11institutetext:  CEA, Irfu, DAp, AIM, Universitè Paris-Saclay, Universitè de
Paris, CNRS, F-91191 Gif-sur-Yvette, France 22institutetext: Department of
Physics & Astronomy, University of California Los Angeles, 430 Portola Plaza,
Los Angeles, CA 90095, USA 33institutetext: Cosmic Dawn Center (DAWN)
44institutetext: Niels Bohr Institute, University of Copenhagen, Jagtvej 128,
DK-2200, Copenhagen N, Denmark 55institutetext: INAF — Osservatorio
Astronomico di Brera, via Brera 28, I-20121, Milano, Italy 66institutetext:
University of Trieste, Piazzale Europa, 1, 34127 Trieste TS, Italy
77institutetext: INAF — Osservatorio Astronomico di Brera, via Brera 28,
I-20121, Milano, Italy 88institutetext: INAF — Osservatorio Astronomico di
Trieste, via Tiepolo 11, I-34131, Trieste, Italy 99institutetext: Institut de
Radioastronomie Millimétrique, 300 Rue de la Piscine, F-38406 Saint Martin
d’Hères, France 1010institutetext: Purple Mountain Observatory & Key
Laboratory for Radio Astronomy, Chinese Academy of Sciences, 10 Yuanhua Road,
Nanjing 210023, People’s Republic of China

# Bulge formation inside quiescent lopsided stellar disks: connecting
accretion, star formation and morphological transformation in a $\rm z\sim 3$
galaxy group

Boris S. Kalita 11 Emanuele Daddi 11 Frederic Bournaud 11 R. Michael Rich 22
Francesco Valentino 3344 Carlos Gómez-Guijarro 11 Sandrine Codis 11 Ivan
Delvecchio 55 David Elbaz 11 Veronica Strazzullo 667788 Victor de Sousa
Magalhaes 88 Jérôme Pety 99 Qinghua Tan 101011<EMAIL_ADDRESS>
(Accepted for publication in A&A)

We present well-resolved near-IR and sub-mm analysis of the three highly star-
forming massive ($>10^{11}\,\rm M_{\odot}$) galaxies within the core of the
RO-1001 galaxy group at $\rm z=2.91$. Each of them displays kpc-scale compact
star-bursting cores with properties consistent with forming galaxy bulges,
embedded at the center of extended, massive stellar disks. Surprisingly, the
stellar disks are unambiguously both quiescent, and severely lopsided.
Therefore, ‘outside-in’ quenching is ongoing in the three group galaxies. We
propose an overall scenario in which the strong mass lopsidedness in the disks
(ranging from factors of 1.6 to $>$3), likely generated under the effects of
accreted gas and clumps, is responsible for their star-formation suppression,
while funnelling gas into the nuclei and thus creating the central starbursts.
The lopsided side of the disks marks the location of accretion streams impact,
with additional matter components (dust and stars) detected in their close
proximity directly tracing the inflow direction. The interaction with the
accreted clumps, which can be regarded as minor-mergers, leads the major axes
of the three galaxies to be closely aligned with the outer
Lyman-$\alpha$-emitting feeding filaments. These results provide the first
observational evidence of the impact of cold accretion streams on the
formation and evolution of the galaxies they feed. In the current phase, this
is taking the form of the rapid buildup of bulges under the effects of
accretion, while still preserving massive quiescent and lopsided stellar disks
at least until encountering a violent major-merger.

###### Key Words.:

Galaxies: high-redshift – Galaxies: evolution – Submillimeter: galaxies –
Galaxies: groups: individual: RO-1001 – Galaxies: star formation – Galaxies:
structure

††offprints: Boris S. Kalita

##  1 Introduction

The formation of massive galaxies ($>10^{11}\,\rm M_{\odot}$) that happened
within the first $\sim 3\,\rm Gyr$ after the Big Bang sustained by cold
streams (Birnboim & Dekel, 2003; Kereš et al., 2005), is still not fully
understood (Somerville & Davé, 2015; Vogelsberger et al., 2020). Cold gas
accretion (which includes smooth gas as well as clumpy material) is expected
to be ubiquitous in high redshift dense environments (Dekel et al., 2009a).
Encouraging observational evidence for cold streams was recently obtained for
a sample of galaxy groups and clusters at $2.0<\rm z<3.3$ and for statistical
samples of massive galaxies (Daddi et al., 2022a, b). Yet there remains a
paucity of direct observations of how this critical process affects individual
galaxies. In general, the need of gas accretion fueling the star formation in
galaxies is abundantly clear, exemplified by the tight correlation between
their star formation rates (SFR) and the stellar mass at least up to $\rm
z\sim 4-6$ (the star-forming main-sequence; Daddi et al., 2007; Elbaz et al.,
2007; Whitaker et al., 2012; Speagle et al., 2014; Schreiber et al., 2015).
Morphologically, this phase is expected to feature secularly growing disks
(Daddi et al., 2010a; Tacconi et al., 2010; Dekel & Krumholz, 2013; Feldmann &
Mayer, 2015).

Meanwhile, to accomodate the existence of compact ($\sim 1\,\rm kpc$),
spheroidal, quiescent galaxies (QGs) observed at $\rm z\sim 2-4$ (e.g.,
Valentino et al., 2020b; Lustig et al., 2021; D’Eugenio et al., 2021) in
contrast to the relatively more extended star-forming disk galaxies (van der
Wel et al., 2014), an intermediate population of compact star-forming galaxies
(cSFGs) have been proposed and widely observed (Barro et al., 2013, 2014; van
Dokkum et al., 2015; Puglisi et al., 2019, 2021) . The feature at the heart of
this hypothesis, quite literally, is the compact star-forming core that is
expected to form the spheroidal bulge characteristic of the compact QGs. When
gas is driven into the central compact region, the increase in the gas surface
density results in a rise in star-formation that rapidly builds up the stellar
mass of the bulge. However, the mode of formation of these cSFGs has been a
matter of debate. On one hand, simulations predict that smooth-gas-accretion
driven violent disk instabilities result in the gas being driven to the core
of secularly evolving disk-like galaxies, once the galaxy mass reaches $\sim
10^{9.5}\,\rm M_{\odot}$ and thereby creating most of the stellar mass in a
compact spheroidal structure (_wet compaction_ ; Dekel et al., 2013; Zolotov
et al., 2015; Tacchella et al., 2016). Whereas observational studies of large
statistical samples advocate the rapid effects of major-mergers between
galaxies leading to the formation of such objects (Cimatti et al., 2008;
Ricciardelli et al., 2010; Fu et al., 2013; Ivison et al., 2013; Toft et al.,
2014, 2017; Elbaz et al., 2018; Gómez-Guijarro et al., 2018). Both scenarios
have its issues however. Wet compaction predicts the presence of high-gas
fractions in cSFGs that is simply not observed (Puglisi et al., 2021; Gómez-
Guijarro et al., 2022a, b). Whereas, a dominance of the merger-driven
starbursts (pushing them a factor of $3-4$ above the main sequence) would
suggest that the galaxy simply transitions through the star-forming main-
sequence on its way to becoming quiescent, making the tight correlation
between the SFR and stellar masses difficult to reproduce. Although, Elbaz et
al. (2018) does provide an tentative solution through a sub-population of
star-bursts ‘hidden’ within the main-sequence.

The morphology of cSFGs could hold clues to disentangling the processes.
Besides their characteristic sub-mm bright highly star-forming cores, the
surrounding stellar regions can also provide valuable information, which is
only possible through near-IR follow-ups of ALMA (sub-mm) detected cSFGs. In
the wet compaction scenario, once the galaxy enters its peak compaction phase
at $\sim 10^{9.5}\,\rm M_{\odot}$, the stellar disk (or a ‘proto-disk’) stays
constant or shrinks while the core rapidly builds up mass (Tacchella et al.,
2016). Whereas in case of major-mergers between massive galaxies, clear signs
of disturbed morphology, especially in the form of clumpy stellar structures
(at least during the initial phases) is anticipated (Lotz et al., 2006;
Bournaud et al., 2011; Rujopakarn et al., 2019; Calabrò et al., 2019) and
extended tidal-tails (e.g., Bridge et al., 2010; Wen & Zheng, 2016; Guo et
al., 2016). Attempts at characterizing the stellar regions are already
underway (e.g., Puglisi et al., 2021; Gómez-Guijarro et al., 2022a), with the
narrative swaying in favour of mergers (Elbaz et al., 2018; Rujopakarn et al.,
2019). Nevertheless, it is imperative to determine whether this is a universal
trend, especially in regions where galaxies are expected to grow under the
influence of high levels of accretion, which might be more conducive for the
wet compaction scenario.

Therefore, to attempt a resolution, one will have to specifically investigate
high-redshift massive dark-matter halos which are expected to allow the
penetration and survival of cold-gas streams into a hot halo (Kereš et al.,
2005; Dekel et al., 2009a). This is primarily driven by the expected evolution
with halo mass ($\propto\rm M_{DM}$) and redshift ($\propto\rm(1+z)^{\alpha}$
with $\alpha\approx 2.25-2.50$). Studying cSFG counterparts within such
accretion-rich environments is our best bet at disentangling the effects of
accretion and mergers. However, observationally establishing the presence of
infalling cold-gas streams in halos has proved to be extremely challenging,
with only a handful of convincing cases yet (using Ly-$\alpha$ emission as a
tracer; Martin et al., 2015, 2019; Umehata et al., 2019; Daddi et al., 2021,
2022a, 2022b). Following up on one of these cases, we investigate the galaxy-
group RO-1001 at $\rm z=2.91$ presented in Daddi et al. (2021). The structure
hosts three massive ($>10^{11}\,\rm M_{\odot}$) star-forming galaxies in its
inner core (along with an additional quiescent galaxy; Kalita et al., 2021b),
at the center of its $\sim 4\times 10^{13}\,\rm M_{\odot}$ dark-matter halo
potential well. They are all $<70$ kpc ($9^{\prime\prime}$) from the peak of
the giant 300 kpc-wide Lyman-$\alpha$ halo centered on the group, and
spectroscopically coincident with the intensity averaged Lyman-$\alpha$
emission within $\pm 500\,\rm km\,s^{-1}$ (Fig.1). Finally, the Lyman-$\alpha$
contours provide tentative identification of accretion-streams that are
expected to feed the central halo and hence the three star-forming galaxies
within.

It needs to be noted that whenever we refer to accretion in this work, we are
including both smooth gas as well as clumpy material. The latter is expected
to make up $\sim 1/3$ of the accreted matter (Dekel et al., 2009a) and its
interaction with the galaxies could be observationally characterised as minor-
mergers of varying mass-ratios. In this paper, we discuss the observational
data in Sec. 2, followed by the analysis and results (Sec. 3). We then discuss
galaxy morphology, star formation and their link to accretion in Sec. 4.
Finally, we provide the conclusions in Sec.8. Throughout, we adopt a
concordance $\Lambda$CDM cosmology, characterized by $\Omega_{m}=0.3$,
$\Omega_{\Lambda}=0.7$, and $\rm H_{0}=70$ km s${}^{-1}\rm Mpc^{-1}$. We use a
Chabrier initial mass function. Magnitudes and colors are on the AB scale. All
uncertainties on measured parameters that have been quoted indicate the $90\%$
confidence interval determined from the limits of $\Delta\chi^{2}=2.71$. All
images are oriented such that north is up and east is left.

##  2 Observational Data

To study the three star-forming galaxies (A, B and C) in RO-1001 (Fig. 1), we
make use of HST/WFC3 imaging in 3 bands (F160W, F125W and F606W) over a total
of 11 orbits during Cycle 27 (Proposal ID: 15190, PI: E. Daddi). The data
reduction was executed using the pipeline grizli
(https://github.com/gbrammer/grizli). The $5\sigma$ point-source sensitivities
reached are 26.25 (F160W), 26.47 (F125W) and 26.39 (F606W) with a pixel scale
of $0.06^{\prime\prime}$ and a half-power beam-width of $0.24^{\prime\prime}$
for F160W. Public COSMOS F814W imaging (Scoville et al., 2007) was also
incorporated into the analysis. Furthermore, we used the Ks-band image from
data release 4 of Ultra-VISTA (McCracken et al., 2012). Finally, IRAC
$3.6\,\mu$m and $4.5\,\mu$m images were taken from the Spitzer Matching Survey
of the Ultra-VISTA Deep Stripes (SMUVS; Ashby et al., 2018), while those at
$5.7\,\mu$m and $7.9\,\mu$m are obtained from the public COSMOS database
(Laigle et al., 2016).

New Atacama Large Millimetre Array (ALMA) band 7 observations, taken in Cycle
7 (Project ID: 2019.1.00399.S, PI: R.M. Rich) provide the sub-millimeter
information of our sources. The data reduction was carried out using the
Common Astronomy Software Application (CASA) and a maximum sensitivity of $\rm
28\,\mu Jy\,beam^{-1}$ was reached, with a synthesised beam size of
$0.49^{\prime\prime}\times 0.46^{\prime\prime}$. Finally, we utilize NOrthern
Extended Millimter Array (NOEMA) spectroscopy data to map the $\rm CO[3-2]$
transition in each of the three galaxies. The synthesized beam size at
$88.3\,\rm GHz$ is $4.0^{\prime\prime}\times 1.8^{\prime\prime}$. The spectra
creation and analysis is carried out using a GILDAS-based pipeline
(http://www.iram.fr/IRAMFR/GILDAS), and has been already discussed in a
previous work (Daddi et al., 2021).

##  3 Analysis

Figure 1: Location of the massive star-forming galaxies in the network of
Lyman-$\alpha$ filaments. (Left) Color image composite of RO-1001, using
observations in F160W, F125W and F606W. The ALMA data has been co-added to
that in F606W since both trace star-formation, differing based on dust
obscuration. The scaling of the ALMA data was done based on its flux to SFR
ratio in comparison to the same for that in F606W. The white dashed contours
trace the Lyman-$\alpha$ halo whereas the cyan arrows show the tentative
directions of the three gas-accretion filaments converging onto the center of
the group potential well (the correspondence to the galaxies is discussed in
detail in Sec. 5.2). (Right) Zoom on the three star-forming galaxies (A, B and
C) as seen in ALMA sub-millimeter dust-emission while the white contours trace
the F160W flux tracing stellar light. The contours begin at $4\sigma$ with
increments of $4\sigma$. The arrows indicate the direction of the streams,
which are shown in green if they are aligned with the major axis of the
galactic disks (in dashed white lines), as discussed in Sec. 5.2. Those which
are not, are in red. In case of Galaxy-A, we rather show the major axis of the
ALMA contour with the white dashed line.

We use the combination of the data listed above (Sec. 2) to derive the
properties of the three star-forming galaxies in RO-1001. Each of them show
extremely compact sub-millimeter bright rotating cores primarily centered on
the much more extended ($4-9\,\times$) near-IR detected stellar components
(Fig.1, right panel), with both being co-planar in at least 2/3 cases
(Galaxies B and C). The stellar regions also show marked lopsidedness in their
emission. We investigate in detail each of these aspects of the galaxies in
this section. Given that Galaxy-B is the most extended and hence best
resolved, we always begin with the description of its analysis for simplicity.
We then proceed to Galaxies A and C, where the same prescription as that for
Galaxy-B is used.

Table 1: Properties of the star-forming massive galaxies in RO-1001

ID |  | A | B | C
---|---|---|---|---
RA |  | 10:01:23.174 | 10:01:22.964 | 10:01:22.369
DEC |  | 02:20:05.57 | 02:20:05.87 | 02:20:02.63
$z_{\rm spec}$ |  | 2.9214 | 2.9156 | 2.9064
$\log\rm M_{\star}$ (1) | $\rm M_{\odot}$ | 11.50${}^{+0.15}_{-0.19}$ | 11.20${}^{+0.07}_{-0.14}$ | 11.26${}^{+0.14}_{-0.10}$
$S_{\nu}$(870 $\mu$m) | mJy | $4.44\pm 0.05$ | $8.69\pm 0.03$ | $4.04\pm 0.11$
SFRcore (2) |  $\rm M_{\odot}$ yr-1 | $345\pm 55$ | $674\pm 106$ | $313\pm 50$
SFRdisk_ALMA (2) |  $\rm M_{\odot}$ yr-1 | $<60^{**}$ | $<19^{**}$ | $<43^{**}$
SFRdisk_SED (1) |  $\rm M_{\odot}$ yr-1 |  $66^{+446}_{-49}$ (3) | $42^{+51}_{-37}$ | $94_{-94}^{+66}$
t50 (1) | $\rm Gyr$ | $1.7^{+0.3}_{-0.7}$ | $0.5^{+0.7}_{-0.2}$ | $0.2_{-0.1}^{+1.3}$
re_disk | kpc | $3\pm 1$ | $9\pm 2$ | $4\pm 1$
rdisk/rcore |  | $4\pm 1$ | $9\pm 2$ | $5\pm 1$
log Mmol | M⊙ | 9.8 | 10.7 | 10.6
FWZVCO[3-2] (4) | km s-1 | 381 | 1114 | 1098
log Mdyn,tot (5) | M⊙ | 10.4 | 11.1 | 11.2
Av |  | $1.8_{1.3}^{2.1}$ | $1.0_{0.4}^{1.2}$ | $1.6^{1.8}_{0.4}$

Notes: (1) Estimated from the composite-$\tau$ model fitting to optical and
near-IR photometry and therefore primarily associated with the disks (2)
Derived from the $870\mu$m flux of individual galaxies assuming the same SED
shape as for their coaddition (Daddi et al., 2021). (3) This high upper-limit
from the composite-$\tau$ model is in agreement with a constant star formation
model being within $90\%$ confidence interval (4) Full Width at Zero Velocity
as previously reported (Daddi et al., 2021). (5) Dynamical mass primarily
associated with the core, rather than the whole galaxy as described in the
main text. ∗∗ $3\sigma$ upper-limits.

###  3.1 Near-IR surface brightness fitting.

Figure 2: (Left panel) The HST F160W cutouts of Galaxies-A and B (top) and
Galaxy-C (bottom) used for the morphological model fitting. (Middle and right
panels) The GALFIT returned models and residuals of the same cutouts. In the
latter, only the RO-1001 galaxy models have been subtracted. The rest of the
sources, although used during the fit, have been left in the image.

We investigate the distribution of rest-frame optical emission in Galaxy-B by
model-fitting (Fig. 2) the intensity profiles using the software GALFIT (Peng
et al., 2002, 2010). The H-band (F160W) image is used since it has the highest
signal-to-noise among the available bands. We find that fitting and
subtracting a double Sérsic profile (with indices $\sim 0.5$) gives the best
result, assessed by the maximum fluctuations in the residual image (found to
be $<1\sigma$). Care is taken to simultaneously subtract all nearby sources
within $\sim 8^{\prime\prime}$. We also fit the same profile, convolved with
the appropriate point-source-functions (PSFs), to the images in all other
observed wavelength windows to ascertain consistency. We find no $>1\sigma$
fluctuations in the respective residual images. We find that the two Sérsic
profiles for Galaxy-B are clearly not spatially coincident with the sub-
millimeter bright compact core (discussed below in Sec. 3.2), but rather fall
$\sim 0.8^{\prime\prime}$ on either side of it (and hence with a spatial
separation of $\sim 0.16^{\prime\prime}$ between the two Sérsic profile
centres). We also find remarkable consistency of the axes ratio and position
angles of the two Sérsic profiles, hence likely part of a continuous stellar
structure. We repeat this procedure for Galaxies A and C. Galaxy-A is found to
have a complex morphology which is fit with a double Sérsic in differing
(almost orthogonal) orientations. Galaxy-C on the other hand is found to
resemble Galaxy-B in terms of an accordance with two co-aligned Sérsic
profiles with low indices ($<1$) on either side of sub-millimeter core. But in
this case the separation is $\sim 0.2^{\prime\prime}$, making it more compact
than Galaxy-B.

To measure integrated effective radii ($\rm r_{e}$) of each of the galaxies,
we did an additional round of fitting using single Sérsic profiles. Besides
using the generic version of the Sérsic profile, we also invoke the $\rm m=1$
Fourier component to account for the lopsidedness of the stellar components.
This is due to quantify the emission asymmetry we observe in each of the cases
which is later discussed in Sec. 5.1. We also measure growth curves using
circular apertures with their centers fixed at the ALMA core of the galaxies
to independently determine the effective radius. For Galaxy-A, we only use the
northern component of its complex near-IR double emission, which we determine
as the primary stellar region due to its proximity to the sub-mm emission. We
use the average of all three methods that are consistent within $15-20\%$, to
obtain the final measurements reported in Table 1: $3\pm 1\,\rm kpc$, $9\pm
2\,\rm kpc$ and $4\pm 1\,\rm kpc$ for Galaxies-A, B and C respectively. It is
noteworthy that for each galaxy, the single profiles are characterised by
Sérsic indices $<1$, indicating disk-like morphology (and hence we refer to
them as disks throughout this work, a conclusion which will be reinforced in
Sec. 4.2). The ellipticities measured for the three galaxies are $0.5\pm
0.1,0.15\pm 0.05$ and $0.5\pm 0.2$ (A, B and C), indicating an almost edge-on
orientation for Galaxy-B.

Table 2: Derived morphological Spergel parameters in sub-millimeter

ID |  | A | B | C
---|---|---|---|---
effective radius${}_{\rm major}^{**}$ | arcsec | $0.092\pm 0.004$ | $0.148\pm 0.002$ | $0.122\pm 0.054$
| kpc | $0.72\pm 0.02$ | $1.15\pm 0.01$ | $0.95\pm 0.42$
Ellipticity |  | $0.62\pm 0.03$ | $0.40\pm 0.01$ | $0.47\pm 0.22$
Position angle | degrees | $-90.6\pm 0.6$ | $-27.4\pm 0.3$ | $-46.4\pm 0.6$
$\Delta$angledisk,bulge (1) | degrees |  – | $3.4\pm 1.5$ | $2.9\pm 1.5$
Spergel index (2) |  | $-0.6\pm 0.2$ | $0.5\pm 0.3$ | $-0.5\pm 0.3$

Notes: (1) The difference between position angles of the stellar disk in HST
F160W and that of the sub-millimeter core. The lack of a value in case of
Galaxy-A is due to its stellar emission having a complex morphology without a
clear position angle for the whole galaxy. (2) Spergel index values 0.5 and
-0.6 correspond to Sérsic indices 1 and 4 respectively. ∗∗ $\sim$ effective
radius of the corresponding Sérsic profile, as has been determined through
modelling Sérsic and Spergel profiles (Tan et al. in prep.)

Figure 3: Components of the three galaxies on the star-forming main-sequence:
star-bursting bulges and quiescent disks. The SFR vs stellar-mass values of
the star-bursting core, the quiescent stellar disk and the combination of the
two placed with respect to the star-forming main-sequence (Schreiber et al.,
2015) at $\rm z=3$, shown as the black solid line. The shaded region
demarcates the 0.3 dex uncertainty in the relation. We use the $3\sigma$ ALMA
upper-limits as the value for SFR with the associated grey error-bars showing
the range allowed by our SED model fitting.The latter have been artificially
offset in the x-axis to emphasize the difference in the method of measurement.

###  3.2 Sub-millimeter emission analysis

Figure 4: The top panel shows the ALMA $870\,\mu\rm m$ image of the core of
RO-1001 with the three star-forming galaxies clearly visible. Each of them
were fit with intensity profiles which were then subtracted to obtain the
residual image displayed in the bottom panel. The ALMA PSF at $870\,\mu\rm m$
is shown in the inset on the top right.

The compact highly star-forming regions of the galaxies are detected thanks to
their dust emission using ALMA at $870\,\mu$m. It is noteworthy that due to a
well characterised PSF and high signal-to-noise, we have the ability to map
structures much smaller than the integrated ALMA PSF (Rujopakarn et al.,
2019). We begin with a detailed morphological analysis of the emission region
in Galaxy-B. Due to the data being distributed over multiple partially
overlapping pointings, we combine the ones with Galaxy-B within their primary
beam. To do so, we follow the procedure outlined in Gómez-Guijarro et al.
(2022a), for combination and stacking of individual pointings in ALMA. We
phase shift each of them to set the source coordinates at their respective
phase center. Finally, the pointings are combined into a single measurement
set which provides the maximum sensitivity available with our data.

Since the Sérsic profile, commonly used to study galaxy morphologies, cannot
be easily extended to the UV space due to its Fourier transform not being
analytically expressible, we use a substitute. We exploit the Spergel profile
(Spergel, 2010), recently incorporated within the MAPPING procedure of GILDAS.
This has been found to correlate well with the Sérsic profile allowing us to
extract Sérsic parameters corresponding to the Spergel parameters we
determine. To also determine the robustness of the fitting procedure (Fig. 4;
Table. 2), we perturb the initial parameters within a factor of 5 over a total
of $\sim 200$ times and repeat the fitting. We also artificially inject $1000$
times the best fitting model of each galaxy at different empty locations (one
at a time) and fit them individually to estimate reliable error for our
measurements based on the a-posteriori dispersion of resulting parameters.
This procedure also shows that there are no detectable systematic biases in
the measured quantities.

For Galaxy-B, we obtain an almost-perfect exponential profile characteristic
of a disk of effective radius $\sim 1.1\,\rm kpc$, with a Spergel index of
$0.55\pm 0.12$ (Sérsic index $\sim 1$) and an ellipticity of $0.40\pm 0.01$.
From the model hence returned, we measure the $870\,\mu$m observed-frame flux.
This is converted to a total-infrared luminosity ($\rm L_{\rm IR}$;
$8-1000\,\mu$m) using the integrated SED from the co-added photometry of
RO-1001 (Daddi et al., 2021). This can then be converted to a SFR of $674\pm
106\,\rm M_{\odot}\,yr^{-1}$ using the widely adopted conversion relation
(Kennicutt, 1998; Daddi et al., 2010b):

$\rm SFR_{\rm IR}[\rm M_{\rm\odot}\,yr^{-1}]=1.0\times 10^{-10}\,\rm L_{\rm
IR}[\rm L_{\odot}]$ (1)

The error for this measurement is determined from the $1\sigma$ dispersion in
the dust-temperature dependent parameter $<\rm U>$, that is usually invoked
during the conversion of the $870\,\mu$m flux to $\rm L_{\rm IR}$. We use this
to account for variations in dust temperature of individual galaxies with
respect to the average value. This approach of evaluating SFR uncertainties is
over-conservative, as it does not take into account that the integrated
bolometric IR luminosity (hence SFR) of the 3 galaxies that is known to better
than $10\%$ accuracy, given the well sampled IR SED including Herschel (Daddi
et al., 2021).

In Galaxy-A, we obtain a much different Spergel index ($-0.61\pm 0.04$) that
translates to a Sérsic index $\sim 4$. The situation is similar in Galaxy-C
with a Spergel index of $-0.48\pm 0.12$, although it has an additional point
source adjacent to it (at $0.14^{\prime\prime}$). The sizes of these profiles
are very compact with effective radii $\sim 0.7\,\rm kpc$ and $0.9\,\rm$kpc.
We measure the SFR using the same prescription as that for Galaxy-B, and
estimate values of $345\pm 55\,\rm M_{\odot}\,yr^{-1}$ and $313\pm 50\,\rm
M_{\odot}\,yr^{-1}$ for Galaxies A and C respectively.

###  3.3 Determining the quiescence of the stellar regions

Besides the measurements for the sub-mm bright compact cores, the high
resolution $870\,\mu\rm m$ map (Sec. 2) also provides us with constraints on
the levels of star formation in the surrounding regions. We are mainly
interested in the estimates for the extended stellar regions detected in near-
IR, that lack any sub-mm emission. Using the H-band models as fixed priors, we
measure $3\sigma$ upper-limits for each of the galaxies by simultaneously
fitting them along with the primary profiles for the cores in the ALMA data
(uv plane). For Galaxy-B, we estimate a $3\sigma$ flux upper-limit of
$0.25\,\rm mJy$ (corresponding to an SFR upper-limit of $19\,\rm
M_{\odot}\,yr^{-1}$) for the stellar disk, while we obtain $0.77\,\rm mJy$ and
$0.55\,\rm mJy$ ($60\,\rm M_{\odot}\,yr^{-1}$ and $43\,\rm
M_{\odot}\,yr^{-1}$) for galaxies A and C respectively. This provides clear
evidence of almost all star formation being concentrated at the core leaving
the massive stellar disks devoid of it and well below the star-forming main-
sequence (Fig. 3).

We note that the estimation of the star formation upper limits in the stellar
disks should be considered as overly conservative. This is because the
conversion to SFR is done based on the average IR SED in the group which is
driven by the co-addition of the emission from all three sub-mm bright
galactic cores in RO-1001 that have a much higher SFR surface density
($\Sigma_{\rm SFR}$; e.g., see Fig. 8). Hence, the dust temperature in the
disks would likely be lower due to a softer radiation field (based on the
star-formation surface density vs. dust temperature relation, Valentino et
al., 2020a, see also Magdis et al. 2012; Magnelli et al. 2014; Daddi et al.
2015), which would in turn drive our $3\sigma$ upper-limit even lower,
probably at least by factors of 2–3.

###  3.4 Star formation history modelling

Figure 5: The best-fit SED models in optical and near-IR for each of the three
star-forming galaxies in RO-1001. The photometry with their respective
errorbars are shown in red. The cyan contours show a modified SED with an
addition of an example $0.1\,$Gyr old highly obscured ($\rm A_{V}=6.5-7.5$)
constant star-formation history SED in each case. In each case, the resulting
stellar-masses are in agreement with our $\rm CO[3-2]$ estimates within 0.1
dex and are hence a representation of contributions of the star-bursting
cores. Figure 6: The UVJ colors of high-z QGs ($\rm z>2.5$) adapted from
D’Eugenio et al. (2020). The post-star burst region is demarcated with the red
box as specified in Belli et al. (2019). The marker sizes are proportional to
the stellar mass. The red and blue stars are the dust uncorrected and
corrected measurements of the quiescent stellar disks in the three star-
forming galaxies within our sample. The final star in orange marks the
location of Galaxy-D, a quiescent galaxy photometrically confirmed to be part
of RO-1001 (Kalita et al., 2021b)

We make use of the photometry obtained in observed frame optical and near-IR,
to estimate a star formation history (SFH) and thereby the age of the stellar
population as well as stellar masses. The measurements can primarily be
attributed to the stellar disks since the prodigious sub-millimeter flux from
the cores is by design at the expense of UV rest-frame flux. However, during
our fitting procedure, we do fix an additional core component in each case
using positional priors obtained in Sec. 3.2. Except in the IRAC bands, all
others return fluxes $<5\%$ of the total galaxy flux. However for IRAC, the
PSF is a factor $\sim 10$ larger than that of HST and a factor $\sim 5$
compared to Ultra-VISTA. Hence in this case, the sources are unresolved and
this leads to the photometry corresponding to the integration over the whole
galaxy. Albeit, in each of the cases the stellar mass within the core is
expected to be $<10\%$ (based on estimates discussed in Sec. 3.5) that ensures
a minimal contribution. Nevertheless, Fig. 5 does suggest progressively higher
fluxes in the IRAC bands, leading to offsets from SED models. To limit the
influence of the rapidly star-forming core, primarily in the IRAC bands with
insufficient resolution to disentangle the core from the disk, we execute the
SED fitting in three stages. The first is done using photometry up to the
bands where the galaxies are well-resolved ($2.1\mu$m). We then include the
remaining 4 bands in pairs of two. We find that the results from the first two
stages are almost identical within their errors and hence use the results of
the second stage (up to the $4.5\mu$m band; due to better constraints). We
show in Fig. 5 that the net photometry at the third stage is reproducible
using the SED derived at stage-two and an additional highly obscured component
for the core.

For a description of the SED model fitting, we refer the readers to Appendix
A. The procedure for Galaxy-B returns the lowest reduced $\chi^{2}$ of $2.0$
for the two declining SFH models used (composite-$\tau$ and delayed-$\tau$).
In case of a constant star-formation model this value is found to be $6.8$
that translates to a $\Delta\chi^{2}=38$, making it highly unlikely. Hence,
this indicates that the disk in Galaxy-B is undergoing a decline in star-
formation, as already conclusively demonstrated by the ALMA upper limts. We
also determine this decline to be significant by measuring the age/$\tau$
ratio from the delayed-$\tau$ models and it is found to be $7\pm 1$. Given
that the composite-$\tau$ models are relatively more robust, we use them to
measure the look-back time of half-mass formation ($\rm
t_{50}=0.5^{+0.7}_{-0.2}\,\rm Gyr$), that can be considered to be the
approximate epoch at which the last major star formation episode had occurred.
However, the results from delayed-$\tau$ models are also in agreement.
Furthermore, we obtain a SFR estimate of $42^{+51}_{-37}\,\rm
M_{\odot}\,yr^{-1}$, consistent with the ALMA $3\sigma$ upper-limit.

The picture is slightly less strict in Galaxy-C followed by Galaxy-A. In the
former, the declining models still give the best fit (reduced-$\chi^{2}=1.9$)
and a $\rm t_{50}=0.2^{+1.3}_{-0.1}\,\rm Gyr$. But the constant star formation
model is relatively less unlikely than for Galaxy-B, with a reduced-$\chi^{2}$
of 3.7. Galaxy-A on the other hand has values of 0.8 and 1.1 for almost
equally plausible declining and constant star formation models, allowing for
possible ongoing star formation in the disk. Nevertheless, the SFR in both
these cases ($94^{+66}_{-94}\,\rm M_{\odot}\,yr^{-1}$ for Galaxy-A and
$66^{+446}_{-49}\,\rm M_{\odot}\,yr^{-1}$ for Galaxy-C) are still in general
agreement with the much more stringent ALMA $3\sigma$ upper-limit.

We also derive UVJ colors (Fig. 6) not so much to ascertain quiescence that is
already unambiguously demonstrated by ALMA, but rather to compare them to more
classical exemples of high redshift quiescent galaxies. Of special interest
are the widely studied post-starburst (PSB) galaxies that have experienced
quenching of star-formation over the last $<0.8\,\rm Gyr$ and generally show
low dust attenuation (Gobat et al., 2012; Schreiber et al., 2018; Forrest et
al., 2020; D’Eugenio et al., 2020; Forrest et al., 2020; Valentino et al.,
2020b). The PSB ages are potentially similar to the mass-weighted ages derived
for our sample, while attenuation in our case is larger (Table. 1). We find
that the observed UVJ colors of our quiescent disks are much redder than those
of known population of quiescent systems at $z\sim 3$. Also, at least in two
cases they are scattered just outside of the formal UVJ-passive boundary.
However, when correcting for dust reddening the colors of the three galaxies
in RO-1001 more closely resemble those of PSBs as well as of the massive
quiescent galaxy with a mass-weighted age $>1\rm\,Gyr$ (Kalita et al., 2021b)
within the same group (Fig. 6).

Finally for Galaxy-B, we pay special attention to the spatial decomposition of
the stellar mass estimates (listed in Table. 1) derived from the SED fitting
procedure – by obtaining separate photometry of the northern and southern
sections of its elongated disk. This is to quantify the lopsidedness in the
stellar structure. We hence find the total stellar mass of $1.6\pm 0.4\times
10^{11}\,\rm M_{\odot}$ for the complete stellar region is divided into
$1.1\times 10^{11}\,\rm M_{\odot}$ and $0.5\times 10^{11}\,\rm M_{\odot}$ for
the northern and southern segments. It is noteworthy that for this analysis,
we only use observations up to the $2.1\,\mu$m band beyond which the
resolution is too low to spatially disentangle the two parts.

###  3.5 Rotating gas traced by $\rm CO[3-2]$ transition.

Figure 7: Two panels showing the rotational properties in Galaxies B and C
with three individual sub-images: (top-left) the NOEMA $\rm CO[3-2]$ emission
profiles for the blue and red-shifted sections with respect to the average
galaxy profile shown as contours superimposed on the F160W image; (bottom-
left) The NOEMA spectra with the $\rm CO[3-2]$ emission line in blue and the
local Lyman-$\alpha$ profile in red; (right) The contours of the stellar disk
(black; beginning at $8\sigma$ with increments of $4\sigma$), the compact core
(white; beginning at $100\sigma$ with increments of $50\sigma$ for Galaxy-B
and at $50\sigma$ with increments of $25\sigma$ for Galaxy-C) and a
representation of the blue and red-shifted $\rm CO[3-2]$ emission locations
with the size of the compact core as seen in ALMA. The expected rotational
axes have been also been provided for each component – disk in red, core in
blue and $\rm CO[3-2]$ emission as black dashed lines. The NOEMA spin axes
uncertainties are large enough to make the difference with the other component
not statistically significant.

A direct spectroscopic tracer of the gas content of the galaxies is available
in the form of NOEMA $\rm CO[3-2]$ transition observations. For Galaxy-B, we
use its integrated luminosity ($\rm log(L^{{}^{\prime}}_{\rm CO(3-2)}/({\rm
K\,km^{-1}pc^{2}}))=10.46$) to estimate a gas mass. This is calculated from
the line flux (Daddi et al., 2021) using the relation prescribed in a recent
work (Silverman et al., 2018). Using a standard $\rm R31=0.5$ (Daddi et al.
2015; Valentino et al. 2020; Boogardt et al. 2020), we hence derive $\rm
log(L^{{}^{\prime}}_{\rm CO(1-0)})=10.76$. The gas mass is finally computed as
M${}_{\rm mol}=\alpha_{\rm CO}\times{\rm L}^{{}^{\prime}}_{\rm CO(1-0)}$ by
adopting a conversion factor $\alpha_{\rm CO}=0.8\ {\rm
M}_{\odot}{\rm(K\,kms^{-1}pc^{2})}^{-1}$ as expected in starbursts (given
location of the cores, with respect to the star-forming main-sequence in Fig.
3, and their very high SFR surface densities). This provides values of
$4.6\times 10^{10}\,\rm M_{\odot}$, $0.7\times 10^{10}\,\rm M_{\odot}$,
$4.2\times 10^{10}\,\rm M_{\odot}$ for Galaxy-B, A and C respectively.
Although, we do acknowledge that this estimate is dependent on our choice of
conversion factors. Nevertheless, we can place a strict upper-limit on the gas
mass using the dynamical mass estimates calculated below (i.e., in the
limiting case in which there was no stellar mass nor dark matter in the
cores), which is less than $2\times$ above the current values in each case. A
Milky-Way-like $\alpha_{\rm CO}$ would have resulted in a factor of 5 higher
gas-mass. Hence, these are in direct conflict with the dynamical mass values.
Moreover, any increase in gas-mass would also indicate almost a negligible
stellar mass, which in turn would place the galaxy-cores at a much higher
offset from the star-forming main-sequence. This would suggest even more star-
burst-like characteristics.

The width of the emission line in Galaxy-B is used to determine the dynamical
mass within the dusty core where the gas is expected to be confined. Given the
sub-millimeter emission profile of the core is found to resemble a disk, we
measure the $\rm M_{\rm dyn,r_{e}}$ within the effective radius $\rm r_{e}$
using the following relation (Daddi et al., 2010a):

$\rm M_{\rm dyn,r_{e}}=1.3\times\frac{\rm r_{e}\times\left(FWZV_{\rm
CO[3-2]}/2\right)^{2}}{G\,{sin^{2}}i}\pm 12.5\%$ (2)

The effective radius returned from the sub-millimeter emission profile is used
in this equation. The width of the line, quantified by the parameter $\rm
FWZV_{\rm CO[3-2]}$ is already reported in Table. 1, while the inclination
angle (i) is determined based on the ellipticity of the sub-millimeter
profile. Subsequently, we measure the total dynamical mass, $\rm M_{\rm
dyn,tot}=2\times\rm M_{\rm dyn,r_{e}}=1.3\pm 0.1\times 10^{11}\,\rm
M_{\odot}$. The factor of 2 in invoked since only half of the mass is
contained within $\rm r_{\rm e}$. We use the same procedure to obtain $\rm
M_{\rm dyn,tot}=2.6\pm 0.3\times 10^{10}\,\rm M_{\odot}$ and $1.7\pm 0.2\times
10^{11}\,\rm M_{\odot}$ for Galaxies A and C. However, given their cores have
morphology closer to a Sérsic index of 4, we re-estimate the $\rm M_{\rm
dyn,tot}$ using the following formula applicable to an elliptical galaxy
dominated by random motion.

$\rm M_{\rm dyn,r_{e}}\approx 5.0\,\frac{\rm r_{e}\,\sigma_{e}^{2}}{G}$ (3)

We measure the total dynamical masses of $\sim 2.2\times 10^{10}\,\rm
M_{\odot}$ and $2.4\times 10^{11}\,\rm M_{\odot}$ for Galaxies A and C
respectively, reasonably consistent with our earlier estimates. Although the
relatively high discrepancy in case of Galaxy-C likely points to the
rotational-dominance expected in a gas-rich structure. Nevertheless, we do not
expect the structures to fully conform to such a dynamical arrangement due to
the inherent dissipative nature of gas within them.

Finally, two separate continuum images are created for Galaxies B and C, by
dividing the whole spectral range into two segments that are separated by the
average location of the $\rm CO[3-2]$ emission of the whole galaxy. The offset
between the peaks trace the plane of rotation, which are found to be in
agreement with the major axes of the respective galaxies in both sub-
millimeter and near-IR (Fig. 7). A similar analysis is not possible for
Galaxy-A due to a low signal-to-noise of the $\rm CO[3-2]$ detection.

##  4 Results

###  4.1 Compact star-forming cores in extended quiescent stellar disks

The spatial decomposition of surface-brightness profiles of the galaxies
reveals extremely compact sub-millimeter bright rotating cores and extended
near-IR detected co-planar stellar disks showing varying levels of
lopsidedness (Fig.1, right panel). The size contrast is evident from the high
near-IR to sub-mm radius ratios: $\sim 5$–8 for Galaxy-B, while in case of
Galaxy-A and C it is $4\pm 1$ and $5\pm 1$. Majority of the star formation is
concentrated in the cores, with the IR-based SFR in the cores being a factor
of $6-36\times$ higher than the $3\,\sigma$ upper-limits in the disks. The
mass concentrations also displays this dichotomy between the cores and the
stellar components. Using the difference between the $\rm CO[3-2]$ derived
dynamical masses and the gas masses, we obtain approximate stellar masses of
the cores for each galaxy ($\approx 2\times 10^{10}\,\rm M_{\odot},8\times
10^{10}\,\rm M_{\odot}$ and $12\times 10^{10}\,\rm M_{\odot}$). These are
concentrated within the areas $>60\,\times$ compact than the extended stellar
regions that feature stellar masses of $3.2\pm 1.3\times 10^{11}\,\rm
M_{\odot}$, $1.6\pm 0.4\times 10^{11}\,\rm M_{\odot}$ and $1.8\pm 0.5\times
10^{11}\,\rm M_{\odot}$.

###  4.2 Morphological characterisation

Figure 8: Spatial distribution of Galaxy-B stellar mass and star formation
rates. (Left) The upper panel shows SFR distribution model of Galaxy-B, with
the morphology determined by the F160W stellar emission in case of the disk,
and the ALMA dust emission for the core. The amplitudes are determined by the
SFR of the two components. The lower panel is a 1-D representation of the plot
above, after a rotation the make the major axis horizontal. (Middle) The
stellar mass distribution following the same procedure. Here the mass in the
core is determined from the difference between the dynamical mass and gas-mass
determined from the $\rm CO[3-2]$ emission line. (Right) The specific SFR
provided by the ratio of the SFR and the stellar mass.

The single-peaked profiles point to these galaxies consisting of singular
(albeit, lopsided) disks with central cores. This is corroborated by the
single Sérsic profile fits (with indices $\lesssim 1$; Sec. 3.1) to their
near-IR surface-brightness profiles. About $10-40\%$ of the stellar mass is
concentrated in the cores occupying $<1\%$ of the surface area of the whole
galaxy. This is illustrated in Fig.8 for Galaxy-B, the most extended of the
three galaxies. We find comparable contrasts in the other two galaxies (based
on their near-IR to sub-mm ratio, Table 1). Hence, the cores of these galaxies
are likely forming the future stellar bulges. This is characterised by their
nuclear location, masses, the extreme compactness similar to $z\sim 2$–3
passive galaxies (Daddi et al., 2005), and their sub-millimeter surface
brightness profiles with Sérsic index $\sim 4$ for Galaxies-A and C, which is
relatively unusual (Barro et al., 2016; Martig & Bournaud, 2008, indicate that
the indices should be closer to that for a disk). Galaxy-B although has an
index $\sim 1$, but the higher ellipticity of the core ($0.40\pm 0.01$) in
comparison to the disk ($0.15\pm 0.05$) still supports the idea of bulge
formation.

For Galaxies B and C, we do not expect their stellar disks to have been
perturbed by major-mergers involving equal-mass galaxies (with ratios 1:1 to
$\sim\,$1:3), which have been studied in multiple simulations over the years
(e.g., Bendo & Barnes, 2000; Bournaud et al., 2005b; Nevin et al., 2019).
Firstly, we conclude a lack of any visible disturbance in the disks from our
well resolved and high signal-to-noise HST imaging (Fig. 1, right). Had these
undergone major-mergers, they would have had to consist of two perfectly
aligned disks at a very early stage of collision (pre-coalescence), the
probability of which is $0.1\%$ and $0.4\%$ for Galaxies B and C respectively
based on the probability of the specific geometrical orientation (having
uncertainties equal to the thickness of the disks). Coupled with the
concurrence of both these galaxies are detected in the same exact scenario,
the probability reduces to a negligible $0.04\%$. Moreover, the temporal
aspect also makes such a scenario even more unlikely – given that both
Galaxy-B and C are detected in the same situation within the observation
window. Furthermore, had a major-merger been the case, one would have detected
a bi-modality in the mass distribution associated with each participating
galaxy rather than a centrally peaked profile, especially seen in Galaxy-B
(Fig.8). An alternate scenario would have been the near-IR detected stellar
disk and the sub-millimeter core are actually two separate galaxies. However,
we also reject such a scenario due to the sub-millimeter bright segment being
perfectly at the geometric center of the stellar emission region in not one
but two separate cases within the same group. In Galaxy-A, with its disturbed
stellar morphology however, the situation is different from its neighbors. As
discussed earlier, the stellar emission can be decomposed into two almost
perpendicular orientations. We observe that one of the two (the northern
component) is better coinciding with the compact ALMA core, similar to that in
Galaxies B and C. We therefore identify it as the primary stellar disk of
Galaxy-A. The additional component is likely an in-falling equal-mass galaxy.

In at least two of the galaxies (B and C), the major axes of both the core and
the disk are aligned within $\sim 3^{\circ}$, as well as with the major axis
implied by the rotational patterns of the gas in the respective cores,
determined from the $\rm CO[3-2]$ emission (Fig. 7). This is dependent on a
reasonable assumption that the gas is confined within the same area as the
dust. Hence, we conclude that these two galaxies have co-planar (and possibly
co-rotating) stellar-disks and compact cores. The current data does not allow
us to measure the major axis direction of the rotational pattern, or the
severely lopsided stellar disk (by a factor $>3$, towards South) of Galaxy-A.
For the latter, we are likely observing only the ‘heavier’ part of the disk
and hence the disk size and shape parameters cannot be satisfactorily
determined. For Galaxy C, the ellipticities of the core and the stellar
component are found to be in agreement (within $0.1$). But in Galaxy-B, where
the stellar component is observed edge-on (with an ellipticity of $0.15\pm
0.05$), the core has a larger ellipticity ($0.40\pm 0.01$). However, it should
be noted that all the three cores have values within $0.4-0.6$.

###  4.3 Young cores within older disks.

For the three cores, we find short gas-consumption timescales of $20\,\rm
Myr$, $70\,\rm Myr$ and $130\,\rm Myr$ and time taken to build the stellar
masses, assuming constant rates of star-formation, $\sim 60\,\rm Myr$,
$120\,\rm Myr$ and $400\,\rm Myr$. However, the short timescales $\sim
100\,\rm Myr$ for three such neighbouring objects makes them statistically
unlikely to be simultaneously observed. Hence we propose that the extreme star
formation levels is rather the culmination of an increase over a larger period
of time. The rate and the beginning of this increase cannot be ascertained.
Nevertheless, these are still similar or smaller compared to the time scales
characterising the decline in star-formation of the stellar components, based
on the goodness-of-fit from the best-fit SED composite $\tau$-models(Schreiber
et al., 2018): the look-back times to the epoch of half-mass formation ($\rm
t_{50}$) are $1.7^{+0.3}_{-0.7}\,\rm Gyr$, $0.5^{+0.7}_{-0.2}\,\rm Gyr$ and
$0.2_{-0.1}^{+1.3}\,\rm Gyr$ for Galaxies A, B and C. Hence, the star-bursting
cores only started getting built after the disks had already formed about half
of their stellar mass and were past their last major episode of star-
formation.

##  5 Discussion

In this section, we revisit the key observational results and discuss how
their interplay leads to a coherent picture of the evolution of the three
star-forming galaxies in RO-1001. Each of them feature extended stellar disks
that are lopsided and quiescent, along with highly star-forming compact cores
within them.

###  5.1 Lopsidedness and quiescence of the disks

We first begin with the severe lopsidedness of the stellar disks (Fig. 1,
right panel). For Galaxy-B, the asymmetry in the stellar emission (of a factor
of 2.0 in F160W/HST) manifests as a mass lopsidedness of 2.2 (Sec. 3.4) along
the major-axis (Fig. 9). In Galaxy-C, the emission asymmetry, also along the
major axis, is 1.6. The current data does not allow us to measure the major
axis direction of the stellar disk of Galaxy-A, but only the lopsidedness
upper limit ($>3$) and direction (South), that is nearly perpendicular to the
East-West ALMA core major axis (Fig. 9). Such asymmetries, not yet recognised
at high redshifts, are in fact a common characteristic among spiral galaxies
in the local Universe (Sancisi et al., 2008; Rix & Zaritsky, 1995; Zaritsky &
Rix, 1997; Reichard et al., 2008), although relatively less pronounced. Since
lopsidedness is usually contributed to tidal interactions and in-situ star-
formation asymmetry (Sancisi et al., 2008), we attribute the strong
lopsidedness in our sample to the accretion of material onto the galaxies,
i.e. asymmetric gas-accretion (Bournaud et al., 2005a) (that is reflected by
stellar-mass distribution hence created) and/or the tidal interaction (or
‘minor-mergers’) with in-falling satellite sub-halos (Zaritsky & Rix, 1997;
Kazantzidis et al., 2008, 2009), that may also include their assimilation into
the primary galaxy halo. These ‘less-severe’ interactions (with mass-ratios
from 1:4 or lower) are expected to preserve the stellar disks (Bournaud et
al., 2005a; Hopkins et al., 2009). Only in Galaxy-A, can we also associate the
imminent major-merger to also be playing a role.

Meanwhile, the quiescence of the stellar disks (albeit possibly not entirely
passive), is the first indication of the presence of an apparent ‘outside-in’
quenching mode in high-redshift massive galaxy populations, in contradiction
to the classic ‘inside-out’ configuration (Lang et al., 2014; Tacchella et
al., 2015; Breda & Papaderos, 2018). We consider various possible modes of
quenching. Since we observe the galaxies to be undergoing an outside-in
quenching, this could not have primarily occurred due to feedback from active
galactic nuclei (AGN; Alatalo et al. 2015), known to quench galaxies inside-
out (Tacchella et al., 2018). We also find no evidence of AGN activity from
X-ray observations (Daddi et al., 2021), although a radio excess in Galaxy-C
is indicative of weak past AGN activity in that galaxy. The process of
morphological quenching (Martig et al., 2009), where the formation of a
stellar bulge stabilises the disk against further star-formation, is also
improbable. The galaxies are far from being bulge-dominated, essential for
this mode of quenching to be applicable, based on their stellar mass
distributions. Also unlikely is cosmological starvation (Feldmann & Mayer,
2015) since the availability of gas has already been established in RO-1001.
Finally, ram-pressure stripping (RPS; Gunn & Gott, 1972) could be regarded as
a possible contributor as it is known to remove gas from external regions of
galaxies (Bravo-Alfaro et al., 2000; Vollmer et al., 2001; Fumagalli et al.,
2009; Boselli et al., 2014; Loni et al., 2021), therefore resulting in an
apparent outside-in quenching (for a review, Boselli et al., 2021). It could
also lead to compression of the gas in the galaxy which could result in the
lopsidedness (although the stellar morphology would not be affected). However,
as shown in Appendix B, a conservative lower-limit of the radius up to which
RPS can remove gas from the sample in RO-1001 would be $10-15\,\rm kpc$. This
is more than an order of magnitude higher than the kpc-scale cores beyond
which the galaxies have suppressed star-formation. Hence we do not expect RPS
to be playing a major role.

The only possible scenarios capable of self-sufficiently explaining the
observed suppression of star-formation are found to be connected to the
aforementioned heavy lopsidedness in the disks. Introduction of such
asymmetry, in a differentially rotating disk-like structure induces loss of
angular momentum, causing mass to rapidly fall into the central regions
(Combes & Gerin, 1985). This process can be characterised as the triggering of
the $\rm m=2$ Fourier component, denoting a bar, by the $\rm m=1$ component
that refers to the asymmetry or lopsidedness (Bournaud et al., 2005a),
observed in our sample. Bars have already been found to efficiently suppress
star-formation up to factors of $\sim 10$ in the disk (Khoperskov et al.,
2018), while driving gas into the core (Carles et al., 2016), albeit on less
spectacular scales than what observed here. This could be a possible case of
an early-phase bar-formation, which are usually scarce at high redshifts
(e.g., Sheth et al., 2008). However, the resolution and sensitivity is not
sufficient to confirm it. The accreted clumpy material driving the
lopsidedness is also expected to feed the star-forming core, and in the
process leading to a stabilization of the disk (Dekel et al., 2009b).
Therefore the same outside-in quenching can be expected in all scenarios
involving lopsidedness and compact star formation.

Moreover, the expected damping time of the lopsidedness is comparable to the
Hubble time (Jog & Combes, 2009), explaining their detection throughout our
sample and allowing them to act as catalysts of bulge formation under the high
redshift accretion conditions. This timescale is not however associated with
the gas being funneled into the core, but rather the survival of the asymmetry
that drives this process. We propose that accreted material is resulting in
the compact star-forming cores within outside-in quenching disks, either
directly (mergers) and/or indirectly (lopsidedness funneling gas to the core).
The accretion may vary from smooth dust (hence presumably gas) components, to
sub-halo stellar ‘clumps’, as in Galaxies B and C (while preserving the disks
in the process), or additional massive stellar structures, observed in
Galaxy-A.

###  5.2 Determining the direction of accretion

Due to the confluence of evidence for influence of accretion on the galaxies,
we try to discuss possible tracers of this process. In an accreting galaxy,
the lopsided part of the disks would be expected to mark the location of
impact for the accreted material. Corroborative evidence can be found in our
sample when the models of the primary disks in the F160W image and the sub-
millimeter bright cores in the ALMA image are subtracted. Residual emission
(stars in near-IR emission and dust in sub-mm) is clearly detected in each
case (Fig. 9). In Galaxy-A, its F160W and the associated ALMA residuals
demonstrate the presence of the similarly-massive companion merging into the
disk. For Galaxies-B and C, their respective F160W residuals are much fainter
(by $\sim 3$ orders of magnitude) and are likely in-flowing small-mass
‘clumps’ within or adjacent to the disks.

These are found to be preferentially located in the direction of the
lopsidedness of the stellar-disks. We hence suggest that these indicators
could be tracing the mass inflow into the core.

##  6 A generalized picture accretion-driven galaxy evolution

In this section, we put forward a way to fit our work within the general
framework of high-z massive galaxy evolution. Throughout, we suggest how our
results indicating accretion onto galaxies is well suited to provide a general
picture of galaxy mass-buildup at these redshifts.

###  6.1 Comparison to high-z compact star-forming galaxies

We start of by making a comparison with the widely studied cSFG population at
similar redshifts (Cimatti et al., 2008; Ricciardelli et al., 2010; Fu et al.,
2013; Ivison et al., 2013; Toft et al., 2014, 2017; Elbaz et al., 2018; Gómez-
Guijarro et al., 2018, 2019; Puglisi et al., 2019, 2021). These cSFGs also
feature compact kpc-scale sub-mm bright regions, as is observed in our sample.
In fact, Puglisi et al. (2019) already suggested these regions/cores to be
above the star-forming main sequence (as seen in our sample, Fig. 3). However,
the surrounding disks being well below the star-forming main sequence as in
our sample (Fig. 3), making galaxies appear to be quenching ‘outside-in’, have
not yet been recognized. A similar scenario might hold for post-starbust
galaxies (e.g., Baron et al., 2022). Another apparent difference is the
average ratio of the near-infrared and sub-millimeter radii for cSFGs, that is
$\sim 3$ (Puglisi et al., 2021; Smercina et al., 2018; Lang et al., 2019).
Although this is likely a lower limit due to many cSFGs remaining unresolved
in large sample studies. It remains thus unclear if examples like the three
galaxies in RO-1001 with ratios $4-9$ could also present among cSFGs.
Moreover, simply the size of Galaxy-B being a factor of $2.0-2.5$ above the
mass-size relation (van der Wel et al., 2014) for star-forming galaxies at
$\rm z=3$, adds to the rarity of our sample, especially with regards to cSFGs.
Another characteristic of cSFGs seemingly in conflict with our results is the
expectation of major-merger dominance within such samples (Elbaz et al.,
2018). Both in galaxies B and C, the stellar disks appear to be well-preserved
(Sec. 4.2).

We can however provide possible reasons behind these apparent discrepancies.
Our high-resolution imaging capabilities in both near-IR and sub-mm for
RO-1001 is usually not reached in larger statistical studies of cSFGs. Hence
we might have simply been able to resolve the galaxies better to determine
their properties. This allowed us to study the lopsidedness, the lack of
dynamical perturbations (in galaxies B and C) and the apparent ‘outside-in’
quenching, based on which we draw the conclusions of our work. Although, we
can also hypothesize a physical reasoning. Large statistical samples usually
comprise of galaxies in the field which do not experience the high levels of
accretion of gas and satellites expected within dense gas-rich environments
like RO-1001 (accretion rate increases with halo mass; Dekel et al., 2009a).
Hence the cSFGs in the regions with less accretion would be more likely to be
results of major-mergers driving gas into compact cores while destroying
extended stellar disks. This is further exemplified by our direct visual
investigation finding a complete lack of similarly massive galaxies with
extended and continuous stellar morphology (like in Galaxy B) in the redshift
window of $2.6<z<3.2$ in both COSMOS and GOODS-South fields. If this is true,
cSFGs with compact star-forming cores and very extended quiescent stellar
disks (similar to our sample) might be more easily found in dense accretion-
rich regions.

Figure 9: Additional stellar and dust components tracing the direction of
accretion. The three panels showing the three residual F160W images of the
galaxies after the subtraction of the primary disks (in green contours;
starting at $4\sigma$ with increments of $4\sigma$). The red solid contours
show the ALMA $870\,\mu$m emission with the lines starting at $50\sigma$ with
increments of $50\sigma$. The red solid lines indicate the respective ALMA
major axes. In case of Galaxies A and B, the dashed red contours starting at
$3\sigma$ with steps of $0.5\sigma$ displays the ALMA residual emission after
the subtraction of the primary emission regions. In case of Galaxy-C, the same
contours show the additional point source adjacent to the core that was found
during the fitting procedure. In this case, the contours are at $15,25\sigma$.
Finally, the arrows indicate the likely directions of gas-accretion onto the
galaxies based on the asymmetric distribution of all the aforementioned
components, which also coincide with the direction in which the disks are
lopsided.

###  6.2 A link to the accretion filaments in RO-1001

Extending on our hypothesis of accretion onto the three star-forming galaxies
in RO-1001, it is imperative to associate the discussed properties with the
large scale narrative of accretion for the galaxy-group (Daddi et al., 2021).
Any ongoing accretion in RO-1001 would likely be coupled with the established
Lyman-$\alpha$-emitting filaments in RO-1001 (Daddi et al., 2021).
Hydrodynamical simulations predict that massive galaxies evolving under the
influence of nearby accretion-streams have their major axes aligned along the
stream direction (Dubois et al., 2014; Codis et al., 2018). We observe a
consistency with this prediction in our observations (Fig. 1, right panel). We
quantify this by finding the probability for the chance alignment of the major
axis of each galaxy with one of the three filaments. The range of allowed
angles is approximated using the centre of the galaxies and the edges of the
‘$-18.0$’ contour (corresponding to a surface brightness of $10^{-18}\,\rm
s^{-1}\,\rm erg\,cm^{-2}\,arcsec^{-2}$) in Fig. 1, since it is the highest
brightness level at which the Ly-$\alpha$ traced filaments are detected. We
also ensure that the tentative direction of the filaments, qualitatively
reported in Daddi et al. (2021), are within this subtended angle ($<\pm
10^{\circ}$). We find total chance probabilities of $13\%$, $17\%$ and $12\%$.
Additionally, the probability of all three galaxies being aligned with one of
the filaments (which is what we observe) is hence $<1\%$. This alignment,
especially in case of disk-like galaxies, is attributable to the process of
tidal torquing (Codis et al., 2015) by the massive accretion filaments.
However, at the core of this lies the tidal interactions the galaxies
experience due to infalling satellites (or minor-mergers). Hence, the apparent
alignments should be regarded as an indication of the galaxies accreting
clumpy material, which has already been suggested in Sec. 5.1.

In each case however, we would still expect a level of ‘bending’ of the
accretion streams before the final impact on to the galaxies, revealed by
offsets between the direction of accretion (Fig.9) and the preferred filament
(Fig. 1, right panel). We propose a scenario where the Galaxy-A, B and C are
being fed by the south-western, northern and south-eastern filaments. The swap
of the preferred filament for Galaxies A and C from those in their proximity
has been made due to better alignment with the major-axis of the galaxies
traced by near-IR and sub-millimeter emissions as well as the direction of
accretion traced by the lopsidedness and residual emission (Fig. 9).
Otherwise, for Galaxy-C the accretion direction would have been opposite to
direction of approach of the filament. Moreover, there is an additional
inconsistency of the line-of-sight velocities of the Lyman-$\alpha$ in the
south-eastern filament at the galaxy position (Daddi et al., 2021). For
Galaxy-A, it has a large spatial displacement from the direction of the
nearest south-western filament. In each case hence, the actual streams of in-
falling material would have needed to drastically bend before the final impact
onto the galaxies. Nevertheless, even in our preferred scenario there is still
a level of bending of the streams necessary as they approach the inner halos
of the galaxies. For Galaxy-A, the major axis (measured here from ALMA) versus
the lopsidedness and in-falling material direction are nearly orthogonal.
Hence the bending is likely occurring in the line-of-sight. The same could
also be true in Galaxy-B, where the northern filament with its reduced length
likely has a major component along the line-of-sight. Hence, the in-falling
stream would need to bend if it has to agree with the expected direction of
accretion along the major-axis, on the plane of the sky (Fig. 9).

###  6.3 A unified picture of accretion-driven evolution

Based on the results of the three star-forming galaxies in RO-1001, we find
evidence of massive disk-like galaxies expected to have secularly evolved
featuring compact star-forming regions at their cores. We propose that the
massive disks build up lopsidedness under the combined effects of gas and
satellite accretion which in turn results in loss of angular momentum of the
material. This drives the prodigous star-formation in the central regions.
Such a scenario is likely being observed in galaxies B and C. Although, gas
can also be driven to the core by much more violent major-mergers (Toft et
al., 2017; Elbaz et al., 2018), but this leads to a destruction of the stellar
disks which is only anticipated in Galaxy-C. However, we conclude that the wet
compaction scenario proposed by simulations (Dekel et al., 2013; Zolotov et
al., 2015; Tacchella et al., 2016), where compact stellar bulges get rapidly
built up as a result of accretion-driven violent disk instabilities, is too
extreme to reproduce the observations in RO-1001. Such a compaction simply
does not allow for creation of extended and massive stellar disks ($\gtrsim
10^{9.5}\,\rm M_{\odot}$) while in our sample we are observing them with
masses $>10^{11}\,\rm M_{\odot}$.

Finally, the presence of massive stellar disks points to the need for a mode
of destruction, since they are not usually observed in dense environments at
lower redshifts (Bundy et al., 2010). Dynamical disturbances caused by mergers
or galaxy harassment can easily be invoked for this (Toth & Ostriker, 1992;
Kazantzidis et al., 2006; Bullock et al., 2009; Purcell et al., 2009; Bournaud
et al., 2011). We might already be observing such a scenario in action in
Galaxy-A, with its signs of a forthcoming major-merger. Finally, a possible
end product may be the compact quiescent spheroidal galaxy(Kalita et al.,
2021b) that has been photometrically confirmed to also be within the group,
although it never grew beyond $10^{11}\,\rm M_{\odot}$. It is curious however,
that we have stumbled upon a galaxy-group with three massive galaxies close
together with recent gas-rich star-bursting cores created within the last few
100 Myr. From each of their observed properties, they seem to have undergone a
recent shift in evolution with a preference for the central region. A possible
reason has recently been discussed in Noguchi (2021), where bulges get rapidly
built-up in $>10^{11}\,\rm M_{\odot}$ galaxies within dark-matter halo cores
that are accessible to cold-gas filaments (Dekel et al., 2009a). This limit is
related to the dependence of migration timescales of clumpy accreted material
(already suggested in our sample by their lopsidedness, as discussed in Sec.
5.1) that feed the central star-forming region on the stellar mass of the
galaxy. Hence, the galaxies in RO-1001, all of which are $>10^{11}\,\rm
M_{\odot}$, could simply be experiencing ideal conditions for a rapid buildup
of bulges. It should be noted however that we refrain from estimating the
timescale of migration of accreted clumps since such a calculation depends on
the relative angular momentum of the inflowing material with respect to the
disk. This can result in a range between a few tens to a few hundred Myrs,
which is highly uncertain and heavily dependent on assumptions that we are not
in a position make with the current data.

##  7 Caveats and future prospects

###  7.1 Further investigations

In our study, we are still lacking information about certain facets of the
three galaxies in RO-1001. A spatially resolved spectroscopic study of the
quiescent stellar regions would be extremely useful to constrain their star-
formation histories. A lot of work in this direction has been done for massive
QGs (e.g., Schreiber et al., 2018; Forrest et al., 2020; Valentino et al.,
2020b), with signatures of rapid quenching of star-formation observed in their
samples. Although we do determine rapid quenching of the stellar disks in our
sample (Sec. 3.4), conclusive proof will only be available after obtaining
spectroscopic data.

Furthermore, this will also allow the tracing of the metallicity of the
stellar disks. It is hypthesized that accreted gas being metal-poor leads to a
fall in the metallicity in the accreting galaxy (Lehner et al., 2013; Sánchez
Almeida et al., 2013, 2014; Wotta et al., 2019). Hence, RO-1001 could be a
test-bed for such theories. Finally, spectroscopy will also provide the
kinematics of the stellar disk and determine the level of rotational dominance
within the structure. This would be necessary to model the evolution of the
galaxies as well as similar galaxies in the future featuring signs of
accretion. This is especially of interest since we have suggested the possible
prevalence of clumps migrating to the core of the galaxies, driving the high
levels of star-formation. The timescales of in-flowing material is coupled
with the rotation timescales of the respective disks (Dekel et al., 2009b).

###  7.2 Extending the search to other structures

Asymmetries in the stellar distribution as well as relative position of the
sub-mm bright cores of cSFGs are rather common. However, they are mostly
associated with galaxy-galaxy interactions (Elbaz et al., 2018; Cibinel et
al., 2019; Puglisi et al., 2019). However, we demonstrate that if studied in
higher resolution, they might reveal effects of accretion of gas and clumps
especially in dark matter halos where cold-gas filaments are expected to
survive in spite of the surrounding hot medium (Dekel et al., 2009a). Hence,
deep observations of star-forming galaxies within dense-environments would be
instrumental in establishing a generalised picture of massive galaxy evolution
in dense environments. A few examples are in fact already available.
CLJ1449+0856 (Gobat et al., 2011, 2013; Strazzullo et al., 2016; Coogan et
al., 2018) has three highly star-forming galaxies that showcase clear offsets
between their near-IR and sub-mm/radio contours, with one of them also
featuring AGN activity (S7-N7 system; Kalita et al., 2021a). Using unresolved
sub-mm data, they were regarded as mergers. However, reconsideration after
obtaining high resolution data might reveal the asymmetries to be due to
comparable features as those seen in RO-1001. Another such case is the highly
star-forming galaxy, GN20, which is part of a proto-cluster at $\rm z=4.05$
(Daddi et al., 2009; Hodge et al., 2015). This too features a similar offset
and is a confirmed member of a high-z dense environment. Additional sources of
interest include galaxies within seven other high-z structures with
Ly-$\alpha$ halos suggesting abundance of gas (Daddi et al., 2022a, b). Future
well-resolved studies of these and additional structures hold much promise.

##  8 Summary and conclusions

Within a $z=2.91$ galaxy-group of dark matter halo mass of $\sim 4\times
10^{13}\,\rm M_{\odot}$, we observe three massive ($>10^{11}\,\rm M_{\odot}$
galaxies (Fig. 1). They have a combined star-formation rate of $\sim 1250\,\rm
M_{\odot}\,yr^{-1}$, and are studied here with high resolution near-IR (HST)
and sub-mm (ALMA) data. Each of the galaxies have extremely compact (effective
radius $\sim 1\,\rm kpc$) sub-millimeter bright cores where almost all of the
star-formation and $10-40\%$ of the stellar mass is confined. They will likely
form the future bulges of their respective galaxies. These are embedded in co-
planar stellar disk-like structures which are $4-8\,\times$ more extended in
radius. The key new results that emerge from our work are the following:

  1. 1.

All three galaxies show marked stellar disk lopsidedness of varying degrees
(from $1.6$ to $>3.0$). The stellar morphology of 2/3 galaxies (B and C) do
not show signs of extreme dynamical disturbances however, hence limiting the
role of major-mergers. Although, the third (galaxy A) is likely at an initial
phase of collision with an equally massive counterpart. These are first,
unique cases of high redshift galaxies in which lopsidedness has been
recognised to play an important role.

  2. 2.

Based on ALMA 3$\sigma$ upper-limits, we also determine that star-formation is
suppressed in the disks. They are found to be located $>1$ dex below the star-
forming main sequence (whose scatter is 0.3 dex), while the star-forming
compact cores are mainly located above it (Fig. 3). These galaxies are among
the first known cases of ‘outside-in’ quenching observed in the distant
Universe.

  3. 3.

Furthermore, the cores could not have been forming stars beyond earlier than a
few $100\,\rm Myr$, which is the same epoch by which the disks had already
formed about $50\%$ of their stellar mass. This bi-modality in star formation
and stellar age coincides with the apparent outside-in quenching of the
galaxies.

  4. 4.

We conclude that the lopsidedness is intrinsically connected to gas being
driven into the centre of the potential well of the galaxies. The reason of
this lopsidedness in at least Galaxies B and C is most likely the combined
effect of accreted gas and clumps, the latter of which can be regarded as
minor-mergers. In case of Galaxy-A, the imminent major-merger would also play
a role.

  5. 5.

The importance of minor-mergers due to accretion is exemplified by the
alignment of the major axes of all three galaxies with one of the accretion
streams established through Ly-$\alpha$ halo morphology in Daddi et al.
(2021). This is expected to also result in the lopsidedness as well as any
residual stellar and dust emission to converge onto the location of impact of
the accretion-stream with the galaxies. We detect these signatures in each of
the cases. Hence we make the first direct connection between accretion streams
and the morphological transformation of galaxies driving compact star-
formation in massive galaxies at high redshifts.

  6. 6.

We show that in the presence of accretion, galaxies can build-up compact
highly star-forming cores without the need of major-mergers and therefore
preserving their stellar disks. A key feature however is an asymmetry in the
stellar distribution, which needs to be studied in high resolution to
determine if it is driven by accretion of gas and clumps or by violent
interactions like major-mergers. Future studies of accretion-rich high-z dense
environments would prove to be crucial.

Based on our results, we suggest an evolutionary pathway in which a secularly
evolving disk within a dense environment with accretion (gas and clumps),
grows substantial mass asymmetry and experiences the creation of a compact
star-bursting core at the expense of the star-formation within the disk. This
is inevitably followed by some form of disruptive event that leads to the
destruction of the quiescent disk (Toft et al., 2017), leaving behind, and
also possibly adding to (Elbaz et al., 2018; Puglisi et al., 2021), a stellar
bulge. However, the ubiquity of such a scenario can only be revealed with more
well-resolved observations of massive galaxies at the heart of well studied
high-redshift dense environments – that will likely become more accessible in
the upcoming James Webb Telescope era.

###### Acknowledgements.

First and foremost, we would like to express our gratitude to the anonymous
referee for the valuable suggestions. We would also like to thank Gabriel
Brammer for assistance with the use of grizli for the HST data reduction.
R.M.R. acknowledges support from GO15910. V.S. acknowledges the support from
the ERC-StG ClustersXCosmo grant agreement 716762. F.V. acknowledges support
from the Carlsberg Foundation Research Grant CF18-0388 “Galaxies: Rise and
Death” and from the Cosmic Dawn Center of Excellence funded by the Danish
National Research Foundation under then Grant No. 140. This paper makes use of
the following ALMA data: 2019.1.00399. 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.

##  Appendix A Spectral Energy Distribution Model Fitting

In order to fit SFH models to the galaxies, we use the results of the surface
brightness distributions in F160W (which also provides the flux in the band)
and then obtain the rest of the photometry using the best-fit models as priors
in all other bands. We fit this photometry with BC03 stellar population models
(Bruzual & Charlot, 2003) to derive the properties of the three massive
galaxies (Fig. 7). The redshift is fixed to the spectroscopic values
previously published for the sources (Daddi et al., 2021). We use
FAST++111https://github.com/cschreib/fastpp to determine the best fitting SED
templates through a $\chi^{2}$ minimisation procedure. We fix the metallicity
to the solar value as is expected in massive galaxies and implement the
Calzetti dust attenuation law(Calzetti et al., 2000), with a range of
extinction values, A${}_{\rm V}=0-5$ in steps of 0.02. Finally, the following
SFH models are used:

  1. 1.

Constant star formation models: We use this model featuring no decline in star
formation (it remains constant throughout) to check if a high attenuation
star-forming scenario is formally consistent with the available photometry.

  2. 2.

Delayed $\tau$-models: This is an exponentially declining SFH here is
characterised as $\propto(t/\tau^{2})\,e^{-t/\tau}$ with a peak of star
formation at $t=\tau$. The $\tau$ varies within [100 Myr, $\rm t_{\rm obs}$]
with steps of 0.1 dex, where $\rm t_{\rm obs}$ is the age of the universe at
the redshift of the galaxy.

  3. 3.

Composite $\tau$-models(Schreiber et al., 2018): This is similar to the
previous model, however with different timescales ($\tau_{\rm rise}$ and
$\tau_{\rm decl}$) for the rising and declining phases separated by the epoch
$\rm t_{\rm burst}$.

$\displaystyle\mathrm{SFR}_{\rm
base}(t)\propto\left\\{\begin{array}[]{ll}e^{(t_{\rm burst}-t)/\tau_{\rm
rise}}&\text{for $t>t_{\rm burst}$}\\\ e^{(t-t_{\rm burst})/\tau_{\rm
decl}}&\text{for $t\leq t_{\rm burst}$}\\\ \end{array}\right.$ (6)

Both $\tau_{\rm rise}$ and $\tau_{\rm decl}$ are varied within the range of
$[10\,\rm Myr,3\,\rm Gyr]$, while for $\rm t_{\rm burst}$ a grid of $[10\,\rm
Myr,\rm t_{\rm obs}]$ is used.

##  Appendix B Prevalence of Ram Pressure Stripping

We investigate the effect RPS may have on the three star-forming galaxies in
RO-1001. We use the following relation from Domainko et al. (2006) for the
minimum radius up to which gas may be stripped from a galaxy ($\rm r_{\rm
strip}$):

$\rm r_{strip}=0.5\rm\,r_{o}\times
ln\left(\frac{G\,M_{star}\,M_{gas}}{\varv^{2}_{gal}\,\rho_{ICM}\,2\pi\,r_{o}^{2}}\right)$
(7)

Here, the $\rm r_{o}$ is the scale radius of the galaxies, while $\rm
M_{star},M_{gas}$ corresponds to the gas and stellar mass of the galaxies.
$\rm\varv_{gal}$ is the relative velocity between the galaxy and the ICM, for
which we use the approximate virial velocity of the galaxies in RO-1001
($500\,\rm km\,s^{-1}$; Daddi et al., 2021). Finally, the density of the ICM
($\rm\rho_{ICM}$) is determined using (Boselli et al., 2021):

$\rm\rho_{ICM}=1.15\,n_{e}\,m_{p}$ (8)

We use the value of $10^{-3}\,\rm cm^{-3}$ for the electron density ($\rm
n_{e}$) as is expected in the core of clusters and groups (Vikhlinin et al.,
2009; Sun et al., 2009; Pratt et al., 2010).

We hence get an $\rm r_{\rm strip}=10-15\,\rm kpc$ for the galaxies in
RO-1001. However, this should be regarded as a conservative lower-limit since
RPS efficiency is expected the steeply decrease at high-redshifts. This is
primarily due to the contribution of non-gravitational heating which
effectively reduces the ICM content (Fujita, 2001). Moreover, the decreasing
efficiency of RPS at high redshifts ($\rm z\gtrsim 2$) is also suggested
through simulations in (Pfeffer et al., 2022). Hence, in each of our sample
galaxies, the $\rm r_{\rm strip}$ is found to be a factor of $\gtrsim 2$
larger than the stellar disks.

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