11institutetext:  Instituto de Estudios Astrofísicos, Facultad de Ingeniería y
Ciencias, Universidad Diego Portales, Av. Ejército Libertador 441, Santiago,
Chile [Código Postal 8370191] 11email<EMAIL_ADDRESS>22institutetext: Las Campanas Observatory, Carnegie Institution of Washington,
Casilla 601, La Serena, Chile 33institutetext: Departamento de Astronomía,
Universidad de Concepción,Barrio Universitario, Concepción, Chile
44institutetext: Sterrenkundig Observatorium, Ghent University,
Krijgslaan281-S9, B-9000 Ghent, Belgium 55institutetext: Department of Physics
& Astronomy, University College London, Gower Street, London WC1E 6BT, UK
66institutetext: Max-Planck-Institut für Extraterrestiche Physik (MPE),
Giessen-bachstr., 85748, Garching, Germany 77institutetext: Department of
Physics and Astronomy and George P. and Cynthia Woods Mitchell Institute for
Fundamental Physics and Astronomy, Texas A&M University, College Station, TX,
USA 88institutetext: Faculty of Engineering, Hokkai-Gakuen University,
Toyohira-ku, Sapporo 062-8605, Japan 99institutetext: Joint ALMA Observatory,
Alonso de Córdova 3107, Vitacura, Santiago, Chile 1010institutetext: National
Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903, USA
1111institutetext: Centre for Astrophysics and Supercomputing, Swinburne Univ.
of Technology, PO Box 218, Hawthorn, VIC, 3122, Australia 1212institutetext:
ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D),
Australia 1313institutetext: Institute of Astrophysics, Foundation for
Research and Technology-Hellas (FORTH), Heraklion, 70013, Greece
1414institutetext: Chinese Academy of Sciences South America Center for
Astronomy (CASSACA), National Astronomical Observatories, CAS, Beijing,
100101, PR China 1515institutetext: Scuola Normale Superiore, Piazza dei
Cavalieri 7, I-50126 Pisa, Italy 1616institutetext: Universidad Andrés Bello,
Facultad de Ciencias Exactas, Departamento de Física, Instituto de
Astrofísica, Fernandez Concha 700, Las Condes, Santiago RM, Chile
1717institutetext: Department of Astronomical Science, SOKENDAI (The Graduate
University for Advanced Studies), Mitaka, Tokyo 181-8588, Japan
1818institutetext: National Astronomical Observatory of Japan, 2-21-1 Osawa,
Mitaka, Tokyo 181-8588, Japan 1919institutetext: Instituto de Astrofísica,
Facultad de Física, Pontiﬁcia Universidad Católica de Chile, Santiago 7820436,
Chile 2020institutetext: Dept. Fisica Teorica y del Cosmos, Universidad de
Granada, Granada, Spain 2121institutetext: Instituto Universitario Carlos I de
Física Teórica y Computacional, Universidad de Granada, E-18071 Granada, Spain
2222institutetext: Max-Planck Institute for Astrophysics, Karl
Schwarzschildstrasse 1, 85748, Garching, Germany 2323institutetext: Cavendish
Laboratory, University of Cambridge, 19 J.J. Thomson Avenue, Cambridge, CB3
0HE, UK 2424institutetext: Kavli Institute for Cosmology, University of
Cambridge, Madingley Road, Cambridge, CB3 0HA, UK 2525institutetext: Leiden
Observatory, Leiden University, NL-2300 RA Leiden, Netherlands
2626institutetext: Department of Astronomy, The University of Tokyo, 7-3-1
Hongo, Bunkyo, Tokyo 113-0033, Japan

# The ALMA-CRISTAL survey

Discovery of a 15 kpc-long gas plume in a $z=4.54$ Lyman-$\alpha$ blob

M. Solimano 11 J. González-López 2211 M. Aravena 11 R. Herrera-Camus 33 I. De
Looze 44 5 5 N. M. Förster Schreiber 66 J. Spilker 77 K. Tadaki 88 R. J. Assef
11 L. Barcos-Muñoz 991010 R. L. Davies 1111 12 12 T. Díaz-Santos 11 13 13 14
14 A. Ferrara 1515 D. B. Fisher 1111 12 12 L. Guaita 1616 R. Ikeda 1717 18 18
E. J. Johnston 11 D. Lutz 99 I. Mitsuhashi 2626 18 18 C. Moya-Sierralta 1919
M. Relaño 2020 21 21 T. Naab 2222 A. C. Posses 11 K. Telikova 11 H. Übler
23232424 S. van der Giessen 44 25 25 22 22 V. Villanueva 33

(Received -; accepted -)

Massive star-forming galaxies in the high-redshift universe host large
reservoirs of cold gas in their circumgalactic medium (CGM). Traditionally,
these reservoirs have been linked to diffuse H i Lyman-$\alpha$ (Ly$\alpha$)
emission extending beyond $\approx$$10\text{\,}\mathrm{kpc}$ scales. In recent
years, millimeter/submillimeter observations are starting to identify even
colder gas in the CGM through molecular and/or atomic tracers such as the [C
ii] $158\text{\,}\mathrm{\SIUnitSymbolMicro m}$ transition. In this context,
we study the well-known J1000+0234 system at $z=4.54$ that hosts a massive
dusty star-forming galaxy (DSFG), a UV-bright companion, and a Ly$\alpha$
blob. We combine new ALMA [C ii] line observations taken by the CRISTAL survey
with data from previous programs targeting the J1000+0234 system, and achieve
a deep view into a DSFG and its rich environment at a $None$ resolution. We
identify an elongated [C ii]-emitting structure with a projected size of
$15\text{\,}\mathrm{kpc}$ stemming from the bright DSFG at the center of the
field, with no clear counterpart at any other wavelength. The plume is
oriented $\approx$$None$ away from the minor axis of the DSFG, and shows
significant spatial variation of its spectral parameters. In particular, the
[C ii] emission shifts from
$180\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ to
$400\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ between the bottom and top
of the plume, relative to the DSFG’s systemic velocity. At the same time, the
line width starts at $400-$600\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$
but narrows down to $190\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ at top
end of the plume. We discuss four possible scenarios to interpret the [C ii]
plume: a conical outflow, a cold accretion stream, ram pressure stripping, and
gravitational interactions. While we cannot strongly rule out any of these
with the available data, we disfavor the ram pressure stripping scenario due
to the requirement of special hydrodynamic conditions.

###### Key Words.:

Galaxies: high-redshift – Submillimeter: galaxies – Galaxies: individual:
J1000+0234

##  1 Introduction

The multiphase gas envelope around galaxies, known as the circumgalactic
medium (CGM; e.g., Tumlinson et al. 2017), plays a major role in galaxy growth
and evolution. In particular, its cool phase
($T\lesssim$1\text{\times}{10}^{4}\text{\,}\mathrm{K}$$) hosts the gas
reservoirs needed to fuel star formation and supermassive black hole
accretion. The regulation of these activities requires cool gas to be
transported in and out of the interstellar medium (ISM), in what is called the
baryon cycle (e.g., Péroux & Howk 2020), a process where the CGM is the main
stage. For example, the CGM is the site where galactic scale outflows expand
into (e.g., Veilleux et al. 2020), and where narrow, cold accretion streams
flow into galaxies (e.g., Dekel et al. 2009).

Observationally, cool CGM gas manifests in several ways. For example, it is
routinely detected as H i and/or metal absorption against the backlight of
distant quasars at any redshift (e.g., Werk et al. 2013; Zhu & Ménard 2013;
Turner et al. 2014). In recent years, high metallicity
($[\mathrm{M}/\mathrm{H}]\approx-1$), high column density
($N_{\mathrm{H}}\gtrsim$2\text{\times}{10}^{20}\text{\,}{\mathrm{cm}}^{-2}$$)
absorbers at $z\gtrsim 4$ have been found at distances as large as
$15\text{\,}\mathrm{kpc}45\text{\,}\mathrm{kpc}$ from their host galaxies
(e.g., Neeleman et al. 2017, 2019), further away than similar galaxy-absorber
pairs at low redshift. These results suggest that at high redshift, the cool
CGM was particularly gas-rich.

Additional evidence comes from the diffuse H i Lyman-$\alpha$ (Ly$\alpha$)
emission that surrounds almost every star-forming galaxy at $z\gtrsim 2$, with
exponential scale lengths of $1\text{\,}\mathrm{kpc}10\text{\,}\mathrm{kpc}$
for individual systems (Ly$\alpha$ halos or LAHs; e.g., Wisotzki et al. 2016;
Leclercq et al. 2017; Claeyssens et al. 2022) and up to
$100\text{\,}\mathrm{kpc}$ for the so-called Ly$\alpha$ “blobs” (LABs; e.g.,
Francis et al. 1996; Le Fevre et al. 1996; Steidel et al. 2000; Venemans et
al. 2002; Matsuda et al. 2004), which often host several galaxies, but not
necessarily AGN (Geach et al. 2009). Given the intrinsic complexities in
interpreting the resonant, and highly dust-sensitive Ly$\alpha$ line, the
origins of extended Ly$\alpha$ emission are still unclear. However, most of
the proposed scenarios involve the presence of neutral hydrogen clouds in the
CGM (see Ouchi et al. 2020, for a recent review).

Moving away from the challenges of Ly$\alpha$, deep (sub)millimeter
observations have revealed extended gas reservoirs of colder gas around
high-$z$ galaxies in a variety of environments. For example, several studies
report extended CO and/or [C i] emission around $z\approx 2$ protocluster
cores (Emonts et al. 2014, 2015, 2016, 2018, 2019; Ginolfi et al. 2017; Frayer
et al. 2018; Li et al. 2021; Umehata et al. 2021; Cicone et al. 2021). At even
higher redshifts, the [C ii] $158\text{\,}\mathrm{\SIUnitSymbolMicro m}$ line
becomes easily observable from the ground, and in the past decade it has
proven very efficient at tracing extended gas in both extremely active (i.e.,
quasars or starbursts, e.g., Carniani et al. 2013; Cicone et al. 2015; Ginolfi
et al. 2020a) and normal, less massive systems (Fujimoto et al. 2019, 2020;
Herrera-Camus et al. 2021; Akins et al. 2022; Lambert et al. 2023). In
particular, Fujimoto et al. (2020) finds that roughly 30% of massive, isolated
main sequence galaxies at $4<z<6$ display $10\text{\,}\mathrm{kpc}$-scale “[C
ii] halos”, defined as the cases where significant [C ii] emission is detected
at $10\text{\,}\mathrm{kpc}$ from the source while the UV and far infrared
(FIR) emission are not. Similar objects have been reported with deeper, higher
angular resolution Atacama Large Millimeter/Submillimeter Array (ALMA)
observations than those used by Fujimoto et al. (e.g., Herrera-Camus et al.
2021; Lambert et al. 2023). In all of these cases, however, the origin of
extended [C ii] line emission remains unclear.

In dense regions, tidal interactions, cold accretion, outflows and AGN
feedback seem to contribute to the presence of extended [C ii] line emission.
In contrast, star-formation-driven outflows are often quoted as the most
likely origin of extended [C ii] emission around individual and more isolated
UV-bright galaxies (Fujimoto et al. 2020; Herrera-Camus et al. 2021; Pizzati
et al. 2020, 2023). However, confirming and understanding extended [C ii]
emission at high redshift requires deeper and higher angular resolution ALMA
observations.

CRISTAL stands for “[C ii] Resolved ISm in STar-forming galaxies with ALma”
(Herrera-Camus et al. in prep.), and is an ALMA Cycle 8 Large Program that
observed the [C ii] line and dust continuum emission of 19 main-sequence,
star-forming galaxies at $4<z<6$ with a $\sim$$$ resolution. CRISTAL builds on
top of the highly successful ALPINE survey (Le Fèvre et al. 2020), which
conducted a wider census of [C ii] and dust at $\approx$$$ resolution in the
COSMOS and GOODS-S fields. Out of the 75 [C ii]-detected galaxies in the
ALPINE sample (Béthermin et al. 2020), and based on the multiwavelength
properties presented by Faisst et al. (2020), CRISTAL selected 19 sources that
(1) have a specific SFR within a factor of 3 of the star-forming main sequence
at their corresponding redshift; (2) have HST imaging available; and (3) have
a stellar mass larger than
$\log\left(M_{\mathrm{star}}/\mathrm{M}_{\odot}\right)\geq 9.5$. In addition,
six sources from the ALMA archive that met the selection criteria were added
to the sample, hence the total size of the sample is 25. The survey is
designed to unveil detailed kinematics, search for resolved outflows,
constrain ISM excitation and also probe extended emission.

Since the CRISTAL program targets the massive end of its parent sample, it is
not surprising that many of them show clear signs of multiplicity or
interaction (e.g., Ikeda et al. in prep, Lee et al. in prep., Posses et al. in
prep.). Among them, CRISTAL-01 stands out due to its proximity ($\sim$$None$)
to the well-known sub-millimeter galaxy AzTEC J100055.19+023432.8 at $z=4.54$
(J1000+0234; Capak et al. 2008; Aretxaga et al. 2011). Here, we present new
ALMA observations of this system and report the discovery of a puzzling [C
ii]-emitting gas plume that extends from the center of the system.

The paper is organized as follows: in Sec. 2 we give an overview of the
literature on this particular system. Sec. 3 describes the observations and
reduction of the new ALMA dataset and the ancillary VLT/MUSE and HST data. In
Sec. 4 we detail the analysis steps and present the results characterizing the
[C ii] plume. Next, in Sec. 5 we explore different physical scenarios that
could give rise to the observed emission. Finally, Sec. 6 closes with a
summary and the main conclusions.

Throughout the paper, we adopt a flat $\Lambda$CDM cosmology with
$H_{0}=$70\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{Mpc}}^{-1}$$
and $\Omega_{m,0}=0.3$. Under this assumption,
$1\text{\,}\mathrm{\SIUnitSymbolArcsecond}$ corresponds to
$6.57\text{\,}\mathrm{kpc}$ of proper physical scale at $z=4.54$. When
relevant, we adopted a Chabrier (2003) initial stellar mass function (IMF).

##  2 The J1000+0234 system

Table 1: Global properties of the two main galaxies in the J1000+0234 system.

Property | J1000+0234-North | CRISTAL-01a
---|---|---
Value | Ref. | Value | Ref.
[C ii] redshift | 4.5391 | 1 | 4.5537 | 2
$\log\left(M_{\mathrm{stars}}\right)\,[$\mathrm{M_{\odot}}$]$ | $10.14\pm 0.08$ | 3 | $9.16\pm 0.07$ | 3
$\log\left(M_{\mathrm{dyn}}\right)\,[$\mathrm{M_{\odot}}$]$ | $11.15\pm 0.19$ | 1 | - | -
UV slope $(\beta_{\mathrm{UV}})$ | $-1.01_{-0.32}^{+0.39}$ | 3 | $-2.04_{-0.11}^{+0.12}$ | 3
SFRUV [$\mathrm{M_{\odot}}\text{\,}{\mathrm{yr}}^{-1}$] | $52.6\pm 8.5$ | 3 | $147.6\pm 7.4$ | 3
SFRIR [$\mathrm{M_{\odot}}\text{\,}{\mathrm{yr}}^{-1}$] | $440_{-320}^{+1200}$ | 3 |  $56\pm 35$aa$a$Estimated from the IRX-$\beta_{\mathrm{UV}}$ relation (Meurer et al. 1999) assuming an SMC attenuation law (Bouchet et al. 1985). | -
SFRtot [$\mathrm{M_{\odot}}\text{\,}{\mathrm{yr}}^{-1}$] | $490_{-320}^{+1200}$ | 3 | $204\pm 35$ | -

(1) Fraternali et al. (2021); (2) Béthermin et al. (2020); (3) GG18. 111

In this paper, we study the core region of the J1000+0234 system at $z=4.54$,
first reported by Capak et al. (2008) as a bright sub-millimeter source with
an associated Ly$\alpha$ blob. This region (see Fig. 1) hosts two highly star-
forming galaxies within $\approx$20\text{\,}\mathrm{kpc}$$ in projection
(Gómez-Guijarro et al. 2018, hereafter GG18). It is embedded in a larger scale
overdensity of galaxies (Smolčić et al. 2017; Loiacono et al. 2021), and
possibly linked to the PCI J1001+0220 protocluster (Lemaux et al. 2018). One
of the central galaxies, previously known as J1000+0234-South (GG18) but
hereafter called CRISTAL-01a, contributes $\approx$75% of the total the rest-
frame UV emission of the pair, and belongs to the sample of Lyman-break
galaxies (LBGs) targeted by both the ALPINE and CRISTAL surveys. The other
galaxy, J1000+0234-North, lies merely $None$ from CRISTAL-01a and accounts for
all of the observed submillimeter flux
($S_{$870\text{\,}\mathrm{\SIUnitSymbolMicro m}$}=$7.8\pm
0.2\text{\,}\mathrm{mJy}$$; GG18) and most of the stellar mass
($\approx$2\text{\times}{10}^{10}\text{\,}\mathrm{M_{\odot}}$$; e.g.,
Schinnerer et al. 2008; GG18). Hereafter, we will also refer to it as “the
DSFG” (dusty star-forming galaxy). The global properties of each galaxy are
extracted from the literature and listed in Table 1.

Multiple follow-up studies have targeted J1000+0234 as one of the brightest
and most extreme non-quasar systems known at $z\gtrsim 4$. Until recently, the
general picture depcits CRISTAL-01a and the DSFG undergoing a merger event,
which potentially drives the elevated SFRs (Capak et al. 2008; Schinnerer et
al. 2008; Smolčić et al. 2015; GG18). Yet ALMA observations of the [C ii] line
later revealed that the DSFG rotates fast at
$V_{\mathrm{rot}}\approx$500\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$
with $V/\sigma\gtrsim 9$, suggesting a dynamically cold gas component (Jones
et al. 2017; Fraternali et al. 2021). In other words, the merger is either not
massive enough or has not had time to dynamically disrupt the internal
kinematics of the DSFG. This is consistent with SED models that put the
stellar mass ratio between CRISTAL-01a and the DSFG at $\sim$1:10 (GG18).

Current Chandra pointings do not detect X-rays from J1000+0234, putting an
upper limit on luminosity of about
$1.3\text{\times}{10}^{43}\text{\,}\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}$ in
the 0.5-2 keV band (Smolčić et al. 2015). This value is considerably higher
than the
$1\text{\times}{10}^{42}\text{\,}\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}$
traditional threshold for AGN identification (e.g., Szokoly et al. 2004).
Moreover the DSFG’s radio emission is weak (Carilli et al. 2008), and
consistent with the infrared-radio correlation (Smolčić et al. 2015). However,
Jiménez-Andrade et al. (2023, hereafter J23) recently obtained VLT/MUSE
observations of J1000+0234, that yielded not only a very high fidelity 3D IFU
map of the LAB in which J1000+0234 is embedded, but also the detection of
spatially extended C iv and He ii emission. The authors argue that the high C
iv/Ly$\alpha$ and He ii/Ly$\alpha$ ratios can be explained by the presence of
an AGN in the DSFG. While this claim still needs confirmation, J23 provided a
first view of the complex CGM of J1000+0234, as well as spectroscopic evidence
for the overdensity, after identifying five Ly$\alpha$ emitters within the
MUSE field of view ($1\times 1\,\mathrm{arcmin}^{2}$).

In parallel to the studies focusing on the massive DSFG, CRISTAL-01a was
independently targeted by the ALMA ALPINE survey of [C ii] emission in bright
LBGs (Le Fèvre et al. 2020, therein labeled as DEIMOS-COSMOS 842313). A
successful detection of the line provided the first systemic redshift of this
source at $z=4.5537$ (Béthermin et al. 2020), closely matching the previously
reported Ly$\alpha$ redshift ($z=$4.5520$$; Hasinger et al. 2018). In the next
section, we describe the high-angular resolution ALMA observations obtained by
CRISTAL, along with the rest of the observations used in this article.

##  3 Observations & data reduction

###  3.1 ALMA

We use casa (version 6.5.2, CASA Team et al. 2022) to combine ALMA
observations of the redshifted [C ii] $158\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ line targeting J1000+0234 from three different programs, namely the ALPINE
survey (Le Fèvre et al. 2020), the CRISTAL survey (Herrera-Camus et al. in
prep.), and an archival dataset from project 2019.1.01587.S (PI: F. Lelli).
The ALPINE observations were carried out with the most compact configuration
(C43-1), tuned to cover the line at $349.1\text{\,}\mathrm{GHz}$ with a
velocity resolution of $40\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ and
a natural weighting beam size of
$$1.25\text{\,}\mathrm{\SIUnitSymbolArcsecond}$\times$0.78\text{\,}\mathrm{\SIUnitSymbolArcsecond}$$
(Béthermin et al. 2020). The CRISTAL data, on the other hand, include deeper
integrations in two antenna configurations, namely C43-1 and C43-4, and with a
higher spectral resolution ($10\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$
per channel) than that of the ALPINE data. These observations were designed to
resolve the [C ii] emission with a beam of
$\sim$$0.25\text{\,}\mathrm{\SIUnitSymbolArcsecond}$, equivalent to
$1.65\text{\,}\mathrm{kpc}$ at $z=4.54$. Finally, the 2019.1.01587.S dataset
was observed using a longer baseline configuration (C43-6), providing a
nominal resolution of $None$. However, the spectral windows were tuned around
the DSFG’s rest-frame velocity, so the frequency overlap with previous data is
partial and only covers the red half of CRISTAL-01a’s emission line. We do not
include data from the Cycle 2 program 2012.1.00978.S (PI: A. Karim; Jones et
al. 2017; Fraternali et al. 2021) into the combined dataset, because its
shallower depth plus the complexities of weighting data that was processed
with old versions of the
pipeline222https://casaguides.nrao.edu/index.php/DataWeightsAndCombination
would have resulted in a marginal improvement.

In addition, thanks to the brightness of the DSFG we performed self-
calibration on the continuum visibilities of both ALPINE and CRISTAL datasets
before combination. This was done in two “phase-only” rounds for each
observation, the first one combining spectral windows and scans, and the
second one only the scans (of average length
$\approx$180\text{\,}\mathrm{s}$$). This process resulted in a $\approx$11%
decrease in continuum rms and the mitigation of patchy patterns in the noise.

Finally, the self-calibrated and combined measurement sets were processed with
CRISTAL’s reduction pipeline as described in Herrera-Camus et al. (in prep.).
Briefly, it starts by subtracting the continuum on the visibility space using
casa’s `uvcontsub` task. After that, it runs `tclean` with automasking
multiple times, producing cubes with different weightings and channel widths.
In all cases the data are cleaned down to $1\sigma$. In this paper, we use
datacubes with $20\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ channel
width and either natural or Briggs (`robust=0.5`) weighting.

Since the data combines different array configurations, it is important to
measure and apply the “JvM” correction (Jorsater & van Moorsel 1995). We do
this by following the method of Czekala et al. (2021). This correction takes
into account the significant deviations from Gaussianity that the core of the
dirty beam can have in multi-array observations and ensures that both the
convolved CLEAN model and the residuals have compatible units. While the
CRISTAL pipeline provides JvM-corrected products, it uses a single correction
factor per spectral window. Since we combine multiple datasets from different
projects, the uv coverage has significant variations within a spectral window.
For this reason, we compute and apply the correction in channel ranges with
similar beam properties. We find a mean multiplicative correction factor of
$\epsilon\approx 0.37$ in the channels covering the [C ii] line emission when
using Briggs weighting, and $\epsilon\approx 0.31$ when using natural
weighting.

###  3.2 MUSE

We retrieved observations of the J1000+0234 field from the ESO archive taken
with the Multi Unit Spectroscopic Explorer (MUSE) instrument mounted on the
Very Large Telescope (UT4-Yepun) using ground-layer adaptive optics and the
Wide Field Mode. These observations, comprising 16 exposures of
$900\text{\,}\mathrm{s}$ (total $4\text{\,}\mathrm{h}$), were taken as part of
ESO GTO programs 0102.A-0448 (PI: S. Lilly) and 0103.A-0272 (PI: S. Cantalupo)
under good weather conditions with average seeing of
$0.9\text{\,}\mathrm{\SIUnitSymbolArcsecond}$ and airmass below 1.4. Here we
use an independent reduction from that of J23, but we refer the reader to
their work for further details about the observations.

The standard calibrations and procedures are performed using the MUSE pipeline
(version 2.8.3; Weilbacher et al. 2020) within the ESO Recipe Execution Tool
(EsoRex) environment (ESO CPL Development Team 2015). The wavelength solution
is set to vacuum. We then apply the Zurich Atmosphere Purge (ZAP, version 2.1;
Soto et al. 2016) post-processing tool to further remove sky line residuals.
As described by J23, half of the exposures were affected by intra-dome light
contamination, resulting in excess counts between
$8000\text{\,}\mathrm{\text{Å}}$ and $9000\text{\,}\mathrm{\text{Å}}$. We
decided to use all the exposures in the combined datacube regardless, since
the issue does not affect wavelengths near the Ly$\alpha$ emission at
$6742\text{\,}\mathrm{\text{Å}}$. We then follow the steps described in
Solimano et al. (2022) to scale the variance cube and match the observed noise
levels. Finally, we apply a simple 2D translation to the WCS to match the
positions of the two Gaia DR2 (Gaia Collaboration et al. 2018) sources in the
field. We check the alignment of the cube with respect to HST by producing
pseudo broadband image from the ACS/F814W filter curve. Matching sources in
the MUSE pseudo-F814W image and the ACS/F814W image yield an astrometric rms
of 220 mas, or about one MUSE pixel.

The resulting datacube yields a $1\sigma$ noise level of
$\approx$$1\text{\times}{10}^{-19}\text{\,}\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{cm}}^{-2}\text{\,}{\mathrm{arcsec}}^{-2}$
per spectral layer around $6750\text{\,}\mathrm{\text{Å}}$, computed from
randomly placed apertures of $1\text{\,}{\mathrm{arcsec}}^{2}$ area. The
datacube is sampled at pixel scale $None$ and spectral layers have a width of
$1.25\text{\,}\mathrm{\text{Å}}$. We fit a Moffat profile to an
$r=19\,\mathrm{mag}$ G-type star in the field and find a point spread function
(PSF) FWHM of $None$ around $6750\text{\,}\mathrm{\text{Å}}$. At this
wavelength, the instrument yields a resolving power of $R=$2538$$.

###  3.3 HST

We retrieved from
MAST333https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html all the
available HST data for the J1000+0234 field. We found observations in the
ACS/F606W, ACS/F814W, WFC3/F105W, WFC3/F125W and WFC3/F160W bands, covering
$1000\text{\,}\mathrm{\text{Å}}3200\text{\,}\mathrm{\text{Å}}$ in the rest-
frame at $z=4.54$. Images were processed using the standard pipeline, co-added
and aligned to Gaia DR2 (Gaia Collaboration et al. 2018). All images were then
drizzled with a square kernel and a pixel fraction of $0.5$ using the
astrodrizzle routine from DrizzlePac (STSCI Development Team 2012; Hack et al.
2021), executed within the grizli pipeline (Brammer 2023). ACS images were
drizzled to a common pixel size of $None$ while for WFC3/IR images we used a
pixel size of $None$.

Figure 1: HST, Ly$\alpha$, and [C ii] morphologies. (a). $$$\times$$$ cutout
of the WFC3/F160W image in grayscale. The blue-filled contours represent
$\left\\{1,5,16,30\right\\}\times
10^{-18}\,$\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{cm}}^{-2}\text{\,}{\mathrm{arcsec}}^{-2}$$
levels of Ly$\alpha$ surface brightness based on the adaptive narrowband image
described in the main text. The diameter of the blue circle represents the
FWHM$=$$$ of the PSF of the VLT/MUSE observations. The orange box outlines the
$$$\times$$$ zoom-in region displayed in the next panels. (b). ALMA Band 7
continuum image in logarithmic stretch. The white contours follow [C ii]
emission at
$\left\\{0.01,0.03,0.07,0.2,0.5\right\\}\times$\mathrm{Jy}\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{beam}}^{-1}$$,
and highlight the non-detection of dust continuum in either CRISTAL-01a or the
plume. (c). Adaptively-masked [C ii] velocity field (moment-1). A single
colormap is assigned separately to the DSFG and CRISTAL-01a. The midpoint of
the colormaps matches their corresponding systemic velocity, with the zero set
at the redshift of the DSFG, $z_{\mathrm{[CII]}}=4.5391$. Again, overlaid
contours show increasing levels of [C ii] SB. The dashed line indicates the
projected rotation axis at a $\mathrm{PA}=$$$ through the [C ii] kinematic
center of the DSFG (see Appendix A). (d). Adaptively-masked [C ii] velocity
dispersion map (moment-2), with [C ii] SB contours.

##  4 Results & Analysis

###  4.1 Adaptive masking of datacubes

Extracting the total flux and spatial extent of the different types of
emission considered here, requires taking into account the contributions of
faint and diffuse components. Now, given the complexity and spatial variations
of the Ly$\alpha$ and [C ii] profiles in the J1000+0234 system, a simple
pseudo-narrowband “collapse” around the line will hide narrow and low surface
brightness (SB) features below the noise level. Instead, we adopt an adaptive
approach based on the “matched filtering” technique. This involves creating a
3D mask that takes into account the line morphology. For the MUSE data, we
used the off-the-shelf software LSDcat (Herenz & Wisotzki 2017), while for the
ALMA cubes we used a custom script.

LSDcat works by building an optimized S/N detection derived from the cross-
correlation of the data with a template signal. Here, we first removed the
continuum emission by running a median filter over the spectral axis across
the full wavelength range of the cube, using the default window width of 151
spectral pixels ($188.75\text{\,}\mathrm{\text{Å}}$). This step yields a
continuum-only datacube which is then subtracted from the original cube. The
next step is optimized for our blind search of Ly$\alpha$ emitters in the
cube, but it also performs well on enhancing the low SB features. The results
of our search and the subsequent characterization of the detected objects will
be presented in a separate paper.

Following Herenz & Wisotzki (2017) we built our template as a point-like
source with a Gaussian spectral profile of
$\mathrm{FWHM}=$250\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$, a choice
that maximizes sensitivity to faint and compact line emitters. After
convolving the continuum-subtracted cube by the PSF (spatial filter), we
convolved the resulting cube with a
$250\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ Gaussian kernel (spectral
filter) to construct the 3D matched filter output. We took into account the
wavelength dependence of the PSF by fitting 2D Moffat profiles to an isolated
bright star in the original cube, using 20 wavelength bins. We simultaneously
fit the Moffat parameters’ dependence on wavelength using 3rd and 2nd order
polynomials, for the FWHM and power index parameters, respectively. These
polynomials were then used to interpolate the PSF to all the channels of the
cube. Then, we computed the detection S/N cube as the voxel-by-voxel ratio
between the filtered datacube and the square root of the propagated variances.

Finally, we selected all voxels with $\mathrm{S/N}\geq 2$ between
$6729\text{\,}\mathrm{\text{Å}}$ and $6776\text{\,}\mathrm{\text{Å}}$
(equivalent to a velocity range of
[$-947\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$,
$1135\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$]). To refine the
selection, we exclude spaxels in which less than three voxels are above the
S/N threshold. Furthermore, we create a 2D mask of the spaxels that satisfy
these conditions and subsequently prune the regions with less than 55
connected spaxels. We find that this number successfully masks any remaining
spurious signal. After we remove the corresponding voxels, we apply the
resulting 3D mask to the data, and integrate along the wavelength axis. The
result is shown in Fig. 1a as filled contours overlaid on top of an HST image.
We recover an irregular and extended Ly$\alpha$ morphology down to
$1\text{\times}{10}^{-18}\text{\,}\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{cm}}^{-2}\text{\,}{\mathrm{arcsec}}^{-2}$,
in agreement with J23. The highest SB emission is centered on CRISTAL-01a, but
extends to a secondary peak $\sim$$$ to the southwest.

We applied a similar procedure to the [C ii] cube. Starting from the
naturally-weighted cube binned in
$20\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ channels, we convolved with
a $\sigma=$30\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$ Gaussian kernel
along the velocity axis, and a $\sigma=$$$ 2D Gaussian kernel in the spatial
axes. We then measured the rms in the signal-free regions of the convolved
cube. Finally, we split cells above and below a $2\times\mathrm{rms}$
threshold into a 3D mask, which we then fed to casa task `immoments` to obtain
the intensity, velocity, and velocity dispersion maps from the original cube
(as shown from panels b to d in Fig. 1).

This approach recovers the bright [C ii] emission from the DSFG but also
reveals faint and extended emission in CRISTAL-01a, and most notably, in a
$None$-long plume extending north of the DSFG. We note, however, that this
elongated diffuse emission was already apparent in the individual channels of
our cubes, as will be discussed in Sec. 4.3. The intensity map spans more than
two orders of magnitude in SB, from
$0.01\text{\,}\mathrm{Jy}\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{beam}}^{-1}$
(outermost contour in Fig. 1b-d) to
$2.5\text{\,}\mathrm{Jy}\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{beam}}^{-1}$
at the center of the DSFG, equivalent to
$5\text{\times}{10}^{5}\text{\,}\mathrm{L_{\odot}}\text{\,}{\mathrm{kpc}}^{-2}$
and
$1.25\text{\times}{10}^{8}\text{\,}\mathrm{L_{\odot}}\text{\,}{\mathrm{kpc}}^{-2}$
respectively at $z=4.54$. If we take the [C ii] SB as a tracer of SFR surface
density, according to the local
$\Sigma_{\mathrm{[CII]}}-\Sigma_{\mathrm{SFR}}$ relation (Herrera-Camus et al.
2015), the lower limit would correspond to
$\Sigma_{\mathrm{SFR}}=$0.01\text{\,}\mathrm{M_{\odot}}\text{\,}{\mathrm{yr}}^{-1}\text{\,}{\mathrm{kpc}}^{-2}$$,
which is well within the regime of normal star-forming galaxies in the Local
Universe from the KINGFISH sample (Kennicutt et al. 2011).

In the velocity space, significant [C ii] emission spans from
$-500\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ to
$850\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ across smooth gradients
(see Fig. 1c). The main gradient goes along the major axis of the DSFG, as
previously found by Jones et al. (2017) and Fraternali et al. (2021).
Interestingly, the plume displays a gradient along its long axis, with a mild
increase in velocity as one moves away from the DSFG. While the plume meets
the DSFG in the approaching side, the velocity of the plume overlaps with that
of the receding side of the DSFG. Finally, CRISTAL-01a’s [C ii] emission is
centered at $v\approx$800\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$, and
shows a more irregular gradient approximately aligned with the minor axis.

The velocity dispersion (Fig. 1d), on the other hand, is largest at the center
of the DSFG, with the other structures showing low values
($\sigma\lesssim$100\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$) and
little to no variation.

###  4.2 Parametric morphology

In this section we study the morphological parameters of the two galaxies,
CRISTAL-01a and the DSFG, in the J1000+0234 system. To this end, we make use
of 2D light profile modeling code PyAutoGalaxy (Nightingale et al. 2023) built
on top of the PyAutoFit (Nightingale et al. 2021) probabilistic programming
framework. While PyAutoGalaxy is capable of directly fitting the
interferometric visibilities, in this paper we used the image-based fitter for
a faster workflow. We account for the noise correlation in the images by
feeding the full covariance matrix into the calculation of the likelihood. The
covariance matrix is estimated in source-free regions of the image using the
method and the code444ESSENCE, Tsukui et al. 2023 presented by Tsukui et al.
(2022).

We start by modeling the DSFG, which shows a regular and almost symmetric
shape. For this reason, we choose to fit a single 2D Sérsic profile (Sersic
1968), with a total of seven free parameters.

We performed two independent fits. One for the rest-frame
$160\text{\,}\mathrm{\SIUnitSymbolMicro m}$ continuum map shown in panel b of
Fig. 1, and the other for the [C ii] integrated intensity map. However, we
refrained from using the adaptive intensity map, since the noise properties
are not well defined after the masking procedure. Instead, we used regular,
unmasked intensity maps integrated within a given velocity range. For the
DSFG, we integrated between $342.293\text{\,}\mathrm{GHz}$ and
$344.006\text{\,}\mathrm{GHz}$, corresponding to a bandwidth of
$1492.7\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$. For the center
coordinates and the effective radius, we adopted broad Gaussian priors
centered on previously published values (Fraternali et al. 2021). For the
intensity parameter we adopted a uniform prior between 0 and the maximum
surface brightness of the image. Finally, based on previous work that
characterized this source as a disk (e.g. Jones et al. 2017), we adopt a
Gaussian prior for the Sérsic index centered at $n=1$ (exponential disk) with
a $\sigma=1$, but allowed $n$ to vary between 0.2 and 10.

The parameter space was explored using the dynesty (Speagle 2020; Koposov et
al. 2022) nested sampler backend with 50 live points. Table 2 lists the
results of fitting with the parameters values and uncertainties drawn from the
Bayesian posterior probability distribution.

Table 2: Results of the parametric 2D fitting of exponential profiles to the
$160\text{\,}\mathrm{\SIUnitSymbolMicro m}$ continuum and [C ii] line maps of
the DSFG.

Property | Value
---|---
$160\text{\,}\mathrm{\SIUnitSymbolMicro m}$ continuum
Center (RA) | $10^{\mathrm{h}}00^{\mathrm{m}}54.49129^{\mathrm{s}}\pm 0.00002^{\mathrm{s}}$
Center (Dec.) | $$$\,\pm\,$$$
$R_{\mathrm{eff}}$ [pkpc] | $0.740\pm 0.003$
Sérsic index ($n$) | $1.29\pm 0.01$
Axis ratio (minor/major) | $0.400\pm 0.002$
Flux density [$\mathrm{mJy}$] | $8.03\pm 0.03$
PA [degrees] | $57.8\pm 0.1$
[C ii] emisison
Center (RA) | $10^{\mathrm{h}}00^{\mathrm{m}}54.4904^{\mathrm{s}}\pm 0.0003^{\mathrm{s}}$
Center (Dec.) | $$$\,\pm\,$$$
$R_{\mathrm{eff}}$ [pkpc] | $1.13\pm 0.04$
Sérsic index ($n$) | $0.71\pm 0.08$
Axis ratio (minor/major) | $0.34\pm 0.01$
Integrated flux [$\mathrm{Jy}\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$] | $7.8\pm 0.3$
PA [degrees] | $57.4\pm 0.8$
555Radii are circularized and given in physical kiloparsecs (pkpc).

Our analysis reveals that the [C ii] and dust morphologies are slightly
different in the DSFG. The effective radius of the gas component is
approximately 1.5 times larger than that of the dust, while the axis ratio is
smaller. However, since the Sérsic indices and the S/N are not equal between
[C ii] line and $160\text{\,}\mathrm{\SIUnitSymbolMicro m}$ continuum, we
refrain from claiming the gas is more extended than the dust. Assuming instead
that the dust and gas both have disk-like geometries, share the same
inclination, and are optically thin, the difference in axis ratio suggests
that the dust component is thicker in the polar direction relative to the gas
component. The higher Sérsic index also indicates that dust is more centrally
concentrated, yet the residual continuum map shows significant features that
extend beyond the central region and do not follow axial symmetry (see middle
row of Fig. 2).

Next, we move to CRISTAL-01a and fit only the [C ii] emission, since the
continuum was not detected. We construct the unmasked intensity map by
integrating the cube between $342.088\text{\,}\mathrm{GHz}$ and
$342.454\text{\,}\mathrm{GHz}$, which encloses only 85% of the total line flux
but maximizes the S/N of the map. The source clearly breaks into two
subcomponents, resembling the rest-frame UV morphology, albeit offset
$\approx$$None$ to the Southwest. We thus model the emission with two
independent profiles, an elliptical 2D Sérsic for the brighter component
(hereafter SW clump) and a circular Gaussian profile for the fainter component
(hereafter NE clump). This model has a total of 11 free parameters. For the SW
clump we use the same prior on the Sérsic index as before. For the rest of the
quantities we use either broad uniform or Gaussian priors covering reasonable
limits in the parameter space.

Figure 2: Results from parametric 2D modeling with PyAutoGalaxy. Each row
shows a different source and/or image. Left column displays the observed
emission, while the right column shows the residuals after subtracting the
maximum likelihood model. The first and second rows show the modeling of the
DSFG’s [C ii] emission and $160\text{\,}\mathrm{\SIUnitSymbolMicro m}$ dust
continuum, respectively. Black contours represent the $\pm 3,9,27$ and
$81\sigma$ levels. Results for the [C ii] emission of CRISTAL-01a (CRISTAL-1)
are shown in the third row. Here, the contours only trace $\pm 3,4$ and
$5\sigma$ levels.

The best-fit parameters and uncertainties from this fit are listed in Table 3.
The right panel of Fig. 2 shows the 2D residuals. Notably, the SW clump alone
has twice the effective radius of the DSFG’s [C ii] emission and more than
three times the radius of its dust emission. This size is comparable to
previous measurements performed on the F814W imaging (Fujimoto et al. 2020).
If we were to associate the [C ii] clumps to the two UV clumps seen by HST, we
notice the brightness order is inverted. The SW clump’s [C ii] line flux
density is about ten times that of than the NE clump. Yet in the UV, the NE
clump is brighter. This discrepancy could be attributed to differences in dust
attenuation. In fact, GG18 provided maps of the rest-frame UV
$\beta_{\mathrm{UV}}$ slope based on the HST imaging, and they show that the
southern part of CRISTAL-01a is slightly redder
($\beta_{\mathrm{UV}}\approx-2.0$) than the northern part
($\beta_{\mathrm{UV}}\approx-2.2$).

Table 3: Results of the parametric 2D fitting to the [C ii] line map of
CRISTAL-01a.

Property | Value
---|---
SW clump
Center (RA) | $10^{\mathrm{h}}00^{\mathrm{m}}54.505^{\mathrm{s}}\pm 0.003^{\mathrm{s}}$
Center (Dec.) | $$$\,\pm\,$$$
$R_{\mathrm{eff}}$ [pkpc] | $2.4\pm 0.4$
Sérsic index ($n$) | $1.0\pm 0.3$
Axis ratio (minor/major) | $0.82\pm 0.09$
Integrated flux [$\mathrm{Jy}\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$] | $0.39\pm 0.08$
PA [degrees] | $175\pm 45$
NE clump
Center (RA) | $10^{\mathrm{h}}00^{\mathrm{m}}54.537^{\mathrm{s}}\pm 0.02^{\mathrm{s}}$
Center (Dec.) | $$$\,\pm\,$$$
$R_{\mathrm{eff}}$ [pkpc] | $0.8\pm 0.3$
Integrated flux [$\mathrm{Jy}\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$] | $0.03\pm 0.02$
Total fluxaa$a$Flux has been corrected by a factor 1.17 to account for emission outside the velocity integration range. (SW + NE)[$\mathrm{Jy}\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$] | $0.5\pm 0.2$
Centroid separation [arcsec] | $0.63\pm 0.06$
666The table separates the fitted parameters for each clump. Radii are
circularized and given in physical kiloparsec (pkpc).

###  4.3 Spectral properties of the [C II]-emitting plume

While the adaptive masking scheme described in Sect. 4.1 helped us identify
all the [C ii] signal present in the cube and unveil the general kinematic
trends, the noise properties of the masked maps in Fig. 1 remain undefined.
Moreover, since our data display a large dynamic range in both surface
brightness and velocity dispersion, the details of the plume are partly
outshined by the DSFG. In order to get a clearer picture of the plume, Fig. 3
displays eight consecutive channel maps of
$40\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ width, covering from
$200\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ to
$480\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ relative to the systemic
velocity of the DSFG.

Figure 3: Selected channel maps from the low-resolution [C ii] datacube binned
to $40\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$. Black contours
represent 3, 5 and 7 times the JvM-corrected noise rms level, while the gray
contours show the negative $3\times\mathrm{rms}$ level. The purple cross in
each channel indicates the origin of the coordinates, at
$\alpha_{\mathrm{ICRS}}=$$$, $\delta_{\mathrm{ICRS}}=$$$.

The limits of the colormap in Fig. 3 were chosen to highlight the faint
extended emission and to give a visual reference of the noise amplitude. On
top of it, we show contours at different levels of statistical significance.
All eight channel maps exhibit large patches of $\geq 3\sigma$ emission
distributed between $None$ and $None$ northward from the DSFG kinematic center
(purple cross). In the first row of panels we can see that the plume grows
longer at higher velocities, reaching a maximum isophotal extent of
$\approx$$=$13.8\text{\,}\mathrm{kpc}$$ at
$360\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ (bottom left panel). In
the subsequent channels, the plume becomes fainter and clumpy in appearance,
possibly due to the lower S/N. We note that the DSFG centroid shifts
coherently to the southeast as a result of rotation.

We now want to quantify the spatial variations of the spectral profile along
the plume with a proper treatment of the noise. To this end, we place six
adjacent rectangular $$$\times$$$ apertures covering the full extent of the
plume as seen in Fig. 4, oriented with a position angle of $None$ east of
north. We extract the spectra from the Briggs-weighted (robust=0.5) datacube
without continuum subtraction. With this weighting, the synthesized beam
($$$\times$$$) fits comfortably within each aperture, making them independent.

We then fit each extracted spectrum independently with a single 1D Gaussian,
except for the first two apertures, where we include a first-order polynomial
to model the continuum from the DSFG. In these apertures we also mask emission
from $-700\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ to
$0\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ to avoid contamination from
the approaching side of the DSFG.

Once again, we use PyAutoFit with the Dynesty (Speagle 2020; Koposov et al.
2022) static nested sampler as a backend. We assume a Gaussian likelihood for
the sum of the rms-weighted residuals (data minus model). For every channel
(of width $20\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$), we measure the
rms as the $3\sigma-$clipped standard deviation of the flux densities of 300
random apertures with the same size and orientation as the extraction
apertures. We adopt uniform priors for the three fitted parameters, namely the
velocity center between $-200\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$
and $1000\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$; the FWHM between
$60$ and $1000\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$; and the total
flux between 0 and
$1.0\text{\,}\mathrm{Jy}\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$.

Figure 4 and Table 4 show the results of these fits as a function of the
distance of each aperture from the center of the DSFG. We recognize radial
trends in all the three parameters, and a large gap between apertures #1 and
#2. This apparent discontinuity could be due to additional contamination in
aperture #1’s spectrum at positive velocities. For this reason, we subtract a
velocity-inverted spectrum from an aperture that mirrors aperture #1 by the
projected rotation axis (dashed line Fig. 4) and repeat the fit. After this
correction, we find both lower fluxes and FWHM, but a consistent central
velocity, as shown by the white-filled markers in Fig. 4. These differences
illustrate the systematic uncertainties associated with aperture #1, that make
flux and FWHM less reliable.

Regardless of which fit we consider for the first aperture, we identify a
radially decreasing trend for the flux density (or surface brightness). From
$5\text{\,}\mathrm{kpc}$ to $15\text{\,}\mathrm{kpc}$ the flux drops almost
exponantially, with an excess at $\approx$$13\text{\,}\mathrm{kpc}$. Summing
apertures from #2 to #6 yields a total flux of $0.50\pm
0.04\text{\,}\mathrm{Jy}\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$, which
closely matches CRISTAL-01a’s total flux (Table 3) and amounts to a [C ii]
luminosity of $(3.1\pm 0.25)\text{\times}{10}^{8}\text{\,}\mathrm{L_{\odot}}$.
Adding aperture #1 will raise this number by a factor of 2.53 under the
original fitting scheme, and by a factor of 1.61 with the corrected fit.

In the middle panel of the left row we can see a decrease in the line width as
one moves further out in the plume. Starting from
$400-600\,$\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$ at
$2.5\text{\,}\mathrm{kpc}$, the plume narrows down to
$180_{-38}^{+64}\,$\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$ in the outermost
aperture. We note that at low S/N the fits tend to bias the FWHM to larger
values, hence the intrinsic FWHMs of the outermost bins might be even lower
than depicted here.

Our aperture-based measurements recover the velocity gradient that we had seen
in the velocity map in Fig. 1c. Here, both methods to extract the spectrum of
aperture #1 yield consistent central velocities at
$v_{\mathrm{cen}}\approx$180\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$.
The next aperture (#2) is already at
$300\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$, suggesting a steep
velocity gradient between apertures #1 and #2. In the subsequent apertures,
the increase in velocity is less abrupt, going from
$\approx$300\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$ to
$\approx$400\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$ in the outer
$10\text{\,}\mathrm{kpc}$.

In addition, we create custom intensity maps for each aperture, integrating
over a velocity window of size 1.1 times the best-fit spectral FWHM for
maximal S/N. On these maps we obtain 1D spatial profiles along the long side
of the corresponding aperture, but extended to
$\pm$3\text{\,}\mathrm{arcsec}$$. We then fit a Gaussian to these profiles to
obtain the transversal (spatial) FWHM of the plume. After deconvolving the
beam width, we obtain FWHMs between $None$ and $None$ with an average of
$None$, but no clear radial trend.

Finally, we put upper limits on the FIR luminosity surface density of each
aperture based on the continuum depth. To this end, we randomly placed $600$
rectangular apertures of size $$$\times$$$ on the rest-frame
$160\text{\,}\mathrm{\SIUnitSymbolMicro m}$, `robust=0.5` continuum map
(without JvM correction). We obtain a distribution of flux densities with
$\sigma-$clipped standard deviation of
$\sigma=$38.8\text{\,}\mathrm{\SIUnitSymbolMicro Jy}$$. Taking $5\sigma$ as
the detection limit, we convert the flux density into FIR luminosity777Defined
as the integral of the rest-frame SED between
$42\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and
$122\text{\,}\mathrm{\SIUnitSymbolMicro m}$. assuming an underlying
$T_{\mathrm{dust}}=$45\text{\,}\mathrm{K}$$ modified blackbody dust SED, with
a dust emissivity index $\beta_{\mathrm{dust}}=1.5$ (a choice that roughly
describes the average SED of star-forming galaxies at $z>4$, e.g., Béthermin
et al. 2020). Such an SED gives the ratio $\nu
L_{\nu}($158\text{\,}\mathrm{\SIUnitSymbolMicro m}$)/L_{\mathrm{FIR}}=0.185$.
After correcting for primary beam gain decrement, we quote the resulting
limits in Table 4, except for aperture #1 where emission from the DSFG
dominates. We note, however, that these values depend on the assumed
temperature. For example, choosing $T_{\mathrm{dust}}=$55\text{\,}\mathrm{K}$$
and $T_{\mathrm{dust}}=$65\text{\,}\mathrm{K}$$ produce $1.7\times$ and
$2.4\times$ higher $L_{\mathrm{FIR}}$ limits, respectively. In any case, these
measurements allow us to estimate the [C ii]/FIR diagnostic, which informs
about the heating mechanism of the gas. At
$T_{\mathrm{dust}}=$45\text{\,}\mathrm{K}$$ we obtain lower limits on the [C
ii]/FIR ratio between $\approx$0.2% (aperture #6) and $\approx$0.6% (aperture
#2). Unfortunately, these lower limits are not high enough to rule out UV
photoelectric heating, characteristic of photodisocciation regions (PDRs; with
typical [C ii]/FIR ratios between 0.01% and 2%, e.g., Herrera-Camus et al.
2018), in favor of other mechanisms such as shock heating ($\gtrsim 4\%$,
e.g., Appleton et al. 2013; Peterson et al. 2018). Only at the coldest
possible temperatures, $T_{\mathrm{dust}}\lesssim$20\text{\,}\mathrm{K}$$
($T_{\mathrm{CMB}}=$15\text{\,}\mathrm{K}$$), the highest limit becomes [C
ii]/FIR $>6.8\%$, and thus harder to explain with UV photoelectric heating
alone.

Figure 4:  Spatial variation of spectral properties of the [C ii] plume. Left:
Radial profiles of fitted 1D Gaussian parameters in six apertures along the
plume, as a function of projected distance from the kinematic center of the
DSFG. The parameters shown are the integrated flux (top), the line FWHM
(middle) and velocity centroid (bottom). White-filled markers in the first bin
indicate best-fit values for the innermost spectrum after reducing
contamination with our symmetric difference method. Center: [C ii] intensity
map integrated from $58\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ to
$536\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$, with black contours at
the $\left\\{\pm 2,3,15,50,150\right\\}\times\sigma$ SB level. Red rectangles
numbered from 1 to 6 delineate the extraction apertures along the plume. The
cyan star and pink cross mark the position of the rest-UV and the [C ii]
kinematic centroids, respectively. The dashed line extrapolates the minor axis
of the DSFG’s [C ii] integrated emission at a PA=$None$ (see Sec. 4.2). The
line intersects the first rectangular aperture, defining a polygonal subregion
where we extract the spectrum for symmetric difference analysis (see Appendix
A). Right: Extracted spectra from the six rectangular apertures, with their
number labeled in red. The black solid line in each panel shows the maximum
likelihood fit, while the orange lines are random samples from the posterior
probability distribution. In panels 1 and 2 the shaded area indicates the
velocity range excluded from the fit. The dash-dotted line shows the best-fit
continuum component.  Table 4: Extracted quantities from the apertures in Fig.
4

Aperture | Flux density | $v_{\mathrm{cen}}$ | FWHM | $\Sigma_{\mathrm{[CII]}}$ |  ${\Sigma_{\mathrm{FIR}}}$bb$b$Limits on the far-infrared luminosity were estimated from the $5\sigma$ depth of the rest-frame $160\text{\,}\mathrm{\SIUnitSymbolMicro m}$ continuum map, and assuming a modified blackbody SED of $T_{\mathrm{dust}}=$45\text{\,}\mathrm{K}$$ and $\beta_{\mathrm{dust}}=1.5$, which yields $\nu L_{\nu}($158\text{\,}\mathrm{\SIUnitSymbolMicro m}$)/L_{\mathrm{FIR}}=0.185$. | $v_{\mathrm{out}}$ | $M_{\mathrm{out}}$ | $\dot{M}_{\mathrm{out}}$
---|---|---|---|---|---|---|---|---
# | $\mathrm{Jy}\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ | $\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ | $\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ | $1\text{\times}{10}^{6}\text{\,}\mathrm{L_{\odot}}\text{\,}{\mathrm{kpc}}^{-2}$ | $1\text{\times}{10}^{10}\text{\,}\mathrm{L_{\odot}}\text{\,}{\mathrm{kpc}}^{-2}$ | $\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ | $1\text{\times}{10}^{7}\text{\,}\mathrm{M_{\odot}}$ | $\mathrm{M_{\odot}}\text{\,}{\mathrm{yr}}^{-1}$
1aa$a$Values in this row were extracted from the spectrum corrected via the symmetric difference scheme (white filled circles in Fig. 4, see Appendix A). | $0.27_{-0.03}^{+0.05}$ | $166_{-54}^{+31}$ | $454_{-81}^{+65}$ | $10.6_{-1.3}^{+2.1}$ | - | $551\pm 75$ | $25\pm 3$ | $83\pm 18$
2 | $0.18_{-0.02}^{+0.03}$ | $297_{-17}^{+19}$ | $377_{-59}^{+73}$ | $7.3_{-0.9}^{+1.0}$ | $<1.3$ | $617\pm 56$ | $17\pm 2$ | $64\pm 11$
3 | $0.10_{-0.02}^{+0.02}$ | $318_{-23}^{+27}$ | $306_{-58}^{+86}$ | $4.0_{-0.7}^{+0.7}$ | $<1.3$ | $578\pm 66$ | $9\pm 2$ | $32\pm 7$
4 | $0.08_{-0.01}^{+0.01}$ | $336_{-25}^{+17}$ | $228_{-42}^{+40}$ | $3.1_{-0.4}^{+0.5}$ | $<1.3$ | $530\pm 41$ | $7\pm 1$ | $23\pm 4$
5 | $0.09_{-0.01}^{+0.01}$ | $379_{-18}^{+15}$ | $210_{-32}^{+36}$ | $3.5_{-0.6}^{+0.5}$ | $<1.3$ | $558\pm 33$ | $8\pm 1$ | $28\pm 4$
6 | $0.05_{-0.01}^{+0.01}$ | $409_{-24}^{+27}$ | $180_{-38}^{+64}$ | $2.0_{-0.5}^{+0.5}$ | $<1.4$ | $561\pm 50$ | $5\pm 1$ | $16\pm 4$
888From left to right, the columns display the aperture number, the flux
density, the central line velocity, the FWHM, and the surface brigthness of [C
ii] line emission, followed by the inferred maximum outflow velocity, gas
mass, and mass outflow rates as described in Sec. 5.1.

##  5 Discussion

The main question we want to answer in this paper is what caused the [C ii]
plume in the J1000+0234 system. In this section we discuss possible scenarios
such as outflows, inflows, ram pressure stripping, and tidal interactions.

###  5.1 Conical outflow

A first hypothesis on the nature of the [C ii] plume is to interpret it as a
collimated outflow launched by the DSFG, driven by stellar feedback, AGN
activity, or both. The first case is compelling because the DSFG hosts a
vigorous starburst in its center, which translates into a high rate of
supernovae explosions that could potentially accelerate gas out of the galaxy.
The theoretical and observational evidence suggests that starburst-driven
outflows escape along the minor axis of disk galaxies, because it is the path
of least resistance, leading to (bi-)conical structures that extend
perpendicular to the disk, with M82 (Bland & Tully 1988) and NGC 1482
(Veilleux & Rupke 2002) being archetypal examples in the local Universe. In
contrast, AGN-driven outflows do not show a preferential alignment with the
host minor axis (e.g., Schmitt et al. 2003; Ruschel-Dutra et al. 2021) and can
have very narrow opening angles ($\theta\lesssim$$$, e.g Sakamoto et al. 2014;
Aalto et al. 2020).

In the J1000+0234 system, the [C ii] plume diverges from the DSFG’s minor axis
by $\sim$$None$ clockwise, thus favoring an AGN origin. Furthermore, the plume
width remains narrow (transversal FWHM of $\approx$$None$, see Sec. 4.3) along
its full extent, showing little to no broadening towards the top (North). In
aperture #6 of Fig. 4, the transversal FWHM is $None$. Taking that as the
opening of the cone at a distance of $None$ of its vertex at the center of the
DSFG, we derive a projected angle of
$\theta_{\mathrm{p}}=2\arctan\left(0.4/2.4\right)\approx$$$, which is a
projection of the true angle
$\theta=2\times\arctan[\sin(i)\times\tan(\theta_{\mathrm{p}}/2)]$. Using the
expectation value for a random uniform distribution of inclination angles,
$\left<\sin{i}\right>=0.79$ (see the derivation in Law et al. 2009), we
estimate $\theta\approx$$$. This angle falls short of typical outflow opening
angle observed in low redshift starbursts ($\gtrsim$$$; e.g., Hjelm & Lindblad
1996; Veilleux et al. 2001; Seaquist & Clark 2001; Westmoquette et al. 2011;
Rubin et al. 2014) and in simulations (e.g., Cooper et al. 2008; Nelson et al.
2019; Schneider et al. 2020). This again favors AGN as the driver of the
outflow, although a high gas density surrounding a central starburst can also
lead to a strong collimation effect, especially in the molecular phase (e.g.,
Pereira-Santaella et al. 2016).

On a side note, the fact we see only one cone instead of a symmetric bi-cone
could be explained by power source being located above the midplane of the
disk. In that case, the outflow would need to be much stronger to blow out
into the other side.

Since [C ii] is the only line available, the dominant gas phase producing the
emission remains unknown. One possibility is that most of the [C ii] flux
arises from a population of clumps of cold (molecular and/or atomic) gas
entrained in the hot outflowing plasma, as illustrated in the upper left panel
of Fig. 5. Such arrangement of the cold medium is predicted by the theory
(e.g., Schneider et al. 2020; Kim et al. 2020; Fielding & Bryan 2022) and
validated by a large set of observations (Shapley et al. 2003; Rubin et al.
2014; Pereira-Santaella et al. 2016, 2018). Yet only a few studies exist
reporting [C ii] outflows at high-$z$. On one hand, high-velocity wings have
been detected in individual (Herrera-Camus et al. 2021) and stacked spectra of
main sequence galaxies (Gallerani et al. 2018; Ginolfi et al. 2020b), and QSO
hosts (e.g., Bischetti et al. 2019), but they usually come without any
constraint on the state of the emitting gas. On the other hand, Spilker et al.
(2020) showed that 7 out of a sample of 11 lensed DSFGs host unambiguous
molecular outflow signatures in the form of blueshifted OH
$119\text{\,}\mathrm{\SIUnitSymbolMicro m}$ absorption, yet none of these
galaxies display broad [C ii] emission. These results led Spilker et al.
(2020) to conclude that [C ii] line is an unreliable tracer of molecular
outflows. Since the DSFG has similar intrinsic properties as the sources in
the Spilker et al. (2020) sample, we argue that it is unlikely for [C ii] to
be tracing molecular gas in the plume. Instead, the gas could be composed of
mainly atomic hydrogen.

Alternatively, the emission is dominated by ionized
($T\gtrsim$1\text{\times}{10}^{4}\text{\,}\mathrm{K}$$) gas and we are seeing
the outflow cone walls from the side, similar to what optical nebular lines
show in low-redshift edge-on outflows. When sufficient spatial resolution
allows it, such cases exhibit a hallmark limb-brightening effect near the
edges of the cone (e.g., Strickland et al. 2004; Westmoquette et al. 2011;
Venturi et al. 2017; Rupke et al. 2019; Herenz et al. 2023). Here, the plume
is resolved in the transverse direction, but the S/N is too low to draw any
conclusion about the structure. Nevertheless, J23 detected C iv at the
position of the DSFG, with a velocity shift comparable to what we measure in
the plume ($\sim$$300\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$). This
would support the idea of a physical association of the [C ii] plume with
warmer gas and hence a with a more energetic origin.

Regardless of the launching mechanism, we can now quantify some outflow
properties based on the [C ii] line emission. In particular, we can estimate
the mass of the plume enclosed in each of the apertures of Fig. 4 from the
measured [C ii] fluxes. In the optically thin limit, and assuming negligible
background emission, the gas mass in each aperture is
$M_{\mathrm{out}}=\kappa_{\mathrm{[CII]}}\times L_{\mathrm{[CII]}}$, where the
conversion factor $\kappa_{\mathrm{[CII]}}$ depends strongly on the
temperature, density and carbon abundance of the gas. Following Herrera-Camus
et al. (2021), we assume the collisions are dominated by atomic hydrogen and
adopt
$\kappa_{\mathrm{[CII]}}=$1.5\text{\,}\mathrm{M_{\odot}}\text{\,}{\mathrm{L_{\odot}}}^{-1}$$
which corresponds to maximal excitation ($T\gg$90\text{\,}\mathrm{K}$$, $n\gg
n_{\mathrm{crit}}\sim$1\text{\times}{10}^{3}\text{\,}{\mathrm{cm}}^{-3}$$),
and solar abundance patterns. Since lower densities, temperatures and
abundances yield higher values of $\kappa_{\mathrm{[CII]}}$, the masses we
derive will effectively represent lower limits. For example,
$\kappa_{\mathrm{[CII]}}$ becomes $3\times$ and $27\times$ larger when the
metallicity drops to half solar, and one-tenth solar, respectively (see
discussion in Herrera-Camus et al. 2021).

In this way, we measure gas masses from
$5\text{\times}{10}^{7}\text{\,}\mathrm{M_{\odot}}$ in the outermost aperture
(#6) to $2.5\text{\times}{10}^{8}\text{\,}\mathrm{M_{\odot}}$ in the innermost
aperture (#1, corrected by symmetric difference method). The sum of all the
apertures gives $(7.1\pm
0.4)\text{\times}{10}^{8}\text{\,}\mathrm{M_{\odot}}$. We now exploit the
spectral information to derive mass outflow rates as
$\dot{M}_{\mathrm{out}}=M_{\mathrm{out}}\times
v_{\mathrm{out}}\times\tan{(i)}/R$, where $v_{\mathrm{out}}$ represents the
projected maximum outflow velocity and $R=$2.63\text{\,}\mathrm{kpc}$$ is the
projected length of the aperture in the short side (parallel to the flow). For
the maximum outflow velocity we use the prescription of Genzel et al. (2011)
for outflows detected as broad emission components with Gaussian profile width
$\sigma_{\mathrm{broad}}$ and velocity offset of $\left|\Delta v\right|$ with
respect to the narrow component: $v_{\mathrm{out}}=\left|\Delta
v\right|+2\sigma_{\mathrm{broad}}$. Since we only detect a single spectral
component along the plume, we take $\left|\Delta v\right|=v_{\mathrm{cen}}$ as
the velocity centroid relative to the DSFG’s systemic velocity. Both
$v_{\mathrm{out}}$ and $M_{\mathrm{out}}$ values are listed in Table 4.

Assuming $\left<i\right>=$$$, we obtain mass outflow rates between
$15\text{\,}\mathrm{M_{\odot}}\text{\,}{\mathrm{yr}}^{-1}$ and
$85\text{\,}\mathrm{M_{\odot}}\text{\,}{\mathrm{yr}}^{-1}$ (see last column of
Table 4). At face value, such an outflow will take several hundreds of mega-
years to deplete the DSFG’s gas reservoir of
$\approx$1\text{\times}{10}^{11}\text{\,}\mathrm{M_{\odot}}$$ (Fraternali et
al. 2021), and hence it’s unlikely to quench the observed SFR anytime soon. We
stress, however, that [C ii] conditions that differ from maximal excitation
and solar abundance would drastically increase the inferred mass outflow
rates.

Mass outflow rates in starburst-driven winds scale with the SFR, and typically
share the same order of magnitude (Veilleux et al. 2020). When taken as lower
limits, our fiducial mass outflow rates are roughly consistent with the DSFG’s
SFR given its large uncertainties.

Are these values consistent with AGN-driven outflows? Recalling that the X-ray
luminosity of the DSFG is
$L_{\mathrm{2-10keV}}<$1.3\text{\times}{10}^{43}\text{\,}\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}$$
(Smolčić et al. 2015), we estimate a bolometric luminosity of
$L_{\mathrm{bol}}<$1.3\text{\times}{10}^{44}\text{\,}\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}$$
assuming a bolometric correction of 10, appropriate for low-luminosity broad
line AGN (Vasudevan & Fabian 2007). According to the AGN wind scaling
relations presented by Fiore et al. (2017), our adopted $L_{\mathrm{bol}}$
upper limit allows for molecular outflows with mass outflow rates of up to
$100\text{\,}\mathrm{M_{\odot}}\text{\,}{\mathrm{yr}}^{-1}$ and maximum
velocities of $\approx$400\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$. In
contrast, ionized outflows yield mass outflow rates of
$\lesssim$0.1\text{\,}\mathrm{M_{\odot}}\text{\,}{\mathrm{yr}}^{-1}$$. In
summary, our mass outflow rates are consistent with the scaling relations for
molecular outflows in both starbursts and AGN.

The main caveat of the outflow interpretation is that it struggles to explain
the kinematic structure of the [C ii] plume. Specifically, most spatially
resolved observations of galactic-scale outflows find a high velocity
dispersion (FWHM $\gtrsim$600\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$)
with a flat, if not increasing, radial profile (e.g. Venturi et al. 2018; Bao
et al. 2019; McPherson et al. 2023). This is also true in idealized high-
resolution simulations such as the one presented by Schneider et al. (2020),
since outflows that start as laminar, low-turbulence flows can develop and
maintain instabilities as they interact with the CGM, thus increasing the
velocity dispersion. These examples contrast with our measurement of radially
decreasing line widths (middle panel of left row in Fig. 4). Also, if the
emission is optically thin, the dispersion must increase with radius because
the volume of the cone slice probed by the beam gets bigger, and thus includes
a larger range of projected kinematic components. In other words, the
dispersion should increase due to beam smearing even if the turbulence remains
low.

In conclusion, the outflow scenario is a natural explanation for the observed
[C ii] plume, as it fits some of the expected properties an outflow would have
given the nature of the DSFG. Future observations will be essential to rule
out or confirm this scenario. For example, upcoming JWST/NIRSpec IFU
observations will tell if there is any broad H$\alpha$ emission–tracer of
ionized gas and a better-established indicator of outflows–associated with the
[C ii] plume. In addition, deep rest-frame UV spectroscopy is needed to probe
absorption by low-ionization metal species against the UV-bright regions of
the system. Blueshifted lines will then unambiguously confirm the presence of
cold outflows.

###  5.2 Gas accretion

We now consider a different possibility: the [C ii] plume traces a filament of
inflowing gas. Cosmological simulations have long predicted that massive halos
at high-$z$ can be fed by narrow streams of cold gas, provided that the
cooling timescale is shorter than the free-fall time (e.g., Dekel & Birnboim
2006). Moreover, if the galaxy at the center is a rotating disk, it is
expected that such streams reach the ISM along its minor axis. If the
accretion is co-rotating with the disk, the disk structure is reinforced,
whereas in the opposite case the disk might be disrupted (e.g., Danovich et
al. 2015).

As pointed out in Sec. 4.1, the plume meets the DSFG at the receding end of
the rotation, although it appears to overlap with the opposite side in the
intensity map. This configuration resembles what could be observed in an
accreting filament along the edge of a disk. Such interpretation would explain
the relatively low-velocity dispersion, since cold streams are protected from
virial shocks.

In cosmological hydrodynamical simulations, cold gas flows in with a speed
comparable to the virial velocity, and the speed is approximately uniform
along the filaments (Goerdt & Ceverino 2015). Following the estimation of
Fraternali et al. (2021) for the J1000+0234 system, we assume a virial mass of
$M_{\mathrm{vir}}=$2\text{\times}{10}^{12}\text{\,}\mathrm{M_{\odot}}$$ and
virial radius of $R_{\mathrm{vir}}=$70\text{\,}\mathrm{kpc}$$, yielding a
virial velocity of
$V_{\mathrm{vir}}=\sqrt{M_{\mathrm{vir}}G/R_{\mathrm{vir}}}\approx$350\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$.
Goerdt & Ceverino (2015) found that halos of similar mass at $z\sim 4$ accrete
at $V_{\mathrm{stream}}\approx 0.9V_{\mathrm{vir}}$, so for the DSFG we would
expect
$V_{\mathrm{stream}}=$315\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$
which is excellent agreement with our measured [C ii] velocities at
5-$10\text{\,}\mathrm{kpc}$. Now, since these velocities are projected into
the line of sight, the actual transversal speed could be much higher,
depending on the inclination of the stream. Using again the average
inclination for a random distribution of viewing angles,
$\left<\sin{i}\right>=0.79$, we obtain
$v/\left<\sin{i}\right>\approx$400\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$.
This implies that the gas is moving faster than expected for a cold inflow
stream. We caution, however, that Goerdt & Ceverino’s simulations only track
gas down to $0.2R_{\mathrm{vir}}$, while the gas plume discussed here appears
projected into smaller radii, from roughly zero to $0.2R_{\mathrm{vir}}$, thus
preventing a direct comparison.

If the gas retains or gradually loses angular momentum, it will follow a
curved path as it falls. In that case, the observed velocity gradient can be
due to a projection of a filament with relatively uniform gas inflow speed
(see Rose et al. 2023, for a similar argument applied to the Abell 2390
central plume). But we observe the plume being approximately straight, so
either the curvature is parallel to the line-of-sight or the gas is truly
following a straight path. The latter seems more likely since it does not
require a special orientation. So, if we assume the gas is falling straight
into the galaxy, the positive velocity gradient we observe implies the gas is
slowing down. This is contrary to the expectation of a free fall, where the
gas will accelerate towards the center of the potential, but it is a plausible
hydrodynamic effect where the pressure in the immediate vicinity of the DSFG
exerts a force against falling gas.

Since we detect the plume in [C ii], the gas cannot be pristine but must have
a significant mixture of processed material, even if the exact amount is not
possible to constrain with the data in hand. Enrichment can occur by mixing of
the infalling gas with the metals already present in the CGM thanks to past
outflow activity. Alternatively, the gas is being enriched by star-formation
ocurring in-situ. In fact, cosmological simulations also predict that
accretion streams carry dwarf galaxies and star-forming clumps into the
central halos (e.g., Dekel et al. 2009; Ceverino et al. 2010; Fumagalli et al.
2011; Mandelker et al. 2018). This idea has been recently proposed to explain
the $100\text{\,}\mathrm{kpc}$ filament of gas that feeds the massive radio-
galaxy 4C 41.17, detected via its [C i] emission (Emonts et al. 2023). To test
this scenario we stacked the HST images from the four WFC3-IR filters
available to search for associated UV sources (see Appendix B). We find two
faint compact sources: one of them lies slightly outside the plume’s [C ii]
footprint to the North, while the other falls within the footprint at the the
Eastern edge of aperture #4, but only at S/N$\approx$3 (see Fig. 7). For this
reason, we deem it a tentative detection and refrain from claiming a physical
association with the plume. Otherwise, we do not detect UV emission in the HST
images at a stacked $5\sigma$ depth of
$26.2\text{\,}\mathrm{mag}\text{\,}{\mathrm{arcsec}}^{-2}$. This corresponds
to an unobscured SFR density limit of roughly
$2.7\text{\,}\mathrm{M_{\odot}}\text{\,}{\mathrm{yr}}^{-1}\text{\,}{\mathrm{kpc}}^{-2}$,
assuming the Kennicutt (1998) prescription scaled to the Chabrier (2003) IMF.

Finally, a third possibility is that of gas recycling in a “galactic
fountain”, this is, gas ejected by the DSFG falls back in. However, recycled
gas in cosmological simulations typically rains down in the outer parts of the
disk, rather than in a collimated stream onto the center (e.g., Anglés-Alcázar
et al. 2017; Grand et al. 2019).

In summary, interpreting the [C ii] plume as a cold accretion filament is
qualitatively sound, although it requires some mechanism to slow down the gas
as it falls, and a significant degree of metal enrichment. Theoretical
predictions for the behavior of cold streams in the inner part of halos (below
$0.2R_{\mathrm{vir}}$) will enable stronger conclusions.

###  5.3 Ram pressure stripping

In certain conditions, galaxies lose their ISM through hydrodynamic
interactions with their environment. Whenever a galaxy encounters a dense
medium at high relative velocity, it will experience a drag force arising from
the ram pressure acting on its ISM gas. If the drag force exceeds that of
gravity, the gas becomes unbound. Known as ram pressure stripping (RPS; Gunn &
Gott 1972) this process is one of the main ways disk galaxies quench their
star formation in galaxy clusters, but it can also be an efficient quenching
mechanism for dwarf satellites around groups or individual massive galaxies
(Boselli et al. 2022). RPS in action is responsible for the existence of
“jellyfish” galaxies, identifiable by their one-sided tails of stripped gas
(e.g., Chung et al. 2009; Bekki 2009; Smith et al. 2010; Ebeling et al. 2014;
Poggianti et al. 2017).

In this section we discuss a scenario where the extended [C ii] feature is one
of such tails (see lower left panel of Fig. 5). Since the integrated [C ii]
luminosity is comparable to that of the CRISTAL-01a galaxy, we could be seeing
gas stripped from a galaxy with similar properties. In fact, the innermost tip
of the feature closely matches the position of the UV-bright spot in the DSFG.
While this light could be escaping through an opening in the dusty ISM of the
DSFG (as suggested by its redder UV slope, $\beta_{\mathrm{UV}}\approx-1$; cf.
Table 1), we cannot rule out it belongs to a separate smaller galaxy currently
orbiting the DSFG. In this interpretation, the UV-bright region plus the [C
ii] tail would represent the farthest example yet of a jellyfish galaxy.

How realistic is this scenario? RPS needs special conditions to be effective.
Since the drag force is proportional to the density and the square of the
relative velocity (e.g., Gunn & Gott 1972), the medium has to be dense,
volume-filling, and fast-moving. Galaxy clusters are thus the ideal
environment for RPS, since they are filled with a hot dense plasma (the
intracluster medium, ICM, e.g., Sarazin 1986), and their huge gravitational
potential allows members to acquire large orbital velocities. The J1000+0234
system is not a galaxy cluster, despite containing an excess number of LAEs
and LBGs (Smolčić et al. 2017; Jiménez-Andrade et al. 2023). If anything, it
could be classified as a protocluster, which means the structure is only
loosely bound and cluster virialization has not happened yet (Overzier 2016).
Gas therefore has not reached the very high temperatures of typical clusters
and is more likely dominated by small clouds and filaments of colder gas
(e.g., Hennawi et al. 2006; Cantalupo et al. 2014; Arrigoni Battaia et al.
2015). Nevertheless, J23 reported extended He ii and C iv emission around the
DSFG, with ratios (relative to Ly$\alpha$) that suggest strong ionization
induced by AGN. The gas is then arguably warmer than
$T=$1\text{\times}{10}^{4}\text{\,}\mathrm{K}$$, increasing the cross section
for a strong RPS interaction in a fast-passing satellite.

Figure 5: Cartoon representations of the four possible scenarios to explain
the [C ii] plume. In all panels the DSFG is depicted as an inclined rotating
disk, with arrows showing the rotation. The spiral arms and the normal vector
are only intended to show the orientation of the disk, although we cannot
determine it from the data. Upper left: In the outflow scenario the extended
[C ii] emission arises from clumps of cold gas entrained within a large-scale,
off-axis conical wind. Alternatively, [C ii] could be tracing ionized gas in
the cone walls. Here, the ISM at the launching site is blown out by the wind,
allowing the escape of UV photons. Upper right: In the inflow scenario, a
C+-bearing stream of gas falls from the north into the receding side of the
disk. Here we depict the disk orientation inverted so that the inflow arrives
in the near side of the disk. Lower left: In the ram pressure stripping
scenario, the UV-bright clump in the DSFG is a satellite galaxy falling
through a hot and dense halo around the system. Ram pressure stripping of the
satellite’s ISM then produces the [C ii] plume in the form of a “jellyfish”
tail. Lower right: In the gravitational interactions scenario, the plume is a
tidal tail from a past gravitational interaction between the DSFG and
(possibly) CRISTAL-01a. This cartoon summarizes the three cases discussed in
the main text: a high-speed flyby of CRISTAL-01a (gray), a late-stage major
merger (green), and the tidal disruption of a minor satellite (purple). The
dashed gray arrow qualitatively describes a possible orbit for CRISTAL-01a in
the first case, that aligns with its morphological major axis.

Given the observed velocity difference $V$ between the DSFG and the base of
the plume, we can estimate the minimum density the CGM must have in order to
induce RPS. According to Gunn & Gott (1972), the requirement of ram pressure
force being larger than the force holding the ISM of the satellite translates
into the criterion

$\rho_{\mathrm{CGM}}V^{2}>\frac{\Sigma_{\mathrm{gas}}v_{\mathrm{rot}}^{2}}{R_{\mathrm{gal}}},$
(1)

where $\Sigma_{\mathrm{gas}}$, $v_{\mathrm{rot}}$, and $R_{\mathrm{gal}}$ are
the gas surface density, rotational velocity, and effective radius of the
satellite, respectively, assuming a thin stellar disk structure. Using the
inferred gas mass and aperture area of aperture #1 (Table 4), we adopt
$\Sigma_{\mathrm{gas}}=$1.6\text{\times}{10}^{7}\text{\,}\mathrm{M_{\odot}}\text{\,}{\mathrm{kpc}}^{-2}$$.
Then, taking
$v_{\mathrm{rot}}=$100\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$,
$R_{\mathrm{gal}}=$200\text{\,}\mathrm{pc}$$ and
$V=$166\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$, we obtain
$n_{\mathrm{CGM}}=\rho_{\mathrm{CGM}}/m_{H}\gtrsim$1\text{\,}{\mathrm{cm}}^{-3}$$.
This is 3 to 4 orders of magnitude denser than typical ICM densities, and is
comparable to the densities of H ii regions and the warm neutral medium in the
Milky Way (Draine 2011). On one hand, these gas phases are normally clumpy in
the Local Universe, so they would not fill enough volume to sustain effective
RPS along $15\text{\,}\mathrm{kpc}$. On the other hand, we know little about
the structure of the high redshift CGM, so this concern may not apply.

The RPS scenario, however, is at odds with our observation of a decreasing
linewidth as a function of distance along the plume. In the context of galaxy
clusters, evidence suggests that stripped cold gas interacts with the hot ICM
either heating it or inducing instabilities that build up turbulence with
time. This effect is most clearly observed in ESO 137-001, a nearby edge-on
jellyfish galaxy with a $40\text{\,}\mathrm{kpc}$ H$\alpha$ tail (Sun et al.
2007). MUSE observations resolve the trailing diffuse H$\alpha$ emisison into
three almost parallel tails, and all of them show a mild but significant
increase in velocity dispersion in the direction away from the disk in the
first $20\text{\,}\mathrm{kpc}$ (Luo et al. 2023; Li et al. 2023). Beyond that
distance the dispersion remains more or less uniform. RPS in idealized
numerical simulations generally reproduce this behavior, regardless of whether
cooling (e.g., Roediger & Brüggen 2008; Tonnesen & Bryan 2010) and/or magnetic
fields are included (e.g., Tonnesen & Stone 2014).

###  5.4 Gravitational interactions

Finally, we consider the scenario where the plume is formed as the result of a
gravitational disturbance. We know that J1000+0234 is a complex multiple
system (see Section 2), so we expect frequent interactions among its members.
It is thus very plausible that a close encounter with the massive DSFG at the
center of the group induced the formation of a tidal tail. This explanation is
simpler than the RPS scenario, as it does not require special hydrodynamic
conditions but only gravity.

Here we present a qualitative discussion of three different ways this
interaction could have happened. First, we consider the case where CRISTAL-01a
made a flyby close to the DSFG. Second, we assume the progenitors already
merged and the plume is the lasting debris of such encounter. And third, we
consider the plume as a separate dwarf galaxy altogether, currently in the
process of being stripped by the tidal forces exerted by the DSFG.

The idea that CRISTAL-01a and the DSFG are interacting was already suggested
by several authors (e.g., Capak et al. 2008; Schinnerer et al. 2008; GG18;
J23), although it was mostly based on the short projected distance between the
two objects. J23 also took the UV and Ly$\alpha$ elongated morphologies of
CRISTAL-01a as evidence of ongoing tidal effects. With reliable [C ii]-based
redshifts at hand, we now know CRISTAL-01a moves at a projected speed of
$800\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ relative to the DSFG,
exceeding by a factor of $2.5$ the escape velocity at a proper distance of
$10\text{\,}\mathrm{kpc}$
($314\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$; assuming a point mass of
$M_{\mathrm{dyn}}=$2.3\text{\times}{10}^{11}\text{\,}\mathrm{M_{\odot}}$$
located in the center of the DSFG, Fraternali et al. 2021). This implies
CRISTAL-01a is not gravitationally bound to the DSFG, indicating that if
CRISTAL-01a actually interacted with the DSFG, it was in a high-speed flyby.

The main issue with this first tidal scenario is the mass ratio between
CRISTAL-01a and the DSFG. Decades of work on numerical simulations of galaxy
collisions have found that the largest and longest-lived tails are produced in
“major” interactions (i.e., where the progenitor mass ratio is 1:3 or lower;
see Duc & Renaud 2013, for a review). In contrast, the stellar mass ratio here
($\sim 1:10$, GG18) belongs to the “minor” regime. Tidal features tend to be
more prominent when the encounter occurs at low speeds, although it has been
shown that high-speed flybys can also lead to the formation of gas-rich tails,
provided the progenitors are both massive (cf. the case of the VIRGOHI21 cloud
in the Virgo cluster Bekki et al. 2005; Duc & Bournaud 2008). In conclusion,
even if CRISTAL-01a shows some evidence of ongoing interaction with the DSFG,
its relatively low mass make it an unlikely candidate to be responsible for
the [C ii] plume.

Based on these considerations, we now discuss the second scenario, where two
massive progenitors already merged into the DSFG, ejecting the [C ii] plume as
a tidal tail. The fact that the DSFG is rotation-supported does not
necessarily rule out a merger origin, since simulations have shown that is
possible for two massive galaxies to collide and result in a disk, provided
they have high gas fractions (e.g., Springel & Hernquist 2005; Peschken et al.
2020). In fact, this type of merger is expected to trigger very intense
starbursts, just as the one we see in the DSFG. But did the merger have time
to coalesce into a disk while still exhibiting a tidal tail? To answer this we
need to estimate the dynamical age of the tail. To first order, we divide the
length of the plume by the velocity difference between its two ends. In
practice, we only consider apertures from #2 to #6, where the radial
velocities are reliable. In this way we get
$\tau_{\mathrm{dyn}}=$13.15\text{\,}\mathrm{kpc}$/$112\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$=$115\text{\,}\mathrm{Myr}$$.
On the other hand, the DSFG has a maximum rotation velocity of
$550\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ at a radius of
$3.5\text{\,}\mathrm{kpc}$ (Fraternali et al. 2021), translating into a
dynamical timescale of merely $\approx$$40\text{\,}\mathrm{Myr}$. Since the
age of the plume is almost three times this value, we deem plausible that the
tail persists after the merger has settled.

Tidal tails in the Local Universe usually come in pairs, as in the well-known
examples of the Antennae Galaxies or the Mice (e.g., Toomre & Toomre 1972). In
contrast, the DSFG only shows one. While some examples of one-sided tails in
late-stage mergers exist (e.g., Mrk 273, Sanders et al. 1988), their formation
involves highly inclined encounters (Howard et al. 1993). However, those
configurations are not well suited for the survival of disks (e.g., Cox et al.
2006; Hopkins et al. 2013).

Finally, we consider the case of extreme tidal stripping of a satellite of the
DSFG. In this picture, a dwarf galaxy orbiting the DSFG passes too close to
the center, where tidal forces are strong enough to disrupt the intruder’s ISM
into a long stream of gas. Depending on the central density of the intruder,
it may not be totally disrupted, leaving its core relatively intact. If that
is the case, the UV-bright region near the DSFG would be a natural candidate
for the remnant, as it appears connected to the bottom of the plume. This idea
could be tested with upcoming spectroscopy from JWST/NIRSpec.

Since gravity also acts on the stars, the three cases discussed here should
produce a stellar stream associated with the plume, similar to those that
populate the Milky Way halo (e.g. Malhan et al. 2018) or the surroundings of
nearby massive galaxies (e.g., Martínez-Delgado et al. 2023). Here, as
mentioned in Sec. 5.2 we do not detect stellar emission from the plume in the
HST images at a $5\sigma$ depth of
$26.2\text{\,}\mathrm{mag}\text{\,}{\mathrm{arcsec}}^{-2}$, corresponding to
an intrinsic SB of $18.8\text{\,}\mathrm{mag}\text{\,}{\mathrm{arcsec}}^{-2}$
after correcting for cosmological dimming. However, typical stellar streams in
the Local Universe are much fainter, and only become detectable at
sensitivities of
$\approx$28.5\text{\,}\mathrm{mag}\text{\,}{\mathrm{arcsec}}^{-2}$$ or higher
(e.g., Bullock & Johnston 2005; Martínez-Delgado et al. 2010). In addition,
our HST filters probe the rest-frame UV emission, and hence only trace young
stars and not the bulk of the stellar mass. Upcoming JWST/NIRCam observations
will be significantly deeper, and trace the rest-frame optical light. But even
then, a detection would need the tail or stream to be remarkably bright.

We conclude that gravitational interactions are more than capable of creating
extended gas structures such as the [C ii] plume we observe, although the
details are very uncertain. In fact, the three tidal scenarios presented here
are only illustrative, and do not pretend to exhaust all the possible
interactions that might produce a [C ii] plume. A more systematic approach
would involve a series of numerical experiments to constrain the parameters
that best reproduce the observed morphology and kinematics, but that goes
beyond the scope of this paper.

##  6 Summary & conclusions

We have presented new ALMA Band 7 observations of the inner region of the
J1000+0234 system at $z=4.54$ located at the center of a bright Ly$\alpha$
blob. These observations are part of the ALMA-CRISTAL Large Program, targeting
[C ii] $158\text{\,}\mathrm{\SIUnitSymbolMicro m}$ emission and the underlying
dust continuum in a sample of 25 star-forming galaxies at $4<z<6$. The high
sensitivity and angular resolution of these data reveal the detailed structure
of the star-forming galaxies in the J1000+0234 system. We report the discovery
of a faint and diffuse [C ii]-emitting plume extending up to $None$
($\approx$$15\text{\,}\mathrm{kpc}$) from the central massive DSFG
(J1000+0234-North). Complemented with archival MUSE and HST data, we analyzed
the spatial and spectral properties of the plume and the two main galaxies of
the system. Our main findings can be summarized as follows:

  1. 1.

The DSFG is detected in both [C ii] and dust continuum, and it shows a compact
disk-like morphology. On one hand, dust emisison is fitted by a single 2D
Sérsic profile with circularized effective radius of
$R_{\mathrm{eff}}\approx$0.74\text{\,}\mathrm{kpc}$$, Sérsic index $n\approx
1.29$ and axis ratio $\approx 0.4$. On the other hand, the [C ii] emission is
fitted by 2D Sérsic profile of
$R_{\mathrm{eff}}\approx$1.13\text{\,}\mathrm{kpc}$$, $n\approx 0.7$ and axis
ratio $\approx$0.34$$.

  2. 2.

CRISTAL-01a sits at a projected distance of $None$ from the DSFG, and recedes
$800\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ faster. It is detected in
[C ii] emission but not in dust continuum, and its [C ii] morphology resembles
that of the rest-frame UV emission. This means it is elongated and resolved
into two clumps, although they are offset by $None$ from the corresponding UV-
bright clumps. We model the northeastern clump with a circular exponential
profile of $R_{\mathrm{eff}}\approx$0.8\text{\,}\mathrm{kpc}$$, and the
southwestern clump with an elliptical exponential of
$R_{\mathrm{eff}}\approx$2.4\text{\,}\mathrm{kpc}$$ and axis ratio $\approx
0.82$.

  3. 3.

The [C ii] plume starts at the center of the DSFG and extends northward with a
position angle that is offset by $None$ clockwise from the DSFG’s minor axis.
The [C ii] surface brightness declines rapidly along the plume, becoming
undetected at $\approx$15\text{\,}\mathrm{kpc}$$ from the center of the DSFG.
In the transverse direction we measure an average FWHM extent of
$\approx$4\text{\,}\mathrm{kpc}$$.

  4. 4.

The plume exhibits a clear velocity gradient, increasing the line central
velocity as a function of radial distance from
$180\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ to
$400\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$, relative to the DSFG’s
systemic velocity. Moreover, the line FWHM also evolves with radius, showing a
smooth drop from $450\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ at the
center of the DSFG to $190\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ at
the farthest measured point.

  5. 5.

We detect no dust continuum at rest-frame
$160\text{\,}\mathrm{\SIUnitSymbolMicro m}$ from the plume down to
$5\sigma=$194\text{\,}\mathrm{\SIUnitSymbolMicro Jy}$$ per $$$\times$$$
aperture. At an assumed dust temperature of
$T_{\mathrm{dust}}=$45\text{\,}\mathrm{K}$$, we obtain lower limits on the [C
ii]/FIR ratio between $\approx 0.2\%$ and $\approx 0.6\%$, consistent with UV
photoelectric heating of the gas.

  6. 6.

We estimate a minimum total mass for the plume of $(7.1\pm
0.4)\text{\times}{10}^{8}\text{\,}\mathrm{M_{\odot}}$, asuming a conversion
factor
$\kappa_{\mathrm{[CII]}}=$1.5\text{\,}\mathrm{M_{\odot}}\text{\,}{\mathrm{L_{\odot}}}^{-1}$$
that corresponds to the limit of maximal excitation of the line in a medium
dominated by atomic hydrogen, with solar-like carbon abundance.

We discuss four scenarios to explain the results outlined above: (1), the
plume is a conical outflow. (2), the plume traces a filament of inflowing gas.
(3), the plume is a ram-pressure stripped tail of an infalling satellite. (4),
the plume is tidal debris from past gravitational interactions.

In the first scenario (1), we infer resolved mass outflow rates between
$16\text{\,}\mathrm{M_{\odot}}\text{\,}{\mathrm{yr}}^{-1}$ and
$83\text{\,}\mathrm{M_{\odot}}\text{\,}{\mathrm{yr}}^{-1}$. The maximum
outflow velocities across the plume range from
$530\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ to
$620\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$. These values are roughly
consistent with literature scaling relations for SFR and $L_{\mathrm{bol}}$ in
the case of starburst-driven and AGN-driven outflows, respectively. Given the
very low ($\theta\approx$$$) opening angle we derive under the assumption of a
simple conical geometry, plus the misalignment with the DSFG’s minor axis, the
putative outflow appears more likely to have originated in a central AGN.
However, the observed kinematic radial trends are in mild tension with the
expected properties of an outflow.

Scenario (2) is qualitatively consistent with theoretical expectations for
cold accretion streams, except for our inference of a slow-down of the gas as
it falls, although this can be accomodated by pressure gradients in the CGM.
Moreover, the fact the putative filament emits in [C ii] rules out a
chemically pristine gas composition. Still, simulations suggest that gas
enrichment can happen concurrently during the inflow, either by gas mixing in
the CGM or by in-situ star formation.

Scenario (3) requires the UV-bright region of the DSFG to be a satellite
galaxy that is crossing the DSFG’s CGM. In addition, the CGM must be dense
($\gtrsim$1\text{\,}{\mathrm{cm}}^{-3}$$) in order to exert a significant ram
pressure capable of stripping off the satellite’s ISM. Moreover, observations
and simulations of ram pressure stripping predict an increase of velocity
dispersion along the stripped tails, contrary to what we observe in
J1000+0234.

Finally, scenario (4) is motivated by the fact J1000+0234 is an overdense
environment and close interactions must be frequent. We explored three
possible ways a gravitational interaction can lead to the formation of a one-
sided tidal tail. Namely, a high-speed flyby of CRISTAL-01a, a late-stage
major merger in which the [C ii] plume is its remaining debris, and the tidal
stripping of a minor satellite in a radial orbit. While a proper assessment of
these configurations using tailored numerical simulations remains pending,
heuristic arguments slightly disfavor the first two.

Besides scenario (3), which requires very special hydrodynamic conditions,
outflows, inflows and tidal tails all have their pros and cons. Further
observations and modeling are needed to discriminate between them.
Promisingly, upcoming JWST/NIRCam and JWST/NIRSpec observations will deliver a
high angular resolution view of the rest-frame optical morphology and spectral
properties. For example, narrow H$\alpha$ spectral imaging with NIRSpec IFU
will constrain the star formation rate density in the [C ii] plume. In
addition, the detection of a broad H$\alpha$ component would support the
outflow scenario. At the same time, NIRCam broad band observations will
uncover the obscured regions of the DSFG and potentially discover a diffuse
stellar stream associated with the [C ii] plume, providing further evidence to
the tidal tail scenario.

Our results highlight the power of ALMA for characterizing the cold CGM in
emission at high redshift, but also the difficulty of their interpretation.
Disentangling the physical mechanisms that produce a given [C ii] observation
is nevertheless very important for understanding how galaxies and their
surroundings evolve.

###### Acknowledgements.

This paper makes use of the following ALMA data: ADS/JAO.ALMA#2017.1.00428.L,
ADS/JAO.ALMA#2021.1.00280.L, ADS/JAO.ALMA#2019.1.01587.S. ALMA is a
partnership of ESO (representing its member states), NSF (USA) and NINS
(Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI
(Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA
Observatory is operated by ESO, AUI/NRAO and NAOJ. This paper is partly based
on observations collected at the European Southern Observatory under ESO
programs 0102.A-0448 and 0103.A-0272. M. S. was financially supported by
Becas-ANID scolarship #21221511, and also acknowledges ANID BASAL project
FB210003. M. A. acknowledges support from FONDECYT grant 1211951 and ANID
BASAL project FB210003. A.F. acknowledges support from the ERC Advanced Grant
INTERSTELLAR H2020/740120. E. J. J. acknowledges support from FONDECYT
Iniciación en investigación 2020 Project 11200263 and the ANID BASAL project
FB210003. I. DL. and S. vdG. acknowledge funding support from ERC starting
grant 851622 DustOrigin. K. T. acknowledges support from JSPS KAKENHI Grant
Number 23K03466. L. G. thanks support from FONDECYT regular proyecto
No1230591. R. I. is financially supported by Grants-in-Aid for Japan Society
for the Promotion of Science (JSPS) Fellows (KAKENHI Grant Number 23KJ1006).
R. J. A. was supported by FONDECYT grant number 123171 and by the ANID BASAL
project FB210003. I.M. thanks the financial support by Grants-in-Aid for Japan
Society for the Promotion of Science (JSPS) Fellows (KAKENHI Number 22KJ0821).
R. L. D. is supported by the Australian Research Council Centre of Excellence
for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number
CE170100013. M. R. acknowledges support from project PID2020-114414GB-100,
financed by MCIN/AEI/10.13039/501100011033.

## References

  * Aalto et al. (2020) Aalto, S., Falstad, N., Muller, S., et al. 2020, A&A, 640, A104
  * Akins et al. (2022) Akins, H. B., Fujimoto, S., Finlator, K., et al. 2022, ApJ, 934, 64
  * Anglés-Alcázar et al. (2017) Anglés-Alcázar, D., Faucher-Giguère, C.-A., Kereš, D., et al. 2017, MNRAS, 470, 4698
  * Appleton et al. (2013) Appleton, P. N., Guillard, P., Boulanger, F., et al. 2013, ApJ, 777, 66
  * Aretxaga et al. (2011) Aretxaga, I., Wilson, G. W., Aguilar, E., et al. 2011, MNRAS, 415, 3831
  * Arrigoni Battaia et al. (2015) Arrigoni Battaia, F., Hennawi, J. F., Prochaska, J. X., & Cantalupo, S. 2015, ApJ, 809, 163
  * Bao et al. (2019) Bao, M., Chen, Y.-m., Yuan, Q.-r., et al. 2019, MNRAS, 490, 3830
  * Bekki (2009) Bekki, K. 2009, MNRAS, 399, 2221
  * Bekki et al. (2005) Bekki, K., Koribalski, B. S., & Kilborn, V. A. 2005, MNRAS, 363, L21
  * Béthermin et al. (2020) Béthermin, M., Fudamoto, Y., Ginolfi, M., et al. 2020, A&A, 643, A2
  * Bischetti et al. (2019) Bischetti, M., Maiolino, R., Carniani, S., et al. 2019, A&A, 630, A59
  * Bland & Tully (1988) Bland, J. & Tully, B. 1988, Nature, 334, 43
  * Boselli et al. (2022) Boselli, A., Fossati, M., & Sun, M. 2022, A&A Rev., 30, 3
  * Bouchet et al. (1985) Bouchet, P., Lequeux, J., Maurice, E., Prevot, L., & Prevot-Burnichon, M. L. 1985, A&A, 149, 330
  * Brammer (2023) Brammer, G. 2023, grizli, Zenodo
  * Bullock & Johnston (2005) Bullock, J. S. & Johnston, K. V. 2005, ApJ, 635, 931
  * Cantalupo et al. (2014) Cantalupo, S., Arrigoni-Battaia, F., Prochaska, J. X., Hennawi, J. F., & Madau, P. 2014, Nature, 506, 63
  * Capak et al. (2008) Capak, P., Carilli, C. L., Lee, N., et al. 2008, ApJ, 681, L53
  * Carilli et al. (2008) Carilli, C. L., Lee, N., Capak, P., et al. 2008, ApJ, 689, 883
  * Carniani et al. (2013) Carniani, S., Marconi, A., Biggs, A., et al. 2013, A&A, 559, A29
  * CASA Team et al. (2022) CASA Team, Bean, B., Bhatnagar, S., et al. 2022, PASP, 134, 114501
  * Ceverino et al. (2010) Ceverino, D., Dekel, A., & Bournaud, F. 2010, MNRAS, 404, 2151
  * Chabrier (2003) Chabrier, G. 2003, PASP, 115, 763
  * Chung et al. (2009) Chung, A., van Gorkom, J. H., Kenney, J. D. P., Crowl, H., & Vollmer, B. 2009, AJ, 138, 1741
  * Cicone et al. (2021) Cicone, C., Mainieri, V., Circosta, C., et al. 2021, A&A, 654, L8
  * Cicone et al. (2015) Cicone, C., Maiolino, R., Gallerani, S., et al. 2015, A&A, 574, A14
  * Claeyssens et al. (2022) Claeyssens, A., Richard, J., Blaizot, J., et al. 2022, A&A, 666, A78
  * Cooper et al. (2008) Cooper, J. L., Bicknell, G. V., Sutherland, R. S., & Bland-Hawthorn, J. 2008, ApJ, 674, 157
  * Cox et al. (2006) Cox, T. J., Dutta, S. N., Di Matteo, T., et al. 2006, ApJ, 650, 791
  * Czekala et al. (2021) Czekala, I., Loomis, R. A., Teague, R., et al. 2021, ApJS, 257, 2
  * Danovich et al. (2015) Danovich, M., Dekel, A., Hahn, O., Ceverino, D., & Primack, J. 2015, MNRAS, 449, 2087
  * Dekel & Birnboim (2006) Dekel, A. & Birnboim, Y. 2006, MNRAS, 368, 2
  * Dekel et al. (2009) Dekel, A., Birnboim, Y., Engel, G., et al. 2009, Nature, 457, 451
  * Draine (2011) Draine, B. T. 2011, Physics of the Interstellar and Intergalactic Medium
  * Duc & Bournaud (2008) Duc, P.-A. & Bournaud, F. 2008, ApJ, 673, 787
  * Duc & Renaud (2013) Duc, P.-A. & Renaud, F. 2013, in Lecture Notes in Physics, Berlin Springer Verlag, ed. J. Souchay, S. Mathis, & T. Tokieda, Vol. 861, 327
  * Ebeling et al. (2014) Ebeling, H., Stephenson, L. N., & Edge, A. C. 2014, ApJ, 781, L40
  * Emonts et al. (2019) Emonts, B. H. C., Cai, Z., Prochaska, J. X., Li, Q., & Lehnert, M. D. 2019, ApJ, 887, 86
  * Emonts et al. (2018) Emonts, B. H. C., Lehnert, M. D., Dannerbauer, H., et al. 2018, MNRAS, 477, L60
  * Emonts et al. (2016) Emonts, B. H. C., Lehnert, M. D., Villar-Martín, M., et al. 2016, Science, 354, 1128
  * Emonts et al. (2023) Emonts, B. H. C., Lehnert, M. D., Yoon, I., et al. 2023, Science, 379, 1323
  * Emonts et al. (2015) Emonts, B. H. C., Mao, M. Y., Stroe, A., et al. 2015, MNRAS, 451, 1025
  * Emonts et al. (2014) Emonts, B. H. C., Norris, R. P., Feain, I., et al. 2014, MNRAS, 438, 2898
  * ESO CPL Development Team (2015) ESO CPL Development Team. 2015, EsoRex: ESO Recipe Execution Tool, Astrophysics Source Code Library, record ascl:1504.003
  * Faisst et al. (2020) Faisst, A. L., Schaerer, D., Lemaux, B. C., et al. 2020, ApJS, 247, 61
  * Fielding & Bryan (2022) Fielding, D. B. & Bryan, G. L. 2022, ApJ, 924, 82
  * Fiore et al. (2017) Fiore, F., Feruglio, C., Shankar, F., et al. 2017, A&A, 601, A143
  * Francis et al. (1996) Francis, P. J., Woodgate, B. E., Warren, S. J., et al. 1996, ApJ, 457, 490
  * Fraternali et al. (2021) Fraternali, F., Karim, A., Magnelli, B., et al. 2021, A&A, 647, A194
  * Frayer et al. (2018) Frayer, D. T., Maddalena, R. J., Ivison, R. J., et al. 2018, ApJ, 860, 87
  * Fujimoto et al. (2019) Fujimoto, S., Ouchi, M., Ferrara, A., et al. 2019, ApJ, 887, 107
  * Fujimoto et al. (2020) Fujimoto, S., Silverman, J. D., Bethermin, M., et al. 2020, ApJ, 900, 1
  * Fumagalli et al. (2011) Fumagalli, M., Prochaska, J. X., Kasen, D., et al. 2011, MNRAS, 418, 1796
  * Gaia Collaboration et al. (2018) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A, 616, A1
  * Gallerani et al. (2018) Gallerani, S., Pallottini, A., Feruglio, C., et al. 2018, MNRAS, 473, 1909
  * Geach et al. (2009) Geach, J. E., Alexander, D. M., Lehmer, B. D., et al. 2009, ApJ, 700, 1
  * Genzel et al. (2011) Genzel, R., Newman, S., Jones, T., et al. 2011, ApJ, 733, 101
  * Ginolfi et al. (2020a) Ginolfi, M., Jones, G. C., Béthermin, M., et al. 2020a, A&A, 643, A7
  * Ginolfi et al. (2020b) Ginolfi, M., Jones, G. C., Béthermin, M., et al. 2020b, A&A, 633, A90
  * Ginolfi et al. (2017) Ginolfi, M., Maiolino, R., Nagao, T., et al. 2017, MNRAS, 468, 3468
  * Goerdt & Ceverino (2015) Goerdt, T. & Ceverino, D. 2015, MNRAS, 450, 3359
  * Gómez-Guijarro et al. (2018) Gómez-Guijarro, C., Toft, S., Karim, A., et al. 2018, ApJ, 856, 121
  * Grand et al. (2019) Grand, R. J. J., van de Voort, F., Zjupa, J., et al. 2019, MNRAS, 490, 4786
  * Gunn & Gott (1972) Gunn, J. E. & Gott, J. Richard, I. 1972, ApJ, 176, 1
  * Hack et al. (2021) Hack, W. J., Cara, M., Sosey, M., et al. 2021, spacetelescope/drizzlepac: Drizzlepac v3.3.0, Zenodo
  * Hasinger et al. (2018) Hasinger, G., Capak, P., Salvato, M., et al. 2018, ApJ, 858, 77
  * Hennawi et al. (2006) Hennawi, J. F., Prochaska, J. X., Burles, S., et al. 2006, ApJ, 651, 61
  * Herenz et al. (2023) Herenz, E. C., Inoue, J., Salas, H., et al. 2023, A&A, 670, A121
  * Herenz & Wisotzki (2017) Herenz, E. C. & Wisotzki, L. 2017, A&A, 602, A111
  * Herrera-Camus et al. (2015) Herrera-Camus, R., Bolatto, A. D., Wolfire, M. G., et al. 2015, ApJ, 800, 1
  * Herrera-Camus et al. (2021) Herrera-Camus, R., Förster Schreiber, N., Genzel, R., et al. 2021, A&A, 649, A31
  * Herrera-Camus et al. (2018) Herrera-Camus, R., Sturm, E., Graciá-Carpio, J., et al. 2018, ApJ, 861, 94
  * Hjelm & Lindblad (1996) Hjelm, M. & Lindblad, P. O. 1996, A&A, 305, 727
  * Hopkins et al. (2013) Hopkins, P. F., Cox, T. J., Hernquist, L., et al. 2013, MNRAS, 430, 1901
  * Howard et al. (1993) Howard, S., Keel, W. C., Byrd, G., & Burkey, J. 1993, ApJ, 417, 502
  * Jiménez-Andrade et al. (2023) Jiménez-Andrade, E. F., Cantalupo, S., Magnelli, B., et al. 2023, MNRAS, 521, 2326
  * Jones et al. (2017) Jones, G. C., Carilli, C. L., Shao, Y., et al. 2017, ApJ, 850, 180
  * Jorsater & van Moorsel (1995) Jorsater, S. & van Moorsel, G. A. 1995, AJ, 110, 2037
  * Kennicutt (1998) Kennicutt, Robert C., J. 1998, ARA&A, 36, 189
  * Kennicutt et al. (2011) Kennicutt, R. C., Calzetti, D., Aniano, G., et al. 2011, PASP, 123, 1347
  * Kim et al. (2020) Kim, C.-G., Ostriker, E. C., Fielding, D. B., et al. 2020, ApJ, 903, L34
  * Koposov et al. (2022) Koposov, S., Speagle, J., Barbary, K., et al. 2022, joshspeagle/dynesty: v2.0.3, Zenodo
  * Lambert et al. (2023) Lambert, T. S., Posses, A., Aravena, M., et al. 2023, MNRAS, 518, 3183
  * Law et al. (2009) Law, D. R., Steidel, C. C., Erb, D. K., et al. 2009, ApJ, 697, 2057
  * Le Fèvre et al. (2020) Le Fèvre, O., Béthermin, M., Faisst, A., et al. 2020, A&A, 643, A1
  * Le Fevre et al. (1996) Le Fevre, O., Deltorn, J. M., Crampton, D., & Dickinson, M. 1996, ApJ, 471, L11
  * Leclercq et al. (2017) Leclercq, F., Bacon, R., Wisotzki, L., et al. 2017, A&A, 608, A8
  * Lemaux et al. (2018) Lemaux, B. C., Le Fèvre, O., Cucciati, O., et al. 2018, A&A, 615, A77
  * Li et al. (2021) Li, J., Emonts, B. H. C., Cai, Z., et al. 2021, ApJ, 922, L29
  * Li et al. (2023) Li, Y., Luo, R., Fossati, M., Sun, M., & Jáchym, P. 2023, MNRAS, 521, 4785
  * Loiacono et al. (2021) Loiacono, F., Decarli, R., Gruppioni, C., et al. 2021, A&A, 646, A76
  * Luo et al. (2023) Luo, R., Sun, M., Jáchym, P., et al. 2023, MNRAS, 521, 6266
  * Malhan et al. (2018) Malhan, K., Ibata, R. A., & Martin, N. F. 2018, MNRAS, 481, 3442
  * Mandelker et al. (2018) Mandelker, N., van Dokkum, P. G., Brodie, J. P., van den Bosch, F. C., & Ceverino, D. 2018, ApJ, 861, 148
  * Martínez-Delgado et al. (2023) Martínez-Delgado, D., Cooper, A. P., Román, J., et al. 2023, A&A, 671, A141
  * Martínez-Delgado et al. (2010) Martínez-Delgado, D., Gabany, R. J., Crawford, K., et al. 2010, AJ, 140, 962
  * Matsuda et al. (2004) Matsuda, Y., Yamada, T., Hayashino, T., et al. 2004, AJ, 128, 569
  * McPherson et al. (2023) McPherson, D. K., Fisher, D. B., Nielsen, N. M., et al. 2023, MNRAS, 525, 6170
  * Meurer et al. (1999) Meurer, G. R., Heckman, T. M., & Calzetti, D. 1999, ApJ, 521, 64
  * Neeleman et al. (2017) Neeleman, M., Kanekar, N., Prochaska, J. X., et al. 2017, Science, 355, 1285
  * Neeleman et al. (2019) Neeleman, M., Kanekar, N., Prochaska, J. X., Rafelski, M. A., & Carilli, C. L. 2019, ApJ, 870, L19
  * Nelson et al. (2019) Nelson, D., Pillepich, A., Springel, V., et al. 2019, MNRAS, 490, 3234
  * Nightingale et al. (2023) Nightingale, J., Amvrosiadis, A., Hayes, R., et al. 2023, The Journal of Open Source Software, 8, 4475
  * Nightingale et al. (2021) Nightingale, J., Hayes, R., & Griffiths, M. 2021, The Journal of Open Source Software, 6, 2550
  * Ouchi et al. (2020) Ouchi, M., Ono, Y., & Shibuya, T. 2020, ARA&A, 58, 617
  * Overzier (2016) Overzier, R. A. 2016, A&A Rev., 24, 14
  * Pereira-Santaella et al. (2016) Pereira-Santaella, M., Colina, L., García-Burillo, S., et al. 2016, A&A, 594, A81
  * Pereira-Santaella et al. (2018) Pereira-Santaella, M., Colina, L., García-Burillo, S., et al. 2018, A&A, 616, A171
  * Péroux & Howk (2020) Péroux, C. & Howk, J. C. 2020, ARA&A, 58, 363
  * Peschken et al. (2020) Peschken, N., Łokas, E. L., & Athanassoula, E. 2020, MNRAS, 493, 1375
  * Peterson et al. (2018) Peterson, B. W., Appleton, P. N., Bitsakis, T., et al. 2018, ApJ, 855, 141
  * Pizzati et al. (2020) Pizzati, E., Ferrara, A., Pallottini, A., et al. 2020, MNRAS, 495, 160
  * Pizzati et al. (2023) Pizzati, E., Ferrara, A., Pallottini, A., et al. 2023, MNRAS, 519, 4608
  * Poggianti et al. (2017) Poggianti, B. M., Moretti, A., Gullieuszik, M., et al. 2017, ApJ, 844, 48
  * Roediger & Brüggen (2008) Roediger, E. & Brüggen, M. 2008, MNRAS, 388, 465
  * Rose et al. (2023) Rose, T., McNamara, B. R., Combes, F., et al. 2023, arXiv e-prints, arXiv:2310.16892
  * Rubin et al. (2014) Rubin, K. H. R., Prochaska, J. X., Koo, D. C., et al. 2014, ApJ, 794, 156
  * Rupke et al. (2019) Rupke, D. S. N., Coil, A., Geach, J. E., et al. 2019, Nature, 574, 643
  * Ruschel-Dutra et al. (2021) Ruschel-Dutra, D., Storchi-Bergmann, T., Schnorr-Müller, A., et al. 2021, MNRAS, 507, 74
  * Sakamoto et al. (2014) Sakamoto, K., Aalto, S., Combes, F., Evans, A., & Peck, A. 2014, ApJ, 797, 90
  * Sanders et al. (1988) Sanders, D. B., Soifer, B. T., Elias, J. H., et al. 1988, ApJ, 325, 74
  * Sarazin (1986) Sarazin, C. L. 1986, Reviews of Modern Physics, 58, 1
  * Schinnerer et al. (2008) Schinnerer, E., Carilli, C. L., Capak, P., et al. 2008, ApJ, 689, L5
  * Schmitt et al. (2003) Schmitt, H. R., Donley, J. L., Antonucci, R. R. J., et al. 2003, ApJ, 597, 768
  * Schneider et al. (2020) Schneider, E. E., Ostriker, E. C., Robertson, B. E., & Thompson, T. A. 2020, ApJ, 895, 43
  * Seaquist & Clark (2001) Seaquist, E. R. & Clark, J. 2001, ApJ, 552, 133
  * Sersic (1968) Sersic, J. L. 1968, Atlas de Galaxias Australes
  * Shapley et al. (2003) Shapley, A. E., Steidel, C. C., Pettini, M., & Adelberger, K. L. 2003, ApJ, 588, 65
  * Smith et al. (2010) Smith, R. J., Lucey, J. R., Hammer, D., et al. 2010, MNRAS, 408, 1417
  * Smolčić et al. (2015) Smolčić, V., Karim, A., Miettinen, O., et al. 2015, A&A, 576, A127
  * Smolčić et al. (2017) Smolčić, V., Miettinen, O., Tomičić, N., et al. 2017, A&A, 597, A4
  * Solimano et al. (2022) Solimano, M., González-López, J., Aravena, M., et al. 2022, ApJ, 935, 17
  * Soto et al. (2016) Soto, K. T., Lilly, S. J., Bacon, R., Richard, J., & Conseil, S. 2016, MNRAS, 458, 3210
  * Speagle (2020) Speagle, J. S. 2020, MNRAS, 493, 3132
  * Spilker et al. (2020) Spilker, J. S., Phadke, K. A., Aravena, M., et al. 2020, ApJ, 905, 85
  * Springel & Hernquist (2005) Springel, V. & Hernquist, L. 2005, ApJ, 622, L9
  * Steidel et al. (2000) Steidel, C. C., Adelberger, K. L., Shapley, A. E., et al. 2000, ApJ, 532, 170
  * Strickland et al. (2004) Strickland, D. K., Heckman, T. M., Colbert, E. J. M., Hoopes, C. G., & Weaver, K. A. 2004, ApJ, 606, 829
  * STSCI Development Team (2012) STSCI Development Team. 2012, DrizzlePac: HST image software, Astrophysics Source Code Library, record ascl:1212.011
  * Sun et al. (2007) Sun, M., Donahue, M., & Voit, G. M. 2007, ApJ, 671, 190
  * Szokoly et al. (2004) Szokoly, G. P., Bergeron, J., Hasinger, G., et al. 2004, ApJS, 155, 271
  * Tonnesen & Bryan (2010) Tonnesen, S. & Bryan, G. L. 2010, ApJ, 709, 1203
  * Tonnesen & Stone (2014) Tonnesen, S. & Stone, J. 2014, ApJ, 795, 148
  * Toomre & Toomre (1972) Toomre, A. & Toomre, J. 1972, ApJ, 178, 623
  * Tsukui et al. (2022) Tsukui, T., Iguchi, S., Mitsuhashi, I., & Tadaki, K. 2022, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 12190, Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy XI, ed. J. Zmuidzinas & J.-R. Gao, 121901C
  * Tsukui et al. (2023) Tsukui, T., Iguchi, S., Mitsuhashi, I., & Tadaki, K. 2023, ESSENCE: Evaluate spatially correlated noise in interferometric images, Astrophysics Source Code Library, record ascl:2306.055
  * Tumlinson et al. (2017) Tumlinson, J., Peeples, M. S., & Werk, J. K. 2017, ARA&A, 55, 389
  * Turner et al. (2014) Turner, M. L., Schaye, J., Steidel, C. C., Rudie, G. C., & Strom, A. L. 2014, MNRAS, 445, 794
  * Umehata et al. (2021) Umehata, H., Smail, I., Steidel, C. C., et al. 2021, ApJ, 918, 69
  * Vasudevan & Fabian (2007) Vasudevan, R. V. & Fabian, A. C. 2007, MNRAS, 381, 1235
  * Veilleux et al. (2020) Veilleux, S., Maiolino, R., Bolatto, A. D., & Aalto, S. 2020, A&A Rev., 28, 2
  * Veilleux & Rupke (2002) Veilleux, S. & Rupke, D. S. 2002, ApJ, 565, L63
  * Veilleux et al. (2001) Veilleux, S., Shopbell, P. L., & Miller, S. T. 2001, AJ, 121, 198
  * Venemans et al. (2002) Venemans, B. P., Kurk, J. D., Miley, G. K., et al. 2002, ApJ, 569, L11
  * Venturi et al. (2017) Venturi, G., Marconi, A., Mingozzi, M., et al. 2017, Frontiers in Astronomy and Space Sciences, 4, 46
  * Venturi et al. (2018) Venturi, G., Nardini, E., Marconi, A., et al. 2018, A&A, 619, A74
  * Weilbacher et al. (2020) Weilbacher, P. M., Palsa, R., Streicher, O., et al. 2020, A&A, 641, A28
  * Werk et al. (2013) Werk, J. K., Prochaska, J. X., Thom, C., et al. 2013, ApJS, 204, 17
  * Westmoquette et al. (2011) Westmoquette, M. S., Smith, L. J., & Gallagher, J. S., I. 2011, MNRAS, 414, 3719
  * Wisotzki et al. (2016) Wisotzki, L., Bacon, R., Blaizot, J., et al. 2016, A&A, 587, A98
  * Zhu & Ménard (2013) Zhu, G. & Ménard, B. 2013, ApJ, 770, 130

##  Appendix A Symmetric difference correction of aperture #1’s [C ii]
spectrum

As described in Sec. 4.3, the aperture #1 in Fig. 4 contains significant
emission from the dust continuum and the approaching side of the DSFG rotator.
To mitigate the contamination, we performed continuum subtraction and masked
negative velocities before fitting the line, yet the resulting 1D Gaussian
parameters deviate significantly from the parameters of the line in the
subsequent apertures, suggesting additional contamination at positive
velocities. Motivated by this, we attempt in this section to remove the
additional emission before repeating the Gaussian fit.

If the DSFG rotator is axially symmetric, we expect any aperture-extracted
spectrum from one side of the DSFG to be similar–although with inverted
velocities–to a spectrum extracted from a mirrored aperture, reflected with
respect to the projected rotation axis. So in principle, differences in these
spectra will uncover asymmetric emission in the cube, such as the plume we are
studying.

Here, we take the projected rotation axis to be parallel to the minor axis of
the DSFG’s [C ii] emission (see dashed line in Fig. 4) and crossing the
position of the steepest velocity gradient. In practice, we choose the point
where the 2nd moment (velocity dispersion) is maximal. Once we have defined
the axis, we calculate the geometrical reflection of aperture #1. However, the
rotation axis crosses through the aperture, which would lead to an overlapping
region between the aperture and its mirrored version. To avoid this, we crop
the corner of aperture #1 that goes over the eastern side of the axis before
the reflection.

We then extract the [C ii] spectrum from the `robust=0.5`,
$20\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ channel width cube without
continuum subtraction, from both the cropped aperture #1 and its reflection.
We then apply a simple continuum subtraction by fitting a first-order
polynomial to channels between
$\pm$1330\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$ and
$\pm$1000\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$ independently for
each spectrum. We show the resulting spectra in Fig. 6.

Figure 6: Symmetric difference analysis for aperture #1. Upper panel: [C ii]
spectra of the cropped aperture #1 (blue), its mirrored version (gray), and
the mirrored version but velocity-inverted (flipped), shifted and matched to
the original peak (orange). Lower panel: Residuals from the difference between
the original and the flipped-and-matched spectra.

After flipping the mirrored spectrum in velocity space and comparing it with
the original, we find the horns have different peak heights and are offset by
$\approx$$47\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$, but have similar
overall shape. We thus shift and scale the mirrored spectrum to match the peak
of the original and then perform the subtraction. The resulting spectrum is
shown in the lower panel of Fig. 6. The difference is mostly consistent with
zero, except for a strong but narrow negative difference around
$-250\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ and a broad positive
difference between $0\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ and
$400\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$. The former arises from an
excess or quirk in the spectrum from the mirrored aperture at
$250\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$, while the latter we
assume to be associated with the [C ii] plume.

Finally, we model the difference spectrum with the method described in Sec.
4.3. This is, we fit a 1D Gaussian using PyAutoFit. Once again, we mask the
negative velocities down to
$-700\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$ to avoid fitting the
residual negative feature. Compared to our fiducial method, this fit yields a
significantly lower flux
($\approx$0.3\text{\,}\mathrm{Jy}\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$)
and FWHM ($\approx$420\text{\,}\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$$),
although the central velocities are consistent. In conclusion, both the flux
and FWHM in aperture #1 are affected by contamination from the host, but the
central velocity is not.

##  Appendix B Stack of HST images

In this section we present the stack of HST imaging in the F105W, F125W, F140W
and F160W filters. We converted the image units to nJy per pixel, and then
computed a pixel-by-pixel weighted sum. The weigths correspond to the inverse
variance of the full frames. We then measure fluxes in 5000 random apertures
of $1\text{\,}{\mathrm{arcsec}}^{2}$ area, and obtain a $5\sigma$ depth of
$26.2\text{\,}\mathrm{mag}\text{\,}{\mathrm{arcsec}}^{-2}$ Fig. 7 shows the
result of the stacking in the region close to the J1000+0234 system, and
reveals two tentative sources near the [C ii] plume that were not detected in
the individual images.

Figure 7: Stack of HST/WFC3-IR imaging of J1000+0234 with the outline of the
[C ii] emission in red. Arrows indicate the positions of the two sources
potentially associated with the plume.