ALMA Deep Field in SSA22: Source Catalog and Number Counts

We observed a 2' × 3' rectangular field and peripheral regions centered at α = 22^h17^m340, δ = +00°17'00'' (J2000) at 1.1 mm, using ALMA Band 6 in cycle 2 (Program ID. 2013.1.00162.S, PI. H. Umehata). Hereafter, we name this field "ADF22," which is an acronym of "ALMA deep field in the SSA22 field." ADF22 is located at the very center of the cosmic large-scale structure (or "Cosmic Web") at z ∼ 3. As illustrated in Figure 1, this area is close to the projected density peak of z = 3.09 LAE candidates selected by Subaru/Suprime-cam observations with a narrow-band filter (NB497) (Hayashino et al. 2004). Previous works have unveiled not only the projected density distribution, but also the density structure in three-dimensions (Matsuda et al. 2005). When we only focus on spectroscopically confirmed z = 3.09 LAEs and draw a three-dimensional map, ADF22 coincides with the junction of a comoving 50 Mpc-scale filamentary structure (Umehata et al. 2015). This means that ADF22 covers a node of the cosmic large-scale structure, and provides a unique opportunity to examine galaxy formation in such a dense field at this early epoch.

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Another important feature is that ADF22 contains a significant number of the most active populations of galaxies that are suggested to preferentially reside in dense environments, including SMGs, QSOs, and Lyα blobs (LABs). There are three 1.1 mm sources discovered by the AzTEC/ASTE survey (Tamura et al. 2009; Umehata et al. 2014). Prior to the present work, one of the three sources, SSA22-AzTEC77 (or SMM J221735+001537), had been proposed as a secure member of the z = 3.09 structure (Chapman et al. 2005; Greve et al. 2005; Bothwell et al. 2013), and the other two sources had been also suggested to be at z ∼ 3.09 (Tamura et al. 2010; Uchimoto et al. 2012; Umehata et al. 2014). One QSO at z = 3.09 discovered by Steidel et al. (1998) and two z ∼ 3.09 LABs listed in Matsuda et al. (2004) are also located within ADF22 (see also Figure 1). ADF22 is thus an excellent region for probing dusty star formation activity in a wide variety of galaxies at the core of the protocluster.

We chose the central observing frequency of 263 GHz (1.14 mm), which is similar to that of our previous AzTEC/ASTE survey, 270 GHz, and allows direct comparison with the flux densities of sources from our AzTEC/ASTE and ALMA surveys. Because the size of primary beam of band 6 is larger than that of band 7, this frequency setup is also beneficial to reduce the number of pointings compared to higher frequency. In order to cover a 2' × 3' rectangular field contiguously, we utilized a 103-field mosaic. The spacing between adjacent pointings was 0.72 times the primary beam (FWHM 23'' at 263 GHz), which was a compromise between the homogeneity of sensitivity and the observing time required to cover as wide an area as possible.

Observations were divided into two campaigns (2014 and 2015 runs), as summarized in Table 1. The first run was conducted on 2014 June 6–10 with 33–36 available 12 m antennas in the C34–4 configuration (longest baseline 650 m) and very good 1.1 mm weather conditions (precipitable water vapor (PWV) of 0.30–1.27 mm). The second run was done on 2015 April 4, 5, and 13 with 32–40 12 m antennas in C32-2 (longest baseline 349 m) and good conditions (PWV of 0.9–1.9 mm). The exposure time per pointing was 30 s for each scheduling block (SB). These observations resulted in an initial on-source time of 2–4.5 minutes per pointing (depending on the individual pointing) and a total on-source time of 386 minutes. We utilized the Time Division Modes correlator, with 4 × 128 dual polarization channels over the full 8 GHz bandwidth, giving an effective bandwidth of 7.5 GHz after flagging edge channels. The correlator was set up to target two spectral windows of 1.875 GHz bandwidth each, at 15.6 MHz (∼20 km s⁻¹) channel spacing in each sideband. The central frequencies of the four spectral windows are 254.0, 256.0, 270.0, and 272.0 GHz. We note that this frequency range enables us to search for the ¹²CO(9–8) line (ν_rest = 1036.912 GHz) at z ∼ 3.09 (we actually found one CO(9–8) emitter, as we describe below. Details will be presented in N. Hayatsu et al. 2016, in preparation.).

Table 1.  Summary of ADF22 Observations

SBa	Date	Antennasb	Baselinec	Fieldsd	Synthesized beame	Flux calibrator
SB1	2014 Jun 06	36	20 m–650 m	1–80	059 × 046 (−37.5 deg)	J2148+069
SB2	2014 Jun 07	34	20 m–646 m	1–40	050 × 045 (+18.6 deg)	J2148+069
SB3	2014 Jun 07	34	20 m–646 m	1–80	056 × 047 (−59.6 deg)	J2148+069
SB4	2014 Jun 09	34	20 m–646 m	1–80	061 × 046 (+63.7 deg)	J2148+069
SB5	2014 Jun 10	34	20 m–646 m	1–80	057 × 048 (−64.9 deg)	J2148+069
SB6	2015 Apr 04	33	15 m–328 m	1–103	118 × 087 (−88.6 deg)	Neptune
SB7	2015 Apr 04	33	15 m–328 m	1–103	139 × 081 (−70.1 deg)	Neptune
SB8	2015 Apr 05	35	15 m–328 m	1–103	130 × 090 (−72.3 deg)	Uranus
SB9	2015 Apr 13	40	15 m–349 m	1–103	167 × 111 (+73.9 deg)	Neptune

Notes.

^aScheduling block. ^bNumber of utilized 12 m antennas. ^cMinimum and maximum baseline. ^dField ID of each pointing (see Figure 2). ^eSynthesized beam size of the map in the case of natural weighting.

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The quasar J2148+0657, with flux 1.2 Jy, was observed regularly for amplitude and phase calibration. The absolute flux scale was set using J2148+0657 (for the 2014 run) and Uranus and Neptune (for the 2015 run). We estimate that the absolute flux accuracy is within 20%. This uncertainty in the absolute flux calibration is not included in the following analyses and discussions.

Data reduction was performed using the Common Astronomy Software Application (casa; McMullin et al. 2007).¹⁶ The calibration and imaging was performed using casa version 4.2.2 of the ALMA pipeline and casa version 4.5.0, respectively. Our analysis is complicated by the fact that our observations were carried out with multiple array configurations. Our observations are composed of nine SBs, as summarized in Table 1. Because each SB has a different antenna setup, the resulting synthesized beam sizes differ among SBs. There are broadly two array configurations; the maximum baseline lengths of SB6–SB9 (taken in 2015) are systematically shorter than SB1–SB5 (taken in 2014). Because of the difference in the observed area in 2014 and 2015, the western edge fields (fields 81–103 in the right panel of Figure 2) lack longer baseline data and have lower sensitivity (Table 1).

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Considering this situation, we first created a 1''-tapered map for the entire field (i.e., fields 1–103), which enables us to achieve nearly uniform angular resolution across the map. This larger synthesized beam is more sensitive to extended sources, but suffers from an increased noise level. As we show in the maps of individual sources (Figure 6) and measured sizes of bright sources (Table 3), the resulting angular resolution, ≈1'', seems to be sufficient to detect the majority of sources in this field. We also discuss the possibility that we are missing very extended components in Section 4.1.1.

The uv-data for individual pointings were first combined into a single uv-data set. We then Fourier-transformed the combined data to create a single "dirty" map with natural weighting, by setting the imager mode to "mosaic" and adopting the taper parameter, outertaper = 120 kλ. After we measured the rms noise level across the whole dirty map, we repeated the clean process down to 1.5σ, putting a tight clean box (1'' × 1'' in size) around each 5σ source (in a manner similar to that reported by Hodge et al. 2013b). The resulting synthesized beam is 116 × 102 in size (P.A. = −80 deg). We denote this map as the FULL/LORES map.

We created another complementary map. Because the five SBs, SB1–SB5, have the longer baseline data with baselines up to 600 kλ, we can achieve a better sensitivity making the best of the longer baselines. For this purpose, we created a second map for 80 pointing field (fields1–80). We have generally adopted the same procedure described above, but we did not apply any tapering to the map. The second map has a synthesized beam of 070 × 059 (P.A. = −80 deg). Hereafter, we call it the DEEP/HIRES map. In the following analyses, we utilize primarily the FULL/LORES map. The DEEP/HIRES map is used for detecting compact faint sources (Section 3) and resolving bright sources (Section 4.2).

The final FULL/LORES map, corrected for the primary beam response, is shown in Figure 2. In the following sections, we consider the effective area; the area in the map within which the primary beam coverage is greater than 50%. This results in a 7.0 arcmin² area in the case of the FULL/LORES map (5.8 arcmin² for the DEEP/HIRES map). A sensitivity map was constructed utilizing an aips task, rmsd, calculating the rms for each 01 × 01 pixel using the surrounding 100 × 100 pixels (or 100 × 100) on an image prior to correcting for primary beam response. The correction results in a range of 1σ depth of 52–170 μJy beam⁻¹ with a median value of 75 μJy beam⁻¹ (Figure 3) for the FULL/LORES map. In the case of the DEEP/HIRES map, we obtained a range of 1σ depth from 50–129 μJy beam⁻¹ with a median value of 60 μJy beam⁻¹ (Figure 3).

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Source extraction was performed using the image map and sensitivity map that were not corrected for the primary beam attenuation. First, we utilized the FULL/LORES map. A source-finding algorithm, aegean v1.9.5-56 (Hancock et al. 2012), was used to extract positive sources above 3.5σ. In parallel, we also counted negative sources with source-like profiles above 3.5σ during the procedure to estimate the fraction of spurious sources among the detected sources. The cumulative number counts of positive and negative sources as a function of signal-to-noise ratio (S/N) is shown in Figure 4. We found 17 positive sources with >5σ and 28 sources with >4σ. There were no negative sources above 5σ, whereas we found seven negative ones with 4σ–4.6σ. The results show that the detection limit of 5σ is secure and conservative. Gaussian statistics also support the validity of the threshold. Because the map contains ≈32,000 beams, we would expect less than one spurious peak above 5σ. Therefore, we adopt these 17 sources as secure detections (ADF22.1–ADF22.17; see Table 2).

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Table 2.  ADF22 Source Properties

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
ALMA ID	ALMA NAME	ID (U15)	AzTEC ID	SAzTEC	σALMA	S/NpkALMA	SALMA	zspec
			(mJy)	(J2000)	(μJy beam−1)		(mJy)
ADF22.1a	ALMAJ221732.41+001743.8	ADF22a	AzTEC1	${11.3}_{-0.7}^{+0.9}$	72	58.1	5.60 ± 0.13	3.092(a)
ADF22.2	ALMAJ221736.11+001736.7	⋯	⋯	⋯	63	31.8	2.02 ± 0.02	⋯
ADF22.3	ALMAJ221735.15+001537.2	ADF22b	AzTEC77	${2.4}_{-0.8}^{+0.9}$	66	27.0	1.89 ± 0.04	3.096(d)
ADF22.4	ALMAJ221736.96+001820.7	⋯	AzTEC14	${4.5}_{-0.8}^{+0.8}$	72	26.6	1.95 ± 0.05	3.091(b)
ADF22.5	ALMAJ221731.48+001758.0	⋯	⋯	⋯	99	20.3	2.43 ± 0.20	⋯
ADF22.6	ALMAJ221735.83+001559.0	ADF22c	⋯	⋯	69	19.1	1.45 ± 0.09	3.089(e)
ADF22.7	ALMAJ221732.20+001735.6	ADF22i	AzTEC1	${11.3}_{-0.7}^{+0.9}$	86	18.7	1.65 ± 0.07	3.097(c)
ADF22.8	ALMAJ221737.11+001712.3	ADF22d	⋯	⋯	77	15.0	1.19 ± 0.06	3.090(f)
ADF22.9	ALMAJ221736.54+001622.6	ADF22e	⋯	⋯	60	12.8	0.82 ± 0.08	3.095(f)
ADF22.10	ALMAJ221737.10+001826.8	⋯	AzTEC14	${4.5}_{-0.8}^{+0.8}$	71	9.8	0.72 ± 0.04	⋯
ADF22.11	ALMAJ221737.05+001822.3	ADF22f	AzTEC14	${4.5}_{-0.8}^{+0.8}$	77	9.5	0.79 ± 0.05	3.093(f)
ADF22.12	ALMAJ221732.00+001655.4	ADF22g	⋯	⋯	71	8.8	0.63 ± 0.03	3.091(f)
ADF22.13	ALMAJ221737.42+001732.4	⋯	⋯	⋯	81	8.0	0.79 ± 0.05	⋯
ADF22.14	ALMAJ221731.34+001639.6	⋯	⋯	⋯	99	7.5	0.98 ± 0.13	⋯
ADF22.15	ALMAJ221732.77+001727.5	⋯	⋯	⋯	79	5.3	0.50 ± 0.08	⋯
ADF22.16	ALMAJ221736.81+001818.0	ADF22h	AzTEC14	${4.5}_{-0.8}^{+0.8}$	77	5.3	0.56 ± 0.07	3.085(f)
ADF22.17	ALMAJ221737.69+001814.4	⋯	AzTEC14	${4.5}_{-0.8}^{+0.8}$	66	5.1	0.60 ± 0.09	⋯
ADF22.18b	ALMAJ221732.23+001527.8	⋯	⋯	⋯	82	5.3	0.44 ± 0.05	2.105(g)

Notes.  (1) ID in this paper. (2) Source name that represents the coordinate in the wcs system. (3) ID defined in Umehata et al. (2015). (4) ID of AzTEC source in Umehata et al. (2014). We list it if an ALMA SMG is located within the 30'' AzTEC beam. (5) Flux density of AzTEC source (Umehata et al. 2014). (6) 1σ sensitivity at a given source position after the primary beam correction. (7) The signal-to-noise ratio, which is defined as a ratio of peak flux density over the 1σ sensitivity. (8) The flux density and uncertainty measured by the casa task, imfit. (9) Spectroscopic redshift (z_spec) if a given source has it. The lines used to determine z_spec and references are as follows. (a) ¹²CO(3–2) (M. Yun et al. 2016, in preparation). (b) ¹²CO(9–8) (H. Umehata et al. 2016, in preparation; N. Hayatsu et al. 2016, in preparation). (c) [C ii] 157.7 μm (H. Umehata et al. 2016, in preparation). (d) ¹²CO(3–2) (Bothwell et al. 2013, see also Chapman et al. 2005, Greve et al. 2005). (e) Lyα (Chapman et al. 2005). (f) [O iii] λ5007 (Kubo et al. 2015, 2016). (g) Lyα (Chapman et al. 2004a).

^aThis source was identified as a primary counterpart of SSA22-AzTEC1 using the Submillimeter Array (SMA) in Tamura et al. (2010). ^bThe properties of ADF22.18 are measured using the DEEP/HIRES map.

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We also performed the same procedures on the DEEP/HIRES map, independently. As a result, 14 sources were detected at >5σ, one of which was not detected in the shallower FULL/LORES map. This source (ADF22.18; see Table 2) was added to the catalog of secure detection because there were no negative sources with >5σ in the DEEP/HIRES map. Therefore, a total of 18 sources were detected at S/N > 5.

In the following analyses and discussion, we mostly focus on the 18 secure sources not affected by spurious features. We show a supplementary catalog of 14 sources detected tentatively in the FULL/LORES and DEEP/HIRES maps, in Appendix A.

The flux densities of the detected sources were measured with the imfit task of casa, using the map after correction for the primary beam attenuation. We adopt the integrated flux density as the flux density of a source, unless it is lower than the peak flux density (e.g., Simpson et al. 2015b). The measurements of fluxes on the two maps are in good agreement with each other. The median ratio of the flux density between the FULL/LORES map and the DEEP/HIRES map is ${S}^{\mathrm{FULL}}/{S}^{\mathrm{DEEP}}={0.96}_{-0.02}^{+0.00}$ for the 13 sources detected above 5σ, in both maps.

We performed a suite of simulations to evaluate the completeness and boosting effect on our flux measurement. We briefly describe the method below (for more detail, see Hatsukade et al. 2016). Model sources created by scaling the synthesized beam are injected into the image map corrected for primary beam attenuation. The input position is randomly selected to be >10 away from ≥3σ sources. We then repeated the same procedures for the source extraction using the artificial map as described in Section 3.1.

The completeness is measured as the recovery rate of the injected model sources; when an input source is detected within 10 of the injected position with ≥4σ, the source is considered to be recovered. Model sources with flux densities over the range S = 0.02–0.6 mJy in steps of 0.02 mJy are considered and the procedures are repeated 1000 times for each flux density bin (ΔS = 0.02 mJy). The results are summarized in Figure 5 as a function of input flux density. The completeness of our source extraction is ∼70% at S/N = 4 and rises to ∼90% at S/N = 5. The completeness reaches ∼100% at S/N ≳ 6.0. We consider the completeness in calculating source counts in Section 4.3, although it does not matter significantly for >5σ sources.

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In the course of the completeness measurement, we also evaluate the effect of flux boosting. It is known that the flux density of sources in a signal-to-noise limited catalog tend to be boosted as a whole due to random noise fluctuations and the shape of the source count distribution (e.g., Hogg & Turner 1998; Scott et al. 2002; Coppin et al. 2006). We plot the ratio of input and output flux density against the input flux density in Figure 5. The results show that the effect is negligible if we consider only those sources detected at >5σ. Hence we do not consider the flux boosting effect in the following discussion.

The measured properties of the ADF22 SMGs are summarized in Table 2. The first column lists the source IDs in this paper, which are generally ranked in terms of S/N. The nine SMGs reported in Umehata et al. (2015) are noted in the second column. There are three AzTEC sources in our field (Umehata et al. 2014). We listed the IDs and flux densities of the corresponding AzTEC source if a given ALMA SMG is located within the AzTEC beam (FWHM; d = 30''). We give the flux density, measured by Gaussian fitting with casa, imfit. We note that these measurements are from the FULL/LORES map except for ADF22.18, which was detected at >5σ only in the DEEP/HIRES map.

We also report the spectroscopic redshift (z_spec), if known. Eleven of the 18 SMGs have z_spec, 10 of which have z ≃ 3.09. In addition to eight z ≃ 3.09 SMGs reported in Umehata et al. (2015), we adopt z_spec for three SMGs, ADF22.4, ADF22.7, and ADF22.18. The redshifts of ADF22.4 and ADF22.7 are determined from our recent ALMA observations (¹²CO(9–8) at z = 3.091 and [C ii] 157.7 μm at z = 3.097, respectively; H. Umehata et al. 2016, in preparation). ADF22.18 coincides with a z = 2.015 radio source, RG J221732.22+001528.2, reported in Chapman et al. (2004a) with a small projected separation (04). We show the ALMA 1.1 mm images of the 18 SMGs in Figure 6.

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One reasonable concern regarding the ALMA source catalog is the overlap between the previously known galaxy populations and our newly discovered ALMA SMGs. Within the survey area of the FULL/LORES map (Figure 2), there are 19 LAEs (Matsuda et al. 2005; Nestor et al. 2013; Erb et al. 2014), five LBGs (Steidel et al. 2003; Nestor et al. 2013; Erb et al. 2014), and 10 K-band selected galaxies (Kubo et al. 2015, 2016) within the protocluster (i.e., with z_spec = 3.06–3.12; Hayashino et al. 2004; Matsuda et al. 2005). None of the ALMA SMGs (including candidates in the supplementary source catalog) have LAE/LBG counterparts, which shows that these rest-frame UV selected galaxies are clearly separated populations, compared to galaxies individually detected by ALMA. In contrast, five out of 10 K-band selected galaxies are securely detected by ALMA. Therefore, such a relatively massive galaxy population (stellar mass, ≳10^10–11 M_⊙; Kubo et al. 2013) selected at rest-frame optical wavelengths appears to significantly overlap with the ALMA population. This trend is broadly consistent with recent works in SXDF (Tadaki et al. 2015) and HUDF (Aravena et al. 2016; Dunlop et al. 2016), as well as previous studies of ALMA SMGs (Simpson et al. 2014). We summarize the relationship to other populations in Appendix B.

Several hundred submm/mm sources discovered by single-dish telescopes have been observed by submm/mm interferometers to date. Some appear to resolve into multiple, individual SMGs, whereas others have a unique counterpart above a given detection limit (e.g., Gear et al. 2000; Tacconi et al. 2006; Younger et al. 2008; Wang et al. 2011; Barger et al. 2012; Smolčić et al. 2012a; Hodge et al. 2013a; Miettinen et al. 2015; Simpson et al. 2015a). For instance, Barger et al. (2012) reported that, using the SMA, three of 16 SCUBA sources are composed of multiple objects. From ALMA observations, Hodge et al. (2013b) and Simpson et al. (2015a) suggested that ∼30–40% of LABOCA or bright SCUBA2 sources (with flux densities of S_870μm = 4–15 mJy and S_850μm ∼ 8–16 mJy, respectively) are resolved into multiple SMGs brighter than S_870μm ∼ 1 mJy, making most of the components "ULIRGs." These results suggest that the relatively poor angular resolution of single-dish imaging (≳15'') causes significant source blending and complicates our interpretation of the nature of SMGs. ALMA enables us now to resolve not only individual single-dish sources, but also relatively faint sources spread over a wider area.

4.1.1. Comparison of the AzTEC and ALMA Map

The AzTEC/ASTE survey of SSA22 by Tamura et al. (2009) and Umehata et al. (2014) presented a 1.1 mm image of ADF22. The 30'' resolution image has a 1σ depth of 0.7 mJy beam⁻¹ and detects three sources above a 3.5σ detection threshold within ADF22 (SSA22-AzTEC1, SSA22-AzTEC14, and SSA22-AzTEC77; hereafter AzTEC1, AzTEC14, and AzTEC77, respectively). Two of the three AzTEC sources, AzTEC1 and AzTEC14, have two and five ALMA SMGs located within the FWHM of the AzTEC beam, respectively. In contrast, AzTEC77 has only one associated ALMA SMG (Figure 7).¹⁷ In summary, three AzTEC sources are resolved into eight ALMA SMGs. The result is in line with previous ALMA studies following up single-dish submm/mm sources with interferometers, which reports that a significant fraction of submm/mm sources detected by single-dish telescopes are found to be intrinsically multiple SMGs (e.g., Hodge et al. 2013a).

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To check the relative flux scales, we compared the flux density between the AzTEC sources and the associated ALMA SMGs. For the AzTEC sources, deboosted flux densities in Umehata et al. (2014) (S^AzTEC) are considered here. Regarding the measurements for the ALMA SMGs, we calculate the sum of the flux densities of the SMGs with ≥5σ within the FWHM of the AzTEC beam (S^ALMA). Figure 8 shows the results for the three AzTEC sources. The ratio between the two, S^ALMA/S^AzTEC, is in agreement within error bars for AzTEC77 and AzTEC14, which suggests that the ALMA SMGs discovered from this survey account for the majority of the flux density of the AzTEC sources. However, the situation is not the same for AzTEC1, the brightest AzTEC source in the SSA22 field, which has S^ALMA/S^AzTEC = 0.64 ± 0.05. The discrepancy could imply the existence of additional components of 1.1 mm emission not accounted for in the ALMA map. One possibility is that we are missing a number of fainter and/or diffuse sources (e.g., Hodge et al. 2013a; Simpson et al. 2015a). If we include sources in the supplementary catalog with S/N = 4–5, then the flux ratio S^ALMA/S^AzTEC gets closer to unity for all three AzTEC sources (Figure 8). However, these sources are still insufficient to explain the case of AzTEC1. Much fainter sources might also contribute to the AzTEC sources for AzTEC1.

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Tamura et al. (2010) gave us another clue. They reported the 860 μm flux density of ADF22.1, S_860μm = 12.2 ± 2.3 mJy, using the Submillimeter Array.¹⁸ They obtained the natural-weighted synthesized beam, 343 × 192 (P.A. 34.3 deg), and found that the source was likely not to be resolved. If we predict a 1.1 mm flux density of ADF22.1, using an averaged SMG template from the ALESS survey (Swinbank et al. 2014) scaled to the 860 μm flux density, the expected value is S_1.1mm ≈ 6.0 mJy. The estimate is broadly consistent with our measurement, which suggests that we are measuring the vast majority of the dust emission from ADF22.1.

There are two ALMA SMGs, ADF22.5 and ADF22.15, located just outside of the beam for AzTEC1 (Figure 7). If we take into account ADF22.5 and ADF22.15, the integral of the flux densities of the ALMA SMGs approach the flux density of AzTEC1 (S^ALMA/S^AzTEC = 0.94 ± 0.07). In order to investigate whether these SMGs indeed contribute to the flux density of AzTEC1 in the AzTEC map, we made a "model" AzTEC image convolving the ALMA map with a Gaussian kernel with a FWHM of 30''. AzTEC1 has flux density 7.1 mJy in the model map, which is consistent with the sum of flux density of the ALMA SMGs within the beam for AzTEC1, not including ADF22.5 and ADF22.15. Therefore, these two nearby SMGs are likely not to account for the discrepancy. We do not consider a systematic error on the absolute flux accuracy for the AzTEC map throughout the above discussion. Although it is difficult to estimate the influence for our small sample, ALMA surveys of a significant number of AzTEC sources will allow us to examine the effect.

As displayed in Figure 7, we compared the spatial distribution of SMGs discovered by ALMA and the contours of the AzTEC 1.1 mm emission, below the AzTEC detection limit (3.5σ). Our ALMA map has discovered 10 SMGs outside the AzTEC source positions. We found that nine of the 10 ALMA SMGs are located within or in the vicinity of the area where the 1.1 mm flux density is 0–2.1 mJy beam⁻¹ in the AzTEC map. This may show that the structure traced by the faint AzTEC emission, below 3σ, reflects the distribution of 1.1 mm sources to a certain degree.

As we reported in Umehata et al. (2014), the AzTEC catalog is significantly incomplete at around 3.5σ (i.e., the detection threshold). The completeness of the AzTEC map is only ∼50% at 2 mJy. Among the ADF22 sources with flux density ∼2 mJy, two SMGs, ADF22.2 and ADF22.5, are found to be located outside of the AzTEC beam. Therefore, our results show that the ALMA mosaic is capable of finding such bright SMGs that were missed by previous submm/mm surveys taken with single-dish telescopes.

4.1.2. The Origin of Multiplicity in a Overdense Environment

Two-dimensional Gaussian fits to the ALMA SMGs in the image plane, using the DEEP/HIRES map, suggest that ADF22 sources are generally resolved. The results for the nine brightest SMGs with S/N > 10 are summarized in Table 3. The deconvolved major axes are 025–085, and the median value for the nine SMGs is $0\buildrel{\prime\prime}\over{.} {32}_{-0\mathop{.}\limits^{\prime\prime }06}^{+0\mathop{.}\limits^{\prime\prime }13}$ (Gaussian FWHM; ${2.4}_{-0.4}^{+1.0}$ physical kpc at z = 3.09). Seven of the nine SMGs have z_spec ≃ 3.09, which leads the almost same median value, $0\buildrel{\prime\prime}\over{.} {32}_{-0\mathop{.}\limits^{\prime\prime }07}^{+0\mathop{.}\limits^{\prime\prime }13}$ if we only consider such robust protocluster members. The size distribution in ADF22 is generally consistent with previous measurements for SMGs in other fields (Figure 9). Simpson et al. (2015b) measured the size for 23 bright SMGs observed at 870 μm and derived a median angular size FWHM = 030 ± 004. Ikarashi et al. (2015) reported that 13 SMGs, which were observed at 1.1 mm and thought to be at z ∼ 3–6, have a median FWHM of $0\buildrel{\prime\prime}\over{.} {20}_{-0\mathop{.}\limits^{\prime\prime }05}^{+0\mathop{.}\limits^{\prime\prime }03}$. These results suggest that dusty star formation occurs in compact regions, a few kiloparsecs in extent. There does not appear to be a significant difference between the size of SMGs within the z = 3.09 protocluster and other SMGs. This might suggest that the local mechanism triggering intense starbursts does not significantly depend on the large-scale environment.

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Table 3.  Summary of Derived Properties for Nine Sources with S/N ≥ 10

ALMA ID	Major Axis		Minor Axis		L8–1000μm	SFRIR	ΣSFR
	('')	(kpc)	('')	(kpc)	(log (L⊙))	(M⊙ yr−1)	(M⊙ yr−1 kpc−2 )
ADF22.1	0.85 ± 0.04	6.5 ± 0.3	0.33 ± 0.03	2.5 ± 0.2	13.0${}_{-0.1}^{+0.2}$	1100${}_{-210}^{+830}$	40
ADF22.2a	0.29 ± 0.05	2.2 ± 0.4	0.05 ± 0.11	0.4 ± 0.8	12.6${}_{-0.1}^{+0.2}$	400${}_{-70}^{+300}$	300
ADF22.3	0.45 ± 0.05	3.4 ± 0.4	0.18 ± 0.08	1.4 ± 0.6	12.5${}_{-0.1}^{+0.2}$	370${}_{-70}^{+280}$	50
ADF22.4	0.25 ± 0.05	1.9 ± 0.4	0.04 ± 0.11	0.3 ± 0.8	12.6${}_{-0.1}^{+0.2}$	380${}_{-70}^{+290}$	420
ADF22.5a	0.57 ± 0.06	4.4 ± 0.5	0.26 ± 0.06	2.0 ± 0.5	12.7${}_{-0.1}^{+0.2}$	480${}_{-90}^{+360}$	30
ADF22.6	0.38 ± 0.08	2.9 ± 0.6	0.30 ± 0.14	2.3 ± 1.1	12.4${}_{-0.1}^{+0.2}$	280${}_{-50}^{+210}$	30
ADF22.7	0.32 ± 0.08	2.4 ± 0.6	0.22 ± 0.10	1.7 ± 0.8	12.5${}_{-0.1}^{+0.2}$	320${}_{-60}^{+240}$	50
ADF22.8	0.26 ± 0.07	2.0 ± 0.5	0.18 ± 0.05	1.4 ± 0.4	12.3${}_{-0.1}^{+0.2}$	230${}_{-40}^{+180}$	50
ADF22.9	0.28 ± 0.14	2.1 ± 1.1	0.26 ± 0.17	2.0 ± 1.3	12.2${}_{-0.1}^{+0.2}$	160${}_{-30}^{+120}$	20

Note. Derived properties of the nine sources with S/N ≥ 10. The second and fourth columns show a deconvolved FWHM of the major and minor axes, derived using imfit. The third and fifth columns represent corresponding physical scale. Infrared luminosity (L_8–1000μm) is estimated using several templates of dusty galaxies as described in Umehata et al. (2015). SFR_IR are calculated from L_8–1000μm, using the empirical calibration by Kennicutt (1998) adjusted for Kroupa initial mass function (Kroupa 2001). We also roughly estimated surface density of SFR (Σ_SFR) using SFR_IR and derived source size.

^aBecause ADF22.2 and ADF22.5 do not have z_spec, we assume z = 3.0, which is a median redshift of the AzTEC sources (Smolčić et al. 2012b).

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The radio continuum also provides a tool to measure the scales of dusty starburst galaxies like SMGs (e.g., Chapman et al. 2004b; Biggs & Ivison 2008; Rujopakarn et al. 2016). These measurements shows relatively extended profile (e.g., a median of 5 kpc; Biggs & Ivison 2008), which is larger than the bright ALMA SMGs discussed above. To date, multiple explanations have been proposed. For instance, Rujopakarn et al. (2016) suggest that the relatively compact star formation is seen in SMGs with higher star formation rate (SFR), whereas main-sequence star-forming galaxies have different scales. Simpson et al. (2015b) indicate that the difference between the diffusion length of cosmic rays and FIR photons can account for it. In the future, deep and high angular resolution radio imaging in ADF22 should provide us with important clues to clarify the origin of the discrepancy between the radio and FIR sizes of SMGs.

The flux density and measured source size allow us to derive star formation rate surface density (Σ_SFR) and investigate the condition of star formation. We estimated L_IR [8–1000 μm] using SED templates of well-studied starburst galaxies (Silva et al. 1998; Swinbank et al. 2010, 2014) in the same manner as in Umehata et al. (2015). The SFR is in turn derived from L_IR, using the empirical calibration by Kennicutt (1998) adjusted to the Kroupa initial mass function (Kroupa 2001). Because ADF22.2 and ADF22.5 do not have z_spec, we assume z = 3.0 (a median value for AzTEC sources; Smolčić et al. 2012b). Finally, Σ_SFR was calculated using the size of the 1.1 mm continuum emission and the SFR divided by a factor of two, following Simpson et al. (2015b) (Table 3). The median value is Σ_SFR = 50 M_⊙ yr⁻¹ kpc⁻², significantly lower than the predicted Eddington limit for radiation pressure supported disks (e.g., Elmegreen 1999; Thompson et al. 2005; Younger et al. 2010; Andrews & Thompson 2011; Riechers et al. 2013, 2014). Therefore, starbursts seen in bright SMGs in ADF22 are not Eddington-limited as a whole. As some authors have noted (e.g., Simpson et al. 2015b), if SMGs have clumpy structure, the individual components might be Eddington-limited, as has been claimed from some recent high angular resolution ALMA images of the brightest SMGs (e.g., Hatsukade et al. 2015; Iono et al. 2016, but see also Hodge et al. 2016). Further observations capable of resolving sub-kpc structures (≲01 angular resolution) are required to probe such a scenario for the SMGs in ADF22.

In this section, we report the 1.1 mm number counts in ADF22, which is one of the most fundamental parameters in describing the evolution of this population. Previously, there have been a number of studies investigating submm/mm number counts from a variety of ALMA data sets; LABOCA/SCUBA2 source follow-up (Karim et al. 2013; Simpson et al. 2015a), the use of a calibration field (Oteo et al. 2016), a wide range of archival data (Hatsukade et al. 2013; Ono et al. 2014; Carniani et al. 2015; Fujimoto et al. 2016), and contiguous mapping (Aravena et al. 2016; Dunlop et al. 2016; Hatsukade et al. 2016). Here, we present the number counts in a ∼7 arcmin² contiguous field, in a remarkably high-density region of the early universe, well-suited for investigating the environmental dependence of SMG source counts.

To minimize contamination by false positives, we utilized only the 17 SMGs detected with S/N > 5σ in the FULL/LORES map. We excluded ADF22.18 because the S/N of this source is <5 in the FULL/LORES map. To investigate how the existence of the z = 3.09 protocluster affects the counts, we calculated the counts in two ways. First, we included all 17 SMGs. Second, we exclude the ten SMGs with known z_spec = 3.09 (Table 2) and used only the remaining seven SMGs. Flux-boosting effects were not considered (see Section 3.2). We corrected for the completeness of the source extraction, although the counts should not be significantly affected by the correction. We calculated the number counts and associated errors in the same way as Hatsukade et al. (2016). Figure 10 shows the differential and cumulative counts (in the left and right panels, respectively). We show the counts from all 17 SMGs, and those obtained when we remove the ten sources with z_spec = 3.09. We also summarize the count statistics in Table 4. For comparison, we also show other ALMA counts in both panels of Figure 10 (Karim et al. 2013; Ono et al. 2014; Simpson et al. 2015a; Fujimoto et al. 2016; Oteo et al. 2016) by scaling to 1.1 mm, assuming a modified black body with typical values for SMGs (spectral index of β = 1.5, dust temperature of 35 K (e.g., Swinbank et al. 2014) and z = 2.5 where necessary).

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Table 4.  Differential and Cumulative Number Counts for all SMGs

Differential Counts					Cumulative Counts
S1.1mm	Nall	dN/dS	Nfield	dN/dS	S1.1mm	Nall	N (>S)	Nfield	N (>S)
(mJy)		(103 mJy−1 deg−2)		(103 mJy−1 deg−2)	(mJy)		(103 deg−2)		(103 deg−2)
0.64	9	${9.4}_{-2.6}^{+6.1}$	5	${5.6}_{-1.9}^{+4.6}$	0.40	17	${9.8}_{-2.2}^{+5.1}$	7	${4.4}_{-1.3}^{+3.3}$
1.59	7	${2.4}_{-0.8}^{+2.1}$	2	${0.7}_{-0.4}^{+1.1}$	1.00	8	${4.1}_{-1.4}^{+3.4}$	2	${1.0}_{-0.6}^{+1.7}$
4.00	1	${0.1}_{-0.1}^{+0.3}$	0	⋯	2.52	1	${0.5}_{-0.4}^{+1.2}$	0	⋯

Note. We calculated the differential and cumulative counts in two ways: using all 17 SMGs (all) or the seven SMGs without z_spec = 3.09 (field). The errors are 1σ Poisson errors (Gehrels 1986).

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As discussed in Umehata et al. (2015), the volume density of the ALMA SMGs at z = 3.09 in ADF22 is, at least, about three orders of magnitude greater than the expected value in general fields. We now investigate whether the protocluster members affect the number counts or not, considering ALMA SMGs at all redshifts. As shown in Figure 10, we see a possible excess in both of the differential and cumulative counts (for all of 17 SMGs). In the case of cumulative counts, the counts in ADF22 are approximately five times higher than those found in ALESS at S_1.1mm > 2 mJy (Karim et al. 2013) and four to five times higher than those obtained at S_1.1mm > 1 mJy (Fujimoto et al. 2016; Oteo et al. 2016). The group of SMGs at z = 3.09 is undoubtedly responsible for this excess. On the other hand, we do not see an excess in the faintest bin (i.e., sub-mJy sources). A possible attribution is that the elevation of dusty star-forming activity in dense environment is significant only for relatively bright SMGs (S_1.1mm ≳ 1 mJy). Deeper observation in the future will provide an answer.

Here, another question naturally arises. What are the counts in typical fields? The core of the SSA22 protocluster is an unusual environment. Therefore, we have to identify ALMA SMGs that are not associated with the protocluster and utilize them in calculating the source counts in a typical field. It is, however, difficult to derive the counts correctly because seven sources with ≥5σ do not yet have z_spec. Here, we conservatively created counts using all seven ALMA SMGs (see Figure 10), some of which may also be at z = 3.09. The cumulative source counts from the seven SMGs and previous counts at bright fluxes (Karim et al. 2013; Simpson et al. 2015a) are fitted to a double-power law function of the form, $N{(\gt S)=N^{\prime} /S^{\prime} {[(S/S^{\prime} )}^{\alpha }+{(S/S^{\prime} )}^{\beta }]}^{-1}$, which yields the best-fit parameters of N' = 200 ± 30 deg⁻², S' = 4.9 ± 0.2 mJy, α = 10.4 ± 1.6, and β = 1.9 ± 0.1 (the right panel of Figure 10). Our counts, excluding known protocluster members, are in reasonable agreement with recent estimates that ought to be relatively free of cosmic variance; those from a number of calibration fields (Oteo et al. 2016) and those from a 2 arcmin² contiguous survey (Hatsukade et al. 2016). On the one hand, those counts from the seven SMGs seem to be several times lower than Fujimoto et al. (2016) at S_1.1mm < 1 mJy. One possible explanation for this discrepancy is that previous counts using 3–4σ sources are seriously affected by contaminants, as pointed out by Oteo et al. (2016). Another explanation involves clustering, although this effect may also contribute to our counts. The counts derived from serendipitously detected sources around other targeted galaxies might be biased or clustered as mentioned in previous papers (e.g., Simpson et al. 2015a; Fujimoto et al. 2016).

Our results suggest that the cluster environments are recognizable in the SMG number counts. At the same time, there are still large uncertainties for submm/mm number counts, including field to field variation, the shape of dust SEDs, and absolute flux uncertainties. Forthcoming, much wider ALMA surveys with sufficient depth, covering a variety of environments, should significantly improve our understanding of the submm/mm counts and their dependence on environment.