# H i Ly$\alpha$ Emission from a Metal-Poor Cool Stream Fueling an Early Dusty
Starburst

Kevin Hall and Hai Fu  Department of Physics & Astronomy, University of Iowa,
Iowa City, IA 52242

(December 6, 2023; April 22, 2024; May 1, 2024)

###### Abstract

The GAMA J0913$-$0107 system is a rare conjunction of a submillimeter galaxy
(SMG) at $z\approx 2.7$ and two background QSOs with projected separations
$<$200 kpc. Previous high-resolution QSO absorption-line spectroscopy has
revealed high H i column density, extremely metal-poor ($\sim 1\%$ solar) gas
streams in the circumgalactic medium of the SMG. Here we present deep optical
integral-field spectroscopy of the system with the Keck Cosmic Web Imager
(KCWI). Reaching a $2\sigma$ surface brightness (SB) limit $\approx 10^{-19}$
erg s-1 cm-2 arcsec-2 with $\sim$2 hrs of integration time, we detect a
filamentary Ly$\alpha$ nebula stretching $\sim$180 kpc from the SMG
intercepting both QSO sightlines. This Ly$\alpha$ filament may correspond to
the same cool gas stream penetrating through the hot halo seen in the
absorption. In contrast to Ly$\alpha$ nebulae around QSOs, there is no obvious
local source for photoionization due to the massive dust content. While
uncertain, we consider the possibility that the nebula is ionized by shocks
induced by the infall, obscured star formation, and/or a boosted UV
background. The SMG-QSOs conjunction multiplied the efficiency of the KCWI
observations, allowing a direct comparison of Ly$\alpha$ nebulae in two
distinct environments. We find that the nebula around the QSOs are much
brighter and show steeper surface brightness profiles than the SMG nebula.
This is consistent with the additional photoionization and Ly$\alpha$
scattering provided by the QSOs. While illustrating the challenges of
detecting Ly$\alpha$ nebulae around SMGs, our work also demonstrates that
important insights can be gained from comparative studies of high-$z$
Ly$\alpha$ nebulae.

###### keywords:

Circumgalactic medium; Starburst galaxies; Quasars

Fu21Paper I

##  1 Introduction

The study of galaxy formation and evolution remains an active field of
research in astrophysics, encompassing a multitude of unanswered questions.
One such question is how galaxies acquire the cold and dense gas to grow their
stellar content. As dark matter (DM) halos grow, gas gradually accumulates
within, marking the inception of galaxy formation from primordial density
fluctuations. Above a mass threshold of $M_{\rm shock}$ $(\sim 10^{12}$
$M_{\odot}$), analytical and numerical models postulated that the inflow of
gas develop shocks in the vicinity of the virial radius of the halo, heating
the gas to the virial temperature ($T_{\rm vir}\gtrsim 10^{6}$ K) (e.g., Rees
& Ostriker, 1977; Silk, 1977; White & Rees, 1978; Birnboim & Dekel, 2003).
Radiative cooling of such hot gaseous halos is so slow that it cannot provide
enough cold gas for the galaxies in these halos to grow at significant rates.
However, more recent numerical simulations showed that this picture may be
incomplete. For massive halos ($M_{\rm DM}>M_{\rm shock}$) at $z\gtrsim 1.5$,
although diffuse shock-heated hot gas still dominates the circumgalactic
medium (CGM), the cosmic web connecting massive halos may be resilient enough
to penetrate through the hot gas halo and supply chemically pristine cool gas
($\sim 10^{4}$ K) from the intergalactic medium (IGM) to the central galaxy.
The newly predicted picture is multiple long filaments of cool gas streams
embedded in hot X-ray emitting halos (Kereš et al., 2005, 2009; Dekel &
Birnboim, 2006; Dekel et al., 2009; Faucher-Giguère et al., 2011; Martin et
al., 2019).

The presence of cool gas streams in hot halos could be a pivotal mechanism in
elucidating the existence of dusty galaxies exhibiting exceptionally elevated
star formation rates (SFRs) at $z>2$, such as the submillimeter-bright
galaxies (SMGs; Smail et al., 1997; Barger et al., 1998; Blain, 2002). Despite
being at significant cosmological distances, the SMGs are the brightest
sources selected between 850 $\mu$m and 2 mm thanks to their huge infrared
luminosity and the negative $K$-correction in the Rayleigh–Jeans tail. Their
pronounced infrared luminosities can be ascribed to the substantial presence
of dust obscuring intense star formation (SFR ¿ 500 $M_{\odot}\,{\rm
yr}^{-1}$). The redshift range and the halo mass of SMGs also fits the cold
accretion picture predicted by the simulations: they are commonly observed at
$z\sim 2.5$ (Chapman et al., 2005), and the clustering of SMGs indicate that
they inhibit massive halos surpassing $M_{\rm shock}$ ($M_{\rm DM}\sim 9\times
10^{12}$ $M_{\odot}$; Hickox et al., 2012). These distinctive attributes
suggest that the halos of SMGs might encompass filaments of cool gas that
permeate through the hot gas halo at the virial temperature. In the absence of
such streams, the radiative cooling of the diffuse hot halo would transpire
over a timescale that is considerably protracted, rendering it insufficient to
sustain the observed high SFR.

Despite their crucial role, definitive observational evidence is required to
confirm their presence. This need grows stronger with recent simulation work
showing cool streams become destabilized as they flow into hot halos due to
Kelvin-Helmholtz Instabilities (Mandelker et al., 2019). In addition, feedback
processes occuring within the galaxy can disrupt the flows from the IGM
(Nelson et al., 2015). To verify their presence, a comprehensive examination
into the CGM of these galaxies is necessary, and this investigation is
typically conducted using two primary observational techniques. The first
approach involves a pairing between emission selected foreground galaxies with
bright Quasi-Stellar Objects (Quasars/QSOs) in the background as probes to
study the CGM along their sightlines. This method leverages the absorption
signatures imprinted by the intervening gas within the CGM onto the quasar
spectrum, facilitating insights into the properties of the CGM. This
methodology has been used for a variety of massive systems at $z\gtrsim 2$,
such as QSOs (e.g., Hennawi et al., 2006; Prochaska et al., 2013), and SMGs
(e.g., Fu et al., 2016, 2021). These close projections on the sky are rare,
and we can only gather a one-dimensional view on the CGM.

The second approach aims to detect and analyze the presence of extended Lyman-
alpha (Ly$\alpha$) emission within the CGM of these galaxies. A cold stream
infalling towards a galaxy is expected to produce Ly$\alpha$ photons through
gravitational heating (Dijkstra & Loeb, 2009; Goerdt et al., 2010; Rosdahl &
Blaizot, 2012). In addition, background radiation (i.e., the Cosmic UV
Background; Gould & Weinberg, 1996; Haardt & Madau, 2012) can ionize the gas
contained within the stream (Faucher-Giguère et al., 2010), leading to
Ly$\alpha$ recombination radiation from recaptured electrons. Consequently, a
detection of Ly$\alpha$ filaments in surface brightness maps can serve as an
indicator for cool streams. However, deep observations are required to detect
the low surface brightness (SB) that is expected (Rosdahl & Blaizot, 2012;
Faucher-Giguère et al., 2010).

The diffuse emission can be enhanced by the presence of a QSO from
photoionization and the resulting recombination radiation, increasing the
surface brightness by a few orders of magnitude (Cantalupo et al., 2005, 2012;
Kollmeier et al., 2010; Hennawi & Prochaska, 2013). Furthermore, the resonant
nature of the Ly$\alpha$ line can introduce scattering off of neutral hydrogen
in the surrounding halo, producing a glow that can contribute to the observed
Ly$\alpha$ luminosities measured in these halos (Hennawi & Prochaska, 2013;
Gronke et al., 2017; Byrohl & Nelson, 2022; Cen & Zheng, 2013). Narrowband
imaging campaigns targeting QSO systems at $z\sim 2-3$ began to find luminous
Ly$\alpha$ halos with surface brightness $\gtrsim 10^{-17}$ cgs (erg s-1 cm-2
arcsec-2 ) (Cantalupo et al., 2014; Hennawi et al., 2015; Cai et al., 2017).
With the advent of integral field spectrographs (IFS) on 8-10 meter class
telescopes, extended Ly$\alpha$ emission is now be regularly detected.
Specifically, Ly$\alpha$ halos are now commonly found within QSO systems at
$z\gtrsim 3$ (Borisova et al., 2016; Arrigoni Battaia et al., 2019; Fossati et
al., 2021) with the Multi Unit Spectroscopic Explorer (MUSE; Bacon et al.,
2010) and at $z\sim 2$ (Cai et al., 2019; O’Sullivan et al., 2020; Lau et al.,
2022; Vayner et al., 2023) using the Keck Cosmic Web Imager (KCWI; Morrissey
et al., 2018). MUSE has also detected Ly$\alpha$ halos in QSO systems out to
$z=6.6$ (Farina et al., 2019).

A selection of these observations have detected filamentary Ly$\alpha$ halos
(Cantalupo et al., 2014; Hennawi et al., 2015; Martin et al., 2019),
suggesting the presence of cool streams. However, the presence of the QSO
complicates the exact nature of those filaments. Outflows can become
photoionized by the QSO and contribute to the observed Ly$\alpha$ emission
(Veilleux et al., 2020). Additionally, the expected surface brightness from
recombination due to photoionization outperforms that of gravitational
heating, so it is challenging to distinguish the two mechanisms. We can
counteract these challenges by focusing on systems devoid of AGN activity,
such as the study performed by Daddi et al. (2021). The authors targeted a
massive galaxy group with KCWI at $z\approx 2.9$ with no on-going AGN activity
and found three extended filaments connecting at the center of the group; they
conclude that the primary energy source for the observed Ly$\alpha$ halo is
gravitational energy from infalling gas - a signature for cold accretion.

Observing campaigns targeting overdense ”protocluster” regions have detected
Ly$\alpha$ nebulae with physical sizes $\sim 100$ kpc and total integrated
Ly$\alpha$ luminosities ($L_{\rm Ly\alpha}$) $\gtrsim 10^{43}$ erg s-1,
commonly referred to as ”Lyman-alpha Blobs” (LABs) (Steidel et al., 2000;
Matsuda et al., 2004; Dey et al., 2005; Nilsson et al., 2006). Gravitational
energy from cold accretion has been proposed as a likely mechanism powering
these bright nebulae. One such protocluster, the SSA22 field at $z\approx
3.1$, is home to several LABs (Matsuda et al., 2004, 2011). The famous LAB1
system (Steidel et al., 2000) is host to bright submillimeter sources,
indicating elevated levels of star formation within dusty galaxies (Chapman et
al., 2001; Geach et al., 2014, 2016; Umehata et al., 2021). While cold
accretion may play a role, UV photons from the active galaxies may escape
through unobscured sightlines and scatter back to the observer (Geach et al.,
2014). Additionally, the UV background is likely boosted by the ongoing star
formation and AGN activity within the large protocluster environment. Umehata
et al. (2019) discovered filaments extending $\gtrsim 1$ Mpc, likely
illuminated by embedded sources. Other examples exist, such as the LAB within
the luminous protocluster region at $z\sim 4$ hosting 10 dusty star-forming
galaxies (Oteo et al., 2018). In all of these examples, it is challenging to
pinpoint a single dominant mechanism. We need to consider highly obscured
targets that are relatively isolated (i.e., not in a clear protocluster
environment). Specifically, SMGs have the potential to increase the contrast
between the mechanisms powering Ly$\alpha$ emission.

The combination between an isolated source and the lack of a UV-continuum
detected from ground surveys (due to high dust obscuration) poses a daunting
challenge on to optical IFU surveys. Recent work by Lobos et al. (2023) found
that extended Ly$\alpha$ nebulae around SMG-QSO composite systems are brighter
than SMGs with no QSO companion. In fact, the latter do not show any extended
Ly$\alpha$ emission above their surface brightness limit. Other examples
include a gas-rich merger consisting of a QSO, Lyman-alpha emitters (LAEs),
and a SMG was targeted at $z\approx 4.7$ by Drake et al. (2020). They detect a
bright Ly$\alpha$ Halo around the QSO, but no associated Ly$\alpha$ nebula
attributed to the SMG. These studies suggest that (1) detecting extended
nebulae around SMGs require ultra-deep observations and (2) local ionization
sources and Ly$\alpha$ emitters, such as the QSOs, play an important role in
powering the extended nebula around QSOs.

Here we carry out deep integral-field spectroscopy of a rare SMG system, GAMA
J0913$-$0107, where there are two QSOs in the background of the SMG. The GAMA
J0913$-$0107 system allows (1) a joint study of the H i CGM in emission and in
absorption and (2) a comparative study of the extended H i Ly$\alpha$ nebulae
around SMG and QSOs. The organization of this paper is as follows. We begin in
§2 by providing an overview of the GAMA J0913$-$0107 system. We describe the
KCWI observations, data reduction, and the procedure used to isolate extended
Ly$\alpha$ signals in §3. We present the resulting Ly$\alpha$ surface
brightness maps and their kinematics for the SMG and the two background QSOs
in §4. In §5, we compare the Ly$\alpha$ emission lines against the H i
absorption lines towards the background QSOs and compare the three nebulae
from this study with QSO extended Ly$\alpha$ nebulae in the literature. We
conclude with a summary and give final remarks in Section 6. We assume the
$\Lambda$CDM cosmology with $\Omega_{\rm m}=0.3$, $\Omega_{\Lambda}=0.7$, and
$h\equiv H_{0}/(100~{}{\rm km~{}s}^{-1}~{}{\rm Mpc}^{-1})=0.7$. Throughout we
adopt the cgs units for surface brightness (erg s-1 cm-2 arcsec-2 ) and column
densities (cm-2).

##  2 Overview of the GAMA J0913$-$0107 System

Figure 1: Overview of the GAMA J0913$-$0107 field. On the left, we overlay the
footprints of the two KCWI pointings (blue rectangles) on a deep $g$-band
image (5$\sigma$ detection limit at 25.4 mag) from the Kilo-Degree Survey
(KiDS; de Jong et al., 2013). On the right, we present the pseudo-$g$-band
image from median averaging all wavelength channels of the coadded KCWI
datacube. Although at a lower spatial resolution, the 2-hr-long KCWI image
detects most of the sources present in the deep KiDS image. The positions of
the SMG, QSO1 and QSO2 with a gold cross, a red star, and a yellow star,
respectively. These same symbols will be used in subsequent figures. In
addition to the three primary galaxies, we also mark the companion galaxies
detected in CO (3$-$2) (Comp a and b) and Ly$\alpha$ (LAE1 and LAE2), as well
as four spectroscopically identified foreground interlopers (Obj 1-4).

This paper represents the fourth installment in a series of papers aimed at
characterizing the CGM of SMGs with projected SMG-QSO pairs. Here we focus on
the GAMA J0913$-$0107 triplet system, which is a particularly rare alignment
between a SMG (at $z_{\rm SMG}=2.674$) and two background QSOs, both within a
projected radius of 22 (see Figure 1). The triplet was initially identified in
Fu et al. (2016) by cross-matching large samples of spectroscopically
confirmed QSOs with Herschel-selected 350 $\mu$m peakers. Followup
observations with ALMA in band-7 (345 GHz/870 $\mu$m) confirmed that the SMG
exhibited an 870 $\mu$m flux density of $S_{870}\approx$ 7.4 mJy and was
designated as ALMA J091339.55$-$010656.4 (hereafter SMG; Fu et al. (2017)).
The improved FWHM resolution from ALMA band-7 imaging ($\sim$ 05) provided
accurate positioning for follow-up spectroscopy to acquire its redshift. In a
focused study of the GAMA J0913$-$0107 system, Fu et al. (2021) (hereafter ),
measured a redshift of $z=2.674$ from H$\alpha$ with Gemini near-IR
spectroscopy and CO (3$-$2) with ALMA band-3 (100 GHz/3 mm) spectral imaging.
They measured a total molecular gas mass of $M_{\rm mol}=1.3\times 10^{11}$
$M_{\odot}$, representing one of the larger gas masses found among SMGs.
Furthermore, the integrated IR Luminosity was $L_{\rm IR}\approx 1.2\times
10^{13}$ $L_{\odot}$, which corresponds to a dust-obscured SFR of $1,200$
$M_{\odot}\,{\rm yr}^{-1}$. Additionally, the ALMA 870 $\mu$m and CO (3$-$2)
maps show no companions within $\lesssim 100$ kpc. However, ALMA did detect
three companion galaxies in CO (3$-$2): Comp a at $z=2.6747$ and Comp b at
$z=2.6884,2.6917$, but both reside $\gtrsim 150$ kpc from the SMG.

The SMG studied here is dominated by star formation with no major contribution
from AGN activity. If we consider the spectral energy distribution (SED) of
the SMG and compare with models for QSOs obscured by a dusty torus, as shown
by Fu et al. (2017), the QSO+torus models underpredict the far-IR emission.
Star formation sits as the dominate contributor to the bolometric luminosity.
Although, SMGs are shown to harbor AGN activity through X-ray observations
(Alexander et al., 2005; Wang et al., 2013), but no data is currently
available.

The main text of the paper focuses on the three primary galaxies in the field
(SMG, QSO1, and QSO2). For a complete inventory of spectroscopically
identified objects in the field, refer to Figure 1 for finder charts and Table
1 for their coordinates and redshifts. In Appendix A, we show the spectra of
the low-redshift interlopers (Objs 1-4), and Appendix B gives a detailed
discussion on the newly discovered Ly$\alpha$ emitter LAE2 and its implication
to the Ly$\alpha$ absorber at $z_{\rm abs}\approx 2.69$ towards both QSOs.

The two QSOs in the field have spectroscopic redshifts from the Sloan Digital
Sky Survey (SDSS), and both lie in the background of the SMG. SDSS
J091338.97$-$010704.6 (hereafter QSO1, $g=20.78$, $r=20.38$, $L_{\rm
bol}=10^{46}$ erg s-1) at $z_{\rm QSO1}=2.916$ has a projected separation of
117 from the SMG, and SDSS J091338.30$-$010708.6 (hereafter QSO2, $g=20.71$,
$r=20.44$, $L_{\rm bol}=10^{46}$ erg s-1) at $z_{\rm QSO2}=2.749$ has a
projected separation of 221. At $z_{\rm SMG}=2.674$, these positions
correspond to impact parameters of 93.1 and 175.5 kpc for QSO1 and QSO2
respectively, within the virial radius of a $10^{13}$ $M_{\odot}$ halo
($\sim$186 kpc), providing a great opportunity to search for neutral hydrogen
and metal ions in the CGM of the SMG.

Indeed, both QSO1 and QSO2 show strong H i Ly$\alpha$ absorbers with velocity
offsets of only $\delta v\approx-300$ km s-1 from the SMG redshift. Towards
QSO1, there is a sub-damped Ly$\alpha$ absorber (sub-DLA; $19<\log N_{\rm
HI}<20.3$) with a total column density of $\log N_{\rm HI}\sim 20.2$. Towards
QSO2, there is a Lyman limit system (LLS; $17.2\leq\log N_{\rm HI}<19$) with a
total column density of $\log N_{\rm HI}\sim 18.6$. Although the sightlines
are separated by 86 kpc in transverse distance, the two absorbers show
remarkable kinematic and metallicity coherence, suggesting that they belong to
the same stream of gas. Their metallicity of [$\alpha$/H] $\approx-2$ places
the absorbers near the 1$\sigma$ upper bound of the metallicity of the
intergalactic medium (IGM), offering strong evidence of inflowing material
from the cosmic web. Can we detect this metal-poor cool gas stream in
emission? How does the CGM around SMG compare with the CGM around QSOs at a
similar cosmic epoch? To address these questions, we have obtained deep
integral-field spectroscopy of GAMA J0913$-$0107 with the 10-meter Keck II
telescope.

Table 1: Spectroscopically Identified Objects in the Field

ID | R.A. (J2000) | Decl. (J2000) | $z_{\rm sys}$ | Comment
---|---|---|---|---
| (h:m:s) | (∘:$\arcmin$:$\arcsec$) |  |
Primary Targets |  |  |  |
SMG | 09:13:39.55 | -01:06:56.4 | 2.674 | CO (3$-$2)
QSO2 | 09:13:38.32 | -01:07:08.6 | 2.750 | CO (3$-$2)
QSO1 | 09:13:38.98 | -01:07:04.5 | 2.916 | Ly$\alpha$
High$-z$ Companions |  |  |  |
Comp a | 09:13:38.28 | -01:06:43.8 | 2.675 | CO (3$-$2)
Comp b | 09:13:38.49 | -01:07:05.5 | 2.688 | CO (3$-$2)
|  |  | 2.692 | CO (3$-$2)
LAE1 | 09:13:40.06 | -01:06:54.2 | 2.674 | Ly$\alpha$
LAE2 | 09:13:39.04 | -01:07:06.4 | 2.692 | Ly$\alpha$
Low$-z$ Interlopers |  |  |  |
Obj 1 | 09:13:39.31 | -01:06:57.0 | 0.054 | H$\gamma$
Obj 2 | 09:13:38.15 | -01:06:58.5 | 0.265 | [O II]
Obj 3 | 09:13:38.41 | -01:06:55.5 | … | M5 star
Obj 4 | 09:13:40.06 | -01:06:37.1 | 0.298 | [O II]

Coordinates for the Primary Targets, Comp a, and Comp b come from ALMA imaging
as reported in ; The remaining coordinates come from KCWI. We comment on the
line used to measure $z_{\rm sys}$ for each target in the last column.

##  3 Observations and Data Analysis

We carried out deep optical integral-field spectroscopy of GAMA J0913$-$0107
with Keck II/KCWI on Jan 30, 2022 (UT). We used a single configuration
throughout the night: the large image slicer, the blue medium grating tilted
to a central wavelength of 4500 Å, and 2x2 binning on the CCD detector. With
this configuration, we achieved a wavelength coverage between 4055Å and 4940 Å
(roughly $g$-band) with a dispersion of $\sim$0.5 Å/pix and a spectral
resolution of $R\sim 2000$. The wavelength coverage includes H i Ly$\alpha$
line between $2.33<z<3.06$ (enclosing the redshifts of the SMG and the two
QSOs). Interloper galaxies emitting the [O ii] $\lambda\lambda$3727,30 doublet
can also be identified between $0.088<z<0.325$.

With the large image slicer at a position angle (PA) of $0^{\circ}$ (i.e., N
is up), the field-of-view (FoV) is 330 wide (24$\times$1.35 slits) and 204
tall (the length of each slit) with an EW spatial resolution of 135/slit and a
NS spatial resolution of 0.294/pix. Although all of the three primary targets
(SMG, QSO1, QSO2) can fit within a single KCWI pointing, we added another
pointing to detect the Ly$\alpha$ nebula to the north of the SMG (see the blue
rectangles in the left panel of Figure 1). For the north pointing, we obtained
$6\times 20$ min (2 hr) frames centered at a Right Ascension (R.A.) and
Declination (Decl) of 09:13:38.98, $-$01:06:47.29. For the south pointing, we
obtained $7\times 20$ min (2.3 hr) frames centered at 09:13:38.98,
$-$01:07:05.50. The north and south pointings are offset by $18\farcs 0$,
leaving a $2\farcs 4$ overlapping region that accumulated a total integration
time of 4.3 hours. To improve the spatial sampling in the EW direction, we
dithered half a slit width ($0\farcs 675$) between adjacent exposures. The
combined FoV for our KCWI observation of GAMA J0913$-$0107 is 33 wide by 38
tall. In the following, we describe the procedures of data reduction,
mosaicing, continuum source subtraction, and optimal extraction of Ly$\alpha$
line emission.

###  3.1 Datacube Construction and Mosaicing

Data reduction was carried out with the IDL version of the KCWI data reduction
pipeline111https://github.com/Keck-DataReductionPipelines/KcwiDRP (Neill et
al., 2018). We compared the reduced science frames using flat fields built
with the internal lamp, the dome lamp, and the twilight, and adopted the
calibrated frames using the dome flats because the sky-subtracted 2D spectra
show the minimum level of systematic artifacts. Feige 56 was used for flux
calibration because it shows less absorption features in our wavelength range
than Hiltner 600 (the other standard star taken during the night). The end
products of the pipeline are fully calibrated datacubes $(x,y,\lambda)$ that
are also corrected for differential atmospheric refraction, along with the
associated variance cubes.

To combine the individual datacubes, we first need to solve for the astrometry
by matching the positions of the sources detected in the wavelength-collapsed
KCWI pseudo-$g$-band image with their equatorial coordinates from the KiDs
catalog. The north pointing contains few bright sources, so we aligned these
frames based on a single point source in the overlapping region between the
pointings (Obj 3 - a M5 star). For the south pointing, additional objects such
as the QSOs were used to improve the astrometric solution.

To coadd the datacubes based on their astrometric solutions, we used a
modified version of the Cosmic Web Imager Tools (CWITools; O’Sullivan & Chen,
2020). The python package combines the datacubes by re-sampling the pixels
onto a common grid using the drizzle algorithm (Fruchter & Hook, 2002). We
chose a final pixel size of $0\farcs 7\times 0\farcs 7$ to match the typical
seeing and the 135 slit width; any pixel size smaller led to noticeable
artifacts. To illustrate the coadding result, we produced a pseudo-$g$-band
image from the coadded KCWI datacube by median-averaging all of the wavelength
channels. As Figure 1 shows, this broad-band image detects almost all of the
sources detected in the deep $g$-band image from KiDS that reached a 5$\sigma$
detection limit of 25.4 magnitude, despite its lower resolution.

To produce the coadded variance cube for S/N estimation, we first pass the
variance cubes through the same drizzle procedure just like the flux cubes. To
account for covariances introduced to the coadded datacube from resampling, we
then use the CWITools covariance estimation function to compute the factor
that should be multiplied to the resampled variance cube (refer to Section 5.2
in O’Sullivan et al., 2020, for details). For our case, we found a
multiplication factor of $\sim 2$.

###  3.2 QSO and Continuum Subtraction

In order to isolate the extended Ly$\alpha$ emission, we need to remove the
bright continuum sources in the datacubes. We found that better results can be
obtained by removing continuum sources in individual datacubes and then
coadding the resulting cubes, as opposed to removing continuum sources from
the coadded datacube. Note that the datacubes from individual exposures
preserve the intial spatial sampling and have a pixel size of
135$\times$0294\. The coadding procedure is the same as outlined in the
previous subsection and the coadded datacube has a pixel size of 07$\times$07.

Inspired by previous analytical methods from optical IFU studies of Ly$\alpha$
nebula (Borisova et al., 2016; Arrigoni Battaia et al., 2019; Cai et al.,
2019; O’Sullivan et al., 2020; Lobos et al., 2023, and references therein), we
first subtract the bright QSOs with empirical PSF models. For both PSF model
construction and subtraction, we only focus on the subregion of $4\farcs
1\times 4\farcs 4$ ($3\times 15$ pixels) centered on each QSO, because the
size is large enough to capture most of the flux from a point source. We build
a high S/N PSF model for each wavelength channel by median-combine the
adjacent 300 channels (150 Å), and subtract the PSF out by scaling it to the
flux within the central $1\farcs 4\times 1\farcs 5$ ($1\times 5$ pixels)
region of each QSO. There are a couple of caveats in this process: (1) the
QSO1 completely disappears in certain wavelength channels because of the DLAs,
making QSO subtraction unnecessary in these channels; we also do not use these
channels when building the PSF because they contain no PSF signal. (2) The
wavelength channels near the systemic redshifts of the three primary galaxies
should not be used to build the PSF model because they may be contaminated by
the extended Ly$\alpha$ emission that we are after. Our analysis code is
flexible enough to account for these caveats.

Next, we subtract the remaining continuum sources with a running average
method. It is necessary to separate each QSO subtraction from continuum
subtraction because the QSOs exhibit sharp spectral features in both emission
and absorption. The main difference is that we build the continuum model for
the full spatial coverage of each datacube and subtract the continuum model
without scaling. Similar to the QSO subtraction, we build a high S/N continuum
model for each wavelength channel by median-combine the adjacent 300 channels,
excluding the channels near the systemic redshifts of the primary galaxies.
This process removed most of the continuum sources seen in Figure 1, but it
did not work well for sources that show narrow emission lines or other sharp
spectral features. So we mask out these high residual foreground sources in
the maps that we will present.

Finally, once the QSOs and other continuum sources have been subtracted from
each individual datacube, we combine the cubes with the same astrometry
solutions and the same drizzle procedure in the previous subsection. To
illustrate the performance of the subtraction procedure, we generated narrow-
band images optimized for extended Ly$\alpha$ nebula around QSO1by summing up
the wavelength channels within $\pm 1500$ km s-1 relative to $z_{\rm
QSO1}=2.916$. Figure 2 shows the narrow-band images from the coadded datacubes
before and after each subtraction stage. It is clear that both the QSO and
continuum sources are adequately removed from the final coadded datacube. More
importantly, the process unveiled a giant Ly$\alpha$ nebula around QSO1, which
we will discuss in more detail along with the nebulosity around the SMG and
the QSO2 in the next subsections.

Figure 2: Demonstration of QSO- and continuum-subtraction results. Each panel
displays a narrow-band image formed by combining wavelength channels within
$\pm 1500$ km s-1 relative to $z_{\rm QSO1}$. From left to right, we show the
narrow-band image from the datacube before any source subtraction, that from
the datacube after QSO subtraction, and that from the datacube after both QSO
and continuum subtraction. Only the extended Ly$\alpha$ nebula remains after
the subtractions.

###  3.3 Optimal Extraction of Ly$\alpha$ Emission

Because extended Ly$\alpha$ line emission display complex kinematics with a
variety of velocities and velocity widths, simply combining wavelength
channels within a fixed velocity range around a systemic redshift (like we did
in Figure 2) does not provide the optimal result. Optimization is especially
important for recovering low S/N signals around high redshift galaxies. The
“optimal extraction” approach solves this problem by finding an optimal
extraction window at each spatial location, and various techniques have been
applied on datacubes produced by both radio interferometers (e.g., Wong et
al., 2022)222https://github.com/tonywong94/maskmoment and optical integral
field spectrographs (e.g., Arrigoni Battaia et al., 2019; Cai et al., 2019).
These extraction windows together is a 3-dimensional mask generated from a
smoothed S/N cube. We begin by constructing a 3D Gaussian kernel to smooth the
the QSO- and continuum-subtracted coadded datacube. For the spatial
dimensions, we use a 2D Gaussian Kernel with a FWHM of 1.5, comparable to the
spatial resolution. For the spectral dimension, we used a Gaussian with a FWHM
matching the spectral resolution (2.25Å). The kernel size is $7\times 7\times
5$ pixels ($4\farcs 9\times 4\farcs 9\times 2.5$ Å). We convolve the 3D kernel
with both the flux cube and the variance cube and divide the two to build a
smoothed S/N cube. All pixels with a S/N less than S/Nmin are masked out. We
then employ the Python module cc3d333https://pypi.org/project/connected-
components-3d/ to discern and categorize all clusters of pixels exhibiting
three-dimensional spatial connectivity. We then exclude clusters with less
than $N_{\rm min}$ pixels to minimize the number of spurious “floating
islands”. The surviving clusters form a 3D mask that can be used to extract
line emission from the unsmoothed datacube to generate the “optimally
extracted” Ly$\alpha$ surface brightness maps and its kinematics maps.

However, the parameters described above ($N_{\rm min}$ and S/Nmin) need to be
chosen to optimize the 3D mask. For example, a too “inclusive” 3D mask would
not only reduce the S/N of the extracted maps but also overestimate the size
of the nebula. We thus devised an iterative procedure to find the parameters
that optimize the 3D mask. For each primary target, we start the iteration by
guessing the initial values of $N_{\rm min}$ and S/Nmin. Once the initial 3D
mask is generated, we apply it to the unsmoothed flux cube and variance cube
and generate a S/N map for the Ly$\alpha$ emission. We then compare the S/N
map with the projected boundaries of the 3D mask. Because only pixels with S/N
$\gtrsim 2$ should be considered as detection, if the projected boundaries of
the 3D mask include too many pixels with S/N $<2$, a more “exclusive” mask
should considered. In the next iteration, the parameters $N_{\rm min}$ and
S/Nmin are modified accordingly and a new 3D datacube produces a new S/N map
and the 2$\sigma$ contour is again compared with the projected boundaries of
the mask. After a few iterations, the mask is considered “optimal” when a good
agreement is found between the two. Through this process, we found that the
optimal parameters are $N_{\rm min}=800$ and S/N${}_{\rm min}=1.2$.

##  4 Results

Both SMGs and QSOs represent the most massive halos ($10^{12.5-13}$
$M_{\odot}$) in the early universe, as indicated by their strong spatial
clustering signals (e.g., Hickox et al., 2012; DaÂngela et al., 2007; Trainor
& Steidel, 2012; White et al., 2012). By design, our KCWI data covers the
redshifted Ly$\alpha$ line around all three primary galaxies, making it
possible to directly compare their observed properties at the same depth and
with the same instrument. We present the Ly$\alpha$ results from three
different angles. First, we build Ly$\alpha$ channel maps to illustrate the
emission detected in the “raw” data. Then, we present optimally extracted
Ly$\alpha$ moment maps to showcase each nebula in more detail. Finally, we
construct azimuthally averaged radial profiles of the Ly$\alpha$ surface
brightness to quantify the similarities and differences among the three
galaxies.

###  4.1 Ly$\alpha$ Channel Maps

Figure 3: Ly$\alpha$ channel maps. The top panel displays the SMG, and each
map has a velocity width of $\approx 150$ km s-1. The middle and bottom panel
show the channel maps for QSO2 and QSO1 respectively with each velocity width
increased to $\approx 650$ km s-1. The white contours corresponds to $\rm
S/N=2$. The position of the SMG, QSO1, and QSO2 are represented by the gold
cross, red, and yellow stars respectively.

We begin our search for extended Ly$\alpha$ emission by producing Ly$\alpha$
channel maps from the QSO- and continuum-subtracted datacube. For each target,
we produce a series of narrow-band images spanning a velocity range of $\sim
1300$ km s-1 relative to the systemic redshift, each covering a velocity range
of $\sim$370 km s-1 (Figure 3). We estimate the 1$\sigma$ noise of each image
by computing the root mean square (RMS) from near empty regions, and overlaid
the 2$\sigma$ contours on each image. Extended Ly$\alpha$ emission is detected
around all three galaxies, and each nebula cover quite a large velocity space.
From these channel maps, it is already clear that the QSOs exhibit
significantly brighter extended Ly$\alpha$ emission than the SMG.

Around the SMG, there is a bright Ly$\alpha$ nebula near the SMG position and
$\delta v=200$ km s-1, and there is also patchy filamentary emission emanating
from the SMG along the diagonal directions in the other channel maps. Next up
in redshift, around QSO2, the channel maps reveal a bright circular Ly$\alpha$
blob centered on the QSO and the emission clearly extends diagonally towards
QSO1. This extended emission is likely connected to the DLA at $z_{\rm
abs}=2.75$ towards QSO1. Lastly, around QSO1, we detect the brightest
Ly$\alpha$ nebula among the three galaxies. Similar to the other two galaxies,
we also observe a bright central Ly$\alpha$ blob with a filamentary extension
(this time towards the NW direction).

###  4.2 Optimally Extracted Ly$\alpha$ Moment Maps

Figure 4: Moment maps of extended Ly$\alpha$ emission around the three primary
galaxies: SMG, QSO2, and QSO1 from left to right, and the Ly$\alpha$ surface
brightness maps, velocity maps, and velocity dispersion map from top to
bottom. For all images, we overlay the $\rm S/N=2$ contours. To indicate the
scale, a dashed circle with a radius of $150$ kpc is drawn around each host
galaxy. The gray circles are masked out areas due to foreground objects. Table
2: Properties of Extended Ly$\alpha$ Nebulae

Parameter | SMG | QSO2 | QSO1 | Unit
---|---|---|---|---
Luminosity | $1.1\pm 0.02$ | $3.4\pm 0.07$ | $7.1\pm 0.04$ |  $10^{43}$ erg s-1
Area | 67 (4200) | 113 (7020) | 159 (9600) | arcsec2 (kpc2)
Extent | 31 (250) | 38 (300) | 26 (200) | arcsec (kpc)
Peak SB | 4.5 | 12 | 27 |  $10^{-18}$ cgs
Mean SB | 1.0 | 1.9 | 3.6 |  $10^{-18}$ cgs
$\langle V\rangle$ | -250 | -51 | 2.4 | km s-1
$\langle\sigma\rangle$ | 180 | 240 | 170 | km s-1
Profile Index | $-0.67\pm 0.22$ | $-1.6\pm 0.3$ | $-1.9\pm 0.3$ | —

All measured within the $2\sigma$ contours of the optimally extracted surface
brightness maps.

To characterize the extended Ly$\alpha$ emission at the highest possible S/N,
we utilize the 3D optimal extraction masks described in § 3.3. While the
channel maps provide crude information on the gas morphology and kinematics,
the optimally extracted emission line maps in Figure 4 provide the full
morphology of each nebula, the total Ly$\alpha$ Luminosity ($L_{\rm
Ly\alpha}$), the total physical size, and detailed kinematics. As usual, the
moment 0, 1, and 2 maps are the Ly$\alpha$ surface brightness maps, the flux-
weighted Ly$\alpha$ radial velocity, and the velocity dispersion maps. All
maps are generated using the optimized 3D mask and the unsmoothed, QSO- and
continuum-subtracted, coadded flux cube. Corresponding noise maps in surface
brightness are from the coadded variance cube. The reader can directly compare
these maps with the channel maps in Figure 3 to evaluate the likelihood of
spurious features. The three galaxies display a variety of Ly$\alpha$
morphology and kinematics as we already started noticing in the channel maps.
The area around QSO1 shows nebulae at a number of redshifts, we rule out the
possibility of mis-identification in Appendix C. In the following, we describe
the nebula around each galaxy in the order of increasing redshift. Table 2
summarizes the properties of the Ly$\alpha$ nebulae measured within the
$2\sigma$ detection contours.

####  4.2.1 SMG at $z=2.674$

With a $2\sigma$ detection limit of $6.7\times 10^{-19}$ cgs, we detect a
clear extended Ly$\alpha$ nebula surrounding the SMG. Similar to the
Ly$\alpha$ channel maps in §4.1, the nebula possesses the brightest SB near
the position of the SMG reaching a peak value of $\approx 4\times 10^{-18}$
cgs. Shifting $\sim 10$ to the northeast of the SMG, we detect the presence of
LAE1 by identifying a local increase in SB up to $\approx 3\times 10^{-18}$
cgs. We also detect clumpy Ly$\alpha$ emission nearly $16$ to the northwest of
the SMG reaching a peak SB of $\sim 1.5\times 10^{-18}$ cgs. From the SB map
alone, it is unclear whether this clumpy emission is associated with the SMG
or other independent sources.

As we shift towards the southwest direction, we identify a large filamentary
structure stretching over $180$ kpc from the SMG intercepting the sightlines
of both QSOs. The structure is not a single solid filament, but a collection
of large regions of clumpy Ly$\alpha$ emission that takes the shape of a
single filament. The mean SB along the filament is $\sim 1.2\times 10^{-18}$
cgs. The presence of this large structure and its position in the CGM of the
SMG suggests a connection with the absorption systems detected previously for
both QSOs.

The total nebula area captured within our $2\sigma$ contour is $67$ arcsec2
($4200$ kpc2). We measure the total extent of the nebula to be $31$ (250 kpc).
The mean SB throughout the entire nebula is $1.0\times 10^{-18}$ cgs, and the
total integrated $L_{\rm Ly\alpha}$ is $1.1\pm 0.02\times 10^{43}$ erg s-1.

Moving onto the kinematics of the gas, we detect a velocity gradient within
the brighter region of the nebula. The Ly$\alpha$ line at the position of the
SMG resides at $\delta v\approx+300$ km s-1. As we shift to the East, the gas
gradually blueshifts to $\delta v\approx-300$ km s-1. The large collection of
Ly$\alpha$ clumps to the northwest of the SMG all exhibit blueshifts
$\lesssim-700$ km s-1, suggesting that they are outside the CGM of the SMG.
The large filamentary structure possesses both redshifted and blueshifted
components with no velocities exceeding an absolute value of $700$ km s-1.
From the moment 2 map, we find that all regions captured within the $2\sigma$
contour possess line widths $\sigma\gtrsim 150$ km s-1. Regions that show
larger line widths ($\sigma\geq 700$ km s-1) are the result of blended
blueshifted and redshifted components (this will be true for both QSO
nebulae). Overall, we measure an average velocity offset of $-250$ km s-1 and
an average line width of $180$ km s-1 for the entire nebula.

####  4.2.2 QSO2 at $z=2.75$

Continuing onto QSO2, we detect a Ly$\alpha$ nebula extended throughout its
CGM at a $2\sigma$ detection limit of $6.3\times 10^{-19}$ cgs. Similar to the
SMG, we find the brightest Ly$\alpha$ SB localized near the position of the
galaxy, which reaches a peak value of $12.0\times 10^{-18}$ cgs. As we shift
away from the QSO, we see a large filamentary structure extending nearly $\sim
150$ kpc to the northeast intercepting the sightline of QSO1. The mean SB
along this filament decreases down to $\approx 2.0\times 10^{-18}$ cgs. Near
the position of QSO1, we measure an increase in SB values approaching $\approx
5\times 10^{-18}$ cgs. The filament disappears from view only a few arcsecs
($\sim 20$ kpc) to the northeast of QSO1’s sightline.

Looking even further to the northeast, we detect a pocket of clumpy Ly$\alpha$
emission with a mean SB of $\approx 1\times 10^{-18}$ cgs. Interestingly, the
clumps take the shape of a narrower filament in a similar fashion to the
structure observed in the CGM of the SMG. Intriguingly, We notice that this
extended structure is positioned in such as way to form an arc with the
filament seen in the southwest. This suggests that this could be one large
extended filamentary structure ($\gtrsim 200$ kpc) within the CGM of QSO2
casting a shadow onto QSO1’s sightline (the DLA at $z=2.75$). The obvious gap
in the filament may be due to the presence of Obj 1, which we masked out due
its strong H$\gamma$ line that was redshifted into the wavelength window of
QSO2’s Ly$\alpha$ line.

If we assume one large structure, the total extent of QSO2’s nebula is nearly
$38$ ($300$ kpc), noticeably larger than the SMG nebula. Furthermore, the
total detected nebula area is $113$ arcsec2 ($7020$ kpc2). The mean Ly$\alpha$
SB is $1.9\times 10^{-18}$ cgs, and the total integrated $L_{\rm Ly\alpha}$ is
$3.4\pm 0.07\times 10^{43}$ erg s-1.

The kinematics seen in QSO2’s nebula also show a large distribution of radial
velocities. Near the position of the galaxy, we find velocities within a range
between $-600<\delta v<0$ km s-1. As we shift towards the position of QSO1, we
measure velocities $0<\delta v<+300$ km s-1. The extended structure to the
northeast does not possess a specific $\delta v$. Rather, we measure a range
of $-500<\delta v<+600$ km s-1. The mean velocity offset of the full nebula is
$\approx-50$ km s-1. Using the moment 2 map, we find that all detected
Ly$\alpha$ emission exhibits line widths larger than $\sigma\gtrsim 180$ km
s-1. The mean line width across the full nebula is $240$ km s-1. Similar to
the SMG’s nebula, we do not detect any clear velocity structure within QSO2’s
nebula.

####  4.2.3 QSO1 at $z=2.916$

Concluding with QSO1, we detect the brightest Ly$\alpha$ nebula out of the
three primary galaxies at a $2\sigma$ detection limit of $6.0\times 10^{-19}$
cgs. The peak Ly$\alpha$ SB is $\approx 27\times 10^{-18}$ cgs, which is
$\approx 2.3\times$ higher than QSO2 and $6\times$ higher than the SMG. The
mean SB of the entire nebula is $\sim 3.6\times 10^{-18}$ cgs. Similar to
QSO2, a rather large structure can be seen over $100$ kpc to the northwest of
the QSO with a SB $\gtrsim 4\times 10^{-18}$ cgs. Given the similarity between
the structures seen in the CGM of both QSO’s, it would be remarkable if both
structures are DLA systems. However, we are unable to speculate since there is
no background target intercepted by the structure in QSO1’s CGM.

The nebula found within the QSO1’s CGM resembles previously observed QSO
Ly$\alpha$ nebulae, particularly those classified as enormous Ly$\alpha$
nebula (ELAN) (Cantalupo et al., 2014; Hennawi et al., 2015; Cai et al., 2017,
2018) that have Ly$\alpha$ surface brightness $\gtrsim 1\times 10^{-17}$ cgs
spanning 100s of kpc with a total integrated $L_{\rm Ly\alpha}\geq 10^{44}$
erg s-1. However, we measure $L_{\rm Ly\alpha}\approx 7\times 10^{43}$ erg s-1
for the entire Ly$\alpha$ halo. The total nebula area is $\approx 159\,\rm
arcsec^{2}$ ($9600\,\rm kpc^{2}$).

Unlike the previous galaxies, we find notable kinematic features present
within QSO1’s nebula. Two distinct velocity components, each with $|\delta
v|\approx 300$ km s-1, are detected within the nebula. If we compute the mean
velocity offset for the nebula, we find that these velocity components average
out to $\sim 0$ km s-1. QSO1’s position coincides with the boundary separating
these velocity regions, spanning the majority of the observed extended nebular
structure. Furthermore, a systematic increase of approximately $50-100$ km
s-1in the absolute velocity value is observed as one moves away from the
galaxy’s position. From the moment 2 map, we find that the mean Ly$\alpha$
line width in the nebula is $\sigma=170$ km s-1. Regions with $\sigma\gtrsim
450$ km s-1 correspond to the boundary between both velocity components.
However, we find line widths approaching $\sim 400$ km s-1 $\approx 5$ to the
south of QSO1, which may not be influenced by line-blending. In Appendix D, we
discuss the remarkable similarities between QSO1’s kinematic features with
those detected in recent observations of the MAMMOTH-1 Ly$\alpha$ nebula
(Zhang et al., 2023b). Overall, the kinematics of QSO1 offer a greater insight
into the dynamics of the cool gas when compared with the SMG and QSO2.

###  4.3 Azimuthally Averaged Radial Profiles

Figure 5: Azimuthally averaged Ly$\alpha$ surface brightness profiles. The
nebulae around the SMG, the QSO2, and the QSO1 are plotted in black, purple,
and red, respectively. The error bars correspond to the 25th and 75th
percentile of the pixels within each annulus. For comparison, we also include
the average profiles of previous QSO surveys at $z\sim 3$ (Arrigoni Battaia et
al., 2019) and $z\sim 2$ (Cai et al., 2019) as dashed and dotted line,
respectively. All surface brightnesses are scaled to the SMG redshift at
$z_{\rm SMG}=2.674$.

We now compare the radial profiles of the three nebulae by constructing
azimuthally averaged surface brightness profiles from the moment 0 maps.
Without information on the inclination angle of the systems relative to the
observer, we simply generate evenly spaced circular annuli around each primary
galaxy and average the Ly$\alpha$ surface brightness from the pixels in each
annulus. The annuli begin at $\sim$25 kpc and end at $\sim$200 kpc, to
encompass the expected virial radii of $10^{13}$ $M_{\odot}$ halos at $z\sim
2.6-2.9$. Because of the clumpy morphologies of the nebulae, not all annuli
have valid measurements. Because of the cosmological surface brightness
dimming ($S(z)\propto(1+z)^{-4}$), the radial surface brightness profiles of
the QSOs are scaled to the SMG redshift by multiplying $(1+z_{\rm
QSO})^{4}/(1+2.674)^{4}$.

Figure 5 shows the resulting surface brightness profiles. In the inner 100 kpc
or so, the QSOs clearly show an enhanced surface brightness profile; but in
the outer region, all profiles converge to a plateau around $4\times 10^{-19}$
cgs. Simple power-law model fits to the radial profiles shows that the power-
law index steepens from $-0.67\pm 0.22$ around the SMG, $-1.6\pm 0.3$ around
QSO2, to $-1.9\pm 0.3$ around QSO1. As shown in the figure, the radial
profiles of two QSO nebulae are comparable to those measured previously around
other QSOs (Arrigoni Battaia et al., 2019; Cai et al., 2019), but the profile
of the SMG nebula is significantly shallower.

##  5 Comparisons

In this section, we first compare the extended Ly$\alpha$ emission line
detected near each QSO with the H i absorption profiles present in the QSO
spectra to connect the ionized hydrogen with the neutral hydrogen in the gas
stream around the SMG, and then compare the general properties of the
Ly$\alpha$ nebulae from this study to those of Ly$\alpha$ nebulae from the
literature.

###  5.1 H i Emission vs. Absorption

Figure 6: H i Ly$\beta$ absorption towards QSO sightlines (top) vs. extended H
i Ly$\alpha$ emission near the sightlines (bottom). The continuum-normalized
QSO spectra on the top are from VLT/X-shooter, while the Ly$\alpha$ emission-
line spectra at the bottom are extracted from our QSO and continuum-subtracted
KCWI datacube. All velocities are with respect to the redshift denoted in the
top right of each column. For each Ly$\alpha$ emission line spectrum, we
overlay the best-fit Gaussian profile in red. Left: H i absorption/emission
towards/near QSO1 around the SMG redshift. Middle: H i absorption/emission
towards/near QSO2 around the SMG redshift. Right: H i absorption/emission
towards/near QSO1 around the QSO2 redshift. The dashed line seen in the middle
panel corresponds to the velocity beyond which QSO subtraction is important;
this explains the large residuals at these velocities. The three cases display
a range of velocity offsets between the main absorption clouds and the
adjacent emission-line nebulae.

While QSO absorption line spectroscopy is an extremely sensitive tool to
detect intervening clouds and their chemical composition, the spatial extent
and distribution of the clouds are difficult to quantify even with multiple
QSO sightlines. A complete picture of the cool gas in the CGM requires deep
integral-field spectroscopy that is sensitive enough to detect diffuse low
surface-brightness line emission. Now with the KCWI data, we can begin to
piece the pictures together.

For the GAMA J0913$-$0107 system, there are two main filaments of cool gas for
which we can compare the gas kinematics in absorption and in emission: (1) the
stream around the SMG that is responsible for the $z_{\rm abs}\approx 2.67$
sub-DLA towards QSO1 and the LLS towards QSO2, and (2) the stream around QSO2
that is responsible for the $z_{\rm abs}\approx 2.75$ DLA towards QSO1. We
have seen the clumpy, filamentary morphology of the streams in the Ly$\alpha$
surface brightness maps in Figure 4, and their connection with the absorption-
line systems is evident because the Ly$\alpha$ filaments appear to pass in
front of their background QSOs. In Figure 6, we compare the kinematics of the
absorption lines with those of the emission lines. Because both filaments
cover a wide range in velocity, for this comparison, we only extract the
emission-line spectra from the parts that are closest in projection to the QSO
sightlines. The SMG stream offers two comparison positions because there are
two background QSOs, while the QSO2 stream offers only one comparison position
at QSO1. Because the Ly$\alpha$ absorption line is highly saturated, we use
the Ly$\beta$ absorption to show the radial velocity distribution of the
absorption clouds. For the SMG stream near the position of QSO1, the
Ly$\alpha$ emission is redshifted relative to the sub-DLA (i.e., subsystem A)
by $\sim$500 km s-1, positioning it between the two absorption subsystems A
and B. On the other hand, near the position of QSO2, the emission line is
blueshifted by $-$150 km s-1 relative to the LLS in subsystem A. At both
positions, relatively narrow line widths are observed in emission
($\sigma\approx 150$ km s-1) and in absorption ($\sigma\approx 30$ km s-1; ,
Table 4). For the QSO2 stream, the Ly$\alpha$ emission is well aligned with
the absorption line and it shows a broad profile with a velocity width of
$\sigma\approx 240$ km s-1, which is comparable to the velocity span of the
absorption-line clouds traced by the optically thin metal lines (see , Figure
C2).

In summary, the comparisons yield a mixed result. The H i Ly$\alpha$ emission
lines can be either blueshifted or redshifted relative to the H i absorption,
but their line widths are comparable to the velocity span covered by the
spectroscopically resolved absorption-line clouds. This discrepancy may be
attributed to the differences between the two methods to infer gas properties.
KCWI measures the average emission over a large area, while absorption lines
are narrower pencil-beam measurements.

###  5.2 Comparison with Ly$\alpha$ Nebulae around Other QSOs

Figure 7: $L_{\rm Ly\alpha}$ as a function of Ly$\alpha$ nebula area. The
Ly$\alpha$ nebula for the SMG, QSO2, and QSO1 are plotted as a gold cross,
blue star, and red star respectively. The additional datapoints come from
previous studies on Ly$\alpha$ Nebula, specifically focused on QSO systems.
The red crosses correspond to the results from QSO MUSEUM (Ref 1; Arrigoni
Battaia et al., 2019), the magenta cross-hairs correspond to Cai et al.
(2019)’s survey on $z\approx 2$ QSOs with KCWI (Ref 2) , the orange triangles
correspond to the QSOs at $z\sim 2.5$ with PCWI (Ref 3; O’Sullivan et al.,
2020). Additionally, we include recent results on the Ly$\alpha$ properties of
QSO pairs with PCWI (Li et al., 2023) as purple squares, as well as QSO-SMG
composite systems from Lobos et al. (2023) (Ref 5) plotted as green diamonds.

We will now direct our focus toward comparing the characteristics of each
nebula. Figure 7 facilitates this comparison by juxtaposing our observed
nebulae with those reported in the previous studies (QSO nebulae), utilizing
the total integrated $L_{\rm Ly\alpha}$ as a function of nebula area. We
convert the angular size of each nebula into its physical area. Since we
overlay other $z>2$ QSO results, we begin our comparison with QSO1 and QSO2.

As Figure 7 illustrates, the Ly$\alpha$ halos enveloping QSO1 and QSO2 adhere
to the established trend between halo $L_{\rm Ly\alpha}$ and nebula area.
Battaia et al. (2023) employed a similar methodology to establish a
Luminosity-Area Relation, which takes the form of $\log(L_{\rm Ly\alpha}^{\rm
Neb})=a_{1}\log(\rm Area^{\rm Neb})+a_{0}$. These relations underscore that
the bolometric luminosity ($L_{\rm bol}$) of the QSO housing the Ly$\alpha$
nebula does not appear to exert a significant influence on the total $L_{\rm
Ly\alpha}$. Our results align with this trend, as both QSO1 and QSO2 exhibit
comparable $L_{\rm bol}$ values, despite differing Ly$\alpha$ nebula
properties. As a final step, we plot the SMG nebula properties and find that
it is comparable to other QSO nebulae.

###  5.3 Previous Non-Detection of Ly$\alpha$ Nebulae around two SMGs

Our KCWI observation of the GAMA J0913$-$0107 system presents a rare
opportunity to make a direct comparison between the Ly$\alpha$ nebula
properties for systems hosting SMGs and QSOs. Discovering the nebulae
surrounding both QSO1 and QSO2 follows the growing trend of extended
Ly$\alpha$ emission surrounding $z>2$ QSOs. However, the same cannot be said
for systems hosting SMGs alone. Specifically, we refer to SMGs residing
outside of clear protocluster environments where the local UV background may
be boosted (e.g., Umehata et al., 2019). The recent study by Lobos et al.
(2023) observed SMG-QSO composite systems, as well as SMGs with no QSOs. The
authors detect bright Ly$\alpha$ nebula within the composite systems, but they
do not detect any Ly$\alpha$ emission from the CGM of the individual SMGs.
This implies that the presence of the QSO could be a dominating mechanism to
power the observed nebulae and other mechanisms such as gravitational heating
may not be as important.

One critical difference between our KCWI observation of the GAMA J0913$-$0107
system and the MUSE observations performed by Lobos et al. (2023) is the
Ly$\alpha$ SB detection limit. The authors report a $2\sigma$ limit of $\sim
2\times 10^{-18}$ cgs for both SMGs at a redshift of $\approx 4.4$. If we
consider cosmological SB dimming and scale this to $z_{\rm SMG}=2.674$, the
limit increases to $\sim 9\times 10^{-18}$ cgs. Our observations reveal that
the nebula reaches a peak Ly$\alpha$ of $\sim 5\times 10^{-18}$ cgs, nearly
$0.5\times$ the limit from the MUSE observations. With this in mind, it is
difficult to make a direct comparison.

##  6 Summary and Discussion

The GAMA J0913$-$0107 system is a rare alignment of three massive $z=2-3$
galaxies on the sky: one SMG in the foreground of two QSOs. Motivated by
previous absorption-line detection of substantial amount of cool gas in their
halos, we have carried out and analyzed deep integral-field spectroscopic
observations to search for extended H i Ly$\alpha$ emission in the halos of
the three massive galaxies. Our main findings can be summarized as follows:

  1. 1.

We discover a bright Ly$\alpha$ nebula surrounding a heavily dust-obscured
starburst. The nebula possesses a large filamentary structure stretching $\sim
180$ kpc from the SMG, intercepting the sightlines of both background QSOs.
The full extent of the nebula is $250$ kpc (31), with a total area of $4200$
kpc2 (67 arcsec2). We find that the peak Ly$\alpha$ SB resides near the
position of the SMG and reaches a value of $\approx 4.5\times 10^{-18}$ cgs
and measure a total integrated $L_{\rm Ly\alpha}$ of $\approx 1.1\times
10^{43}$ erg s-1. The velocity map shows that all Ly$\alpha$ emission,
including the filamentary structure, is consistent with gas that is
gravitationally bound to a $10^{13}$ $M_{\odot}$ DM halo.

  2. 2.

We detect Ly$\alpha$ nebulae surrounding both QSOs at equivalent detection
limits and compare their characteristics with the SMG. Both QSO2 and QSO1 have
peak Ly$\alpha$ SB values that exceed the SMG by $2.7\times$ and $6\times$,
respectively. The total $L_{\rm Ly\alpha}$ for each nebula is $\approx 2.7$
and $6.3\times 10^{43}$ erg s-1. Each nebula has comparable nebula properties
with other $z>2$ QSOs from the literature. The CGM of QSO2 possesses a large
filamentary structure stretching $\gtrsim 200$ kpc from the host galaxy
intercepting the sightline of QSO1. The DLA towards QSO1 (at $z=2.75$) is
attributed to this structure. Furthermore, we find another filament within
QSO1’s nebula that spans nearly $\sim 150$ kpc to the northwest.
Interestingly, the velocity map for QSO1 reveals clear kinematic structure,
where we find two regions that have a radial velocity equal to $|\delta
v|\approx 300$ km s-1.

  3. 3.

We create circularly-averaged SB profiles for each nebula and perform a direct
comparison. The SMG has a flatter profile than the QSOs with a power-law index
of $\approx-0.7$. Meanwhile, the QSO nebulae exhibit steeper profiles with a
power-law index near $\sim-1.8$, which is in agreement with previous $z>2$ QSO
surveys.

  4. 4.

Our KCWI observations enable a direct kinematic comparison between the
absorption line systems found within each QSO sightline and the associated
Ly$\alpha$ emission line. The Ly$\alpha$ line associated with the sub-DLA
(subsystem A) towards QSO1 at $z\approx 2.67$ is redshifted by $\sim+500$ km
s-1, but the Ly$\alpha$ line is blueshifted by $\sim-150$ km s-1 with respect
to the LLS towards QSO2. Both emission lines share a narrow line width of
$\sigma\approx 150$ km s-1. For QSO2, we find that the Ly$\alpha$ emission has
a broader line width of $\sigma\approx 240$ km s-1 and shares equal kinematic
properties with its associated DLA system towards QSO1.

The GAMA J0913$-$0107 system is a truly remarkable opportunity to study the
extended environments of different high$-z$ galaxies. The two background QSOs
enabled a direct study of the SMG’s CGM and led to the discovery of a large
”shadow” cast by a long filament of gas flowing towards the dusty starburst.
Now, with KCWI, we discover the Ly$\alpha$ signal emanating from this extended
structure. If we consider all of the evidence gathered thus far, it guides us
to the conclusion that this is indeed a cool stream fueling the star formation
within the SMG, but could there be another scenario that can adequately
explain the observations?

One possibility is the role of the obscured AGN/QSO within the dusty starburst
ionizing the Ly$\alpha$ nebula through unobscured sightlines. This would not
be too dissimilar to the KCWI observation of the SMM J02399-0136 system, which
revealed a Ly$\alpha$-emitting dark cloud powered by an obscured QSO (Li et
al., 2019). Additionally, luminous Ly$\alpha$ nebula have been detected around
obscured QSOs as shown by den Brok et al. (2020) for Type-II AGN. Even though
AGN activity is not dominant within the SMG, we still need to consider its
role. To do this, we predict the required bolometric luminosity ($L_{\rm
Bol}^{\rm required}$) that an obscured QSO would need to power the Ly$\alpha$
nebula. This $L_{\rm Bol}^{\rm required}$ value can then be compared with the
SMG’s total $L_{\rm IR}$ as reported by  and estimate the escape fraction
($f_{\rm esc}$) of ionizing photons. Additionally, if we find that $L_{\rm
Bol}^{\rm required}>L_{\rm IR}$, then we can rule out the possibility of an
obscured source.

We begin by utilizing the simple model outlined by Hennawi & Prochaska (2013).
The QSO is surrounded by cool ($\sim 10^{4}$ K) gas clouds with a uniform
volume density ($n_{\rm H}$). From the QSO absorption lines along both
sightlines, we know the gas is optically thick (). As a result, shelf-
shielding kicks in and a thin shell surrounds the clouds, converting a
fraction of ionizing photons into Ly$\alpha$ photons that travel back to the
observer. This implies that the Ly$\alpha$ SB is proportional to $L_{\nu_{\rm
LL}}$, where $L_{\nu_{\rm LL}}$ is the specific luminosity at the Lyman limit
for the QSO, and will decrease at greater distances following $R^{-2}$. If we
use the observed characteristics of the Ly$\alpha$ filament within the CGM
($R\approx 180$ kpc, $\rm SB_{\rm Ly\alpha}\sim 10^{-18}$ cgs) and rearrange
Equation 12 from Hennawi & Prochaska (2013), we estimate that $\log
L_{\nu_{\rm LL}}$ would be $\sim 29.6$ erg s-1 Hz for the unobscured QSO.

To get $L_{\rm Bol}^{\rm required}$, we must perform a bolometric correction.
We convert $\log L_{\nu_{\rm LL}}$ to the rest-frame $1350$ Å luminosity
($L_{1350}$) by assuming the QSO’s SED follows the power-law:
$L_{\nu}=L_{\nu_{\rm LL}}(\nu/\nu_{\rm LL})^{-1.7}$ (Lusso et al., 2015).
Next, we perform the bolometric correction on to $L_{1350}$ following Equation
10 in Fu et al. (2017), which utilizes the QSO SEDs from Hopkins et al.
(2007). We find that $L_{\rm Bol}^{\rm required}\approx 1.7\times 10^{12}$
$L_{\odot}$. Finally, we estimate $f_{\rm esc}$ by taking the ratio $L_{\rm
Bol}^{\rm required}/L_{\rm IR}$ and compute a value of $\sim 15\%$. This is
larger than expected for the SMG if we consider its dust content. However, it
is still within a plausible limit of the true $f_{\rm esc}$ value because of
the large uncertainty in our calculation due to the assumptions used.
Furthermore, this estimate did not consider any possible local enhancements to
the ionizing background in which the SMG resides. As a result, it is unclear
from this estimate whether an obscured source can explain our observations,
but it can likely be excluded due to the lack of AGN activity within the SMG.

We also consider the role of obscured star formation within the nebula. First,
the SMG is heavily obscured. This can be appreciated by the undetected UV
continuum in the deep KiDS image (Figure 1), as well as the dust properties
measured by ALMA (). Assuming all Ly$\alpha$ photons are produced by the
internal SFR under Case-B recombination444We utilize Equation 2 from Robert C.
Kennicutt (1998) and convert the SFRIR to SFRUV (Kennicutt & Evans, 2012)
assuming a constant star-formation history., we would expect a total $L_{\rm
Ly\alpha}$ of $\sim 1.2\times 10^{44}$ erg s-1. This would require $f_{\rm
esc}\sim 10\%$, which is similar to the previous estimate. Again, this is
likely higher than the true value for the SMG due to the lack of a detected
continuum.

Furthermore, several Ly$\alpha$ nebulae are found to host dusty star forming
galaxies (Geach et al., 2007, 2016; Oteo et al., 2018; Umehata et al., 2021).
However, these bright nebulae are host to several galaxies within a relatively
small physical size. Umehata et al. (2021) identified 9 galaxies within LAB1
and measured a total SFR $\approx 200$ $M_{\odot}\,{\rm yr}^{-1}$. If we
compare the Ly$\alpha$ properties of LAB1 and other filamentary emission
associated with SMGs from the SSA22 protocluser (Umehata et al., 2019), we
find that the Ly$\alpha$ SB is noticeably lower around the SMGs (with no
associated AGN). If obscured star formation plays a dominant role, we would
expect these isolated SMGs to display either equal or higher Ly$\alpha$ SB
since they possess higher rates of star formation (Umehata et al., 2017).
Umehata et al. (2021) suggests an additional mechanism may be needed to
explain the Ly$\alpha$ nebula, such as cooling flows or galaxy mergers. The
observations by Lobos et al. (2023) also support this conclusion. If star
formation is the dominant mechanism, then the authors should have detected
Ly$\alpha$ nebulae around their SMGs at their detection level. However, this
argument assumes a homogeneous environment surrounding SMGs such as the cold
gas density and clumpiness. As a result, these comparisons alone cannot
eliminate the role of star-formation.

utilized UV background radiation models from Haardt & Madau (2012)
(interpolated to $z=2.67$) to act as the ionizing source in their
photoionization models. However, if this is the sole ionizing source, we would
expect a mean Ly$\alpha$ SB of the order $\sim 10^{-20}$ cgs (Gould &
Weinberg, 1996), which is an order of magnitude lower than our detection
limit. However, the UV background may be boosted by nearby star forming
galaxies or AGN. Indeed, overdense regions, such as the environment of the
SMG, can possibly supply the necessary photon budget to power the observed
Ly$\alpha$ nebula. It has also been shown that overdensities of LAEs are
associated with bright Ly$\alpha$ nebulae (Matsuda et al., 2011; Zhang et al.,
2023a), and the identification of LAE1 near the SMG may suggest a similarity.
However, it is unclear whether the GAMA J0913$-$0107 system represents a newly
discovered protocluster region, such as the observations presented by Umehata
et al. (2019). In the ALMA CO (3$-$2) () and 870 $\mu$m (Fu et al., 2017)
maps, it was confirmed that the bright submillimeter source was not a blend of
multiple interacting galaxies, which was the case for LAB1 early on (Matsuda
et al., 2007; Geach et al., 2014). With KCWI, we do not identify any
additionally galaxies near the SMG outside of LAE1.

Despite the uncertainty in classifying the environment of the SMG as a
protocluster, we can be confident that it does indeed reside within an
overdense environment. The identification of other CO emitters within 30 of
the SMG would require a survey size that covers $\sim 10\times$ the area for
detections of companions (). This estimated overdensity is comparable to one
of the largest overdensities of CO emitters (Pensabene et al., 2024). This
supports the possibility of the Ly$\alpha$ stream being photoionized by a UV
background higher than the models from Haardt & Madau (2012). Nevertheless,
future observations at larger scales will be needed to better constrain the UV
background.

We now consider the role of gravitational energy. The gas will dissipate
gravitational potential energy during infall and form shocks as they flow
closer to the starburst. Cosmological hydrodynamical simulations predict
Ly$\alpha$ nebulae with $L_{\rm Ly\alpha}\approx 10^{43}-10^{44}$ erg s-1 for
$\sim 10^{12-13}$ $M_{\odot}$ DM halos (Faucher-Giguère et al., 2010; Rosdahl
& Blaizot, 2012), which is consistent with our measurements for the SMG.
However, these predictions are highly uncertain, as local boosts in UV photons
from embedded star formation can increase the expected $L_{\rm Ly\alpha}$.
Specifically, LAE1 likely contributes Ly$\alpha$ photons that can ionize
regions of the nebula, as it is an unobscured source. Interestingly, the $\pm
300$ km s-1 velocity gradient detected $\sim 5$ arcsecs to the East of the SMG
may also indicate gas infall from a second filament that is cutoff from our
KCWI FOV. Similar velocity structure was detected by Daddi et al. (2021) for
the RO-1001 group at $z=2.91$. Furthermore, the SMG resides at the region of
highest surface brightness. This indicates that the nebulae is at the center
of mass of the DM halo, which is an expectation if gravity plays a role.
Furthermore, the Ly$\alpha$ filament itself, if we interpret as a cooling
flow, is an indicator for the influence of gravity. The filament may also be
ionized by the surrounding hot CGM as it flows towards the starburst. Overall,
the evidence provided by the absorption study and the KCWI observations
suggests cool gas accretion can serve as a plausible scenario.

The results presented here demonstrates the advantage of tying together QSO
absorption line spectroscopy probing the CGM of SMGs with deep optical IFU
observations. The presence of the optically thick absorbers towards both QSOs
suggested that the SMG holds exciting dynamics within its CGM. More
importantly, it provided the metallicity of the gas and excluded the
possibility of metal enriched outflows. Searching for other conjunctions
between QSOs and foreground SMGs can aide our effort for further observational
evidence for cool streams flowing through hot CGMs, as well as help us
prioritize future targets. Additionally, searching for spatially extended
Ly$\alpha$ emission within the trough of the DLA at $z=2.75$ towards QSO1
revealed an unexpectedly large extended Ly$\alpha$ filament within the CGM of
QSO2. Could filamentary structure be a characteristic of CGMs that possess
DLAs? The primary challenge we face is the rarity of the GAMA J0913$-$0107
system. We will need to search for more QSO constellations with foreground
SMGs. Utilizing the latest data releases from large sky surveys, such as the
Dark Energy Spectroscopic Instrument (DESI), can aide our search and enable
future discoveries. Similar to the ongoing QSO Ly$\alpha$ halo studies,
performing large IFU surveys on SMGs, similar to the one studied here, can
help us better understand the CGM of these extreme starbursts.

###### Acknowledgements.

We thank the anonymous referee for their detailed comments that helped improve
the paper. This work is supported by the National Science Foundation (NSF)
grants AST-1614326 and AST-2103251. 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. All analysis software and data used in this study can be found on
the corresponding author’s Github page555https://github.com/kevhall23
Facilities: Keck/KCWI, KiDS

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##  Appendix A Spectroscopic Identifications of Low Redshift Objects in the
Field

Our deep observations of the GAMA J0913$-$0107 system enabled us to acquire
spectroscopic redshifts for multiple low-$z$ objects within the field-of-view.
In this Appendix, we present the spectra of the four foreground objects listed
in Table 1.

Obj 1 at $z=0.054$ is of significant interest due to its nearly overlapping
position relative to the SMG (Figure 1). As a result, we need to make sure
that the emission lines from the foreground galaxy do not interfere with our
analysis of the Ly$\alpha$ line at the SMG redshift ($z=2.674$). To illustrate
any possible line blending, we show KCWI spectra extracted from two slightly
offset aperture in Figure 8. In the top panels, the aperture encloses Obj 1
but avoids the SMG; in the bottom panels, the aperture is more centered on the
SMG. As expected, the Ly$\alpha$ line from the SMG shows up clearly in the
bottom right panel. The SMG Ly$\alpha$ line is well separated from the
H$\gamma$ and H$\delta$ lines of Obj 1. Given this result, it is deemed
unnecessary to mask out Obj 1 while studying extended Ly$\alpha$ emission
around the SMG, although we do need to remove the continuum from the
foreground galaxy.

Figure 9 shows the spectra from the other three foreground objects along with
the positions of their extraction apertures. As the plots illustrate, we
identified that Obj 2 and Obj 4 are [O ii] emitters near $z\sim 0.3$ and that
Obj 3 is a M5-type star666Luminosity class is undetermined from the spectrum
in the Galaxy.

Figure 8: Spectra extracted near Obj 1 from the coadded KCWI datacube. The
left column shows the extracted region by the red aperture, and the right
column displays the spectrum. In the top panel, we shift the aperture away
from the SMG, while we include the position of the SMG by increasing the
aperture in the bottom panel. We mark emission lines from Obj 1 at $z=0.054$,
as well as the Ly$\alpha$ line from the SMG at $z=2.674$.

Figure 9: KCWI spectra from three foreground objects within our field-of-view.
Top: Obj 2 - an [O ii] emitter at $z=0.265$. Middle: Obj 3 - a foreground
M5-type star. For comparison, we overlay a spectrum of a M5V star from Kesseli
et al. (2017). Bottom: Obj 4 - another [O ii] emitter at $z=0.297$.

##  Appendix B Discovery of a Ly$\alpha$ emitter at $z=2.6918$

As we search the KCWI datacube for emission near our three primary targets, we
detected a bright Ly$\alpha$ signal near the position of QSO1. We designate
the Ly$\alpha$ emitter as LAE2 and show its Ly$\alpha$ surface brightness map
in Figure 10. The total integrated Ly$\alpha$ Luminosity within the $\rm
S/N=2$ contour is $3.6\pm 0.1\times 10^{42}$ erg s-1. We show the integrated
spectrum in the right panel of Figure 10 and fit its profile with a Gaussian
profile. The best fit places the redshift of the Ly$\alpha$ line at
$z=2.6918\pm 0.0006$, which is in agreement with the second redshift of the CO
emitter Comp b at $z=2.6917$ (Table 1). The Ly$\alpha$ emission is clearly
extended, it covers a total area of $\approx 20$ arcsec2 ($\approx 1200$
kpc2), and the longest extent of $\approx 90$ kpc along the EW direction.

LAE2 is at $\delta v=+1500$ km s-1 relative to the SMG, making it unlikely to
be part of its CGM. However, there is a DLA near the redshift of LAE2 along
the line of sight towards QSO1 (designated as subsystem C in ; see Figure 6
top left panel). The DLA has two sub-components (C1 and C2) that correspond to
the two CO emission redshifts of Comp b. The proximity of LAE2 to QSO1 and its
redshift establishes it as the most likely host galaxy of the C2 absorber.

We now know that the DLA “subsystem C” has two possible hosts: LAE2 detected
in Ly$\alpha$ by KCWI and Comp b in CO(3-2) by ALMA. The two hosts are
separated by $\sim$7 on the sky. Interestingly, LAE2 is undetected in the deep
ALMA CO datacube, and Comp b does not show any Ly$\alpha$ emission in the KCWI
data. This case illustrates that both optical IFU observations and ALMA
spectral line imaging are needed to unveil the diverse host galaxies of
Ly$\alpha$ absorbers.

Figure 10: Ly$\alpha$ signal at $z=2.692$. In the left panel, we show the
”optimally extracted” Ly$\alpha$ surface brightness map. The position of Comp
b is marked by the red crosshair. The white contours correspond to $\rm
S/N=2$, $5$, $10$. In the right panel, we integrate the flux within the $\rm
S/N=2$ contour and plot the spectrum as a function of the observed wavelength.
The gray region corresponds to the maximum width of the 3D aperture used to
generate the optimally extracted image ($\sim\pm 400$ km s-1). A 1D Gaussian
is used to fit the emission line, and the red curve corresponds to the line of
best fit. The green curve is the error spectrum taken from the same 3D
aperture. The vertical dashed line represents the redshift of LAE2 from the
observed Ly$\alpha$ line.

##  Appendix C Overlapping Ly$\alpha$ Nebulae near QSO1

Figure 11: Full KCWI spectrum extracted from the QSO and continuum subtracted
datacube with an aperture of 2 in radius and centered 15 to the southwest of
QSO1. The spectrum is plotted in the rest-frame of QSO1 ($z=2.916$). The rest-
frame wavelengths of possible UV nebular emission lines are marked by red
vertical lines. The Ly$\alpha$ emission lines associated with the SMG and the
QSO2 are marked by blue and green lines, respectively. The inset provides a
closer look at the Ly$\alpha$ lines associated with the two foreground CGMs
and LAE2 (purple line). No prominent emission lines near the QSO2 redshift is
expected to blend with the Ly$\alpha$ emission lines of the two foreground
targets.

The area around QSO1 is crowded. First, there is a luminous Ly$\alpha$ nebula
around QSO1. Further, the sightline intercepts three (sub-)DLAs at the
redshifts of the SMG, the LAE2 (Appendix B), and the QSO2; and it appears that
the two foreground gas streams seen in Ly$\alpha$ emission also pass in front
of QSO1. Finally, a Ly$\alpha$ emitter LAE2 appears just to the south of QSO1.
Given that QSO1 itself hosts the brightest Ly$\alpha$ nebula among the three
primary galaxies, it is worth investigating whether the detected Ly$\alpha$
emission lines apparently in its foreground were actually shorter wavelength
emission lines at the redshift of QSO1.

In Figure 11, we display the full KCWI spectrum taken from the region of
enhanced Ly$\alpha$ SB at the position of QSO1 in the CGMs of the SMG and QSO2
(Figure 4). Plotted in the rest frame of QSO1, we indicate the wavelengths of
other nebular lines between Ly$\beta$ and Ly$\alpha$ that could have produced
a mis-identified “Ly$\alpha$” line at lower redshifts. The composite spectra
of Lyman break galaxies (Shapley et al., 2003; Jones et al., 2012; Berry et
al., 2012) show an absence of emission lines in this wavelength range. So we
looked into the composite QSO spectrum from the SDSS (Berk et al., 2001) and
found four lines: C iii $1176$ Å, Fe iii $1117$ Å, Ar i $1067$ Å, and O vi
$1034$ Å. As the Figure shows, none of these lines could explain the emission
lines detected between 1135 and 1175 Å in the rest-frame of QSO1. Therefore,
we conclude that it is correct to interpret them as the Ly$\alpha$ lines at
the redshifts of the SMG, the QSO2 redshift, and LAE2.

##  Appendix D Gas Infall/Outflow in QSO1?

The Ly$\alpha$ nebula surrounding QSO1 is not only the brightest out of the
three galaxies studied here, but the moment 1 map reveals clear kinematic
structure. We find that the filamentary structure, that extends nearly $\sim
150$ kpc, is divided into two radial velocity components ($\delta v\sim\pm
300$ km s-1), and the QSO sits near the beginning of this velocity gradient.
We may be observing an outflow within the CGM emanating from the QSO, which
can power the observed Ly$\alpha$ nebula through shocks that form from the
exiting gas. In this scenario, our sightline is edge-on to the direction of
the outflow, and the $\pm\delta v$ components correspond to gas flowing
towards and away from our line of sight, respectively. The large outflow may
explain why QSO1 has a brighter Ly$\alpha$ nebula than QSO2 despite both QSOs
having similar bolometric luminosities.

Recent KCWI observations by Zhang et al. (2023b) of the MAMMOTH-1 Ly$\alpha$
nebula at $z=2.3$ (Cai et al., 2017) show remarkable similarities with QSO1.
Their moment 1 map revealed similar kinematic structure. Specifically, the
velocities are comparable with those detected in QSO1 and the nebula has a
similar morphology. The authors utilize other emission lines (He ii and C iv)
to conclude that the bright nebula may be gas recycling back into the galaxy
from a previous outflow event. From the Ly$\alpha$ line alone, we cannot
speculate any further on the true nature of QSO1’s nebula, but it may warrant
future investigation.