# NOEMA Redshift Measurements of Extremely Bright Submillimeter Galaxies Near
the GOODS-N

Logan H. Jones Department of Astronomy, University of Wisconsin-Madison, 475
N. Charter Street, Madison, WI 53706, USA  Michael J. Rosenthal Department of
Astronomy, University of Wisconsin-Madison, 475 N. Charter Street, Madison, WI
53706, USA  Amy J. Barger Department of Astronomy, University of Wisconsin-
Madison, 475 N. Charter Street, Madison, WI 53706, USA  Department of Physics
and Astronomy, University of Hawaii, 2505 Correa Road, Honolulu, HI 96822, USA
Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu,
HI 96822, USA  Lennox L. Cowie Institute for Astronomy, University of Hawaii,
2680 Woodlawn Drive, Honolulu, HI 96822, USA

(Received XXX; Revised YYY; Accepted ZZZ)

###### Abstract

We report spectroscopic redshift measurements for three bright submillimeter
galaxies (SMGs) near the GOODS-N field, each with SCUBA-2 850 µm fluxes $>10$
mJy, using the Northern Extended Millimeter Array (NOEMA). Our molecular
linescan observations of these sources, which occupy an $\sim 7$ arcmin2 area
outside of the HST coverage of the field, reveal that two lie at $z\sim 3.14$.
In the remaining object, we detect line emission consistent with CO(7–6), [C
i], and H2O at $z=4.42$. The far-infrared spectral energy distributions of
these galaxies, constrained by SCUBA-2, NOEMA, and Herschel/SPIRE, indicate
instantaneous star formation rates $\sim 4000~{}{\rm M_{\odot}~{}yr^{-1}}$ in
the $z=4.42$ galaxy and $\sim 2500~{}{\rm M_{\odot}~{}yr^{-1}}$ in the two
$z\sim 3.14$ galaxies. Based on the sources’ CO line luminosities, we estimate
$M_{{\rm gas}}\sim 10^{11}M_{\odot}$ and find gas depletion timescales of
$\tau_{{\rm depl}}\sim 50$ Myr, consistent with findings in other high-
redshift SMGs. Finally, we show that the two $z\sim 3.14$ sources, which alone
occupy a volume $\sim 10$ Mpc3, very likely mark the location of a
protocluster of bright SMGs and less dusty optical sources.

Submillimeter astronomy (1647) — High-redshift galaxy clusters (2007) — CO
line emission (262) — Galaxy evolution (594)

††journal: ApJ††facilities: Subaru (Suprime-Cam), JCMT (SCUBA-2), SMA, NOEMA,
Herschel, JVLA††software: astropy (Astropy Collaboration et al., 2018)

##  1 Introduction

Submillimeter galaxies (SMGs) are home to some of the most extreme regions of
star formation in the Universe. These highly dust-obscured sources, with far-
infrared (FIR) luminosities $L_{\rm IR}$ in excess of $10^{12}~{}L_{\odot}$,
have star formation rates (SFRs) of hundreds to thousands of
$\mathrm{M_{\odot}~{}yr^{-1}}$ and typically lie at redshifts $z=2-3$ (e.g.,
Chapman et al., 2005; Simpson et al., 2014; Neri et al., 2020), though a
significant tail in their redshift distribution has been found out to $z>6$
(e.g., Daddi et al., 2009a, b; Riechers et al., 2020). SMGs are major
contributors to the SFR density of the early Universe, accounting for as much
as half of all star formation at $z>1$ (e.g., Cowie et al., 2017; Dudzevičiūtė
et al., 2020). The rapid buildup of stellar mass that results from their
prodigious SFRs also suggests that SMGs are likely progenitors of compact
quiescent galaxies at moderate redshifts and of massive ellipticals locally
(e.g., Simpson et al., 2014; Toft et al., 2014).

In addition to being an important phase in massive galaxy evolution, dusty
starbursts may also trace the most massive dark matter halos in the early
Universe (e.g., Chen et al., 2016; Dudzevičiūtė et al., 2020; Long et al.,
2020). In the last ten years, a growing number of $z>2$ overdensities and
protoclusters of galaxies have been discovered through an excess of SMGs and
luminous active galactic nuclei (AGNs), each containing several (sometimes
$>10$) such sources (e.g., Chapman et al., 2009; Daddi et al., 2009a, b; Capak
et al., 2011; Walter et al., 2012; Casey et al., 2015; Miller et al., 2018;
Oteo et al., 2018; Gómez-Guijarro et al., 2019; Hill et al., 2020; Long et
al., 2020; Riechers et al., 2020; Zhou et al., 2020).

However, the relatively short duration ($\lesssim 100$ Myr, e.g., Carilli &
Walter, 2013) of a dusty starburst phase means that such structures may pose
challenges to our understanding of galaxy evolution. Perhaps activation of the
SMG phase is somehow correlated over the volume of a protocluster, though it
is unclear how the canonical mechanisms for triggering a starburst in
SMGs—gas-rich mergers (e.g., Toft et al., 2014) or the smooth accretion of gas
from the surrounding medium (e.g., Tadaki et al., 2018)—could synchronize over
large distances and short timescales. Alternatively, the gas depletion
timescales $\tau_{\rm{depl}}$ in these environments may be significantly
longer than previously thought, up to $\sim$1 Gyr in duration (e.g., Casey,
2016, and references therein). However, this conflicts with observations that
suggest the most massive ellipticals in low-redshift clusters formed most of
their stellar mass in short ($\lesssim$ 1 Gyr) bursts at high redshift (Thomas
et al., 2010). Long $\tau_{\rm{depl}}$ would also imply impossibly massive
end-product galaxies, if an SMG were to sustain its $\gtrsim 500~{}M_{\odot}$
yr-1 SFR for 1 Gyr.

In any case, the existence of SMG-rich structures in the early Universe
provides new and interesting constraints on the growth of individual massive
galaxies and the assemblage of large-scale structures. Moreover, the diversity
of observed properties of distant protoclusters (e.g., Casey, 2016, and
references therein) illustrates the need for a statistical sample of such
structures if we are to make robust inferences about the growth of galaxy
clusters and of massive galaxies across cosmic time.

In the first paper of their SUPER GOODS series, Cowie et al. (2017) presented
a deep 450 µm and 850 µm survey of the region around the GOODS-N field using
SCUBA-2 on the 15 m James Clerk Maxwell Telescope (JCMT), along with
interferometric followup of most of the more luminous SMGs with the
Submillimeter Array (SMA). (Note that observations of the field have continued
since that published work, and we use the latest images when quoting SCUBA-2
flux densities below.)

Of the six SCUBA-2 sources in the field with 850 µm fluxes greater than
$\sim$10 mJy, four reside in a small ($\sim 7$ arcmin2) region to the
northwest of the field center, just outside the HST/ACS and WFC3 footprints of
the GOODS (Giavalisco et al., 2004) and CANDELS (Grogin et al., 2011;
Koekemoer et al., 2011) surveys; see the upper-right panel of Figure 1. This
includes one of the brightest SCUBA-2 850 µm sources in the entire extended
GOODS-N with an 850 µm flux density of 18.7 mJy; cf. GN20 (Pope et al., 2005)
at 16.3 mJy.

The three brightest SMGs in this grouping appear to be single sources at the
resolution of the SMA observations, with the fourth only recently observed (M.
Rosenthal et al., in preparation). More than being projected neighbors, their
similar 20 cm flux densities, $K_{s}$ magnitudes, and photometric redshifts
$z_{phot}\sim 3$ (Yang et al., 2014; Hsu et al., 2019) suggest they may also
lie at similar redshifts and may even belong to a single, massively star-
forming structure. Two more moderately-bright SCUBA-2 sources, each with
$S_{850}>$8 mJy and $z_{phot}\sim 3$, also lie in this region.

In this work, we present the first results of a spectroscopic campaign with
the IRAM Northern Extended Millimeter Array (NOEMA) to detect CO line emission
towards SMGs in this northwest offshoot of the GOODS-N. From these data, we
determined spectroscopic redshifts of the three brightest sources and
confirmed that two are at nearly identical redshifts. In Section 2, we
describe our NOEMA observations and data reduction, along with public
multiwavelength imaging for our field. We present the redshifts and observed
continuum and line properties of our sources in Section 3. In Section 4, we
discuss the nature of these sources as well as their physical properties
derived from our NOEMA data and from optical-through-mm spectral energy
distribution (SED) fitting. We also discuss the evidence for these sources
signposting a galaxy overdensity, concluding that they very likely belong to a
protocluster that is relatively rich in SMGs. Finally, we give a brief summary
in Section 5. Throughout this work we use a $\Lambda$CDM cosmology with
$H_{0}=70.5$ km s-1, $\Omega_{{\rm m}}=0.27$, and $\Omega_{\Lambda}=0.73$.

##  2 Data

###  2.1 NOEMA Observations

Figure 1: Top left: SCUBA-2 850 $\mu$m image of the extended GOODS-N.
Displayed fluxes include a multiplicative factor of 1.1 to correct for the
SCUBA-2 PSF. The blue contour shows the CANDELS HST/WFC3 F160W footprint. Top
right: A zoom-in to the portion of the field that contains our target galaxies
(marked by the white box in the top left panel). Our 3 target galaxies are
circled in solid white. An additional 3 galaxies with $S_{850}>8$ mJy, which
may also belong to the $z\sim 3.1$ protocluster, are circled in solid green.
Bottom: CFHT/WIRCam $K_{s}$-band images of GN-CL-1, GN-CL-2, and GN-CL-3. Each
panel is 12″ on a side. Pink crosshairs mark the position of each object’s
nearest $K$-band counterpart (except for GN-CL-1, which has no catalogued
counterpart in Hsu et al. (2019) due to its proximity to a bright star).
Contours show the 3, 7, 12, 18, and 25$\sigma$ levels of the CO(7–6) emission
line in GN-CL-1 and CO(5–4) in GN-CL-2 and GN-CL-3. In the bottom-right corner
of each panel, we show the beam profiles for the CO maps as yellow ellipses.

We targeted the three brightest SCUBA-2 sources in the northwest offshoot of
the GOODS-N using the NOEMA interferometer in the compact D configuration
(project ID W19DG; PI: Jones). We used two spectral tunings each in the
PolyFix 2 mm and 3 mm bands, which cover the frequency ranges 78.384–109.116
GHz and 131.384–162.116 GHz. GN-CL-1 and 2 were observed only in the 2 mm
band, as 3 mm observations towards these sources had already been carried out
in 2019 August; to our knowledge, these data have not yet been published. GN-
CL-3 was observed with all four spectral setups. Observations were carried out
in track-sharing mode in good weather conditions over the course of 2020 April
10–16, with average atmospheric phase stability of $\sim 10$–30% degrees rms
and typical precipitable water vapor levels of 1–4 mm. Tracks executed on 2020
April 10 used nine antennas, while all others used ten. In all observations,
the quasar 1030+611 was used as the phase and amplitude calibrator.
Observations carried out on 2020 April 10 used 0851+202 as the flux
calibrator, while all others used LkH$\alpha$101\. Calibration and imaging of
the uv data were carried out in gildas. We estimate that the absolute flux
calibration is accurate at the $\sim$15% level. Images were produced using
natural weighting, with typical synthesized beam sizes of
$7^{\prime\prime}\times 4^{\prime\prime}$ ($3^{\prime\prime}\times 2\farcs 5$)
at 3 (2) mm (see bottom panels in Figure 1).

Identification of lines in each tuning and sideband, as well as separation of
line- and continuum-only information, were carried out using an iterative
process. First, cleaned spectral cubes were binned to $\sim$75 km s-1 channel
widths to better identify potential emission and absorption features. Strong
emission features were identified by eye and then masked with the uv_filter
task in gildas/mapping using a $\sim$800–1000 km s-1 wide window around the
frequency of the line peak. This somewhat aggressive method of line-masking
ensures that our continuum measurements remain uncontaminated by strong
emission features at the cost of slightly underestimating the continuum flux
density. The remaining channels were then collapsed to form our continuum-only
images. RMS noise values in a given window were essentially uniform for all
sources observed in that window, ranging from 16–19.8 $\mu$Jy in the 3 mm band
and 23.2–30.1 $\mu$Jy in the 2 mm band. Continuum-subtracted spectral cubes
were created with the uv_base task in gildas/mapping using the same windows as
described previously to mask out strong lines.

###  2.2 Multiwavelength Data

Table 1: NOEMA Line and Continuum Measurements Name | R.A.a | Dec.a | ${S_{\rm 850\mu m}}^{b}$ | ${S_{158.2{\rm GHz}}}^{c}$ | Line | $\nu_{{\rm obs}}$ | $z$ | $\nu_{0}$ | $\Delta v_{\rm FWHM}$ | $S_{{\rm peak}}$
---|---|---|---|---|---|---|---|---|---|---
|  |  | [mJy] | [mJy] |  | [GHz] |  | [GHz] | [km s-1] | [mJy beam-1]
GN-CL-1 | 188.96404 | 62.36311 | 18.7$\pm$0.5 | 2.40$\pm$0.03 | CO(7–6) | 148.76 | 4.422 | 806.65 | 513$\pm$49 | 3.1$\pm$0.3
|  |  |  |  | [C i](3P2–3P1) | 149.24 | 4.423 | 809.34 | 362$\pm$63 | 2.0$\pm$0.3
|  |  |  |  | H2O($2_{11}$–$2_{02}$) | 138.72 | 4.421 | 752.03 | 430$\pm$85 | 1.2$\pm$0.2
GN-CL-2 | 188.98283 | 62.37750 | 11.2$\pm$0.5 | 0.87$\pm$0.03 | CO(5–4) | 138.92 | 3.148 | 576.27 | 369$\pm$23 | 4.3$\pm$0.2
GN-CL-3 | 188.94433 | 62.33703 | 11.5$\pm$0.6 | 0.90$\pm$0.03 | CO(5–4) | 139.46 | 3.132 | 576.27 | 500$\pm$41 | 3.0$\pm$0.2
|  |  |  |  | CO(3–2) | 83.71 | 3.131 | 345.80 | 459$\pm$40 | 2.0$\pm$0.2

Because HST data are not available for our sources, we instead used the
compilation of deep ultraviolet (UV), optical, and near-infrared (NIR)
photometry of the extended GOODS-N from Hsu et al. (2019) and references
therein to constrain the stellar properties of our sources. Specifically, for
our SED fits (see Section 4.1), we used Subaru/Suprime-Cam BVRIz data from
Capak et al. (2004); CFHT/WIRCam JHKs data from Wang et al. (2010) and Hsu et
al. (2019); and Spitzer/IRAC 3.6 µm and 4.5 µm data from Ashby et al. (2013).
Two of our three sources (GN-CL-2 and 3) have counterparts in the Hsu et al.
(2019) catalog within 1″ of the SMA 870 µm centroid, and we used their
photometry directly for these sources. GN-CL-1 is very near a bright ($H=7.8$)
star and thus no nearby optical-NIR counterpart is listed in the Hsu et al.
(2019) catalog. Instead, we performed our own aperture photometry on the JHKs
data from Wang et al. (2010) and Hsu et al. (2019) at the SMA position of GN-
CL-1. In each band, we measured fluxes in a 2″ diameter aperture and a local
median “background” (which largely comes from the saturated foreground star)
in a 2.4″–6″ diameter annulus, both centered on the SMA position of GN-CL-1.
We use the median background values to correct our fluxes for spillover light
from the star.

At long wavelengths, we use data from the GOODS-Herschel program of Elbaz et
al. (2011) to measure SPIRE 250 $\mu$m, 350 $\mu$m, and 500 $\mu$m fluxes for
our sources. Finally, we use the Very Large Array (VLA) 20 cm observations of
Morrison et al. (2010) to search for radio counterparts, though the radio
fluxes are not included in our SED fits.

##  3 Results

Figure 2: Full millimeter spectra of our three bright SCUBA-2 sources. The
source name and band are labeled in the top left corner of each panel.
Continuum-subtracted spectra were extracted from the spaxel with the brightest
continuum emission. The triangles denote the frequencies of common molecular
and atomic emission and absorption lines in the spectral ranges of our
observations. Given the rms noise in these spectra, we can only securely
identify the CO, H2O, and [C i] emission lines listed in Table 1. However, for
completeness, we also label several weaker transitions that are known to exist
in these ranges. Red triangles show commonly observed transitions in SMGs from
Spilker et al. (2014). Because that work does not extend to the highest rest-
frame frequencies at which we observed GN-CL-1, we mark transitions from the
NRAO’s Splatalogue database as blue triangles on its spectrum.

For GN-CL-1 and GN-CL-2, we extract four continuum flux densities in windows
centered at 135.3, 142.8, 150.7, and 158.2 GHz. For GN-CL-3, we extract four
at the above frequencies and another four in windows centered at 82.3, 89.8,
97.7, and 105.2 GHz. All of our sources are securely detected in continuum (at
the $\gtrsim 4\sigma$ level) in all sidebands of all tunings in which they
were observed, though for brevity, we report only the 158.2 GHz flux densities
in Table 1, as this sideband is devoid of obvious line emission or absorption
in all of our sources and thus provides a clean continuum measurement. As may
be expected from their relative 850 µm fluxes, the 158.2 GHz flux densities of
GN-CL-2 and 3 are similar at around 0.9 mJy, while that of GN-CL-1 is
brighter; we give exact values in Table 1.

We show the full NOEMA spectra of each of our sources in Figure 2, and mark
common molecular and atomic transitions in these bands. We do not detect most
of the weaker emission features, but GN-CL-1, 2, and 3 all have at least one
millimeter emission line detected at $>$5$\sigma$. We show the spectra from
the spaxel with the brightest line emission in Figure 3. Below we discuss the
continuum flux densities, line properties, and redshifts of the sources
individually.

GN-CL-1: This source is extremely well-detected in continuum, with flux
densities rising from 1.3 $\pm$ 0.03 mJy (SNR$\sim$43) in the 135.3 GHz window
to 2.4$\pm$0.03 mJy (SNR$\sim$80) in the 158.2 GHz window. We detect two
strong emission features towards this source at 148.762 and 149.243 GHz and a
weaker emission feature at 138.721 GHz, consistent with the frequency ratios
of CO(7–6), [C i](3P2–3P1), and H2O($2_{11}$–$2_{02}$) at $z\approx 4.42$. We
fit the CO(7–6) and [C i](3P2–3P1) lines simultaneously with two Gaussians,
without fixing their line ratios, widths, or frequencies relative to one
another, and we fit a single Gaussian to the H2O feature. The three lines have
peak flux densities of $3.1\pm 0.3$, $2.0\pm 0.3$, and $1.2\pm 0.2$ mJy beam-1
for CO(7–6), [C i](3P2–3P1), and H2O($2_{11}$–$2_{02}$), respectively, with
line widths ranging from $\sim$360 to 510 km s-1. As we discuss below, this
redshift identification shows that GN-CL-1 is not physically associated with
either of the remaining two sources.

Figure 3: Continuum-subtracted CO or H2O emission from our three bright
SCUBA-2 sources, zoomed in from the full spectra show in Figure 2. Spectra are
extracted from the spaxel with the brightest continuum emission. Red lines
show Gaussian fits to the data, with the transition labeled in red below the
line. The fitted peak flux densities, FHWM velocities, and peak frequencies
are listed in Table 1. Figure 4: Portion of the Keck/MOSFIRE $K$-band spectrum
of optical source 77630 in the catalog of Hsu et al. (2019), the most likely
optical-NIR counterpart to GN-CL-2. The data have been median filtered using a
window that is 5 wavelength bins wide. We mark the observed positions of the
redshifted [Oiii] doublet and H$\beta$ at $z=3.15$.

GN-CL-2: The second brightest SCUBA-2 source in our sample has NOEMA continuum
flux densities ranging from 0.41$\pm$0.02 mJy in the 135.3 GHz window to
0.87$\pm$0.03 mJy in the 158.2 GHz window. We detect a single strong emission
line towards GN-CL-2 at 138.917 GHz, with a peak flux density of $4.3\pm 0.2$
mJy beam-1 and a FWHM of $\approx$ 370 km s-1. For this redshift range, based
on the most common millimeter transitions in high-redshift SMGs (e.g., Spilker
et al., 2014), a line of this strength is most likely to be CO with $J_{\rm
up}=$ 4, 5, 6, or 7 at $z=$ 2.32, 3.15, 3.98, or 4.81, respectively, [C
i](1–0) at $z=2.54$, or H2O(211–202) at $z=4.41$.

Our near-continuous coverage from 131.4–162.1 GHz allows us to rule out most
of these redshift identifications by the non-detection of other strong lines
at the expected frequencies. If the feature at 138.917 GHz were CO(4–3) at
$z=2.32$, for example, we would expect to detect [Ci](1–0) at $\nu_{\rm
obs}\approx 148.2$ GHz, but no significant line emission is seen there.
Redshifts of $z=3.98$, 4.41, and 4.81 are similarly ruled out by the absence
of strong ($\gtrsim 1$ mJy beam-1) H2O($2_{11}-2_{02}$), CO(7–6), and
[Ci](3P2–3P1) emission at their respective expected frequencies.

This leaves CO(5–4) at $z=3.15$ and [Ci](1–0) at $z=2.54$ as the only viable
redshift identifications from the NOEMA data alone. Follow-up Keck/MOSFIRE
$K$-band spectroscopy from M. Rosenthal et al., in preparation, of this
source’s nearest optical-NIR counterpart (source 77630 in Hsu et al. 2019,
with $K=22.7$ and a separation of 0$\farcs$709 from the SMA position of GN-
CL-2) finds a redshift of $z$ = 3.15 based on the [Oiii] doublet and H$\beta$
(see Figure 4). This confirms the higher redshift identification.

GN-CL-3: GN-CL-3 was the only source we observed in both the 2 mm and 3 mm
bands. The nearest optical-NIR counterpart to this SMG (separation of
0$\farcs$473 from its SMA position) is source 85384 in Hsu et al. (2019). Its
millimeter continuum flux densities rise smoothly from 82.5$\pm$16 $\mu$Jy in
the 82.3 GHz window to 0.9$\pm$0.03 mJy in the 158.2 GHz window. We detect
strong emission features at 83.706 GHz and 139.458 GHz, consistent with the
frequency ratio of CO(3–2) and CO(5–4) at $z\approx 3.13$. Separate Gaussian
fits to each of these lines yield peak flux densities of $2.0\pm 0.2$ and
$3.0\pm 0.2$ mJy beam-1, respectively, with FWHM $\approx$ 480 km s-1. GN-CL-2
and GN-CL-3 are therefore confirmed to lie a mere $\Delta z\sim 0.02$ apart in
redshift, with a projected separation of 1.2 Mpc and a 3D separation of 2.7
proper (14.6 comoving) Mpc, if the difference in recession velocities is due
only to the Hubble flow. A sphere of diameter equal to the proper distance
between these two galaxies would have a volume of, at most, $\sim$10 Mpc3.
However, as we discuss in the next section, these galaxies very likely belong
to a larger overdensity of rare, submillimeter-bright galaxies. If the
difference in their redshifts is due to peculiar velocities within a common
structure, then the separations quoted above would be overestimates.

Finally, we note that GN-CL-3 appears to have a projected companion about 5″
to the southeast. This neighboring source is extremely faint in continuum,
with a $<2\sigma$ detection in the $\sim 2$ mm data and completely invisible
in the lower-resolution 3 mm data. However, its presence is revealed by a
single strong emission feature (peak flux density $\sim 2.5$ mJy) at 149.3
GHz. No line emission from an SMG at $z=3.13$ is expected at this frequency,
which suggests that the companion is not associated with GN-CL-3. The line
emission is spatially coincident with an optically-bright $z=0.543$ radio
source (Barger et al., 2014), which suggests this line may be CO(2–1).

Table 2: Derived Properties of Candidate Protocluster Members | GN-CL-1 | GN-CL-2 | GN-CL-3
---|---|---|---
SFRa [${\rm M_{\odot}~{}yr}^{-1}$] | $3900\pm 580$ | $2530\pm 130$ | $2990\pm 770$
${\rm SFR_{100}}^{b}$ [${\rm M_{\odot}~{}yr}^{-1}$] | $1070\pm 300$ | $630\pm 30$ | $390\pm 140$
$M_{\star}$ [$10^{10}~{}{\rm M_{\sun}}$] | $10.7\pm 3.1$ | $5.8\pm 0.3$ | $4.5\pm 1.2$
sSFR [${\rm Gyr^{-1}}$] | $37\pm 12$ | $44\pm 3$ | $67\pm 25$
$M_{\rm d}$ [$10^{9}~{}{\rm M_{\sun}}$] | $4.5\pm 0.4$ | $2.2\pm 0.2$ | $2.0\pm 0.1$
$T_{\rm d,char}$ [K] | $33.4\pm 0.8$ | $34.9\pm 0.5$ | $34.8\pm 0.6$
$M_{\rm gas}$ [$10^{11}~{}{\rm M_{\sun}}$] | $2.0\pm 0.5$ | $1.3\pm 0.2$ | $1.2\pm 0.2^{c}$
${\tau_{\rm depl}}$ [Myr] | $52\pm 15$ | $51\pm 9$ | $41\pm 13^{c}$
$M_{\rm gas}/M_{\rm d}$ | $45\pm 12$ | $59\pm 11$ | $61\pm 12^{c}$

##  4 Discussion

###  4.1 Star Formation Rates, Masses, and Dust Temperatures

The rich photometric data from the rest-frame optical to the radio allow us to
constrain the physical properties of these galaxies with SED fitting. We use
the Code Investigating GALaxy Emissions (cigale, Noll et al., 2009), which
calculates SEDs using an energy balance principle, where the energy absorbed
by dust in the UV to NIR equals that re-radiated in the MIR to FIR. We use the
updated python version of the code, which has been shown to produce comparable
results for high-redshift starbursts to other SED fitting codes (Boquien et
al., 2019), to constrain the SFRs, stellar masses, dust masses, and dust
temperatures of the three SMGs.

We used Bruzual & Charlot (2003) stellar population libraries with a Chabrier
(2003) initial mass function (IMF) for the full range of available
metallicities. Stellar spectra are attenuated using a modified Charlot & Fall
(2000) dust law with fixed power law indices $\delta_{\rm ISM}=-0.7$ and
$\delta_{\rm BC}=-1.3$ and a separation age between old and young stellar
populations of 10 Myr. We use the dust emission models from Draine et al.
(2014), with an input minimum radiation field of $1.0\leq U_{\rm min}\leq
50.0$111$U$ has units of 1 Habing $=1.6\times 10^{-3}~{}{\rm
erg~{}cm^{-2}~{}s^{-1}}$ and an input mass fraction of $0.005\leq\gamma\leq
0.05$ irradiated by $U>U_{\rm min}$. We fix the radiation field power law
slope $\alpha=2.0$, and we fit for polycyclic aromatic hydrocarbon (PAH) mass
fractions $0.47\%\leq q_{\rm PAH}\leq 3.90\%$. The mean intensity
$\left<U\right>$ is used to derive a characteristic dust temperature, $T_{\rm
d,char}=18~{}{\rm K}\times\left<U\right>^{1/6}$ (Draine et al., 2014), which
we report in Table 2.

The properties estimated by cigale, especially the SFR, are strongly dependent
on the input star formation history (SFH). Given these galaxies have FIR
fluxes indicative of ongoing starbursts, we model the SFH as having formed
50-99% of stars by mass in a short, ongoing, flat burst of age $\leq 100$ Myr,
and the remainder of stars in an exponentially declining SFH of age 0.25-1.5
Gyr, with $e$-folding time $250~{}{\rm Myr}\leq\tau_{\rm main}\leq 6~{}{\rm
Gyr}$. cigale returns a maximum likelihood instantaneous SFR for each galaxy,
as well as SFRs averaged over the preivous 10 and 100 Myr. Different methods
of SFR estimation in the literature report either averaged or instantaneous
SFRs, so we report both the instantaneous and 100 Myr-averaged SFR for each
galaxy in Table 2. We use the instantaneous SFRs to compute gas depletion
times (see Section 4.2). The 100 Myr-averaged SFR is appropriate for
comparisons with SFRs output from codes such as magphys (da Cunha et al.,
2015) and works that use it (e.g. Dudzevičiūtė et al., 2020).

We ran cigale on FIR to millimeter photometry from Herschel/SPIRE, SCUBA-2,
and NOEMA, along with observed-frame optical to NIR photometry from Hsu et al.
(2019) (for GN-CL-2 and 3) or our own JHKs aperture photometry (for GN-CL-1).
In addition to the cataloged measurement uncertainties, we included a 10%
systematic uncertainty on the absolute photometry/flux calibration in our
input flux errors. We fixed the redshifts at the spectroscopic redshift of
each source; that is, $z_{spec}=4.42$ for GN-CL-1 and $z_{spec}=3.14$ for GN-
CL-2 and GN-CL-3. We show the best-fit SEDs for the three SMGs in Figure 5.

Based on its best-fitting SED, GN-CL-1 has an 8–1000 $\mu$m luminosity $L_{\rm
IR}\approx 1.1\times 10^{13}~{}{\rm L_{\sun}}$, making it a high-redshift
hyper-luminous infrared galaxy (HyLIRG). Its instantaneous ${\rm SFR}=3900\pm
580~{}{\rm M_{\sun}~{}yr^{-1}}$ is one of the largest in the field. With $\sim
10^{11}~{}{\rm M_{\sun}}$ of stars already in place by $z=4.42$, this source
is the likely progenitor of a massive elliptical at $z\approx 0$. GN-CL-2 and
GN-CL-3 are also massive star-forming galaxies, with 8–1000 $\mu$m luminosity
$L_{\rm IR}\approx 5\times 10^{12}~{}{\rm L_{\sun}}$, comparable to nearby
ultraluminous infrared galaxies, and instantaneous ${\rm SFR}\approx
2500~{}{\rm M_{\sun}~{}yr^{-1}}$. The similarities between GN-CL-2 and GN-
CL-3, as well as the difference in their values compared with GN-CL-1, are
consistent with rough expectations from the 850 $\mu$m flux densities.

Figure 5: Best-fit SEDs from cigale for each SMG. The black curve shows the
total SED, while the red and yellow curves show the relative contributions to
the SED of the dust and the attenuated stellar emission, respectively. The
purple and red dots show the measured and fit fluxes, respectively.

###  4.2 Gas Mass and Depletion Timescale

Molecular hydrogen’s low emissivity makes it hard to detect even in nearby
galaxies, so the luminosity of the CO(1–0) emission line is often used as a
proxy for the mass of molecular hydrogen, $M_{{\rm H_{2}}}$. We follow the
methodology of Bothwell et al. (2013) to convert our higher $J$ CO transitions
to CO(1–0), and subsequently into a molecular gas mass for each galaxy,
$M_{{\rm gas}}$.

We compute the line luminosity $L^{\prime}_{\rm CO}$ using the standard
relation from Solomon & Vanden Bout (2005):

$L^{\prime}_{\rm CO}=3.25\times 10^{7}\times S_{\rm CO}\Delta V\nu_{\rm
obs}^{-2}D_{\rm L}^{2}(1+z)^{-3},$ (1)

where $L^{\prime}_{\rm CO}$ is the line luminosity with units ${\rm
K~{}km~{}s^{-1}~{}pc^{2}}$, $S_{\rm CO}\Delta V$ is the integrated line
luminosity in Jy km s-1, $\nu_{\rm obs}$ is the observed line frequency in
GHz, and $D_{\rm L}$ is the luminosity distance in Mpc. We take $S\Delta V$ to
be the area underneath the Gaussian fits to each detected CO line and convert
our measured luminosities from higher $J$ lines to CO(1–0) using Table 4 of
Bothwell et al. (2013). Errors on $L^{\prime}_{\rm CO}$ are dominated by
errors on $S\Delta V$ and on the $J$-conversion factors $r_{76/10}$,
$r_{54/10}$, and $r_{32/10}$. We assume an $L^{\prime}_{\rm CO(1-0)}$ to
$M_{{\rm H_{2}}}$ conversion factor $\alpha=1~{}{\rm
M_{\sun}(K~{}km~{}s^{-1}~{}pc^{2}})^{-1}$. Finally, we multiply a correction
of $M_{\rm gas}=1.36M_{\rm H_{2}}$ to account for the addition of helium.

For a given SFR and $M_{\rm gas}$, the depletion timescale is approximately
given by

$\tau_{\rm depl}=\frac{M_{\rm gas}}{{\rm SFR}}.$ (2)

We list the gas masses and depletion times for our galaxies in Table 2. For
GN-CL-3, which has both CO(5–4) and CO(3–2) detections, we show values for
CO(5–4) for consistency with GN-CL-2, but the values derived from both lines
are consistent within errors222Specifically, $M_{\rm gas}=(12.3\pm 2.3)\times
10^{10}~{}{\rm M_{\sun}}$ and $\tau_{\rm depl}=41\pm 13~{}{\rm Myr}$ for
CO(5–4), and $M_{\rm gas}=(12.8\pm 2.7)\times 10^{10}~{}{\rm M_{\sun}}$ and
$\tau_{\rm depl}=43\pm 14~{}{\rm Myr}$ for CO(3–2).. The depletion times of
$\sim$50 Myr are consistent with values for other high-redshift SMGs based on
high-$J_{\rm up}$ CO lines (e.g., Casey, 2016). Based on the calculations in
Casey (2016), we would not be likely to observe two SMGs in the same structure
with such short depletion times, though we note that values of $\tau_{\rm
depl}$ are dependent on the SFR measurement methods used, and, by extension,
the assumed SFH, IMF, and conversion factor, $\alpha$.

###  4.3 (Sub)Millimeter Evidence of a Protocluster

As mentioned previously, the three SMGs we targeted with NOEMA are part of a
larger grouping of seven bright SCUBA-2 sources to the northwest of the HST
coverage of the GOODS-N. One is confirmed by our NOEMA observations to lie at
high redshift ($z=4.42$), while another (source 7 in Figure 1) has a $U$-band
counterpart and $z_{phot}=1.58$, making it unlikely to belong to the same
$z\approx 3.14$ halo as GN-CL-2 and GN-CL-3. The remaining three sources (4,
5, and 6 in Figure 1) have SCUBA-2 850 $\mu$m fluxes of 9.8 mJy, 8.6 mJy, and
8.2 mJy, respectively. NOEMA redshift scans of these additional sources, which
will determine whether they are part of the same system as GN-CL-2 and GN-
CL-3, will be carried out in 2021. In the meantime, we can use the known
number counts of bright SMGs to estimate the probability that these sources
belong to a larger structure or protocluster.

The S2COSMOS survey of Simpson et al. (2019) presents number counts of SCUBA-2
850 $\mu$m sources in the COSMOS field over 2.6 deg2, with a typical $1\sigma$
noise level of 1.2 mJy beam-1 in the central region of the field. Their
incompleteness-corrected cumulative number counts (their Table 2) suggest that
one can expect 61.9${}^{+7.2}_{-7.7}$ sources per deg2
(0.017${}^{+0.002}_{-0.002}$ arcmin-2) at a flux density $S_{850}>7.7$ mJy.
However, there are seven $S_{850}>8$ mJy galaxies in the northwest offshoot of
the GOODS-N that occupy an area only $\sim 4.6\times 4.1$ arcmin2 in size, for
a cumulative source density of $N(S_{850}>8$ mJy) = 0.371 arcmin-2. If we
assume that the positions of bright SMGs are completely random on the plane of
the sky and uncorrelated in redshift space, then the number counts in Simpson
et al. (2019) suggest that we should expect an average of just 0.321 sources
with $S_{850}>8$ in a given $4.6\times 4.1$ arcmin2 area, a factor of $21.8$
lower than what is observed in our field. Even removing sources 1 and 7 (for a
total of 5 galaxies across a $4\times 4$ arcmin2 area) yields a projected
overdensity 14 times higher than what would be expected if the remaining
sources were not part of a single structure.

Alternatively, let us assume that whether or not a bright SMG is seen in a
unit area is a Poissonian process so that we can use small number statistics
(Gehrels, 1986) to determine the raw likelihood of seeing multiple randomly-
distributed $S_{850}>8$ mJy sources in an 18.9 arcmin2 box. Specifically, if
we treat GN-CL-2 and GN-CL-3 as a single system due to their nearly-identical
redshifts, then we may compute the chances of observing $2<N<6$ projected
systems via $P(N;0.321)=\frac{\lambda^{N}e^{-\lambda}}{N!}$, where
$\lambda=0.321$ is the mean expected number of sources in a $4.6\times 4.1$
arcmin2 area. As may be expected, the probability of such a projection drops
rapidly with increasing $N$, falling from 3.7% at $N=2$ to $1.1\times
10^{-4}$% at $N=6$. For $N=5$ (6), only $\sim$2500 (160) such projections are
expected to be seen across the entire sky.

However, we know from the combination of our NOEMA observations and the UV
through radio photometry of Hsu et al. (2019) that sources 1 and 7 are,
indeed, a chance projection with one another and with sources 2 and 3. In
other words, all three systems are independent “events” such that $N$ is at
least 3. If even one of the remaining three bright SMGs is also a chance
projection with these systems, then we begin to move into a regime of such
extraordinarily low probability that it defies our assumption of independent
and physically unassociated systems.

###  4.4 Optical Evidence of a Protocluster

Figure 6: Projected 2D density of all sources in the extended GOODS-N with
$3.1<z_{phot}<3.2$ in Hsu et al. (2019) (top) and those in the interval
$2.9<z_{phot}<3.3$ that meet the LBG criteria of Capak et al. (2004) (bottom).
In both panels, a Gaussian kernel density estimate has been applied, and each
cell is $2\times 2$ arcmin2. Contours on the top (bottom) panel indicate
regions where the source density is 3$\sigma$, 4$\sigma$, and 5$\sigma$
(2$\sigma$ and 3$\sigma$) higher than the mean in the CANDELS portion of the
field. Filled stars show the positions of SMGs observed as part of this work
(blue if they are spectroscopically confirmed to lie at $z\sim 3.14$, and
brown otherwise). Blue open stars show the positions of other $S_{850}>8$ mJy
SMGs in the region that do not yet have spectroscopic confirmation but may
belong to the overdensity. The brown open star is an SMG with a bright
$U$-band counterpart and $z_{phot}=1.58$. Upward- and downward-pointing open
triangles, respectively, mark the positions of the GN20 overdensity (Pope et
al., 2005; Daddi et al., 2009a) and the $z=1.99$ SMG-rich protocluster of
Chapman et al. (2009).

The region we consider in this work is well outside the HST coverage of the
GOODS-N. Thus, spectroscopic followup is extremely incomplete, even for
relatively bright objects, compared to the GOODS/CANDELS portion of the field.
Within a 5′ radius of the mean position of all seven bright SMGs, there are
316 (2949) sources with $R$ magnitudes brighter than 22 (25), of which only 3
(8) objects have a published spectroscopic redshift in the multiband catalog
of Hsu et al. (2019), with none at $z>2$.

In M. Rosenthal et al., in preparation, we will use our Keck/MOSFIRE
spectroscopy of optical-NIR sources in the northwest region of the GOODS-N,
together with our existing and upcoming NOEMA data, to characterize the
$z\approx 3.14$ protocluster. For now, we use the multiband catalog of Hsu et
al. (2019) to see whether evidence of an optical overdensity is present based
on photometric redshifts only. We restrict to objects with Kron $R$ magnitudes
brighter than 25 and $R$ magnitude errors fainter than 26.75, corresponding to
a $>5\sigma$ detection. We further restrict to regions where the per-pixel
$J$-band flux uncertainties are less than twice the median rms in the central
part of the field. This results in the loss of 139 arcmin2 of the $JHK_{s}$
survey area but also removes the bulk of spurious or extremely noisy sources
near the edge of the field. Over the redshift interval $3.1<z_{phot}<3.2$, we
find a mean density of 0.58 galaxies per arcmin2. However, when we perform a
similar analysis in an area of radius 4′ centered on the bright SMG
overdensity, we find a mean density of 0.89 galaxies per arcmin2. The total
number of objects in the overdense region is 45 compared with an expected
value of 29.

We next compare the distribution of the number of sources in $1^{\prime}$
square cells in the full field with that in an $8^{\prime}$ square area
centered on the SMGs (64 cells). A one-tailed Mann-Whitney test of these two
samples yields a $p$ value of 0.0014, which implies that they are not drawn
from the same distribution and that the optical-NIR overdensity is
statistically significant.

For visualization purposes, we show in the top panel of Figure 6 a 2D
histogram of the source density in this narrow photometric redshift interval.
This density map has been “smoothed” using a Gaussian kernel density estimate
with $2^{\prime}\times 2^{\prime}$ bins. We note a clear maximum in the
density of optical sources that is coincident with the grouping of bright
SMGs.

As an additional check, we examine the spatial distribution of candidate Lyman
Break Galaxies (LBGs) across the extended GOODS-N in the bottom panel of
Figure 6. We use the color criteria of Capak et al. (2004) to select LBGs in
the redshift interval $2.9<z_{phot}<3.3$. While the photometric redshift
interval is too broad to constrain the number of LBGs that may belong to a
single, coherent structure at $z\approx 3.14$, we nevertheless note that the
maximum density of LBGs is again coincident with the (projected) overdensity
of bright SMGs (see the bottom panel of Figure 6).

Finally, we note that the $\sim 0\fdg 07\times 0\fdg 07$ angular extent of our
extremely bright SMG overdensity is intermediate in size compared to other
high-redshift, SMG-rich protoclusters in the literature. For example, this
structure is quite compact compared to the $z=1.99$ structure in the GOODS-N
(Chapman et al., 2009, 0$\fdg$17 $\times$ 0$\fdg$17), the SSA22 protocluster
at $z=3.1$ (Steidel et al., 1998, 0$\fdg$33 $\times$ 0$\fdg$50), and the
$z=5.18$ HDF850.1 overdensity (Walter et al., 2012, 0$\fdg$10 $\times$
0$\fdg$13). However, it is more extended than the GN20 overdensity (Pope et
al., 2005; Daddi et al., 2009a, b, 0$\fdg$01 $\times$ 0$\fdg$01) and the
Distant Red Core (Oteo et al., 2018; Ivison et al., 2020, 0$\fdg$02 $\times$
0$\fdg$02), both at $z\sim 4$. We defer a fuller discussion of the total SFR,
stellar mass, halo mass, and physical extent to M. Rosenthal et al., in
preparation.

##  5 Summary

We report the results of a millimeter spectroscopic campaign with NOEMA to
measure redshifts for three of the 850 µm-brightest SMGs in the extended
GOODS-N, which lie in a close (projected) grouping. We determined unambiguous
spectroscopic redshifts for two of our three targets using the NOEMA data
alone (GN-CL-1 at $z=4.42$ and GN-CL-3 at $z=3.13$) and for the remaining
target using both NOEMA and Keck/MOSFIRE spectroscopy (GN-CL-2 at $z=3.15$).
With nearly identical redshifts, GN-CL-2 and 3 are likely part of a single
system and may signpost an overdensity of galaxies at $z\approx 3.14$. More
importantly, there are three more bright, neighboring SMGs which, based on
number counts and simple probability estimates, are extremely likely to belong
to the same structure, constituting a protocluster of short-lived SMGs in the
high-redshift Universe. Finally, our best-fit SEDs suggest that GN-CL-1, one
of the brightest SCUBA-2 850 µm sources in the extended GOODS-N field, is an
extremely FIR-luminous, high-redshift dusty starburst with $\sim
10^{11}~{}{\rm M_{\sun}}$ already formed when the Universe was only 1.4 Gyr
old.

We thank the anonymous referee for a useful report that helped us to improve
the manuscript. We gratefully acknowledge support for this research from a
Wisconsin Space Grant Consortium Graduate and Professional Research Fellowship
(L.J.), NASA grant NNX17AF45G (L.L.C.), the William F. Vilas Estate (A.J.B.),
and the Kellett Mid-Career Award from the University of Wisconsin-Madison
Office of the Vice Chancellor for Research and Graduate Education with funding
from the Wisconsin Alumni Research Foundation (A.J.B.). This work is based on
observations carried out under project number W19DG with the IRAM NOEMA
Interferometer. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN
(Spain). L. Jones thanks Vinod Arumugam for many helpful discussions on the
reduction and processing of NOEMA observations.

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