11institutetext:  Department of Physics, Colorado College, 14 E. Cache La
Poudre Street, Colorado Springs, CO 80903, USA 22institutetext: Academia
Sinica Institute of Astronomy and Astrophysics (ASIAA), No. 1, Sec. 4,
Roosevelt Rd., Taipei 10617, Taiwan
22email<EMAIL_ADDRESS>33institutetext: Max-Planck-Institut fur
Astrophysik, Karl-Schwarzschild-Str 1, D-85748 Garching bei München,
Germany44institutetext: Dipartimento di Fisica G. Occhialini, Università degli
Studi di Milano Bicocca, Piazza della Scienza 3, 20126 Milano, Italy
55institutetext: Centre for Extragalactic Astronomy, Durham University, South
Road, Durham DH1 3LE, UK 66institutetext: Institute for Computational
Cosmology, Durham University, South Road, Durham DH1 3LE, UK 77institutetext:
Department of Astronomy, Tsinghua University, Beijing 100084, China
88institutetext: Dipartimento di Fisica e Astronomia, Università di Firenze,
Via G. Sansone 1, 50019 Sesto Fiorentino, Firenze, Italy 99institutetext: INAF
– Osservatorio Astrofisico di Arcetri, 50125 Florence, Italy
1010institutetext: UCO/Lick Observatory, University of California 2013 Santa
Cruz, Santa Cruz, CA 95064, USA 1111institutetext: Kavli Institute for the
Physics and Mathematics of the Universe (Kavli IPMU), 5-1-5 Kashiwanoha,
Kashiwa, 277-8583, Japan 1212institutetext: Korea Astronomy and Space Science
Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Republic of Korea

# A Multiwavelength Study of ELAN Environments (AMUSE2)

Ubiquitous dusty star-forming galaxies associated with enormous Ly$\alpha$
nebulae on megaparsec scales

Marta Nowotka 11 Chian-Chou Chen 22 Fabrizio Arrigoni Battaia 33 Michele
Fumagalli 445566 Zheng Cai 77 Elisabeta Lusso 8899 J. Xavier Prochaska
10101111 Yujin Yang 1212

(To be submitted to A&A)

We have been undertaking a systematic survey at 850 $\mu$m based on a sample
of four prototypical $z\sim 2-3$ enormous Ly$\alpha$ nebulae (ELANe) as well
as their megaparsec-scale (Mpc-scale) environments to study the physical
connections between ELANe and their coeval dusty submillimeter galaxies
(SMGs). By analysing the SCUBA-2 data with self-consistent Monte Carlo
simulations to construct the number counts, here, we report on the
overabundance of 850 $\mu$m-selected submillimeter sources around all the four
ELANe, by a factor of 3.6$\pm$0.6 (weighted average) compared to the blank
fields. This suggests that the excessive number of submillimeter sources are
likely to be part of the Mpc-scale environment around the ELANe, corroborating
the co-evolution scenario for SMGs and quasars; this is a process which may be
more commonly observed in the ELAN fields. If the current form of the
underlying count models continues toward the fainter end, our results would
suggest an excess of the 850 $\mu$m extragalactic background light by a factor
of between 2-10, an indication of significant background light fluctuations on
the survey scales. Finally, by assuming that all the excessive submillimeter
sources are associated with their corresponding ELAN environments, we estimate
the SFR densities of each ELAN field, as well as a weighted average of
$\Sigma$SFR=1200$\pm$300 $M_{\odot}$ yr-1 Mpc-3, consistent with that found in
the vicinity of other quasar systems or proto-clusters at similar redshifts;
in addition, it is a factor of about 300 greater than the cosmic mean.

###### Key Words.:

Galaxies: clusters: general – Galaxies: halos – Galaxies: high-redshift –
Cosmology: cosmic background radiation – Submillimeter: galaxies

##  1 Introduction

Galaxies that are selected at submillimeter wavelengths, in particular at 850
micron, contain sites that exhibit some of the most intensive star formation
across the Universe, with estimated star-formation rates up to thousands of
solar masses per year (e.g., Barger et al. 2012; Swinbank et al. 2014; Cowie
et al. 2017; Dudzevičiūtė et al. 2020). They are predominantly located at
$z=1-3,$ with a long tail toward $z>4$ (Barger et al. 2000; Chapman et al.
2005; Wardlow et al. 2011; Simpson et al. 2014; Chen et al. 2016a; Stach et
al. 2018; Dudzevičiūtė et al. 2020; Smail et al. 2021), matching the trend of
cosmic star formation rate (SFR) densities (Madau & Dickinson 2014a). Evidence
that has been collected since the discovery of the first submillimeter
galaxies (SMGs; Smail et al. 1997; Barger et al. 1998; Hughes et al. 1998)
points to an evolutionary scenario whereby these massive (1010-1011 M⊙ in
stellar masses; da Cunha et al. 2015; Michałowski et al. 2017) dusty star-
forming galaxies would evolve into the likes of local massive elliptical
galaxies, undergoing subsequent multiple phase transitions that include
optically bright quasars, compact quiescent galaxies, and dry mergers (e.g.,
Toft et al. 2014).

The latest evidence supporting this hypothetical evolution comes from galaxy
clustering analyses, which have been enabled thanks to the sufficiently large-
scale submillimeter surveys that have only recently become available (e.g.,
Geach et al. 2017). These studies have found, via the measurements of both
auto-correlation functions and cross-correlation functions, that SMGs are
predominantly located in dark-matter halos with masses of around 1012-1013 M⊙
at $z\sim 1-3$ (Hickox et al. 2011; Chen et al. 2016a, b; Wilkinson et al.
2017; An et al. 2019; García-Vergara et al. 2020; Lim et al. 2020). This is
consistent with their being the predicted progenitors of local massive
elliptical galaxies, as is the case for the bright quasars at similar
redshifts (White et al. 2012; Timlin et al. 2018, and references therein.)

In general, subsequent active black hole accretion that coincides with or
follows intensive star-forming events has long been proposed, even in the
local Universe (e.g., Hopkins et al. 2006), to partly explain the rapid
quenching of star formation through feedback. This hypothesis, together with
the clustering analyses, would suggest an intimate co-evolution between black
hole growth and star formation, such that detecting star formation in and
around quasar host galaxies is expected. Indeed, the correlated signals found
via cross-correlation analyses between infrared background measurements and
quasar samples have further supported, on average, the co-existing nature of
the two populations on halo scales (Wang et al. 2015). In addition, targeted
submillimeter observations on well-defined AGN samples have revealed
overdensities of submillimeter sources, as indicated by excessive
submillimeter source counts, around some high-redshift radio galaxies (e.g.,
Stevens et al. 2003; Dannerbauer et al. 2014), as well as IR luminous AGN
selected by the WISE satellite (e.g., Jones et al. 2017a), again suggesting
the possible co-evolution and co-existence of both active black hole accretion
and dusty star formation on Mpc scales around massive halos. However, these
studies have often reported overdensity only in a few fields over a larger
parent sample, casting the question that the co-evolution may not be universal
and can only occur under certain conditions or preferentially around a certain
type of quasar (Rigby et al. 2014; Zeballos et al. 2018).

Figure 1: SCUBA-2 signal-to-noise maps at 850 $\mu$m for the Fabulous,
Jackpot, MAMMOTH-1, and Slug ELANe (yellow star). Sources detected at over 4
$\sigma$ are marked by cyan circles, and the size of the circles represents
$2\times$ the FWHM of the beam. The white curve bounds the effective area of
every map, which is about 10′ ($\sim$5 Mpc) in diameter. The quasars that
contribute significantly to the powering of the corresponding ELAN are marked
as yellow stars (coordinates in Table 1).

To improve our understanding of this co-evolution and to expand the quasar
types studied, as part of the A MUltiwavelngth Study of ELAN Environment
(AMUSE2; Arrigoni Battaia et al. 2021; Chen et al. 2021), we have been
conducting submillimeter observations around Enormous Lyman Alpha nebulae
(ELANe). ELANe represent the extreme of known Ly$\alpha$ nebulae with
exceptionally bright (SB${}_{\rm Ly\alpha}\sim 10^{-17}$ erg s-1 cm-2
arcsec-2) Ly$\alpha$ emission over $>100$ kpc in physical scales, normally
embodying multiple powering sources such as AGN, quasars, and other galaxy
populations. Current statistics show that only $\sim 4\%$ of bright quasars
are associated with ELANe, translating into a number density of few times
$10^{-6}$ Mpc-3 (Arrigoni Battaia et al. 2019; Cai et al. 2019; Arrigoni
Battaia et al. submitted). Spectral analyses focusing on the powering of ELANe
have suggested a large amount of cool and dense gas ($\gtrsim 10^{10}$M⊙ and
$\gtrsim$1 cm-3; Arrigoni Battaia et al. 2015; Hennawi et al. 2015), a finding
that is further strengthened by the detection of molecular gas via CO in the
circumgalactic medium (CGM) around a central group of galaxies in the
MAMMOTH-I ELAN (Emonts et al. 2019). ELANe therefore represent one of the
ideal quasar samples for a comprehensive study of the co-evolution between
SMGs and quasars and extending the studies to one of the rarest and likely
densest regimes.

Our first results intriguingly show a factor of four in overdensities for
submillimeter sources around one ELAN, MAMMOTH-1 ($z=2.32$; Cai et al. 2017;
Arrigoni Battaia et al. 2018a). In this paper, we report our results on three
more ELANe, the Jackpot nebula ($z=2.04$; Hennawi et al. 2015), the Slug
nebula ($z=2.28$; Cantalupo et al. 2014), and the Fabulous nebula ($z=3.17$;
Arrigoni Battaia et al. 2018b), the first discovered ELANe that marked the
start of studies regarding this new class of Lyman alpha nebulae. We present
our data and analyses in Sections 2 and 3, along with a summary and discussion
of the impact of our results in Section 4. We assume the cosmological
parameters $H_{0}=70$ km s-1 Mpc-1, $\Omega_{\rm M}=0.3,$ and
$\Omega_{\Lambda}=0.7$. In this cosmology, 1′′ corresponds to about 7.6 – 8.4
physical kpc at the redshift range of our sample (Table 1). All distances
reported in this work are proper. Finally, in this paper we define overdensity
as $n_{\rm src}/n_{\rm field}$, in which $n_{\rm src}$ is the number density
of the submillimeter sources in the ELAN fields and $n_{\rm field}$ is that
for the blank fields.

##  2 Observations and data reduction

The dataset for the four ELAN fields studied in this work were acquired with
the Submillimetre Common-User Bolometer Array 2 (SCUBA-2; Holland et al. 2013)
on the James Clerk Maxwell Telescope (JCMT) during flexible observing in 2017
September 02,16,17,23,24, 2018 January 16-18, February 12 and March 29
(programs ID: M17BP024, M18AP054) under good weather conditions
($\tau_{225{\rm GHz}}\leq 0.06$). For each target, the observations covered a
field-of-view of $\simeq 13.7\arcmin$ in diameter using a daisy scanning
pattern centered on each ELAN position. Each field was scheduled with cycles
(scans) of about 30 minutes, resulting in 3 hours (6 scans) for the MAMMOTH-1,
the Slug and the Jackpot ELANe, while in 2.7 hours (5 scans) for the Fabulous
ELAN. Even though SCUBA-2 acquires simultaneously data at 850 and 450 $\mu$m,
here we focus only on the dataset at longer wavelengths as the 450 $\mu$m
dataset is not deep enough to obtain proper number counts.

The data reduction follows the method outlined in Chen et al. (2013a) and
Arrigoni Battaia et al. (2018a), which rely on the Dynamic Iterative Map Maker
(DIMM) included in the SMURF package from the STARLINK software (Jenness et
al. 2011; Chapin et al. 2013). Each scan has been reduced adopting the
standard configuration file, dimmconfig_blank_field.lis, which is best for our
science purposes. The coaddition of the reduced scans into final maps was then
performed with the MOSAIC_JCMT_IMAGES recipe in PICARD, the Pipeline for
Combining and Analyzing Reduced Data (Jenness et al. 2008).

Figure 2:  Differential number counts recovered from 500 realizations of the
number counts models determined through Monte Carlo simulations (orange) and
the fiducial model (gray). The shaded regions represent the $90\%$ confidence
intervals of the counts recovered from the simulated maps. The black points
are raw differential number counts, as defined in section 3. The underlying
counts models and the fiducial model (Geach et al. 2017) are plotted in blue
and gray, respectively. The effect of flux boosting can be observed as the
shaded regions are lying above their input model. We note that the lower zero
limits of the fiducial model realizations at faint fluxes reflect the non-
uniform noise structure of our maps, where incompleteness increases with the
distance, from the center of the map.

Point source detectability is increased by applying a standard matched filter
to these final maps. For this purpose, we used the PICARD recipe
SCUBA2_MATCHED_FILTER. As a last step, we adopted the standard conversion
factor for 850 $\mu$m (537 Jy pW-1), with upwards of 10% correction for flux
calibration. The uncertainty of the flux conversion factor at 850 $\mu$m is
typically 5% (Dempsey et al. 2013)

The final noise level at the centers of our maps (ELAN positions) is 0.88,
0.97, 1.02, 1.01 mJy beam-1, respectively, for the MAMMOTH-1, the Jackpot, the
Slug, and the Fabulous ELANe. In this work, we focus on effective areas
characterized by noise levels smaller than 2.5 times this central noise (Table
1 and white curves in Figure 1).

Furthermore, we produced a true noise map (jackknife map) for each field by
subtracting two maps, each representing the sum of approximately half of that
source’s dataset. Therefore, the residual map should represent source-free
noise data because all real sources should be subtracted irrespective of their
significance. Importantly, we multiply these true noise maps by the scaling
factor $\sqrt{t1\times t2}/(t1+t2),$ with t1 and t2 being the exposure time of
each pixel from the two maps, to correct for the difference in exposure time.
The central noise in these jackknife maps is consistent with the noise in the
science data (0.88, 0.95, 1.03, 1.01 mJy beam-1, respectively, for MAMMOTH-1,
the Jackpot, the Slug, and the Fabulous ELANe).

##  3 Differential number counts

Figure 3: Histogram of signal-to-noise ratio for pixels located within the
effective area of the Jackpot map (blue) and the corresponding jackknife map
(yellow). The solid vertical line represents the 2.5$\sigma$ cut used in our
simulations. The dashed line represents the threshold of 4$\sigma$ above which
we catalog sources. We note that the excessive negative signals compared to
the jackknife map are a result of matched filtering, which can be properly
accounted for during source extraction processes using a correct PSF.

We extracted point sources from the SCUBA-2 maps by following the procedure
from Chen et al. 2013a. The source extraction algorithm identifies the pixel
with the highest signal-to-noise ratio (S/N) and subtracts a scaled point
spread function (PSF) centered at the location of that pixel. The process
continues until the highest S/N in the map falls below the detection
threshold. In all four ELAN fields, we detect 73 sources with $>$ 4 $\sigma$
located within effective areas of the maps. The locations of the detected
sources, plotted over (S/N) maps, are shown in Figure 1, and their relevant
information is listed in Tables A.1-A.4

To obtain the raw number counts, we first sum the number of sources in every
flux bin and divide the sum by the width and detectable area of the bin. The
detectable area is defined as the region of the map within which the sources
with a given flux density can be detected above the S/N threshold. The flux
bins are roughly in equal partition in logarithmic scale between the minimum
and maximum flux densities of the detected sources. To correct for the
detection of spurious sources, counts obtained from the jackknife maps using
the same procedure are subtracted off, and the results are the raw number
counts. The number of sources detected in the jackknife maps can be used to
determine the fraction of spurious detections, which is 40% at the simulation
threshold of 2.5 $\sigma$, and 7% at the catalog threshold of 4 $\sigma$.

The raw number counts are affected by observational biases, including flux
boosting, source blending, and incompleteness. Instead of making corrections
for these biases separately, we chose to account for these effects altogether
through Monte Carlo simulations. Our goal in the simulations is to determine
underlying count models that correctly reproduce the raw number counts in
every field. We chose to model the differential number counts using a
Schechter function of the form

$\frac{dN}{dS}=\frac{N_{0}}{S_{0}}\left(\frac{S}{S_{0}}\right)^{-\gamma}\exp\left(-\frac{S}{S_{0}}\right),$
(1)

where $N_{0}$ is the normalization and $S_{0}$ is the characteristic flux.

The Schechter function or a double power-law function have been typically
adopted for analyzing submillimeter number counts (e.g., Chen et al. 2013a;
Geach et al. 2017). Here, the Schechter function is preferred over a double
power-law because of a smaller number of free parameters involved. It is also
the model adopted by the fiducial blank-field counts and, thus, more
straightforward comparisons can be made. Experimentally, we find that the
Schechter function reproduces the distribution of faint fluxes in our sample
more accurately. We note, however, that the choice of the function does not
significantly affect our results.

Accurate positional information and low contamination rates are not critical
for statistical analyses of number counts (Chen et al. 2013a). To probe the
faintest sources in our data set, we looked for the lowest detection threshold
corresponding to statistically significant excess counts. The adopted
detection threshold of 2.5 $\sigma$ is consistent with the excess in the
positive signal, which is evident in Figure3.

The simulation proceeds as follows. First, we fit the Schechter function to
raw number counts using the least-squares method. The obtained initial
parameters are used to populate the jackknife map with mock sources. The
positions of mock sources are selected randomly. The lowest fluxes we inject
are 1 mJy, the same as that adopted by the fiducial blank-field model (Geach
et al. 2017) that we later use to compare our results. At this value, the
integrated flux density of our models is statistically consistent with the
extragalactic background light (EBL; e.g., Puget et al. 1996). Our results are
not, in fact, sensitive to the adopted flux levels of the faintest injected
sources. For a given set of model parameters, we create 100 simulated maps and
calculate the mean recovered counts. The ratios of the raw counts to mean
recovered counts, which are typically different in different flux bins, are
used to create a new set of counts by multiplying the raw counts by these
ratios. This new set of adjusted counts are then used for the next round of
Schechter function fitting, for which the best fit is adopted as the new input
model for the next iteration of the simulations. For each field, the process
is repeated until the convergence, which is when the recovered counts fall
within $1\sigma$ error of the raw counts.

The parameters of the underlying models obtained through this procedure are
listed in Table 1. Given the limited dynamical range of the measured counts,
$N_{0}$ and $S_{0}$ tend to be degenerate. We therefore keep the value of
$S_{0}$ fixed to 2.5, same as the fiducial blank-field model (Geach et al.
2017), but the other two parameters free. By doing so, we confirm that the
simulations can converge and the results from each run are consistent with
each other. We also confirm that changing $S_{0}$ to other values does not
significantly alter the results. To verify our methods, we run the same
analyses on the SCUBA-2 images of one known blank field, CDF-N, and we confirm
that CDF-N shows no evidence of overdensity, which is consistent with the
published results (Chen et al. 2013a).

Table 1: Information of the four ELANe in our sample, along with their best-fit parameters for the underlying counts models formulated as Schecter functions. ELAN Name | R.A. | Decl. | Redshift | Effective area | N0 | S0 | $\gamma$
---|---|---|---|---|---|---|---
| (J2000; h:m:s) | (J2000; ∘:′:′′) |  | (arcmin-2) | (mJy-1 deg-2) | (mJy) |
Fabulous | 10:20:09.99 | +10:40:02.7 | 3.17 | 106.7 | $27000\pm 6400$ | 2.50 | $1.45\pm 0.25$
Jackpot | 08:41:59.26 | +39:21:40.0 | 2.04 | 108.9 | $39900\pm 7300$ | 2.50 | $2.68\pm 0.24$
MAMMOTH-1 | 14:41:27.62 | +40:03:31.4 | 2.32 | 109.8 | $31200\pm 4300$ | 2.50 | $2.12\pm 0.18$
Slug | 00:52:03.26 | +01:01:08.6 | 2.28 | 109.5 | $26200\pm 10900$ | 2.50 | $2.05\pm 0.41$

We tested whether the models determined through Monte Carlo simulations
reproduce the raw number counts. We created 500 simulated maps for each ELAN
field by injecting sources into the respective jackknife map according to the
derived counts model. The mean recovered counts along with $90\%$ confidence
intervals are shown in Figure 2. We find good agreements between the simulated
counts and the raw counts in all four ELAN fields, confirming that our Monte
Carlo simulations have properly accounted for observational biases. We note
that the brightest bin in MAMMOTH-1 ELAN contains only two sources and its
counts do not, in fact, differ substantially from the model; however, given
the low probability of chance detection, they are often suspected to be
associated with the ELAN system (Arrigoni Battaia et al. 2018a).

To further verify that our procedure is able to constrain the overdensity, we
constructed another set of 500 simulated maps using a blank field model. By
injecting sources into the jackknife maps following a blank-field model, we
simulated the number counts that would have been observed in each of the four
fields if an overdensity were not present. As a blank field model, we selected
the Schechter function from Geach et al. (2017), with the following
parameters: $N_{0}=7180\pm 1220$ deg-2, $S_{0}=2.5\pm 0.4$ mJy, and
$\gamma_{0}=1.5\pm 0.4$, referred to as the fiducial model throughout this
paper. As shown in Figure 2, the realizations of the blank field model result
in recovered counts that are significantly lower than the raw counts from the
ELAN fields, confirming the presence of overdensities.

##  4 Discussion

Figure 4: Best-fit number counts models and their integrated energy densities.
Left: Derived number counts models underlying distribution of sources in ELAN
fields compared to blank field models (gray). To highlight the typical
uncertainties in these models, we show the confidence bands for the Geach et
al. model and for the Jackpot field. Right: Extragalactic background light as
a function of flux. In both panels, the models for ELANe are plotted in solid
at the flux range of the measured counts, and dashed in flux regimes fainter
than our measurements.

In the previous section, we determine the number count models that reproduce
the observed density of sources in ELAN fields. We plot these models in the
left panel of Figure 4, along with blank field models from the literature
(Chen et al. 2013b; Casey et al. 2013; Geach et al. 2017; Zavala et al. 2017).
A comparison between ELANe and blank fields reveals the presence of
overdensities that extend from the lowest fluxes up to $6-7$ mJy. Above that
threshold, the ELAN models become indistinguishable from the fiducial model
based on the current statistics. We have tried splitting the counts by the
distance to the ELAN, meaning the inner $<2^{\prime}$ and outer $>2^{\prime}$
regions, but we do not find any significant differences, so there is no
evidence of counts overdensity as a function of radial distance, contrary to
what was found in other submillimeter or millimeter counts studies toward
other AGN samples or dense fields at high redshifts (Zeballos et al. 2018;
Cooke et al. 2019).

As a test, we have tried different radial binning procedures but we found the
results insensitive to these choices. There are a few factors that could be
the root of the variety in the results compared to the previous work that
suggested otherwise. First, there is the sample size. Previous studies have at
least twice the number of fields compared to ours and some also have
significantly deeper data. This is despite the fact that the observed
differences in overdensity between the inner and outer regions reported in
these studies are marginal, that is, close to or less than 3 sigma. We
therefore expect that our current data quality would not have allowed us to
make the detection if the SMGs around ELANe behave similarly to those in other
dense fields. Second, while the first factor argues from a purely statistical
point of view, it is also possible that the SMGs intrinsically span a wider
physical range in the environments around ELANe compared to those around HzRGs
or X-ray selected clusters targeted by other studies. The fact that the
footprint of our SCUBA-2 observations (Figure 1) matches the expected span
($\sim$10-20 cMpc) of a protocluster hosting a massive (1013-1014 M⊙) halo at
the redshift of our sample ELANe (Chiang et al. 2013) makes the scenario of
more widespread SMG distribution around ELANe a plausible hypothesis.

To quantify the overdensity factor for each of the ELANe, we adopted two
approaches. In the first approach, which was also adopted in other studies
(Arrigoni Battaia et al. 2018b), for each field we first correct the raw
counts for observational biases by dividing the raw counts in each flux bin by
the ratios of the mean recovered counts to its underlying model obtained from
the simulations. We then fit the fiducial model to these corrected counts,
allowing only the normalization $N_{0}$ to vary. The overdensity factor is
defined as the ratio of the obtained normalization to fiducial model
normalization. As a result, we find that the overdensity factors for each
field are $2.7\pm 0.5$, $2.0\pm 0.4$, $1.8\pm 0.5$, $3.8\pm 0.7,$
respectively. for MAMMOTH-1, the Jackpot, the Slug, and the Fabulous ELANe.
The uncertainties in each field have taken into account both Poisson noises
and those from the simulations. The weighted average overdensity factor in our
sample is $2.3\pm 0.2$111If we instead adopt 0.1 mJy as the faintest injected
sources for the simulations, the factor would be $2.2+/-0.3$, consistent to
within 1 $\sigma$ to the adopted method..

The first approach is appropriate if the shape of the model in ELANe agrees
with that of the fiducial model. However, as shown in Figure 2 and Table 1
there is tentative evidence that the models in ELANe are steeper, so the
overdensity could be flux dependent. In such cases, estimating overdensity
factors by only fitting the normalization would bias the results to the lower
end. To mitigate this bias we therefore estimate the overdensity factors by
simply comparing the cumulative number of sources between each ELAN field and
the fiducial field. The cumulative number of sources are obtained by
integrating the models within the flux range probed by our SCUBA-2
observations ($S_{850}\sim 2.5-10\,{\rm mJy}$). As a result, we find
overdensity factors of $3.6\pm 0.9$, $3.8\pm 1.2$, $2.9\pm 1.8$, and $3.9\pm
1.5$ for MAMMOTH-1, the Jackpot, the Slug, and the Fabulous ELANe,
respectively. These give a weighted overdensity factor of $3.6\pm
0.6$2223.5$\pm$0.7 if we instead adopt 0.1 mJy as the faintest injected
sources for the simulations.. As expected, the overdensity factors using the
cumulative approach are slightly larger than the normalization approach in the
three fields where the best-fit underlying models have slightly steeper
slopes. In addition, since the cumulative method additionally includes the
uncertainties from the bright-end slope, $\gamma$, the uncertainties of the
overdensity factors would be larger compared to those of the first approach
with fittings only to the normalization. The results from both approaches
however are consistent with each other, thus we chose to adopt this second
approach since it does not suffer from any possible bias due to the
assumptions of the model shape.

Our results are consistent with those found in our pilot study on the
MAMMOTH-1 ELAN alone (Arrigoni Battaia et al. 2018a). By expanding the
measurements to include three more ELANe, we have found overabundant
submillimeter sources around all four ELANe and obtained a more precise
average overdensity factor. With these results, we conclude that there are
significantly (with a $>4\,\sigma$ confidence level) more SMGs around ELANe in
general. We postulate that this overdensity is likely caused by additional
SMGs that are physically associated with each ELAN, but future emission line
measurements are needed to confirm this hypothesis; this would also allow us
to measure the three-dimensional overdensity factors. Our results are also in
agreement with submillimeter and millimeter surveys in other samples of AGN,
such as high-redshift radio galaxies (HzRGs) and WISE-selected AGN, in which
(on average) a factor of 2-6 in overdensity was found (e.g., Rigby et al.
2014; Jones et al. 2017b; Zeballos et al. 2018). What we found to be different
is that, while it comes with a varying range of significance, the overabundant
submillimeter sources is found in all the surveyed ELAN fields; this ubiquity
was not observed in other studies where typically less than half of the
targeted fields show any signs of overdensity. While surveying more ELAN
fields is needed, these findings support the fact that certain levels of co-
evolution exist between SMGs and AGN, as they are likely part of similarly
dense environments, and the co-evolution may be more commonly observed in the
ELAN fields.

On the other hand, if our best-fit count models continue to the fainter end,
our findings could have implications for the extragalactic background light
(EBL) measurements at 850 $\mu$m. In the right panel of Figure 4, we plot the
integrated flux density above a given flux density based on the best-fit
models for each ELAN field as well as the fiducial model. By comparing the
results to the background light measurements from the COBE satellite (Fixen et
al. 1996), we find that in the ELAN fields, the background light can already
be fully accounted for by integrating the counts models down to $1-2$ mJy, and
there would be significantly excessive background light if the models are
integrated down to 0.1 mJy level – which is the faintest detection level
reported for other fields (e.g., Chen et al. 2014; Fujimoto et al. 2016; Hsu
et al. 2017; González-López et al. 2017, 2020). Our results therefore suggest
that there could be up to an order of magnitude in fluctuations with regard to
the 850 $\mu$m background on the survey scales toward these dense fields. On
the other hand, if this level of fluctuation does exist, we would expect these
extreme fluctuations to be rare; otherwise, a deficit of background light at a
similar level would have to exist in some other fields to bring the average
down to the observed level by COBE. Deeper observations are key for
constructing the shape of the number count distribution at the faint end,
which, in turn, will provide better constraints in this area.

Figure 5: Cosmic SFR density in physical volumes. The estimates based on our
counts measurements are plotted in black points, with the corresponding field
names indicated. The gray points mark the values reported in the literature
around samples of overdense regions (Clements et al. 2014; Kato et al. 2016)
that are not known to host ELANe. The cosmic mean is plotted in gray dashed
based on eqn. 15 of Madau & Dickinson (2014b) but converted to physical volume
density, whilst the black curve shows the cosmic mean multiplied by a factor
of 300.

Finally, we attempted to estimate the total obscured star formation within the
Mpc scale environments of ELAN, which can be achieved by assuming that the
excess number of submillimeter sources are all associated with the respective
ELAN. To compute the SFR densities we first seek a proper conversion from
$S_{\rm 850}$ to SFRs. We utilized a sample of ALMA-identified SMGs in the
UKIDSS-UDS field, which has been studied in detail with proper SED fittings
(Dudzevičiūtė et al. 2020). Similarly to our observations, the sample of
Dudzevičiūtė et al. (2020) was drawn from a flux-limited sample produced by
the SCUBA-2 Cosmology Legacy Survey (Geach et al. 2017). Their results should
therefore be representative, on average, of SCUBA-2 sources uncovered in other
fields. These authors found a linear correlation of log10[SFR(M⊙yr-1)] =
(0.42$\pm$0.06)$\times$log10[$S_{\rm 870}$(mJy)]+(2.19$\pm$0.03) for their
SMGs, which span a flux range of $\sim 1-10$ mJy, appropriate for the SCUBA-2
sources discovered in our target ELAN fields. We then computed the total SFR
densities by integrating over a given $S_{\rm 850}$ range in which the SFR
contribution at a given $S_{\rm 850}$ is the product of the excess number
density of the submillimeter sources and their corresponding SFR based on the
conversion. For each field, by considering a flux range of $S_{\rm 850}=1-20$
mJy and assuming a sphere with an equivalent circular radius of the
corresponding effective area, we obtain SFR densities of 1100$\pm$500,
1100$\pm$500, 2300$\pm$1100, and 1400$\pm$1100 $M_{\odot}$ yr-1 Mpc-3 for
Fabulous, Slug, Jackpot, and MAMMOTH-1 ELAN, and a weighted average SFR
density of $\Sigma$SFR= 1200$\pm$300 $M_{\odot}$ yr-1 Mpc-3. We plot the
results in Figure 5, showing that they are consistent with those found in the
Mpc-scale environments of other quasar samples or proto-clusters at $z\sim
2-3$ (Clements et al. 2014; Dannerbauer et al. 2014; Kato et al. 2016). This
result suggests that the star formation activities around ELANe are at a
similar level of other dense systems in this redshift range, or, in other
words, at a factor of about 300 greater than the cosmic mean.

##  5 Summary

In this second paper of the AMUSE2 series, we present the results of a SCUBA-2
850 $\mu$m survey around four ELANe, with the aim of understanding the dust-
obscured star formation around these massive systems on Mpc scales. We
summarize our findings in the following.

  1. 1.

By carefully performing the number counts analyses through self-consistent
simulations, we find that the number of submillimeter sources with $S_{\rm
850}\gtrsim 3$ mJy are overabundant in all four ELANe fields, by a factor of
2-4 within $\sim$5 Mpc. The significance of overdensity detection in each
field varies between 1-4 $\sigma$, depending on the precise methods used in
computing these overdensity factors. The weighted average overdensity factor
is 2.3$\pm$0.2, if normalized to the fiducial blank-field counts, or $3.6\pm
0.6,$ if instead adopting a cumulative method over the flux density range
probed.

  2. 2.

By integrating the number count models in the ELAN fields, we find that the
850 $\mu$m EBL would be fully accounted for at 1-2 mJy, and up to an order of
magnitude higher when integrating down to about 0.1 mJy; thereby suggesting an
order of magnitude fluctuations of the 850 $\mu$m EBL on the survey scales
toward these dense fields. Deeper observations are key to constraining the
count shapes at the faint end, which, in turn, will provide better constraints
in this regard.

  3. 3.

Finally, assuming that all the excessive sources can be attributed to SMGs
associated with the corresponding ELANe, and by adopting a linear $S_{\rm
850}$-to-SFR relation reported by a general SMG study (Dudzevičiūtė et al.
2020), we find SFR densities of 1000-2000 M⊙ yr-1 Mpc-3 with a weighted
average of $\Sigma$SFR=$1200\pm 300$ M⊙ yr-1 Mpc-3, which is a factor of about
300 larger than the cosmic mean. These are consistent with those found in
other quasar samples or proto-clusters, suggesting that the presence of ELANe
in the central $\sim$100 kpc regions does not significantly affect the dust-
obscured star-forming activities on Mpc scales.

This work represents the first step into systematically quantifying the Mpc-
scale environments around ELAN from the perspective of dusty star formation.
Follow up observations with spectroscopic measurements to confirm member
associations would be the next step to understand their spatial and kinematic
distributions, key to unlock the formation processes on $z\sim 2-3$ massive
proto-clusters.

###### Acknowledgements.

We thank the first ever ESO summer research program (Manara et al. 2019) that
facilitated the start of this research project; Ian Smail for providing useful
comments on this work; and the reviewer for a thoughtful report that has
improved the manuscript. C.C.C. acknowledges support from the Ministry of
Science and Technology of Taiwan (MOST 109-2112-M-001-016-MY3). MN and FAB
warmly thank the JCMT staff for their hospitality and support during the
observatory visits and observing runs. This project has received funding from
the European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation programme (grant agreement No 757535). Y.Y.’s research
was supported by Basic Science Research Program through the National Research
Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future
Planning (NRF-2019R1A2C4069803). The James Clerk Maxwell Telescope is operated
by the East Asian Observatory on behalf of The National Astronomical
Observatory of Japan; Academia Sinica Institute of Astronomy and Astrophysics;
the Korea Astronomy and Space Science Institute; Center for Astronomical Mega-
Science (as well as the National Key R&D Program of China with No.
2017YFA0402700). Additional funding support is provided by the Science and
Technology Facilities Council of the United Kingdom and participating
universities and organizations in the United Kingdom and Canada. Additional
funds for the construction of SCUBA-2 were provided by the Canada Foundation
for Innovation. This research made use of Astropy,333http://www.astropy.org a
community-developed core Python package for Astronomy (Astropy Collaboration
et al. 2013, 2018). The authors wish to recognize and acknowledge the very
significant cultural role and reverence that the summit of Maunakea has always
had within the indigenous Hawaiian community. We are most fortunate to have
the opportunity to conduct observations from this mountain.

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##  Appendix A Source catalogs

In this appendix, we provide the source catalogs for $\geq$4 $\sigma$
detection. The last two columns of each table represent the deboosted flux
densities ($f_{850}^{\rm Deboosted}$) and the positional uncertainties
($\Delta(\alpha,\delta)$), which are estimated as follows. We use the 500
simulated maps described in section 3 in every field to estimate the flux
boosting factors and positional uncertainties. In every map, we search for an
injected source corresponding to a detected source. An injected source is
considered a match if it is located within the beam area of a detected source.
We define flux boosting as the ratio of the recovered source flux to the
intrinsic source flux. Both flux boosting and positional offsets are recorded
for each injected source and we find they are both a function of S/N, which is
consistent with previous findings (e.g., Geach et al. 2017). In the catalogs,
we therefore apply the median flux boosting correction for each source given
its S/N and we quote the corresponding positional uncertainty.

Table 2: SCUBA-2 850 $\mu$m detected sources within the assumed effective area around the Slug ELAN Name | R.A. | Decl. | S/N | $f_{850}$ | $f_{850}^{\rm Deboosted}$ | $\Delta(\alpha,\delta)$
---|---|---|---|---|---|---
| (J2000; h:m:s) | (J2000; ∘:′:′′) |  | (mJy) | (mJy) | arcsec
Slug-850.1 | 00:52:01.6 | +01:03:41.2 | 8.7 | $11.4\pm 1.3$ | $9.6\pm 1.1$ | 0.8
Slug-850.2 | 00:51:54.4 | +01:05:31.2 | 5.4 | $10.1\pm 1.9$ | $7.1\pm 1.3$ | 1.6
Slug-850.3 | 00:52:16.4 | +00:58:57.2 | 5.1 | $9.0\pm 1.8$ | $6.1\pm 1.2$ | 1.6
Slug-850.4 | 00:52:20.5 | +01:01:07.2 | 4.9 | $8.9\pm 1.8$ | $5.8\pm 1.2$ | 1.8
Slug-850.5 | 00:52:00.9 | +01:01:55.2 | 4.4 | $4.6\pm 1.0$ | $2.7\pm 0.6$ | 2.0
Slug-850.6 | 00:51:54.5 | +01:01:23.2 | 4.3 | $5.0\pm 1.2$ | $2.9\pm 0.7$ | 2.0
Slug-850.7 | 00:52:15.2 | +01:05:31.2 | 4.2 | $9.0\pm 2.1$ | $5.0\pm 1.2$ | 2.2
Table 3: SCUBA-2 850 $\mu$m detected sources within the assumed effective area around the Jackpot ELAN Name | R.A. | Decl. | S/N | $f_{850}$ | $f_{850}^{\rm Deboosted}$ | $\Delta(\alpha,\delta)$
---|---|---|---|---|---|---
| (J2000; h:m:s) | (J2000; ∘:′:′′) |  | (mJy) | (mJy) | arcsec
Jackpot-850.1 | 08:41:58.8 | +39:21:51.0 | 10.9 | $11.0\pm 1.0$ | $9.0\pm 0.8$ | 0.9
Jackpot-850.2 | 08:42:06.9 | +39:20:37.0 | 6.0 | $6.4\pm 1.1$ | $3.8\pm 0.6$ | 1.8
Jackpot-850.3 | 08:42:16.9 | +39:19:28.9 | 5.5 | $7.9\pm 1.4$ | $4.4\pm 0.8$ | 2.0
Jackpot-850.4 | 08:42:14.7 | +39:23:12.9 | 5.2 | $7.5\pm 1.4$ | $4.0\pm 0.8$ | 2.0
Jackpot-850.5 | 08:41:46.6 | +39:20:07.0 | 5.1 | $8.0\pm 1.6$ | $4.3\pm 0.8$ | 2.0
Jackpot-850.6 | 08:42:19.2 | +39:18:50.9 | 5.0 | $7.8\pm 1.6$ | $4.0\pm 0.8$ | 2.2
Jackpot-850.7 | 08:42:03.3 | +39:17:33.0 | 5.0 | $7.7\pm 1.6$ | $4.0\pm 0.8$ | 2.2
Jackpot-850.8 | 08:42:00.5 | +39:18:45.0 | 4.9 | $6.6\pm 1.3$ | $3.4\pm 0.7$ | 2.2
Jackpot-850.9 | 08:42:05.0 | +39:19:57.0 | 4.6 | $5.1\pm 1.1$ | $2.5\pm 0.5$ | 2.2
Jackpot-850.10 | 08:42:11.9 | +39:26:35.0 | 4.6 | $9.7\pm 2.1$ | $4.8\pm 1.0$ | 2.2
Jackpot-850.11 | 08:41:59.2 | +39:20:43.0 | 4.6 | $4.6\pm 1.0$ | $2.3\pm 0.5$ | 2.2
Jackpot-850.12 | 08:42:19.0 | +39:21:04.9 | 4.6 | $6.4\pm 1.4$ | $3.2\pm 0.7$ | 2.2
Jackpot-850.13 | 08:42:09.0 | +39:21:03.0 | 4.6 | $5.1\pm 1.1$ | $2.5\pm 0.6$ | 2.2
Jackpot-850.14 | 08:42:00.7 | +39:25:15.0 | 4.5 | $6.6\pm 1.5$ | $3.2\pm 0.7$ | 2.3
Jackpot-850.15 | 08:42:23.1 | +39:23:00.8 | 4.4 | $6.9\pm 1.6$ | $3.3\pm 0.8$ | 2.3
Jackpot-850.16 | 08:42:25.5 | +39:21:26.8 | 4.3 | $7.0\pm 1.6$ | $3.4\pm 0.8$ | 2.3
Jackpot-850.17 | 08:42:10.7 | +39:19:19.0 | 4.3 | $5.9\pm 1.4$ | $2.9\pm 0.7$ | 2.3
Jackpot-850.18 | 08:42:06.2 | +39:17:59.0 | 4.3 | $6.9\pm 1.6$ | $3.2\pm 0.8$ | 2.4
Jackpot-850.19 | 08:42:00.5 | +39:20:53.0 | 4.2 | $4.1\pm 1.0$ | $1.9\pm 0.5$ | 2.4
Jackpot-850.20 | 08:42:02.3 | +39:19:49.0 | 4.2 | $4.5\pm 1.1$ | $2.1\pm 0.5$ | 2.4
Jackpot-850.21 | 08:41:53.5 | +39:21:47.0 | 4.1 | $4.4\pm 1.1$ | $2.0\pm 0.5$ | 2.4
Jackpot-850.22 | 08:42:05.7 | +39:18:35.0 | 4.0 | $5.8\pm 1.5$ | $2.7\pm 0.7$ | 2.4
Jackpot-850.23 | 08:42:00.5 | +39:16:11.0 | 4.0 | $7.0\pm 1.8$ | $3.3\pm 0.8$ | 2.4
Jackpot-850.24 | 08:41:51.7 | +39:22:43.0 | 4.0 | $5.0\pm 1.2$ | $2.3\pm 0.6$ | 2.4
Table 4: SCUBA-2 850 $\mu$m detected sources within the assumed effective area around the Fabulous ELAN Name | R.A. | Decl. | S/N | $f_{850}$ | $f_{850}^{\rm Deboosted}$ | $\Delta(\alpha,\delta)$
---|---|---|---|---|---|---
| (J2000; h:m:s) | (J2000; ∘:′:′′) |  | (mJy) | (mJy) | arcsec
Fabulous-850.1 | 10:20:10.0 | +10:40:08.0 | 11.1 | $11.3\pm 1.0$ | $9.9\pm 0.9$ | 0.5
Fabulous-850.2 | 10:20:19.5 | +10:36:40.0 | 8.9 | $12.0\pm 1.3$ | $10.4\pm 1.2$ | 0.7
Fabulous-850.3 | 10:20:28.9 | +10:39:34.0 | 7.9 | $12.6\pm 1.6$ | $10.5\pm 1.3$ | 0.8
Fabulous-850.4 | 10:20:27.1 | +10:41:54.0 | 5.8 | $10.4\pm 1.8$ | $7.9\pm 1.4$ | 1.4
Fabulous-850.5 | 10:20:23.3 | +10:40:10.0 | 5.1 | $7.0\pm 1.4$ | $5.1\pm 1.0$ | 1.6
Fabulous-850.6 | 10:20:26.3 | +10:41:36.0 | 5.1 | $8.2\pm 1.6$ | $5.8\pm 1.2$ | 1.7
Fabulous-850.7 | 10:20:08.5 | +10:38:52.0 | 5.0 | $5.2\pm 1.0$ | $3.7\pm 0.7$ | 1.7
Fabulous-850.8 | 10:20:22.2 | +10:40:48.0 | 5.0 | $6.5\pm 1.3$ | $4.6\pm 0.9$ | 1.7
Fabulous-850.9 | 10:20:25.2 | +10:41:18.0 | 4.9 | $7.3\pm 1.5$ | $5.2\pm 1.1$ | 1.7
Fabulous-850.10 | 10:19:58.7 | +10:36:46.0 | 4.8 | $8.7\pm 1.8$ | $6.2\pm 1.3$ | 1.7
Fabulous-850.11 | 10:20:02.5 | +10:37:16.0 | 4.7 | $8.0\pm 1.7$ | $5.5\pm 1.2$ | 1.8
Fabulous-850.12 | 10:20:17.5 | +10:36:46.0 | 4.7 | $5.9\pm 1.3$ | $4.1\pm 0.9$ | 1.8
Fabulous-850.13 | 10:20:03.4 | +10:39:14.0 | 4.6 | $5.2\pm 1.1$ | $3.6\pm 0.8$ | 1.8
Fabulous-850.14 | 10:20:08.8 | +10:39:22.0 | 4.4 | $4.5\pm 1.0$ | $3.0\pm 0.7$ | 1.9
Fabulous-850.15 | 10:20:06.7 | +10:35:10.0 | 4.3 | $7.7\pm 1.8$ | $5.1\pm 1.2$ | 1.9
Fabulous-850.16 | 10:20:06.6 | +10:34:28.0 | 4.3 | $8.3\pm 1.9$ | $5.5\pm 1.3$ | 1.9
Fabulous-850.17 | 10:19:51.5 | +10:42:18.0 | 4.3 | $7.4\pm 1.7$ | $4.8\pm 1.1$ | 2.0
Fabulous-850.18 | 10:19:52.1 | +10:36:18.0 | 4.3 | $9.7\pm 2.3$ | $6.3\pm 1.5$ | 2.0
Fabulous-850.19 | 10:20:10.1 | +10:40:00.0 | 4.0 | $4.1\pm 1.0$ | $2.6\pm 0.7$ | 2.0
Table 5: SCUBA-2 850 $\mu$m detected sources within the assumed effective area around the MAMMOTH-1 ELAN Name | R.A. | Decl. | S/N | $f_{850}$ | $f_{850}^{\rm Deboosted}$ | $\Delta(\alpha,\delta)$
---|---|---|---|---|---|---
| (J2000; h:m:s) | (J2000; ∘:′:′′) |  | (mJy) | (mJy) | arcsec
MAMMOTH-850.1 | 14:41:25.5 | +40:00:31.4 | 16.0 | $21.0\pm 1.3$ | $18.3\pm 1.1$ | 0.6
MAMMOTH-850.2 | 14:41:29.0 | +40:01:19.4 | 15.9 | $18.8\pm 1.2$ | $16.4\pm 1.0$ | 0.6
MAMMOTH-850.3 | 14:41:45.6 | +40:08:13.3 | 7.7 | $13.9\pm 1.8$ | $10.9\pm 1.4$ | 1.1
MAMMOTH-850.4 | 14:41:40.2 | +40:01:01.4 | 7.4 | $10.0\pm 1.3$ | $7.8\pm 1.1$ | 1.1
MAMMOTH-850.5 | 14:41:44.7 | +40:02:19.3 | 6.9 | $8.9\pm 1.3$ | $6.7\pm 1.0$ | 1.3
MAMMOTH-850.6 | 14:41:25.5 | +40:07:29.4 | 6.2 | $8.1\pm 1.3$ | $5.8\pm 0.9$ | 1.5
MAMMOTH-850.7 | 14:41:14.9 | +40:07:59.4 | 5.9 | $9.3\pm 1.6$ | $6.3\pm 1.1$ | 1.5
MAMMOTH-850.8 | 14:41:47.5 | +40:00:01.3 | 5.4 | $8.5\pm 1.6$ | $5.8\pm 1.1$ | 1.8
MAMMOTH-850.9 | 14:41:35.6 | +39:59:27.4 | 5.2 | $7.6\pm 1.5$ | $4.8\pm 0.9$ | 1.8
MAMMOTH-850.10 | 14:41:15.2 | +40:06:01.4 | 5.1 | $7.2\pm 1.4$ | $4.5\pm 0.9$ | 1.8
MAMMOTH-850.11 | 14:41:49.4 | +40:01:27.3 | 5.1 | $7.3\pm 1.4$ | $4.6\pm 0.9$ | 1.8
MAMMOTH-850.12 | 14:41:30.8 | +40:03:07.4 | 4.9 | $4.5\pm 0.9$ | $2.8\pm 0.6$ | 1.8
MAMMOTH-850.13 | 14:41:46.8 | +40:05:29.3 | 4.9 | $6.7\pm 1.4$ | $4.2\pm 0.9$ | 1.8
MAMMOTH-850.14 | 14:41:24.5 | +40:03:07.4 | 4.9 | $4.6\pm 0.9$ | $2.9\pm 0.6$ | 1.8
MAMMOTH-850.15 | 14:41:15.3 | +40:01:41.4 | 4.7 | $6.7\pm 1.4$ | $3.9\pm 0.8$ | 2.1
MAMMOTH-850.16 | 14:41:33.9 | +40:01:41.4 | 4.5 | $5.2\pm 1.2$ | $3.0\pm 0.7$ | 2.1
MAMMOTH-850.17 | 14:41:35.6 | +40:06:09.4 | 4.2 | $5.2\pm 1.2$ | $3.0\pm 0.7$ | 2.1
MAMMOTH-850.18 | 14:41:29.9 | +40:07:43.4 | 4.2 | $5.4\pm 1.3$ | $3.1\pm 0.7$ | 2.1
MAMMOTH-850.19 | 14:41:44.5 | +40:01:23.3 | 4.2 | $5.7\pm 1.4$ | $3.3\pm 0.8$ | 2.1
MAMMOTH-850.20 | 14:41:25.0 | +40:06:29.4 | 4.1 | $5.2\pm 1.3$ | $3.0\pm 0.7$ | 2.1
MAMMOTH-850.21 | 14:41:44.2 | +40:00:49.3 | 4.1 | $5.7\pm 1.4$ | $3.3\pm 0.8$ | 2.1
MAMMOTH-850.22 | 14:41:28.7 | +39:59:31.4 | 4.0 | $5.7\pm 1.4$ | $3.3\pm 0.8$ | 2.1
MAMMOTH-850.23 | 14:41:17.7 | +39:58:09.4 | 4.0 | $8.1\pm 2.0$ | $4.7\pm 1.2$ | 2.1