26.69 ± 0.07	2.22	$6.359^{+0.001}_{-0.001}$	−20.25 ± 0.12	14.07 ± 0.71	6.41 ± 0.32	58.1 ± 8.4	8.28 ± 2.03
28	13:24:06.5	+27:16:34.3	26.97 ± 0.09	1.94	$6.549^{+0.001}_{-0.001}$	−20.92 ± 0.10	4.39 ± 0.64	2.14 ± 0.31	9.3 ± 2.0	3.86 ± 1.35

Notes. ^aThe galaxies with ID = 1–15 were identified by previous observations, and have the same ID as in Table 3 of Toshikawa et al. (2012). The others (ID = 16–28) were newly identified in this observation. ^bThe redshifts were derived by the peak wavelength of the Lyα emission line, assuming the rest wavelength of Lyα to be 1215.6 Å. These measurements could be overestimated in the case of significant damping wings by IGM. When emission lines are located near strong sky lines, line profiles are affected by them, and the position of the peak could be shifted. These effects of sky lines and the wavelength resolution are taken into account estimating the error. ^cThe absolute magnitudes of the UV continuum (at 1300 Å in the rest-frame) were derived from z' band magnitudes using Equation (1) of Kashikawa et al. (2011), assuming that the UV continuum slopes (f_λ∝λ^β) are β = −2, and the continua blueward of Lyα are entirely absorbed by intergalactic medium. No aperture correction was applied. The error was estimated using the following Monte Carlo simulation: (1) Gaussian random errors were assigned to the measured Lyα flux and z' band magnitude and M_UV was re-calculated; (2) the process is repeated 100,000 times; (3) the error of M_UV was determined from the rms fluctuation. The systematic error depending on the assumption of β was not taken into account, since the scatter of i' dropout galaxies' β is not well constrained (e.g., Bouwens et al. 2012; Wilkins et al. 2011). Even if β was varied from −3.0 to −1.0, the variation of the UV continuum flux is a few percent. ^dThe observed line flux corresponds to the total amount of the flux within the line profile. The error was estimated from the noise level at wavelengths blueward of Lyα. ^eThe rest-frame equivalent widths of Lyα emission were derived from the combination of M_UV and L_Lyα. The error was estimated from M_UV, L_Lyα and their errors. The systematic error of β is not taken into account.

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We found a protocluster with 6σ overdensity at z = 6.01, but how large is the dark matter halo that it will evolve into at z = 0? To answer this question, it is necessary to compare our observations with theoretical predictions about the descendants of high redshift overdensities by tracing hierarchical merging histories. Overzier et al. (2009) and Chiang et al. (2013) investigated the relation between galaxy overdensity at high redshift and dark matter halo mass at z = 0 by using a combination of N-body dark matter simulations and semi-analytic galaxy formation models. They systematically studied cluster development from z ∼ 6 to z = 0 and found clear correlations between overdensity at high redshift and halo mass at z = 0, depending on, e.g., the sample selection, search volume, and redshift accuracy of the tracer galaxies, as well as the mass of the clusters. Here, we perform a new simulation specifically designed to match the observational details of our i' dropout survey as closely as possible. This design is important because our target selection is characterized by a rather broad photometric selection at z = 6 ± 0.5 compared with the cases described by Chiang et al. (2013). We will connect directly the observed quantity, the significance of the overdensity of the surface number density, to the dark matter halo mass at z = 0.

We used the light-cone model constructed by Henriques et al. (2012). A brief outline of the construction of light-cone models is presented below. First, the assembly history of the dark matter halos was traced using an N-body simulation (Springel et al. 2005), in which the length of the simulation box was 500 h⁻¹ Mpc and the particle mass was 8.6 × 10⁸ h⁻¹ M_☉. The distributions of dark matter halos were stored at discrete epochs. Next, the processes of baryonic physics were added to dark matter halos at each epoch using a semi-analytic galaxy formation model (Guo et al. 2011). Based on the intrinsic parameters of galaxies predicted by the semi-analytic model, such as stellar mass, star formation history, metallicity, and dust content, the photometric properties of simulated galaxies were estimated from the stellar population synthesis models developed by Bruzual & Charlot (2003). Then, these simulated galaxies in boxes at different epochs were projected along the line-of-sight, and intergalactic medium (IGM) absorption was applied in order to mimic a pencil-beam survey using the Madau (1995) IGM light-cone set from Overzier et al. (2013). Finally, 24 light-cone models with 1.4 × 1.4 deg² FoV were extracted using these procedures.

The same color selection applied to the observations (Toshikawa et al. 2012) was also applied to the simulated catalog of each light-cone model. In this analysis, we only used the galaxies whose dark matter halos are composed of more than 100 dark matter particles (∼1 × 10¹¹ M_☉ halo mass), because galaxies' spectral energy distributions (SEDs) in small halos are not stable between redshift snapshots. A color correction was also made to transform the light-cone's SDSS filter system to Subaru/SprimeCam's one. We detected ∼3000 i' dropout galaxies per 2 deg² FoV down to the same limiting magnitude of z' band, as in the SDF. The number counts of the simulated i' dropouts were found to be nearly consistent with those observed in the SDF (Figure 4). Although there is some deviation at the bright end, this is probably caused by the contamination of dwarf stars, which are not included in the model. As in Figure 4, the observed number counts well agree with the simulated ones by correcting for the contamination of dwarf stars, which is estimated by the star count model developed by Nakajima et al. (2000). We also compared the simulated number counts with those of z ∼ 6 galaxies in Bouwens et al. (2014), applying the selection window for z ∼ 6 galaxies presented in Bouwens et al. (2014) to light-cone models. Both number counts are almost consistent with each other. Next, we investigated the sky distribution and estimated the local surface number density in the light-cone catalogs in the same way as in the SDF. For each overdense region, the dominant structure was identified as follows. First, we selected the strongest spike in the redshift distribution for that region. Next, we determined the halo ID of the most massive halo in that redshift spike. Finally, the descendant halos at z = 0 for each overdense region were identified by tracing the halo merger tree of those z ∼ 6 halos. Figure 5 shows the relation between the significance of the overdensities at z ∼ 6 and the halo mass at z = 0. Although there is large scatter, these two quantities are correlated quite closely. The Spearman's rank correlation coefficient is 0.55, indicating that the probability of no correlation is <10⁻⁵. We find that 95% (100%) of >4σ (>6σ) overdense regions are expected to include protoclusters. This result suggests that we can detect a real protocluster with high confidence by measuring the overdensity significance if it is more than 4σ away from the observed surface number density, and also that we can infer its descendant halo mass at z = 0 based on Figure 5. The protocluster that we found with 6σ significance at z ∼ 6 is predicted to evolve into a dark matter halo with a mass of 5 × 10¹⁴ M_☉ on average and at least 1 × 10¹⁴ M_☉ at z = 0, suggesting that this is a progenitor of a local galaxy cluster. We also estimated the number density of such overdense regions at z ∼ 6 based on the large survey volume covered by the simulations. The average number density of regions with >6σ significance is 0.42 deg⁻² (0.83 per light-cone), though the scatter from field to field is as large as 0.43 deg⁻². Considering that our finding was made in a field measuring only 0.24 deg², this discovery must have been quite serendipitous.

In addition, we estimated the probability for a galaxy located at a certain position relative to the protocluster center to become a cluster member at z = 0. Based on the simulation, we can map the galaxy distribution of a protocluster at z ∼ 6 by tracing back the merger tree of a cluster at z = 0. Although protoclusters have different structural morphologies, such as filamentary or sheet-like, we estimated the probability by counting the numbers of both descendant cluster members and non-members as a function of the distance to the protocluster center. The center of each protocluster is defined as the peak of the three-dimensional density field, and a spatial map of these probabilities is derived for each protocluster. We extracted 19 z ∼ 6 protoclusters with >6σ overdensity and made a median stack in order to derive a spatial map of the probability that a galaxy will merge into a single halo by z = 0 as a function of distance from the center of the protocluster (Figure 6). Additionally, we plotted the observed protocluster members within a narrow redshift range (ID = 3–10, 21, 22) measured by our spectroscopy, as shown in Figure 6. The center of the protocluster is simply defined by the middle values between the maximum and the minimum of R.A./decl./redshift of 10 galaxies, which is around (ΔR.A., Δdecl.) = (− 4, −2) Mpc in Figure 1 and z = 6.02. We found that these 10 (nine without ID = 22) galaxies will become a single halo by z = 0 with a probability of >80% (>95%). Based on the model prediction, even two galaxies, which are located around (ΔR.A., Δdecl.) = (− 11, 3) Mpc in Figure 1, are expected to coalesce into a cluster even though they are located in a region of only <2σ significance. This illustrates well that our 10 protocluster members are indeed expected to become members of a cluster at z = 0. It should be noted that the estimate of the center of the observed protocluster involves some uncertainties, because only Lyα emitting galaxies can be identified as protocluster members; detection completeness also grows some uncertainties. In this study, the number of protocluster members is only 10; therefore, we estimated the center of the observed protocluster in various ways, using the average, median, or biweight (Beers et al. 1990) of the 10 members' positions, and checked the differences between these methods. As a result, the uncertainties in the center are <1.5 arcmin (3.6 Mpc) in the spatial and <0.01 (4.2 Mpc) in the redshift direction. Although the most outer galaxy could have a probability of only 50% or less in the worst case, most galaxies have a high probability of >80%. Therefore, we conclude that these 10 galaxies are likely protocluster members.

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Based on comparison with the model prediction in the previous section, we classified 28 spectroscopically confirmed galaxies into two groups: 10 protocluster members (ID = 3–10, 21, 22) and 18 non-members (ID = 1, 2, 11–20, 23–28). The members are clustered in the redshift range between z = 5.984 and z = 6.047 (Δz ≲ 0.06), which corresponds to a radial separation of 26.1 Mpc. The properties and distribution of the galaxies within the protocluster are discussed in this section.

5.1. Galaxy Properties

We compared several galaxy properties between members and non-members to investigate whether there was any difference due to their environments at this early epoch. The average and standard deviation of L_Lyα, M_UV, and EW_rest in the protocluster and field galaxies were estimated, and found that all of these properties of protocluster and field galaxies are consistent with each other within 1σ scatter, as shown in Table 2. Figure 7 shows that there are no significant differences between the M_UV and LyαEW_rest distribution between protocluster and field (the p-value derived by the Kolmogorov–Smirnov (K-S) test is >0.3); however, a possible difference can be seen at the lowest EW_rest bin (EW_rest < 20 Å). Because both protocluster and field galaxies were observed in the same observing runs, it is unlikely that this difference was caused by a difference in the completeness limit of the spectroscopic observations. Taking into account the completeness limit, the sample in the lowest EW_rest bin mostly consists of the brightest galaxies in M_UV. This may imply that the brightest galaxies in the overdense region are older and have more dust, suppressing the Lyα emission compared with those in the field galaxies. Lee et al. (2013) also reported that the median EW_rest of z = 3.78 protocluster galaxies is higher than that of field galaxies. However, the Lyα emission, which is a resonantly scattered line, can be affected by many physical parameters such as SFR, dust amount, and geometry of dust and neutral gas (e.g., Shibuya et al. 2014). It is therefore difficult to identify the reason of the possible difference at the lowest EW_rest. In this study of a z = 6.01 protocluster, it should be noted that the difference can be only seen in the lowest EW_rest bin, and there is no significant difference between the EW_rest distribution of the protocluster and the field galaxies as a whole.

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Table 2. Average of Observed Properties of Protocluster and Field Galaxies

	LLyα	MUV	EWrest
	(1042 erg s−1)	(mag)	(Å)
Protocluster	5.51 ± 3.78	−20.16 ± 0.49	50.74 ± 31.66
Field	4.21 ± 2.44	−20.34 ± 0.61	45.53 ± 52.60
p-valuea	0.78	0.78	0.32

Note. ^aUsing the K-S test, the distribution of observed properties are compared between protocluster and field galaxies.

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We measured the Lyα fraction, which is the fraction of Lyα emitting galaxies among our dropout galaxies. This has been widely studied at 4 < z < 8 (e.g., Stark et al. 2010; Schenker et al. 2012; Treu et al. 2013), and the fraction steadily increases toward higher redshift, while it gradually decreases beyond z = 6, possibly as a signature of reionization. However, those measurements were made using only field galaxies. It is important to compare the Lyα fraction between field galaxies and galaxies in overdense regions in order to ascertain whether it has environmental dependence or not. Since it is impossible to distinguish between member and non-member galaxies in the spectroscopically undetected galaxies, we measured the Lyα fraction in the projected overdense region over 8 × 8 arcmin², including Lyα emitting galaxies, even if they were found in the field behind and in front of the protocluster. We assumed that the Lyα undetected galaxies are all at z = 6.0, and calculated their M_UV. In this estimate, expected IGM absorption at z = 6.0 in the z' band was also corrected for though the correction is as small as 0.08 mag. We here apply the same color selection criterion of i' − z' > 1.3 as in Stark et al. (2011). Our spectroscopic completeness still remains high (>95%) in the overdense region because i' dropout galaxies with 1.3 < i' − z' < 1.5 were also observed as secondary targets. We compare our result with the bright sample of Stark et al. (2011), which has the same M_UV range as ours. The fraction in the overdense region was found to be $0.0^{+6.4}_{-0.0}\%$ and 20.0 ± 11.0% for EW_rest > 50 Å and >25 Å, which are almost the same as in the field at z ∼ 6.

These results show that we do not find any significant differences in the observed properties between protocluster and field galaxies. This would indicate that this protocluster is still in the early phase of cluster formation, before any environmental effect works on galaxy properties. However, the observed properties of protocluster galaxies in this study are very limited. According to other works for lower-redshift protoclusters, differences in galaxy properties between protocluster and field galaxies begin to appear at z ∼ 2–3: protocluster galaxies are ∼ two to three times more massive than field galaxies at the same redshift (Steidel et al. 2005; Kuiper et al. 2010; Hatch et al. 2011). In this study, the UV and Lyα properties of the protocluster galaxies are almost the same as those of field galaxies. These properties are closely related to star-formation activity. This could imply that galaxy mergers could scarcely happen even in the high-density region at z ∼ 6 because galaxies basically contain large amounts of gas in their young phase. Under such conditions, galaxy mergers can ignite bursty star formation. Therefore, the stellar-mass difference as seen at z = 2–3 could emerge in a later cluster formation phase rather than in this early stage; overdense regions would result in a higher rate of galaxy mergers, which could prolong star formation. However, direct stellar mass measurements using deep infrared imaging of the protocluster at z = 6.01 will be required to investigate this issue further.

5.2. Protocluster Structure

As has been discussed in Toshikawa et al. (2012), the protocluster appears to have some substructure: there are no spectroscopically identified galaxies at the central region of the protocluster, and it is far from virial equilibrium. In this study, the number of spectroscopically identified member galaxies was increased to 10, but their velocity dispersion was found to be still too high (869 ± 85 km s⁻¹) to consider virial equilibrium. Figure 8 presents an updated version of the three-dimensional galaxy distribution in the protocluster after including new spectroscopically identified galaxies; it reveals that the protocluster seems to consist of four subgroups of close pairs. Protocluster galaxies having almost the same redshifts happen to be located near to each other in the spatial dimension as well. To discuss this more quantitatively, the histogram of the spatial separation from the nearest galaxy is shown in the left panel of Figure 9. The K-S test suggests that the observed histogram is significantly different from a random distribution (the p-value is less than 0.01); random distribution was generated from a uniform distribution in the limited-size box of 17 × 19 × 29 Mpc³, which corresponds to the volume occupied by the 10 member galaxies. Furthermore, Figure 9 shows a histogram of the separation from the nearest neighbor of field LAEs. The data were taken from the spectroscopic LAE samples at z = 5.7 and 6.5 (Kashikawa et al. 2011), which have a high degree of spectroscopic completeness (∼80%–90%). To compare protocluster and field galaxies more accurately, the difference in average number density between protocluster and field are corrected. The separation of field LAEs is multiplied by (n_field/n_protocluster)^1/3 ∼ 0.6, where n_protocluster and n_field are the average number density of the protocluster and field, respectively. The p-value of a K-S-test between the distribution of field LAEs and that of the protocluster was found to be less than 0.03, suggesting that the excess of close pairs cannot be attributed to the clustering nature of LAE alone.

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We also evaluated the separations from the second nearest galaxies (the right panel of Figure 9) based on the same procedure as for the first nearest neighbors. Its separation distribution was found to be reproduced by the random distribution with the p-value of 0.23. Moreover, the separations from Nth nearest galaxies were also calculated, and shown in Figure 10. The separation, D, was fitted as a function of the Nth (N > 2) nearest galaxy: log (D) = a × log (N) + b (a and b are free parameters). The values of a and b were a = 0.53 ± 0.04 and b = 1.82 ± 0.07 (blue dashed line in Figure 10). The separation was found to be well approximated by this formula for N > 2, while the observed separation from the first nearest galaxies was found to be smaller with 1.8σ significance than the extrapolation from the formula. Even if we exclude two galaxies that have exceptionally small separations from the first nearest galaxy, the trend was confirmed with 1.8σ significance. Actually, as seen in Figure 10, all individual separations from the first nearest galaxy are smaller than the best fitted line. It is a statistically reliable result that galaxy separation from the first nearest galaxy is significantly smaller in this protocluster. Therefore, the protocluster galaxies tend to make galaxy pairs rather than triplets or larger structures. However, the typical separation length (>100 kpc in physical units) is too large for galaxy mergers or interactions. This is consistent with Cooke et al. (2010) who found that the fraction of Lyα emission in LBGs is larger in pairs with separation of only ⩽70 kpc in physical units. We could not find any strong correlation between the separation length and observed properties (M_UV, L_Lyα, and EW_rest).

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The inset in Figure 10 shows the same relations in the case of protoclusters at lower redshifts taken from the literature (Steidel et al. 1998; Venemans et al. 2007; Kuiper et al. 2012). Most of the protoclusters, whose members have been identified by Lyα emission, show the smooth relation without a bend at the first nearest neighbor. Interestingly, the protoclusters, SSA22 and MRC 0316-257, whose members are selected by the dropout technique, show a similar trend as our study: smaller separations from the first nearest galaxies than those from the second or higher nearest galaxies. Generally, LBGs have brighter UV luminosity than LAEs; thus, this trend would imply that bright galaxies are located at the core of a protocluster and make pair-like structures, while faint galaxies are more widely distributed. Bright galaxies, presumably more massive, would form structures faster than less massive galaxies. However, this comparison requires many caveats because the limiting magnitudes and spectroscopic completeness are different; in most lower-redshift protoclusters, only 40%–60% galaxies are spectroscopically observed. We only selected LBGs or LAEs in the above analysis, but various galaxy populations were found in z ∼ 2–3 protoclusters. For example, Kuiper et al. (2011, 2012) found large subgroups in protoclusters at z ∼ 2–3, which contain Hα and [O iii] emitters as well. These results would be consistent with the hierarchical structure formation model: at first, galaxies form small groups like galaxy pairs, and these small groups grow to larger structures through mergers. The cosmic epoch of z ∼ 6 may be the onset of cluster formation.

5.3. Ancestors of Large-scale Structure

An interesting distribution of galaxies can be found behind the protocluster region. Four galaxies at z ∼ 6.2 (color coded by light green in Figure 11) seem to align in the east–west direction at Δdecl. ∼ 6 Mpc, like a filamentary structure, along the 2σ overdense region. This filamentary structure, which is 80 Mpc away from the protocluster, is unlikely to merge with the protocluster by z = 0. However, it is possible that these four galaxies may become another galaxy group by z = 0 because they span only <6 arcmin and Δz < 0.06. It should be noted that the length of large-scale filaments, as seen in the local universe, can reach more than 100 Mpc (e.g., Park et al. 2012; Smargon et al. 2012; Alpaslan et al. 2014). These galaxies would thus be part of the large-scale structure around a cluster at z = 0. Therefore, the protocluster at z = 6.01 might be embedded in a large-scale overdense region. Einasto et al. (2014) found that galaxy properties depend on the global environment like a supercluster, as well as the local environment like a galaxy group. Thus, it will be interesting to carry out further follow-up observations with infrared imaging on this protocluster region in order to investigate galaxy properties in various environments, such as protoclusters, filaments, and fields.

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In this study, we have presented a systematic spectroscopic observation of the highest redshift protocluster known to date. We performed spectroscopy for all 53 i' dropout galaxies down to 27.09 mag in z' band in/around the protocluster region, and Lyα emission of EW_rest ≳ 11 Å should be completely detected with S/N > 3 in our spectroscopy. The results and implications of this study are summarized below.

• 1.  
  From this observation, 13 galaxies were newly identified as real z ∼ 6 galaxies by detecting their Lyα emission lines. Combined with the sample from Toshikawa et al. (2012), 28 galaxies were confirmed to be located at z ∼ 6. Ten of these are clustered in a narrow redshift range between z = 5.984 and z = 6.047 (Δz ≲ 0.06), corresponding to a radial separation of 26.1 Mpc.
• 2.  
  We compared our results with the light-cone models, in which we applied the same i' dropout selection and the same overdensity measurements as in the observation. We obtained a relation between the observed overdensity significance at z ∼ 6 and the predicted dark matter halo mass at z = 0. Based on this relation, the observed protocluster with 6σ significance is predicted to grow into a galaxy cluster (∼5 × 10¹⁴ M_☉) at z = 0.
• 3.  
  We also derive the spatial map of probability for a galaxy located at a certain position relative to the protocluster center to become a cluster member at z = 0. Based on the map, the 10 galaxies within 10 Mpc from the center of the protocluster are found, with more than an 80% probability, to merge into a single dark matter halo by z = 0. This clustering of galaxies is consistent with the progenitor of a galaxy cluster.
• 4.  
  No significant difference in observed galaxy properties, such as M_UV, L_Lyα, and EW_rest, between the protocluster and the field are found except for the brightest galaxies. This suggests that this protocluster is still in the early phase of cluster formation before the onset of any obvious environmental effects. Further multi-wavelength imaging to trace their SEDs from the rest-frame optical to far-infrared wavelength will provide us with clues about possible differences in stellar mass, dust, and gas mass.
• 5.  
  The velocity dispersion of this protocluster is too high (869 ± 85 km s⁻¹) to consider virial equilibrium. This high velocity dispersion would be caused by the internal three-dimensional structure of the protocluster. We also obtained a statistically reliable result that galaxies tend to form close pairs in the protocluster. These pair-like subgroups will coalesce into a single halo and grow into more massive structures through accretion of material from their surroundings. Filamentary structure was found to be 80 Mpc away from the protocluster. Although it is not expected to merge with the protocluster, this could become a large-scale structure around the galaxy cluster, as seen in the local universe.

As we have shown, the results obtained in this study are qualitatively and, in many ways, also quantitatively, consistent with the hierarchical structure formation model. The epoch of z ∼ 6 may be the time when galaxies start to coalesce in order to form a cluster as seen in the local universe. It is necessary to increase the number of observations of protoclusters at z ∼ 6 and even at lower redshifts to obtain statistical samples of protoclusters across cosmic time, in order to clarify the general features of cluster formation and galaxy evolution in dense regions. Using the new instrument Hyper SuprimeCam on the Subaru telescope, we are carrying out an unprecedentedly wide and deep survey over the next five years. Based on the number density estimate of protoclusters in Section 4, >10 z ∼ 6, >500 z ∼ 5–4 protoclusters, and even one z ∼ 7 protocluster would be discovered from this Subaru strategic survey. These will enable us to derive a more complete picture of cluster formation and galaxy evolution in high density environments.

Some of the data presented here were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The other data were collected with the Subaru telescope, which is operated by the National Astronomical Observatory of Japan. We are grateful to the W. M. Keck and Subaru Observatory staff for their help with the observations. We are also grateful to Dr. Takashi Hattori, Subaru Sr. Support Astronomer, who helped us reduce the spectroscopic data obtained by Keck/DEIMOS. The Millennium Simulation databases used in this paper and the web application providing online access to them were constructed as part of the activities of the German Astrophysical Virtual Observatory (GAVO). We thank the anonymous referee for valuable comments and suggestions which improved the manuscript. This research was supported by the Japan Society for the Promotion of Science through Grant-in-Aid for Scientific Research 23340050 and 12J01607.

Facilities: Subaru (FOCAS) - Subaru Telescope, Keck:II (DEIMOS) - KECK II Telescope