LARGE-SCALE STRUCTURE AROUND A z = 2.1 CLUSTER

Large-scale structure plays a critical role in the evolution and assembly of galaxies. Red and massive elliptical galaxies are preferentially located in high-density environments today (e.g., Dressler 1980; Postman & Geller 1984; Hogg et al. 2004), where star formation is strongly suppressed (e.g., Hashimoto et al. 1998; Gómez et al. 2003; Goto 2005). In a hierarchical structure formation paradigm, these correlations with local environments should become less significant and even overturn at earlier epochs (e.g., Hopkins et al. 2008). Although some studies have observed the reversal of the star formation–density relation at $z\sim 1$ (Elbaz et al. 2007; Cooper et al. 2008), exactly when and where these correlations with local environments are established remains highly uncertain (e.g., Patel et al 2009; Tran et al. 2010; Brodwin et al. 2013; Darvish et al. 2014, 2016; Smail et al. 2014). In fact, the existence of mature cluster cores and evidence of early mass assembly of brightest cluster galaxies at z ∼ 1–2 suggest that the formation of these rare objects takes place rapidly at even higher redshifts (e.g., Collins et al. 2009; Gobat et al. 2011; Zeimann et al. 2012). It is thus critical to probe beyond $z\sim 2$ so we can observe the formation of massive galaxy clusters and directly infer the early environmental influences on galaxy evolution.

Common probes of galaxy clusters (e.g., X-ray emission from hot intracluster gas, red galaxy sequence, inverse Compton scatter of the Cosmic Microwave Background photons off the hot intracluster medium; Allen et al. 2011) reach their limits at $z\sim 2$ due to the combination of survey sensitivity and the less-evolved nature of large-scale structure. Identification of protoclusters at $z\gtrsim 2$ thus often rely on significant overdensities of galaxies on the sky and in the redshift space (e.g., Steidel et al. 1998; Miley et al. 2004). One successful strategy to identify high-z protoclusters is to place the survey area around highly biased galaxies like radio galaxies and quasars since they are likely progenitors of massive elliptical galaxies in the core of present-day galaxy clusters (e.g., Kurk et al. 2000; Miley et al. 2004; Venemans et al. 2007; Utsumi et al. 2010; Capak et al. 2011; Hatch et al. 2011; Hayashi et al. 2012; Koyama et al. 2013a; Wylezalek et al. 2013). Meanwhile, some protoclusters have also been discovered serendipitously via narrow-band imaging or spectroscopic surveys (e.g., Steidel et al. 1998; Shimasaku et al. 2003; Toshikawa et al. 2012; Lee et al. 2014b). In either case, the $z\gtrsim 2$ protoclusters are often traced by optically selected galaxies like (spectroscopically confirmed) Lyman Break galaxies (LBGs), Lyα emitters (LAEs), and/or Hα emitters (HAEs).

The recent advent of large submillimeter surveys has enabled an alternative window to search for $z\gtrsim 2$ protoclusters. Clustering analysis of submillimeter galaxies (SMGs, Blain et al. 2002) show that SMGs are located in massive halos at $z\sim 2$ (e.g., Blain et al. 2004; Hickox et al. 2012), yet it remains highly debated whether SMGs indeed trace the densest environments at z = 0 (Capak et al. 2011; Carilli et al. 2011; Cowley et al. 2015; Miller et al. 2015). Observations of SMG overdensities have led to contradictory interpretations. Casey et al. (2015) discover a highly unusual filamentary structure at z = 2.47 containing seven dusty star-forming galaxies (DSFGs with star formation rates (SFRs) $\gtrsim 200$ M_⊙ yr⁻¹; Casey et al. 2014), five active galactic nuclei (AGNs with ${L}_{X}\,\gtrsim$ ${10}^{43.5}$ erg s⁻¹), and 33 other spectroscopically confirmed LBGs within a comoving volume of 15,000 Mpc³. Such overdensities in DSFGs (${\delta }_{{\rm{DSFG}}}=10$) and AGNs (${\delta }_{{\rm{AGN}}}=35$) are unlikely to be a result of survey incompleteness or biases, and Casey et al. (2015) argue that this structure is a possible progenitor of the present-day Coma-like cluster. On the other hand, Blain et al. (2004) and Chapman et al. (2009) identify an association of SMGs at z = 1.99 in the GOODS-N field, in which Chapman et al. (2009) find a strong overdensity of SMGs (${\delta }_{{\rm{SMG}}}=10$), but only a moderate overdensity of UV-selected galaxies (${\delta }_{{\rm{UV}}}=2.5$). Based on the linear theory of spherical collapse, Chapman et al. (2009) conclude that the structure traced by UV-selected galaxies will not collapse by¹¹ z = 0, and they attribute the contradictory conclusions based on SMG overdensities as a result of an even larger galaxy bias of SMGs than they assumed.

Protoclusters that are identified through both submillimeter and optical windows can provide crucial insights to understand the nature of DSFG-rich structures and their differences with protoclusters traced by optically selected galaxies. Tamura et al. (2009, also see Umehata et al. 2014, 2015) present an imaging survey of 1.1 mm emission in SSA 22 (a z = 3.09 protocluster, Steidel et al. 1998), and they find that the population of SMGs is enhanced near the protocluster core and there is a spatial correlation between SMGs and LAEs. In MRC1138−262 (a z = 2.16 protocluster, Kurk et al. 2000), Dannerbauer et al. (2014) find an excess of SMGs in the protocluster, yet the concentration of SMGs does not coincide with the central radio galaxy. Such offset between the dusty starburst population and the densest regions of protocluster is also seen in a z = 1.62 structure (Smail et al. 2014). Does the spatial distribution of dusty starbursts represent the evolutionary status of protoclusters? What are the implications when using DSFGs as tracers of large-scale structure? A systematic search of DSFG populations in the known protoclusters is necessary to shed light on these questions.

In this paper, we present a search of DSFGs and large-scale structure around a bona-fide galaxy cluster at z = 2.095 (Yuan et al. 2014, hereafter Y14). We provide an overview of this z = 2.095 cluster in Section 1.1, and we detail our analysis in Section 2. In Sections 3–5, we present our results on the large-scale structure found around the z = 2.095 cluster, the environmental dependence of galaxy properties, and a detailed scrutiny of DSFGs in the structure. We discuss the implications of our results and provide a brief summary in Section 6. Throughout this paper, we adopt a ΛCDM cosmology with ${H}_{0}=70$ km s⁻¹ Mpc,${}^{-1},{{\rm{\Omega }}}_{M}=0.3$, and ${{\rm{\Omega }}}_{{\rm{\Lambda }}}=0.7$.

1.1. A z = 2.095 Cluster in the COSMOS Field

To search for the populations of DSFGs within and near the ZFIRE cluster, we draw a sample of spectroscopically confirmed galaxies at $2.07\leqslant z\leqslant 2.12$ from a number of redshift surveys. We note that the ZFIRE cluster members in Y14 span a redshift range of $2.08\lesssim z\lesssim 2.11$, and here we enlarge this redshift range by 0.01 to search for galaxies in the large structure that may also be associated with the cluster core. However, all of the cluster members defined based on the friends-of-friends (FoF) analysis (Section 3.1) fall within a similar redshift range as the ZFIRE cluster members. The redshift surveys included in this work are listed below.

• 1.  
  The ZFIRE survey from Y14 and Nanayakkara et al. (2016, submitted). The targets were originally selected based on photometric redshifts from Spitler et al. (2012) as part of the ZFOURGE survey and observed with Keck I Multi-Object Spectrometer For Infra-Red Exploration (MOSFIRE). The ZFIRE survey achieves a detection limit (S/N ∼ 5) of objects with ${Ks}\sim 25$.
• 2.  
  The redshift survey of Herschel SPIRE-selected and Scuba 2-selected sources from Casey et al. (2012) and C. M. Casey et al. (2016, in preparation). The submillimeter-bright galaxies were observed with the Keck I Low Resolution Imaging Spectrometer (LRIS), the Keck II DEep Imaging Multi-Object Spectrograph (DEIMOS), and MOSFIRE.
• 3.  
  The zCOSMOS-deep redshift survey from Lilly et al. (2007) and S. Lilly et al. (2016, in preparation). The targeted galaxies were selected based on BzK criteria (Daddi et al. 2004) and UGR criteria (Steidel et al. 1996) with ${K}_{{\rm{AB}}}\lesssim 23.5$ (Lilly et al. 2007; Diener et al. 2013), in which the sample yields a set of SFGs that are mostly at $1.3\lesssim z\lesssim 3$. We exclude sources with insecure redshift measurements that are also inconsistent with photometric redshift estimates (flag 1.1 and 2.2 defined by Lilly et al. 2009). These SFGs were observed with the VLT VIMOS spectrograph.
• 4.  
  Additional public MOSDEF and VUDS redshift catalogs are also included our analysis (Kriek et al. 2015; Tasca et al. 2016). Both of these redshift surveys cover the CANDELS-COSMOS field, and thus the ZFIRE cluster.

We obtain the full UV-near-IR multiwavelength data set of spectroscopically confirmed sources through the COSMOS photometric redshift catalogs (Capak et al. 2007; Ilbert et al. 2009; McCracken et al. 2010). When available, mid-far-IR photometry are obtained from the Spitzer-COSMOS survey (Sanders et al. 2007), the PACS Evolutionary Probe program (Lutz et al. 2011), the Herschel Multitiered Extragalactic Survey (HerMES Oliver et al. 2012), and the Scuba 2 450 and 850 μm survey from Casey et al. (2013). The MIPS 24 μm through SPIRE 500 μm catalog is compiled in Lee et al. (2013). The spectroscopically confirmed sources from all redshift catalogs were also cross-correlated with the Chandra-COSMOS catalog (Elvis et al. 2009; Civano et al. 2012) to search for X-ray luminous AGNs in and near the ZFIRE cluster. In this study, we focus only on X-ray selected AGNs, and we refer the reader to Cowley et al. (2016) for the population of mid-IR selected and radio-selected AGNs in the ZFIRE cluster.

We require potential DSFGs to have 24 μm detections and to be detected (S/N $\geqslant$ 3) in at least two additional bands from PACS 100, 160 μm, SPIRE 250, 350, 500 μm, or Scuba 2 450, 850 μm. We measure the far-infrared luminosity (${L}_{{\rm{IR}}}$ $\equiv \,{L}_{8-1000\mu {\rm{m}}}$ in the object rest-frame), dust temperature, and dust mass of these sources by fitting their FIR spectral energy distributions (SEDs) to a coupled modified graybody and mid-IR power law (Casey 2012). We assume a dust emissivity (β) of 1.5, and the results do not change significantly with $\beta =1.5\mbox{--}2.0$. Furthermore, we assumed the slope of mid-infrared power law (α) to be 2. In the cases where more than three data points are available at rest-frame wavelengths shorter than ∼70 μm, we do not see significant differences when leaving α as a free fitting parameter. Within a 10' circle from the center of the ZFIRE cluster¹³ and a redshift range of $2.07\leqslant z\leqslant 2.12$, we find a total of nine sources with ${L}_{{\rm{IR}}}$ $\geqslant$ 10¹² L_⊙.¹⁴ Four X-ray luminous AGNs are found within the same search area, and all of them are DSFGs. The IR and X-ray properties of the nine DSFGs (including four X-ray luminous AGNs) identified within a 10' circle from the center of the ZFIRE cluster are summarized in Table 1, and the best-fit FIR SEDs are shown in Figure 1.

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Table 1.  Properties of DSFGs Associated with the ZFIRE Cluster

Name	z	Redshift	S24	S100	S160	S250	S350	S450	S500	S850	${L}_{{\rm{IR}}}$	LX
		Survey	(μJy)	(mJy)	(mJy)	(mJy)	(mJy)	(mJy)	(mJy)	(mJy)	(1012 L⊙)	(1043 erg s−1)
J100017.9+021807.2	2.094	(1)a Hαb	198 ± 14	⋯	⋯	10.7 ± 2.2c	10.0 ± 2.9	⋯	9.9 ± 3.4	⋯	${2.58}_{-0.75}^{+1.05}$	20.2 ± 2.8
J100030.0+021413.1	2.098	(1) Hα	153 ± 101	⋯	14.0 ± 3.1	8.1 ± 2.2	8.8 ± 3.1	⋯	⋯	⋯	${3.19}_{-1.58}^{+3.12}$	⋯
J100031.8+021242.7	2.104	(1) Hα	746 ± 18	15.3 ± 1.6	25.9 ± 4.7	40.0 ± 2.2	37.1 ± 3.2	⋯	31.8 ± 4.3	⋯	${9.47}_{-0.87}^{+0.96}$	⋯
J100020.2+021725.7	2.104	(2) Hα	401 ± 16	⋯	⋯	20.0 ± 2.2	12.6 ± 3.5	⋯	22.3 ± 3.7	2.6 ± 1.1	${5.23}_{-0.88}^{+1.06}$	23.9 ± 2.7
J100035.9+021128.1	2.103	(2) Lyα	158 ± 17	⋯	11.2 ± 2.9	11.6 ± 2.2	12.9 ± 3.0	⋯	12.1 ± 3.1	⋯	${2.50}_{-0.70}^{+0.97}$	⋯
J100039.2+022220.9	2.085	(2) Hα	544 ± 17	9.7 ± 1.5	22.6 ± 4.5	41.5 ± 2.2	35.8 ± 2.7	19.3 ± 4.8	19.2 ± 3.0	5.8 ± 1.1	${7.47}_{-0.69}^{+0.76}$	⋯
J100032.7+021331.1	2.091	(3) Lyα	301 ± 15	⋯	⋯	20.2 ± 2.2	14.7 ± 3.2	⋯	⋯	⋯	${3.94}_{-0.86}^{+1.10}$	5.6 ± 1.5
J100056.7+021720.9	2.076	(3) Lyα	278 ± 17	⋯	⋯	13.5 ± 2.2	15.7 ± 2.7	⋯	10.5 ± 3.1	⋯	${3.47}_{-0.74}^{+0.94}$	20.5 ± 2.4
J100018.2+021842.6	2.102	(4) Hα	490 ± 99	⋯	9.1 ± 2.6	13.5 ± 2.2	9.5 ± 7.3	⋯	⋯	⋯	${4.28}_{-1.28}^{+1.83}$	⋯

Notes.

^aRedshift surveys: (1) ZFIRE, (2) SPIRE and Scuba 2-bright sources, (3) zCOSMOS, and (4) MOSDEF. ^bThe main spectral line used to determine redshift. ^cUncertainties of SPIRE photometry refer to the quadrature sum of instrumental and confusion noise (Smith et al. 2012).

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3.1. Distribution of SFGs and Rare Sources

Figure 2 shows the spatial distribution of all spectroscopically confirmed sources at $2.07\leqslant z\leqslant 2.12$ (${\rm{\Delta }}z=0.05$ corresponds to a velocity range of ${\rm{\Delta }}v\sim 4800$ km s⁻¹) and their distribution in the redshift space. Within a 10' (corresponds to a proper distance of ∼5 Mpc) radius from the ZFIRE cluster center, the redshift distribution of SFGs from the zCOSMOS survey peaks at similar redshift (median $z={2.097}_{-0.003}^{+0.001}$, the error represents the bootstrapped uncertainties) as the ZFIRE cluster members. We perform the FoF analysis (Huchra & Geller 1982) to determine which galaxies from the zCOSMOS, SPIRE/Scuba 2 surveys and MOSDEF/VUDS can be linked to the ZFIRE cluster members (from redshift survey (1); blue dots in Figure 2) with a linking length of 2 Mpc, a scale that accommodates the large spatial extent of unvirialized structure at $z\gt 2$ (e.g., Chiang et al. 2013; Muldrew et al. 2015). The structure identified from the FoF algorithm (black circles in Figure 2) spans a comoving volume of ∼25,000 Mpc³, and its spatial extent is consistent with the z = 2.07 structure identified based on photometric redshifts (Chiang et al. 2014). This structure also covers three candidate galaxy groups selected based on zCOSMOS survey (Diener et al. 2013).

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The rare sources (DSFGs and AGNs) identified via all redshift surveys span an area of $\sim 20^{\prime} \times 20^{\prime}$ on the sky. For the nine DSFGs (four of them are X-ray luminous AGNs) that fall within a 10' radius from the ZFIRE cluster center, they have comparable median redshift ($z={2.099}_{-0.005}^{+0.004}$) as the ZFIRE cluster members and zCOSMOS SFGs (we note that here three DSFGs are drawn from ZFIRE and two DSFGs are drawn from zCOSMOS surveys). If we define potential cluster members using the FoF analysis instead of a fixed 10' aperture, then there are also nine DSFGs (four of them are X-ray luminous AGNs) included in the large-scale structure. Such an excess of DSFGs and AGNs within and around the ZFIRE clusters is comparable to several DSFG- and AGN-rich structures at $z\gtrsim 1.5$ (Chapman et al. 2009; Tamura et al. 2009; Digby-North et al. 2010; Dannerbauer et al. 2014; Smail et al. 2014; Casey et al. 2015; Ma et al. 2015, see a compilation by Casey 2016).

In the 11' × 11' deep medium-bandwidth NIR survey area presented by Spitler et al. (2012) and Allen et al. (2015), the cluster shows four prominent cores that are linked by a filamentary structure. The spatial metallicity distribution of the galaxies in the ZFIRE cluster indicates a few low-metallicity substructures that could be recently accreted on (T. Yuan 2016, private communication). Based on the spatial and redshift distribution traced by zCOSMOS SFGs and the population of DSFGs, it is possible that the large-scale structure associated with the ZFIRE cluster may extend beyond the ZFIRE survey area. In fact, Chiang et al. (2015) also detect three LAEs a few arcmins offset from the ZFIRE cluster (their positions are also shown in Figure 2). Such a large spatial extent traced by these various galaxies is consistent with the cosmological simulations (e.g., Chiang et al. 2013), where the $z\sim 2.1$ cluster may still be actively accreting from large-scale structure while more mature cluster cores begin to assemble in the densest regions.

3.2. Significance of this Structure

The ZFIRE cluster (Spitler et al. 2012, Y14) and its associated large-scale structure traced by Herschel-selected DSFGs and color-selected SFGs represent a site that the cluster assembly may be actively taking place. It is thus an ideal laboratory to test whether any early environmental impacts have begun to influence galaxy evolution. In this section, we examine the environmental dependence on galaxies' physical properties: M_*, SFR, gas content, and morphology.

4.1. M_* and SFR

We measure the M_* and SFR of all spectroscopically confirmed galaxies by fitting the full SEDs using the Magphys code (da Cunha et al. 2008), and the HIGHZ extension (da Cunha et al. 2015) is used here since it includes stellar and dust emission priors that are more comparable to $z\gt 1$ galaxies. Since SED fitting-based SFRs often suffer from large uncertainties for highly obscured sources (e.g., Wuyts et al. 2011), we convert ${L}_{{\rm{IR}}}$ of DSFGs to their SFRs using the relation SFR/M_⊙ yr⁻¹ = 9.5 × 10⁻¹¹ ${L}_{{\rm{IR}}}$/L_⊙(Kennicutt 1998, adjusted for a Chabrier initial mass function). The zCOSMOS SFGs (galaxies from redshift survey 3) that are linked to the ZFIRE cluster have mean M_* $=\,(1.23\pm 0.36)\times {10}^{10}$ M_⊙ and mean $\mathrm{SFR}=47\pm 12$ M_⊙ yr⁻¹, where the uncertainties correspond to the standard deviation of the mean. For the control sample, we use those SFGs from the same redshift survey (zCOSMOS; redshift survey 3) at the same redshift range ($2.07\leqslant z\leqslant 2.12$) but are not linked to the ZFIRE cluster based on the FoF analysis in Section 3.1. This selection yields 140 SFGs with their mean M_* $=(7.17\pm 0.80)\times {10}^{9}$ M_⊙ and mean $\mathrm{SFR}=34\pm 10$ M_⊙ yr⁻¹.

Figure 3 takes a closer examination of the M_* and SFR distributions of all SFGs in the large-scale structure and the control sample (here we include all SFGs from redshift surveys 2 and 3). A Kolmogorov–Smirnov (K–S) test does not reject either consistent or different distributions of M_* between the protocluster and the field (the p-value is 0.61). However, the lack of an excess of massive galaxies in the protocluster environment may be a bias introduced by primarily selecting star-forming populations (e.g., Muldrew et al. 2015). Despite the fact that protocluster and field SFGs have similar mean SFR, their SFR cumulative distributions show a slight discrepancy in which the cluster members are composed with slightly more high-SFR galaxies but fewer low-SFR galaxies (the p-value from the K-S test is 0.04). This excess of high-SFR galaxies in the large-scale structure is consistent with the significant overdensity of DSFGs found within and around the ZFIRE cluster.

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4.2. Gas Content

4.3. Galaxy Morphology

One important question to address is the origin of excess DSFGs in this $z\sim 2.1$ structure (both in the ZFIRE cluster and its associated large-scale structure). A possible explanation is that the underlying SFG main sequence (e.g., Brinchmann et al. 2004; Noeske et al. 2007) in the protocluster environments are intrinsically different from the field. An elevated galaxy main sequence can naturally lead to an increase of high-SFR population at a given M_*. However, Koyama et al. (2013b) have shown that the SFR–M_* relation of SFGs is independent of environments at $z\sim 2$, and in this $z\sim 2.1$ structure, the mean specific SFR of protocluster SFGs does not differ significantly from the control sample. We thus conclude that there is no obvious evidence to attribute the excess DSFGs to an elevated galaxy main sequence.

The excess of DSFGs in the protoclusters represents an enhanced population of galaxies that are "outliers" of the SFR–M_* relation at $z\sim 2$, and these DSFGs may be triggered by an enhanced gas supply (with respect to the SFGs on the galaxy main sequence) or through galaxy interactions (e.g., Engel et al. 2010; Tacconi et al. 2010). However, based on the stacking and morphological analysis in Sections 4.2 and 4.3, we find no evidence that the protocluster SFGs exhibit more gas supply or higher merger fraction than the field. Among the eight DSFGs that have CANDELS WFC3 images available (Figure 4), four of them may exhibit ongoing interaction (J100031.8, J100030.0, J100039.2, and J100032.7). This leads to a merger fraction of 0.5, which is also consistent with the field DSFGs at $z\sim 2$ (Kartaltepe et al. 2012).

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We present a search of large-scale structure around a z = 2.095 cluster (Spitler et al. 2012, Y14). Within a 10' (corresponds to a proper distance of ∼5 Mpc) radius from the cluster center and a redshift range of $2.07\leqslant z\leqslant 2.12$, there are nine DSFGs (including four X-ray luminous AGNs), and 34 BzK- and UV-selected SFGs. This leads to galaxy overdensities of ${\delta }_{{\rm{DSFG}}}\sim 12.3$ and ${\delta }_{{\rm{SFG}}}\sim 2.8$. An estimation based on the linear theory of spherical collapse model suggests that only the overdensity traced by DSFGs can collapse by $z\sim 0$. However, ${\delta }_{{\rm{SFG}}}$ of 2.8 is only slightly under the collapsing threshold, and it is expected to collapse to a Virgo-type structure when comparing to the prediction of cosmological simulations with M_* $\gt \,{10}^{10}$ M_⊙ in a 25 (comoving) Mpc window (Chiang et al. 2013). The ZFIRE cluster and its associated DSFG- and SFG-rich structure represents an active cluster formation phase, in which the $z\sim 2.1$ cluster is still accreting from large-scale structure while more mature cluster cores begin to assemble. This structure is thus an ideal site to explore early environmental dependence of galaxy properties, and the interplay between intergalactic medium and galaxies during the formation of massive clusters (e.g., Lee et al. 2014a, 2016; Cai et al. 2015).

The identification of this $z\sim 2.1$ structure, along with previous findings of DSFG- or AGN-rich structures in known protoclusters (Tamura et al. 2009; Digby-North et al. 2010; Dannerbauer et al. 2014; Smail et al. 2014), demonstrate that the excess of these rare systems indeed traces bona-fide overdensities (of mass) and protoclusters (also see Casey et al. 2015). In fact, searching for the overdensities of DSFGs or AGNs can be an efficient probe¹⁵ of large structure across several tens of Mpc at $z\gtrsim 2$, and there is potentially a large population of such DSFG-rich protoclusters as revealed by Herschel and Planck observations (Planck Collaboration et al. 2015). Without prior knowledge of the ZFIRE cluster, it is still possible to identify this structure relying only on the excess of DSFGs. The redshift survey targeted on SPIRE/Scuba 2-bright sources finds four DSFGs within an area of ∼140 arcmin² on the sky and ${\rm{\Delta }}z=0.02$ (orange dots with red circle in Figure 2), which leads to an overdensity of ${\delta }_{{\rm{DSFG}}}\sim 10.4$.

A clear picture that explains the triggering of excess DSFGs/AGNs has not yet emerged. It is plausible that galaxies in dense environments at $z\gtrsim 2$ exhibit elevated gas supply and higher chances of galaxy interactions. However, our morphological analysis shows that the merger fraction of the protocluster galaxies is consistent with the control sample, and there are also no obvious enhancements of mergers/interacting systems in protocluster DSFGs as compared to the field populations. Follow-up high-resolution observations with integral field spectrographs can provide further information on the dynamics and/or reveal recent merger histories of these DSFGs (e.g., Hung et al. 2016). The stacking results based on 850 μm images are not yet sensitive enough to constrain the gas content of both protocluster and field galaxies, and it is necessary to incorporate additional submillimeter imaging or pursue follow-up molecular gas observations for both SFGs and DSFGs.

C.-L.H. thanks J. R. Martínez-Galarza for helpful discussion on SED fitting. C.-L.H. acknowledges support from the Harlan J. Smith Fellowship. C.M.C. thanks the University of Texas at Austin, College of Natural Science for support. G.G.K. acknowledges the support of the Australian Research Council through the award of a Future Fellowship (FT140100933).

The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. 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 and made possible by financial support of the W.M. Keck Foundation.

Part of the data presented in this paper has been made available by the COSMOS team (http://cosmos.astro.caltech.edu). COSMOS is based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA Inc, under NASA contract NAS 5-26555; also based on data collected at the Subaru Telescope, which is operated by the National Astronomical Observatory of Japan; the XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA; the European Southern Observatory, Chile; Kitt Peak National Observatory, Cerro Tololo Inter-American Observatory, and the National Optical Astronomy Observatory, which are operated by the Association of Universities for Research in Astronomy, Inc. (AURA) under cooperative agreement with the National Science Foundation; the National Radio Astronomy Observatory, which is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc; and the Canada–France–Hawaii Telescope operated by the National Research Council of Canada, the Centre National de la Recherche Scientifique de France and the University of Hawaii.