2023 %=11

[1,2]Francesco D’EugenioThese authors contributed equally to this work. These
authors contributed equally to this work.

1]Kavli Institute for Cosmology, University of Cambridge, Madingley Road,
Cambridge, CB3 OHA, UK

2]Cavendish Laboratory - Astrophysics Group, University of Cambridge, 19 JJ
Thomson Avenue, Cambridge, CB3 OHE, UK

3]Centro de Astrobiología (CAB), CSIC-INTA, Ctra. de Ajalvir km 4, Torrejón de
Ardoz, E-28850, Madrid, Spain

4]Department of Physics and Astronomy, University College London, Gower
Street, London WC1E 6BT, UK

5]European Space Agency (ESA), European Space Astronomy Centre (ESAC), Camino
Bajo del Castillo s/n, 28692 Villanueva de la Cañada, Madrid, Spain

6]European Space Agency, c/o STScI, 3700 San Martin Drive, Baltimore, MD
21218, USA

7]University of Oxford, Department of Physics, Denys Wilkinson Building, Keble
Road, Oxford OX13RH, United Kingdom

8]Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy

9]Sorbonne Université, UPMC-CNRS, UMR7095, Institut d’Astrophysique de Paris,
F-75014 Paris, France

10]INAF - Osservatorio Astrofisico di Arcetri, largo E. Fermi 5, 50127
Firenze, Italy

11]Centre for Astrophysics Research, Department of Physics, Astronomy and
Mathematics, University of Hertfordshire, Hatfield AL10 9AB, UK

12]AURA for European Space Agency, Space Telescope Science Institute, 3700 San
Martin Drive. Baltimore, MD, 21210

13]Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg,
Germany

14]Department of Astronomy and Astrophysics University of California, Santa
Cruz, 1156 High Street, Santa Cruz CA 96054, USA

15]NRC Herzberg, 5071 West Saanich Rd, Victoria, BC V9E 2E7, Canada

# A fast-rotator post-starburst galaxy quenched by supermassive black-hole
feedback at z=3

*<EMAIL_ADDRESS>Pablo G. Pérez-González  Roberto Maiolino  Jan Scholtz  Michele Perna  Chiara Circosta  Hannah Übler  Santiago Arribas  Torsten Böker  Andrew J. Bunker  Stefano Carniani  Stephane Charlot  Jacopo Chevallard  Giovanni Cresci  Emma Curtis-Lake${}^{\textit{{11}}}$ Gareth C. Jones  Nimisha Kumari  Isabella Lamperti  Tobias J. Looser  Eleonora Parlanti  Hans-Walter Rix  Brant Robertson  Bruno Rodríguez Del Pino  Sandro Tacchella  Giacomo Venturi  Chris J. Willott  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [

###### Abstract

There is compelling evidence that the most massive galaxies in the Universe
stopped forming stars due to the time-integrated feedback from their central
super-massive black holes (SMBHs). However, the exact quenching mechanism is
not yet understood, because local massive galaxies were quenched billions of
years ago. We present /NIRSpec integral-field spectroscopy observations of , a
massive, quiescent galaxy at redshift $z=3.064$. From the spectrum we infer
that the galaxy has a stellar mass of = $1.6\pm 0.2\times 10^{11}$ and a
dynamical mass . Half of its stellar mass formed at $z=3.7\text{--}4.6$, and
the system is now quiescent, with the current star-formation rate SFR $<9$ .
We detect ionised- and neutral-gas outflows traced by emission and absorption.
Outflow velocities reach $\vout\approx 1,000~{}\kms$, comparable to the galaxy
escape velocity and too high to be explained by star formation alone. hosts an
Active Galactic Nucleus (AGN), evidence that these outflows are due to SMBH
feedback. The outflow rates are $0.14\text{--}2.9$ and
$30\text{--}300~{}\MSun~{}\peryr$ for the ionised and neutral phases,
respectively. The neutral outflow rate is ten times higher than the SFR, hence
this is direct evidence for ejective SMBH feedback, with mass-loading capable
of interrupting star formation by rapidly removing its fuel. Stellar
kinematics show ordered rotation, with spin parameter $\lambdar[\re]=0.62\pm
0.07$, meaning is rotation supported. This study shows direct evidence for
ejective AGN feedback in a massive, recently quenched galaxy, thus clarifying
how SMBHs quench their hosts. Quenching can occur without destroying the
stellar disc.

The Universe today is not what it used to be (madau+dickinson2014, ). Local,
massive quiescent galaxies stand like colossal wrecks of glorious but remote
star-formation histories, and mighty and rapid quenching the likes of which
have no present-day equals (thomas+2010, ; mcdermid+2015, ). enables us for
the first time to witness these monumental galaxies during the long-gone epoch
when they arose and fell. By redshift $z=1.5\text{--}2$, 3–4 Gyr after the Big
Bang, massive quiescent galaxies have little to no cold gas, the fuel for star
formation (whitaker+2021, ; williams_alma_2021, ). But the question whether
the missing fuel was consumed by starbursts or if it was removed by ‘ejective’
feedback from SMBHs remains open (man+belli_quenching_2018, ;
somerville+dave2015, ). We present a NIRSpec/IFS impression of , a massive,
quiescent galaxy at redshift $z=3.064$ (look-back time 11.7 Gyr). Observed as
part of the Galaxy Assembly with NIRSpec Integral Field Spectroscopy GTO
programme (GA-NIFS), this galaxy (Fig. 1) was selected as a ‘blue nugget’
(barro+2013, ), a class of massive, extremely compact galaxies (stellar mass
$\Mstar=3\text{--}30\times 10^{10}~{}\MSun$, half-light radius
$\re=0.5\text{--}2~{}\kpc$), thought to be the progenitors of compact
quiescent galaxies at $z=2$ (‘red nuggets’, (damjanov+2009, )). Blue nuggets
are believed to be undergoing ‘gas-rich compaction’, that is, a central
starburst driven by disc instability or gas-rich major mergers, followed by
rapid quenching (dekel+2014, ) and leaving a compact, quiescent red-nugget
galaxy. As we will show, is instead already a red nugget in an advanced stage
of quenching. The system is merging with multiple low-mass satellites and is
undergoing powerful, ejective feedback from its SMBH.

Figure 1: Panel 1. False-colour image of from NIRCam. The grey dashed square
is the field of view of NIRSpec/IFS (with dithering). The solid white contour
is a stellar isophote from NIRSpec/IFS prism spectroscopy, the red dashed
ellipse is the best-fit deconvolved model, with semi-major axis equal to 1 .
The cyan contours are rest-frame UV from NIRCam F090W, displaying complex
morphology, probably due to foreground dust. The orange/blue contours are
isosignificance lines for the –and –blended lines, from the prism data. The
nebular emission is significantly more extended than the stellar light,
indicating the ability of mergers/feedback to enrich the circum-galactic
medium (CGM). Panel 1. Comparing the model isophote (red dashed ellipse) to
NIRCam isophote morphology, there is a clear wavelength-dependent offset to
the north west. Panel 1. Brightest emission from g235h/f170lp data, showing a
slight offset from the centre of the stellar emission (cf. red dot, distance
$<1$ spaxel) and a remarkably different position angle, almost /2 compared the
stars. Panel 1. Neutral gas absorption, which is clearly asymmetric and
located where the rest-UV photometry is faintest. Panels 1–1. Spectrum from
the dotted black spaxel highlighted in panels 1 and 1, showing the data
(grey), best-fit continuum and nebular-line model (red and blue, respectively)
and the best-fit model (orange); the horizontal bar in the top right corner of
each panel is $\delta v=500\,\kms$. Panels 1 and 1 show the complex, multi-
component emission-line profile of and $\Halpha\text{--}\NII$. Panels 1 and 1
show the same spaxel. The vertical dotted lines mark the position of the
stellar , and -doublet absorption; the deep absorption, blueshifted with
respect to the stars, betrays the presence of a neutral-gas outflow.

NIRCam imaging (eisenstein_overview_2023, ; rieke_jades_2023, ;
williams_jems_2023, ) reveals a system with several smaller companions, all
within 8 kpc in projection (labelled [b]–f in Fig. 1, of which [b]–d are
spectroscopically confirmed to be satellites). Multiple low-mass satellites
are a common occurrence for massive quiescent galaxies at high redshift
(suess_buddies_2023, ). shows a regular, elliptical shape at 2.77–4.44 , but
the light distribution is increasingly lopsided blueward of 2 (Fig. 1), with
the brightest region at 0.9 clearly offset to the north west (by 0.5 ) and
displaying two peaks.

Figure 2:  Panels 2–2. Stellar-population surface mass-density and mass-
weighted age maps from full spectral fitting of the low-resolution
spectroscopy data, showing that most of consists of 0.5-Gyr-old stars. Merging
satellites have lower mass-to-light ratios than the , and do not contribute to
the mass-weighted properties. Panel 2. The star-formation history from the
same models, integrated over the 2-d map, shows the main episode of star
formation occurred 0.5 Gyr ago. The shaded region is the 1-uncertainty. The
cyan diamond and black circle are the mass outflow rates from and ,
respectively. Unlike the ionised-gas outflow, the neutral-gas outflow has mass
loading high enough to stop star formation. Panel 2. SED of the individual
spaxels summed inside a circular aperture of radius 1.15 arcsec, for both the
NIRSpec/IFS data (black) and the best-fit model (red). We also show the
aperture photometry as errorbars. The model does not include an AGN, therefore
it does not capture the emission lines or the flux redder than 6 , which is
dominated by host-dust emission from the AGN torus.

We use the NIRSpec/IFS data with the low-resolution prism disperser to perform
spaxel-by-spaxel full spectral energy distribution (SED) modelling, to measure
the surface stellar mass density, spatially resolved stellar population
properties and star-formation history (SFH; see Methods). The resulting mass
distribution is symmetric, with no strong signs of asymmetry (Fig. 2). The
asymmetric light distribution at rest-frame UV wavelengths arises from younger
stellar populations (luminous but with low stellar mass), and/or from an
asymmetric dust distribution. Integrating the 2-d properties inside a circular
aperture of 1.2 arcsec radius, and correcting for aperture losses, we measure
a total stellar mass $\Mstar=1.6\pm 0.2\times 10^{11}~{}\MSun$ (surviving
stellar mass). The total SFH from all spaxels shows that the main star-
formation episode happened at $z=3.7\text{--}4.6$, 0.4–0.8 Gyr prior to
observation. Afterwards, the star-formation rate (SFR) rapidly declined. There
is some evidence of a recent upturn, but our models do not include an Active
Galactic Nucleus (AGN), therefore this upturn could be due to the nebular
emission being interpreted as due to star formation. The SFR averaged over the
last 100 Myr, is $40\pm 20~{}\MSun~{}\peryr$. This is five times below the
star-forming main sequence at $z=3$ (popesso+2023, ), and comparable to the
quiescence threshold of 19 (pacifici+2016, ). However, part of the SFR is
likely due to the satellites, and the nebular emission is mostly powered by
the AGN, meaning that the true SFR is likely much lower. This implies that is
currently quenched and on its way to quiescence, which is consistent with the
empirical UVJ-colour diagnostic (williams+2009, ), and with the SFR inferred
from the emission-line analysis.

The NIRSpec/IFS observation in the low spectral-resolution configuration
reveals extended nebular emission in both the –and –spectrally blended
complexes (Fig. 1). This nebular emission is elongated in a different
direction compared to the stellar major axis, but in the same direction as
[b], which suggests that the ionised gas comes from inter-stellar medium (ISM)
material stripped by the interaction with the satellite. An outflow origin is
also possible, but in this case, the alignment with the satellite would be a
coincidence.

Figure 3: Emission-line diagnostic diagram for compared to selected samples
from the literature; the line ratios of our target place its ionisation source
firmly beyond the range that can be explained by star formation (dashed line,
(kauffmann+2003c, )). For the main target, we show the emission-line ratios
from spectra integrated inside elliptical apertures (colour coded by the semi-
major axis of the aperture). The yellow circle is the eastern satellite. We
show a number of samples for comparison: the contours and the small empty
circles trace the distribution of galaxies at $z=0.1$ (from SDSS) and $z=2$
(from KLEVER, (curti+2020, )), respectively. The sand symbols and upper limits
are the MRG sample of post-starbust galaxies at $z=1\text{--}2$ (newman+2018a,
), while the grey star is one of the most extreme post-starburst galaxies in
SDSS. The extreme values we find for are similar to what is found for other
post-starburst galaxies.

Unlike the low-resolution observations, NIRSpec high-resolution data (Fig. 1–1
and 1–1) are able to separate from , and (which in we observe mostly in
absorption) from . The emission lines show a broad, multi-component profile,
indicating complex kinematics. The BPT diagnostic diagram (Fig. 3) shows that
has everywhere a high /ratio (emission-line ratios are measured inside
concentric elliptical annuli, following the shape and position angle of the
stellar isophotes). From the outmost to the innermost annulus around ,
/increases from 4 to 10, whereas /remains approximately constant at 5–8. All
annuli are in the AGN region of the diagram, well beyond the demarcation curve
between starburst-driven and AGN-driven photoionisation (kauffmann+2003c, );
moreover, all annuli lie far outside the 99th percentile of the distribution
of local galaxies and AGN (grey and black contours). Star-forming and AGN
galaxies at $z=2$ also have much smaller /ratios (empty circles), but we find
our values to be similar to post-starburst galaxies (PSB) at $z=1\text{--}2.5$
(newman+2018b, ) and to the most extreme PSBs in the local Universe (grey
star). Assuming all emission was due to star formation, the extinction-
corrected SFR on timescales of 3–10 Myr is 9 (inside 2 , where =1.1 kpc from
(vanderwel+2014, )). Varying the aperture size, the SFR ranges between 4
(inside 1 ) to 19 (summing over the entire map, including the satellites).
These values are similar to the result from the SED analysis. However, as we
have seen, is dominated by emission from the AGN, therefore the true SFR is
likely much lower, and we treat all these values as upper limits within their
apertures. Overall, the low SFR values are in agreement with the quiescent
interpretation. In addition to the BPT diagram, direct evidence for an AGN
comes from the X-ray detection ($L_{X}=8$ [44] (luo+2017, )) and from the SED
excess at MIR wavelengths, which can be explained by the presence of a dusty
torus around the accreting SMBH (Fig. 2, cf. model and photometry at 24 ).
Modelling the photometry using both stellar and AGN emission models gives an
AGN bolometric luminosity $L_{\mathrm{AGN}}=2.6\pm 0.9$ [45] (see Methods;
(circosta+2019, )).

Figure 4:  Flux and kinematic maps of the , and nebular lines. The three rows
show (top), (middle) and (bottom). Panels 4–4. Flux maps, obtained fitting one
or two Gaussians to the emission lines (see Methods). Panels 4–4. Non-
parametric median velocity. Panels 4–4. Inter-percentile line width. Panels
4–4. 10th percentile velocity. Panels 4–4. 90th percentile velocity. For
(whose continuum emission is highlighted by the red dashed ellipse), most of
the emission is in a broad, blue-shifted component. Together with information
from the BPT diagram (Fig. 3), this is evidence for an AGN-powered outflow.

Spatially resolved emission-line kinematics (Fig. 4) display line broadening
in excess of 500 , and centroids that are blueshifted relative to the stellar
absorption (the stellar distribution is traced by the red dashed ellipse in
Fig. 4). Most of the nebular flux comes from the central regions, but is
offset from the centre of the stellar emission and is elongated almost at
right angle compared to the stellar isophote (Fig. 1). We also see a clear
kinematic transition between this bright central region and the more diffuse
emission at larger radii. The central region has velocity offset of -400 ,
while the extended emission is at velocities of $\pm 100~{}\kms$. Furthermore,
the central regions have inter-percentile line widths $\mbox{\rm\bf w}_{8}$0
in excess of 1,000 . The extent and elongation of the diffuse nebular emission
suggest a merger origin, but most of the flux is likely associated with the
blueshifted component which we interpret as an outflow. The large velocity
offset and velocity width of the nebular lines – and the fact that the
contours of highest flux are directed along the galaxy minor axis (Fig. 1 and
Fig. 4–4) – are evidence for an outflow normal to the disc
(cresci+maiolino2018, ; harrison+2018, ). The fast outflow velocity, the low
SFR, and the AGN are evidence for SMBH-feedback driven outflows
(forsterschreiber+2019, ; nelson+2019, ; concas+2022, ). We estimate a mass
outflow rate $\Mdotout[\OIII]=0.14\text{--}2.9$ (see Methods), meaning the
ionised-gas outflow is much lower than the SFR (Fig. 2).

What sets apart from other high-redshift sources, however, is the clear
detection of spatially resolved, deep absorption features. These include the
prominent hydrogen absorption lines characteristic of 0.5-Gyr-old stellar
populations (equivalent width EW $\hda=6.6\text{--}8.1$ Åand
$\hga=4.1\text{--}6.8$ Å; Figs. 1 and 5–5) and resonant absorption (Fig. 1).
The Balmer absorption confirms the results of the SED analysis (which is based
on spectroscopy with much lower spectral resolution). The absorption is offset
both spatially and kinematically from the stars, therefore we rule out a
stellar origin. The highest EW translates into a column density of $6\times
10^{22}$ cm-2, ten times lower than the column density towards the X-ray AGN
($6\times 10^{23}$ cm-2, (circosta+2019, )). The EW maps (Fig. 1) show that
the absorption extends from the centre of the galaxy to the south-east,
avoiding completely the north-western half, where we detect the brighest rest-
UV emission. This fact, combined with the blueshifted line-of-sight velocities
($\vnai=-(250\text{--}350)$ ), indicate that the absorption is due to a
neutral gas outflow, with a cone-like geometry possibly tilted with respect to
the stellar disc. We estimate the disc inclination from the best-fit Sérsic
model of (vanderwel+2014, ), which gives a projected axis ratio $q=0.44$ (we
assume an intrinsic axis ratio $q_{0}=0.2$). After correcting for inclination
by a factor $\cos\,i$, we obtain an outflow velocity of order $-1,000~{}\kms$
– again too fast to be explained by star formation alone. Assuming a maximal
escape velocity of $\vesc=1,200~{}\kms$, we infer a velocity ratio
$\vnai/\vesc=0.8\pm 0.2$, meaning the outflows are certainly capable of
removing material from the star-forming disc, with a fraction possibly
escaping the galaxy altogether.

We assume an outflow extent $\Rout=2.7~{}\kpc$, based on the largest distance
between the detection and the centre of the galaxy. With this and a thin-shell
geometry, the mass outflow rate is $\Mdotout[\NaI]\approx
100~{}\MSun~{}\peryr$, with uncertainties of a factor of 3. This value is
larger than the SFR – particularly if we recall that the SFR is overestimated
(Fig. 2). This indicates that the neutral-gas outflow is capable of halting
star formation by removing the necessary fuel.

In Fig. 5 we show the stellar kinematics of . We measure a clear velocity
gradient between the east and west sides (cf. Fig. 5 and 5). Could this
gradient be due to a major merger? In favour of this hypothesis, the two sides
of have different continuum shapes, with the south-east side (panel 5)
displaying flatter continuum slope and broader, less deep absorption. Rest-
frame UV photometry shows multiple peaks, and the stellar velocity-dispersion
is highest in the south east, rather than at the centre of the galaxy.
However, contrary to the merger expectation, both UV peaks are located on the
same (receding) region of the velocity map (cyan contours in Fig. 5),
therefore these two peaks are unlikely to trace two distinct galaxies merging.
In case of a merger, would be highest between the two galaxies, where
absorption lines of different redshift blend. Moreover, the mass maps and the
red-wavelength NIRCam imaging show an elliptical morphology centred at – or
very near – the kinematic centre of the maps, which is also in contrast with
the merger hypothesis (Fig. 2, and orange contours in Fig. 5, see also Figs.
1). Finally, the putative rotation axis is aligned with the minor axis of the
isophotes (and isodensity contours), as expected from regular rotation. Under
the rotation hypothesis, the different spectral shapes between the receding
and approaching halves of the velocity map could be due to a combination of
more dust in the south east (where we also detect the neutral-gas outflow,
Figs. 1 and 5), a slightly younger stellar population in the north west (Fig.
2), and stronger absorption-line infill due to nebular emission in the south
east. Most likely, all three factors contribute to the observed spectral
differences.

By applying the virial theorem to the aperture velocity dispersion inside 1 ,
$\sigmaestar=356\pm 36$ , we find a dynamical mass of (using the calibration
of (vanderwel+2022, )), which is comparable to . In case of a major merger,
both and would be severely overestimated, meaning the true would be much lower
than what inferred from the virial theorem, in tension with . Based on all
this evidence, we classify as a regular (fast) rotator – the most distant yet
found from stellar kinematics. An alternative possibility, is that is a system
in an advanced stage of merger, with the orbital angular momentum of the two
progenitors locked in the stars (bois+2010, ). To measure the degree of
rotation support, we use the [] spin parameter, a proxy for the angular
momentum per unit mass (emsellem+2007, ), defined by

$\lambdar[\re]\equiv\dfrac{\sum_{r<\re}F_{i}r_{i}|v_{i}|}{\sum_{r<\re}F_{i}r_{i}\displaystyle\sqrt{v_{i}^{2}+\sigma_{i}^{2}}}$
(1)

where we calculate the radius $r_{i}$ of each spatial element along the best-
fit ellipse (brough+2017, ), the aperture is the observed isophote of semi-
major axis one , $F_{i}$ is the continuum flux, and $v_{i}$ and $\sigma_{i}$
are the stellar velocity and velocity dispersion. We measure
$\lambdar[\re][\text{(observed)}]=0.46$, then apply a model-based point-spread
function (PSF) correction (dependent on the galaxy size and light profile
(harborne+2020, )) for a Gaussian PSF with full width at half maximum
FWHM=0.09 arcsec, obtaining $\lambdar[\re]=0.62\pm 0.07$ (the uncertainties
include the uncertainties due to the correction).

In Fig. 6 we compare to other quiescent galaxies. Based on its location on the
[]-plane (where is the ellipticity of the isophote at 1 ), is a clear fast-
rotator (FR) galaxy (emsellem+2007, ), i.e., it is consistent with being an
oblate spheroid with mild anisotropy, dominated by rotation support. FRs are
rare among galaxies of similar mass in the local Universe (trujillo+2009, ;
comeron+2023, ), but were much more common at high redshifts(newman+2018b, ).
Fig. 6 shows on the mass-size plane: its compact size would again make it a
strong outlier at $z=0$ and even possibly at $z=2$. Taken together, Figs. 6
and 6 imply that galaxies like must undergo significant dynamical and
morphological evolution between $z=3$ and present. This evolution has to
decrease the angular momentum and increase the size – all while not exceeding
the stellar mass of local massive galaxies. It has been postulated that this
kind of growth can only be achieved via gas-poor minor mergers (naab+2009, ;
bezanson+2009, ), because gas-rich merger trigger starbursts and disc
(re-)formation – which would increase the light-weighted [] parameter
(lagos+2018a, ; lagos+2022, ). Our target is surrounded by three and up to
five faint, low-mass satellites, which may represent the fuel for the
postulated size growth (suess_buddies_2023, ).

Figure 5: Panels 5–5. Voronoi-binned 2-d maps of , showing the empirical S/N
(panel 5), stellar velocity (panel 5), instrument-deconvolved velocity
dispersion (panel 5) and neutral-gas velocity (panel 5). In these four panels
the dashed ellipse traces the shape and of the best-fit Sérsic model to the
stellar continuum. Panel 5 also shows the contours of the Voronoi bins (white
dotted lines). Panel 5 shows an enlarged region of the RGB image from Fig. 1
in the background, for comparison. Panel 5 shows clear evidence for ordered
rotation, with the rotation axis along the minor axis of the stellar
distribution. Panels 5–5. Detail on the and stellar absorption features from
two Voronoi bins (white dotted squares in panel 5), chosen to highlight the
velocity offset that we attribute to stellar rotation. The line colours are
the same as Fig. 1–1.

Figure 6: Panel 6. []–diagram showing that – interpreting the velocity field
as stellar rotation – is rotation supported, a so-called fast-rotator galaxy
(slow rotators fall inside or near the dashed box, (cappellari2016, )). This
is similar to other quiescent galaxies at high redshift (MRG sample, diamonds;
(newman+2018b, )) and unlike local quiescent galaxies (SAMI sample, circles;
(brough+2017, )), including the most massive local quiescent galaxies (MASSIVE
sample, squares; (veale+2017, )). Panel 6. Mass–size diagram, illustrating
that is extremely compact; to join the $z=0$ distribution, our galaxy must
grow in size by a factor of 10.

represents a unique opportunity to study how the most massive galaxies in the
Universe became – and stayed – quiescent. Even though we cannot draw general
conclusions from a single target, we show that AGN feedback is capable of
powering neutral-gas outflows with high velocity and high mass loading,
sufficient to interrupt star formation by removing its cold-gas fuel. In
contrast, the ionised-gas outflows appear to have much lower mass loading and
may be ineffective at halting star formation, in agreement with studies of
other AGNs at high redshift. It is unclear how much cold gas an AGN like the
one active in may leave behind. Non-detection from existing sub-mm
observations of CO emission give a molecular-gas mass fraction $f<10$ per cent
circosta+2019 , lower than the value of coeval star-forming galaxies
(tacconi+2020, ), but not sufficiently constraining. Current evidence from
redshifts $z=1.5\text{--}2$ suggests that quiescent galaxies have low (3 per
cent) molecular-gas fractions (whitaker+2021, ; williams_alma_2021, ) – an
order of magnitude lower than coeval star-forming galaxies. Any leftover gas
may have low star-forming efficiency, perhaps due to stabilisation against
gravitational collapse and/or (AGN-induced) turbulence, similar to local PSB
galaxies (smercina_after_2022, ) and AGN hosts (venturi+2021, ). The ISM/CGM
around suggest that a combination of AGN feedback and mergers may be providing
the energy required to sustain this turbulence against dissipation. The
presence of a stellar disc suggests that feedback was ‘gentle’ enough to
preserve the dynamical structure of throughout its quenching phase, therefore
dynamical transformation from disc-like FRs to spheroid-like SRs happens after
quenching. A census of the emission-line properties of high-redshift, massive
quiescent galaxies is essential to clarify if strong, ejective SMBH feedback
is episodic or if it is a key mechanism for driving and maintaining
quiescence.

##  1 Methods

###  1.1 NIRSpec observations and data reduction

Our observations are part of the GA-NIFS survey, a large NIRSpec GTO survey
targeting extended galaxies and AGNs at $z>3$ with the NIRSpec Integral Field
Spectroscopy (IFS, (boker+2022, )) mode (PIs: S. Arribas, R. Maiolino). Data
for was obtained from programme PID 1216 (PI: N. Lützgendorf) and consist of
two disperser/filter combinations. Observations with the prism/clear setup
cover the full wavelength range of NIRSpec with spectral resolution
$R=30\text{--}300$ (jakobsen+2022, ), whereas the g235h/f170lp observations
probe only 1.66–3.17 but with higher resolution $R=2,700$. Both observations
had a position angle of -99°, resulting in a NIRSpec position angle of
39.5°(measured north to east). For prism/clear we used the IRS2RAPID readout
pattern, 33 groups per integration and 8 exposures, for a total of 1.1 h on
source; for g235h/f170lp we used the IRS2 readout pattern, 25 groups per
integration and 8 exposures, for a total of 4.1 h on source. The exposures
were dithered following the medium cycling pattern to improve the PSF sampling
and to marginalise against detector defects and leakage/open shutters from the
NIRSpec Micro-Shutter Assembly.

For the data reduction, we follow the procedure described in (perna+2023, );
here we report a brief summary and highlight any differences. We reduced the
data with the publicly available jwst pipeline, version 1.8.2, using static
calibrations from the context file version 1014 (for g235h/f170lp) and context
file version 1068 (for prism/clear). The pipeline was patched to include a
number of corrections and improvements, as described in (perna+2023, ).
Compared to the default reduction, we used an additional correction for the
1/f noise. For g235h/f170lp, flux calibration was done in post-processing
using data from the standard star TYC 4433-1800-1 (PID 1128, observation 9).
To detect and flag outliers we used a custom algorithm, similar to
(vandokkum+stanford2003, ). Their algorithm was developed specifically for
(spatially) undersampled images. However, NIRSpec/IFS data is undersampled
only in the spatial direction, therefore we calculated the derivative of the
count-rate maps only along the detector x axis, which is the approximate
direction of the dispersion axis (the trace curvature can be neglected on
scales of two detector pixels). The absolute value of the derivative was then
normalised by the local flux (or by 3$\times$ the noise, whichever was
highest) and we rejected pixels where the normalised derivative was higher
than the 95th-percentile of the resulting distribution. For the cube-building
stage, we used the drizzle algorithm to produce cubes with a scale of 0.05
arcsec per spaxel, for both the prism/clear and the g235h/f170lp datacubes.
For the PSF modelling (Method III), we used a cube with 0.03 arcsec per
spaxel.

We use publicly available photometry for additional flux calibration (see
$\mbox{\rm\bf S}_{~{}}$1.4). At wavelengths 0.4–1.6 we use /ACS data from
GOODS (giavalisco_goods_2004, ; illingworth+2016, ) and /WFC3 IR data from
CANDELS (grogin+2011, ; whitaker+2019, ); at wavelengths 0.9–4.8 we use
/NIRCam data from the Advanced Deep Extragalactic Survey (JADES; PID 1180, PI:
D. J. Eisenstein; (eisenstein_overview_2023, ; rieke_jades_2023, )) and from
the Extragalactic Medium-band Survey JEMS (PID 1963, PIs: C. C. Williams, S.
Tacchella and M. Maseda; (williams_jems_2023, )).

###  1.2 Point-spread function determination

We present three independent measurements of the shape and size of the
NIRSpec/IFS PSF. The first measurement uses observations of a standard star
with the g235h/f170lp grating/filter combination. The second method uses a
serendipitous star inside the NIRSpec/IFS field of view of . The third method
uses NIRCam imaging from the JADES and JEMS surveys (for which the PSF is well
understood) to infer the NIRSpec/IFS PSF.

Method I – Standard star observations. We used the standard star TYC
4433-1800-1 (V3=188°, PA=146.5°), reduced using the same pipeline and context
file as the galaxy data, and modelled the PSF using the multi-Gaussian
expansion algorithm mgefit (MGE; cappellari+emsellem2004, ). We divide the
datacube in one hundred wavelength intervals between 1.66–3.17 , then find the
PSF position angle from the second moment of the light distribution, and the
best-fit MGE model by minimising 2. The formal flux uncertainties on the
wavelength-collapsed datacube are very small, and likely dominated by
systematic uncertainties. Our 2-minimisation uses therefore flux weighting
instead of error weighting. The resulting FWHM is shown in Fig 7; filled and
empty stars are the model FWHM along the major and minor axis of the PSF,
respectively; the solid lines are the running median (note the detector gap at
2.5 ). In panel 7 the solid line is the position angle of the PSF with respect
to the NIRSpec position angle; a value of 0°indicates that the PSF major axis
has the same direction as the slices long axes (hereafter: along slices; 90°is
across slices). We find the NIRSpec/IFS PSF to be preferentially aligned close
to along slices. At short wavelenghts, the PSF is larger than the NIRCam PSF
(coloured dots), and there seems to be a drop in FWHM around 3 .

Figure 7:  Panel 7. NIRSpec PSF as a function of wavelength, using three
methods. Method I (stars and solid lines) uses the calibration star TYC
4433-1800-1. Method II (dot-dashed line) uses the serendipitous star inside
the NIRSpec/IFS field of view for the observations of . Method III uses NIRCam
wide- and medium-band imaging to model the PSF with a 2-d Gaussian with
orthogonal axes, with one axis closer to the slice direction (filled symbols)
and one closer to across slices (empty symbols). The dots show the FWHM of the
NIRCam empirical PSF for comparison. Panel 7. Position angle of the PSF major
axis (points with error bars) compared to the NIRSpec position angle (dashed
horizontal line). The major axis of the PSF is closer to the direction of the
slices.

Method II – Serendipitous Star. For this method, we use the relatively bright
star inside the NIRSpec field of view (Fig. 1; $F775W=25$ mag), modelled as a
Gaussian. The prism/clear datacube for is summed over six wavelength elements,
and each synthetic image is fit independently. We then model the resulting
FWHM as a function of wavelength with the function:

$FWHM(\lambda)=(0.13+1.6\cdot\lambda[\mum]\cdot\exp(-21.4/\lambda[\mum])~{}\mathrm{arcsec}$
(2)

This model is shown as a dot-dashed grey line in Fig. 7; we remark that this
determination may suffer from edge effects – particularly at the longest
wavelengths.

Method III – Matching NIRCam imaging. For this method, we select a NIRCam
wide- or medium-band filter, integrate the NIRSpec/IFS prism/clear cube (0.03
arcsec/spaxel) under the filter transmission curve to create a synthetic image
in that band, then proceed to find the kernel convolution that best matches
the available NIRCam image to the synthetic NIRSpec image. The NIRSpec/IFS PSF
is then estimated as the convolution of the NIRCam PSF with the best-fit
kernel. The model consists of six free parameters; the kernel is assumed to be
a pixel-integrated, bivariate Gaussian, with three free parameters $\sigma$,
axis ratio $q$ and position angle. In addition, we allow a small pixel
adjustment to align the NIRCam and NIRSpec images and a flux scaling factor.
The model is optimised using the Markov-Chain Monte-Carlo algorithm emcee
(foreman-mackey+2013, ). We use flat priors for the kernel parameters
($0.003<\sigma<0.5$ arcsec, $-90<$position angle $<90$°and $0<q<1$) and
informative, Gaussian priors for matching the NIRCam image position and flux
(the pixel shifts are Gaussians with mean 0 and standard deviation three
pixels, and the flux scaling factor is a Gaussian with mean equal to the mean
flux ratio and standard deviation of 10 per cent). An example posterior
distribution is shown in Fig. 8, which shows that – as for Method I above –
the PSF is not circular. Fig. 7 shows the results from method III as coloured
ellipses, with the filled and empty symbols denoting the PSF FWHM along the
major and minor axes of the PSF, respectively. The position angle is once
again close to 0, i.e., the PSF tends to be aligned with the IFS slices (panel
7). This method also finds a drop in the PSF FWHM between the NIRCam F210M and
F277W filters; the origin of this drop is unclear and we do not model it in
the subsequent analysis. We tested that our results are consistent when
modelling the convolution kernel as a superposition of two Gaussians with the
same axis ratio and position angle. In addition to , we also model GS-3073, a
AGN-host galaxy at $z=5.55$ (uebler+2023, ). The results are shown by the
GS-3073-shaped markers, with filled and empty symbols having the same meaning
as for . Using both and GS-3073, we model the PSF FWHM along the major axis
(i.e., along slices) as

$FWHM(\lambda)=(0.12+1.9\cdot\lambda[\mum]\cdot\exp(-24.4/\lambda[\mum])~{}\mathrm{arcsec}$
(3)

(dotted grey line in panel 7) and along the minor axis (across slices) as

$FWHM(\lambda)=(0.09+0.2\cdot\lambda[\mum]\cdot\exp(-12.5/\lambda[\mum])~{}\mathrm{arcsec}$
(4)

(dashed grey line in panel 7).

Figure 8: Example posterior distribution for our PSF estimation based on
matching NIRCam imaging to synthetic NIRCSpec/IFS imaging (method II).
$\sigma$ is the semi-major axis standard deviation of the Gaussian kernel we
apply to the NIRCAM F182M imaging to best match NIRSpec. The kernel has axis
ratio $q=0.55$, but the NIRSpec/IFS PSF is the result of convolving this
kernel with the NIRCam PSF. The kernel position angle is 34°, meaning the
NIRSpec/IFS PSF is elongated preferentially along the IFS slices.

Neither of the three methods adopted is ideal. For method I, we are using
observations with a different number of dither positions than , which may
affect the image and PSF reconstruction; the limited number of dithers means
we can only reconstruct the image with a scale of 0.05 arcsec/spaxel, which
may limit the accuracy of the PSF modelling. For method II, the serendipitous
star is close to the edge of the NIRSpec/IFS field of view, and may therefore
suffer from edge effects. For method III, the starting NIRCam image has a
different PSF than the NIRSpec/IFS image, therefore, there is no guarantee
that a Gaussian (or two Gaussians) kernel can model the resulting image
adequately. However, the fact that the three methods agree on the elongated
shape of the PSF leads credence to our conclusion. Furthermore, the elongation
of the PSF along the instrument slicers has already been reported by other
authors (Parlanti et al., in prep., Perna et al., in prep.), was already
expected from the instrument design and had already been noted during ground-
based evaluations (Böker, T., priv. comm.).

When measuring the spin parameter [], we apply an empirical correction to
obtain the intrinsic value from the observed measurement (harborne+2020, ). We
assume a PSF FWHM of 0.09 arcsec (at 2 ); a larger FWHM value would increase
the intrinsic and make our results more significant.

###  1.3 Redshift determination.

One would think that spectroscopy with spectral resolution of $R=2,700$ ought
to yield redshift uncertainties better than 10 , i.e., a fraction of a pixel
for well-sampled spectra (as is the case for NIRSpec). However, our data
consists of two kind of spectral features, both of which are scarcely
conducive of precise redshift determination. Nebular emission consists of
broad lines and of multiple narrow lines. Even when a precise redshift can be
determined, it is unclear which narrow lines can be used to trace the redshift
of the galaxy. For the stellar features, the physical association with the
systemic redshift is unambiguous, but all the absorption features belong to
the Balmer series of hydrogen and are therefore subject to nebular-line
infill. Line infill may consist of multiple components too.

To take into account the different ways the absorption lines can be filled we
use a Monte Carlo approach. We consider the central spectrum as the unweighted
sum of the spectra within the elliptical aperture of semi-major axis equal to
/2, axis ratio $q=0.75$ and position angle 111.5°; spaxels partially inside
the aperture are weighted according to the fractional overlap between the
spaxel and the ellipse. We then create one thousand random-noise realisations
of this spectrum by adding white noise from the uncertainty spectrum.

This procedure yields an ensemble of spectra that have 40 per cent lower S/N
than the actual data, but crucially preserve any systematics compared to e.g.,
bootstrapping based on a best-fit model spectrum. We fit each random
realisation with the same procedure used in $\mbox{\rm\bf S}_{~{}}$1.5, but we
also use a random starting guess for the redshift, chosen between
$3.04<z<3.09$. The resulting redshift distribution is bimodal, with the
strongest peak at $z=3.06404$ and a secondary peak at $z=3.06568$ (the two
distributions contain 63 and 37 per cent of the total probability). We
therefore adopt a systemic redshift $z_{\mathrm{sys}}=3.06404$. The random
uncertainties (from a Gaussian fit to the posterior distribution) are of order
0.0004, but this value is overestimated, because we added random noise to the
already noisy spectrum. However, the systematic uncertainty (defined as the
distance between the strongest and secondary peak) is much larger at 0.0016.
The random and systematic redshift uncertainties correspond to velocity
uncertainties of 31 and 120 , respectively. Our final redshift determination
is $z_{\mathrm{sys}}=3.06404\pm 0.0004(\text{rand.})\pm 0.0016(\text{syst.})$.

Spectroscopy in band 1 (g140m and g140h gratings) may remove the systematic
uncertainty entirely, by targeting the higher-order Balmer lines where the
stellar absorption is much stronger than the nebular emission. However, even
this region may present complex features (e.g., ISM absorption with high
equivalent width in the doublet, which overlap with other stellar features
(stellar and ).

###  1.4 Spectral energy distribution modelling and star-formation history

To study the physical properties of the stellar populations present in , the
prism/clear NIRSpec/IFS observations were analysed in a spaxel-by-spaxel basis
(0.05 arcsec on a side) following a similar method to that described in
(2023ApJ…946L..16P, ). Before comparing with models, the NIRSpec prism/clear
data was PSF-matched using a Gaussian kernel to match the FWHM of the PSF at
4.5 , 0.16 arcsec FWHM (see Fig. 7, dotted line) The spectra were also re-
calibrated in flux (with correction factors ranging from 0.86 at 1 to 1.29 at
2.0–2.5 ) to match the integrated magnitude (in a 1.2 arcsec radius circular
aperture) NIRCam wide- and medium-band data obtained by JADES
eisenstein_overview_2023 ; rieke_jades_2023 . We considered a 5 per cent
constant error added in quadrature to the formal observational values to
account for the absolute flux calibration uncertainties.

The spectrum for each spaxel counting with more than 10 wavelengths with
$S/N>5$ was compared to a grid of stellar population models constructed with
the (bruzual+charlot2003, ) library, assuming a star formation history
described by a delayed exponential characterised by a timescale $\tau$
(ranging from 1 Myr to 1 Gyr in 0.1 dex steps) and age $t_{0}$ (ranging from 1
Myr to the age of the Universe at the redshift of the galaxy, 2 Gyr). The
stellar metallicity $Z$ was left as a free parameter, allowing to take all the
discrete values provided by the (bruzual+charlot2003, ) library from 2 per
cent solar to 2.5 times solar. Nebular (continuum and line) emission was taken
into account as described in (2003MNRAS.338..508P, ; 2008ApJ…675..234P, ). The
attenuation of the stellar and nebular emission was modelled with a
(calzetti+2000, ) law, with $A_{V}$ values ranging from 0 to 5 magnitudes in
0.1 mag steps. The (surviving, i.e., without including remnants and gas re-
injected by winds and supernova explosions into the interstellar medium)
stellar mass is obtained by scaling the (mass-normalised) stellar model to the
spectrum (i.e., the stellar mass is not a directly fitted quantity).

The stellar population synthesis method includes a Monte Carlo algorithm to
estimate uncertainties and degeneracies of the modelling (see
(2008ApJ…675..234P, ; 2016MNRAS.457.3743D, )), consisting in varying the data
points according to their uncertainties, refitting the spectrum, and analysing
the clusters of different solutions identified in the multi-dimensional
parameter space defined by $\tau$, $t_{0}$, $Z$, and $A_{V}$.

Based on this method, we constructed the stellar mass and mass-weighted age
maps presented in Fig. 2–2. The mass-weighted age was calculated by
integrating the star formation history multiplied by the time from 0 to the
age $t_{0}$ of the stellar population.

The integrated SFH and stellar mass evolution as well as the global spectral
energy distribution, all presented in Fig. 2, were constructed by adding all
the spaxels included in the stellar population synthesis analysis. To account
for low surface brightness pixels that were not included in the modelling, we
applied an aperture correction obtained by comparing the flux of the analysed
spaxels compared to the integrated photometric aperture.

####  1.4.1 Modelling the panchromatic SED with cigale

The panchromatic SED of the target was built by considering the multi-
wavelength UV-to-NIR photometry available in (Merlin2021, ) as well as the
NIRCam photometry released by the JADES and JEMS collaborations
(eisenstein_overview_2023, ; rieke_jades_2023, ; williams_jems_2023, ). The
MIR-to-FIR photometry was taken from (Shirley2021, ). The counterpart in the
different catalogs was found by using a positional matching radius of 1
arcsec. The SED was then analyzed by using the galaxy SED-fitting tool cigale
(Code Investigating GALaxy Emission; (Boquien2019, )). This code performs a
multi-component fitting to separate the AGN contribution from the host galaxy
emission. We used the following models to reproduce the different emission
components: i) the stellar emission was modelled by adopting a delayed-$\tau$
(exponentially declining) SFH, the stellar population models of
(bruzual+charlot2003, ), a Chabrier initial mass function (IMF; (chabrier2003,
)), and solar metallicity. Dust attenuation was taken into account through the
modified version of the (Calzetti2000, ) curve available within cigale. ii)
The emission from dust heated by star formation was reproduced using the model
library by (Dale2014, ), where we assumed an AGN contribution equal to 0 in
order to treat it separately. iii) The AGN emission component was reproduced
by using the models presented by (Fritz2006, ). We run cigale by adopting the
same input grid used by (Circosta2018, ) and the cigale version v2018.0.2.

###  1.5 Stellar kinematics

We present the first spatially resolved stellar kinematics beyond redshift
$z=2.5$, and the first 2-d stellar kinematics beyond $z=0.8$. For these
measurements we use , which models simultaneously the stellar continuum and
nebular lines with a non-linear 2 minimisation (cappellari+emsellem2004, ;
cappellari2017, ; cappellari2022, ), all while taking into account the
instrument line-spread function. The stellar continuum is modelled as a (non-
negative) linear superposition of simple stellar population (SSP) spectra. As
input, we use a subset of the SSPs library based on the MIST isochrones
(choi+2016, ) and C3K model atmospheres (conroy+2019, ). The SSP templates
span a logarithmically spaced grid of ages and metallicities, covering the
ranges 10–2,500 Myr with 0.2 dex sampling and =-2.00–0.25 dex with 0.25 dex
sampling. The maximum age is set to 500 Myr older than the age of the Universe
at the redshift of , to avoid edge effects (changing this setting does not
alter our conclusions). The nebular emission and absorption lines are modelled
as multiple Gaussians. It is common practice to also use additive Legendre
polynomials when fitting stellar kinematics (vandesande+2017a, ), but we found
that tended to fit a strongly negative and almost featureless polynomial, akin
to an over-subtracted background as bright as the target, which – given our
flux calibration – is unphysical. We therefore used a 15th-order
multiplicative Legendre polynomial to model residual flux-calibration issues.
For the line-spread function, we use a uniform spectral resolution of
$R=2,700$, using the nominal resolution curve for g235h (jakobsen+2022, ).

We find that our results depend critically on the wavelength range adopted.
This is due to the already mentioned degeneracy between Balmer emission and
absorption ($\mbox{\rm\bf S}_{~{}}$1.3). For example, restricting the fit to
the range where only and are present, we measure a that is 25 per cent lower
(in this case the degree of the multiplicative polynomial is only 3). It is
common practice to assess this uncertainty by repeating the fit and masking
the Balmer lines (newman+2018b, ), but in our case these lines are the only
prominent stellar absorption features in the observed spectroscopic
configuration. Therefore, as for the redshift, a conclusive test may require
new observations at shorter wavelengths.

####  1.5.1 Aperture-integrated kinematics

We use two sets of aperture-integrated kinematics: inside an ellipse of semi-
major axis equal to one (for calculating the second moment of the line-of-
sight velocity distribution of the stars, ), and inside elliptical annuli (for
use in the BPT diagram, Fig. 3). In both cases, we use emission lines coupled
in four sets called ‘kinematic components’, which share the same line-of-sight
velocity and intrinsic velocity dispersion (i.e., before convolution with the
NIRSpec g235h line spread function). The first kinematic set consists of the
Balmer series of hydrogen –(using the intrinsic line ratios appropriate for
Case B recombination, electron density $n_{e}=100~{}\mathrm{cm}^{-3}$ and
temperature $T_{\mathrm{e}}=10,000$ K; note the relative line fluxes are then
modified with a dust attenuation model), , and the doublet. The second
component consists of the , and doublets. The third component consists of and
. The fourth and last component is the resonant $D_{1}$ and $D_{2}$ absorption
features. The , and doublets have line ratios fixed to the appropriate values
from atomic physics; the doublet has line ratio constrained between 0.44 and
1.47 (kewley+2019, ), and the $D_{2}/D_{1}$ ratio of is constrained between
0.89 and 1.94 (poznanski+2012, ). For nebular emission only, we use the
(calzetti+2000, ) attenuation law.

From the elliptical aperture at 1 we find $\sigmaestar=356\pm 10$ . The
uncertainties are likely dominated by systematics, so we consider the fiducial
uncertainties to be 10 per cent. Using the virial theorem calibration of
(vanderwel+2022, ) and the light profile measurements from CANDELS
(grogin+2011, ) F160W imaging (vanderwel+2014, ), we find a dynamical mass
$\Mdyn=k(n)k(q)\sigmaestar^{2}\re/\mathrm{G}=(2.0\pm 0.1)\times 10^{11}$ ,
dominated by the scatter in the calibration, which are of order 25 per cent.
For a single-burst stellar population of age 1 Gyr, the surviving stellar mass
fraction is 0.7 (assuming a Chabrier initial mass function and solar
metallicity). Down-scaling the stellar mass formed by this factor, we obtain a
dynamical-to-stellar mass ratio of 70 per cent.

We also use the 1 apertures to measure the Balmer EW indices and , using the
Lick definition (worthey1994, ). For , the Lick bands lie partially outside
the wavelength range of the g235h/f170lp datacube. We therefore measure the
absorption strength using the best-fit model. The resulting values are
$\hda=6.63\pm 0.01$ and $8.06\pm 0.08$ Å(rest frame), where for the second
value we subtracted the nebular emission. The uncertainties are from
bootstrapping the uncertainties on the data. Clearly, the true stellar EW must
be higher than the non-subtracted measurement, which lies itself well into the
range that defines PSB galaxies ($\hda>4\text{--}5$ Å, e.g., (wu+2020, )). For
, we can measure the index from the data, and find respectively $\hga=4.07\pm
0.01$ and $6.83\pm 0.09$ Åfor the unsubtracted and subtracted spectra. Both
values are again in the PSB regime.

####  1.5.2 Spatially resolved stellar kinematics

Measuring spatially resolved stellar kinematics with typically requires
$S/N\gtrsim 10\text{--}15~{}\AA^{-1}$, unless specific constraints are applied
(vandesande+2017a, ). Our data has a continuum $S/N$ as low as 3–5 $\AA^{-1}$,
therefore we need to adopt a careful approach. We measure spatially resolved
stellar kinematics with two different setups: Voronoi-binned data (Method I)
and spaxel-by-spaxel measurements (Method II). Briefly, Voronoi bins have the
advantage of higher $S/N$ (cappellari+copin2003, ), but for data with low
spatial resolution they risk averaging over regions with different stellar
populations and kinematics (vandesande+2017a, ); spaxel-by-spaxel fitting
overcomes the low-$S/N$ limitations by restricting the set of input templates
(vandesande+2017a, ; foster+2021, ). The results in the article are based on
Method I. The other method is described only briefly, to show that our
findings do not depend on the procedure adopted.

Method I – Voronoi-binned data. We measure the $S/N$ per spaxel with a
preliminary fit to each spaxel independently, using the the best-fit template
from the fit to the aperture spectrum as the only input template (1.5.1). The
$S/N$ is then measured from the standard deviation of the residuals between
the spaxel best-fit model and the data. Having determined the $S/N$
empirically, we proceed to create the Voronoi bins using vorbin
(cappellari+copin2003, ). We select a target $S/N=12~{}\AA^{-1}$. The
resulting bins are outlined in Fig. 5 and are colour-coded by their empirical
$S/N$, estimated from the residuals of the fit (see below); we note that in
the outer bins ($1<R<2~{}\re$) the empirical $S/N$ is lower than the target
$S/N$. This outcome is in fact expected from correlated noise, which becomes
more relevant as the average size of the Voronoi bins increases outward from
the galaxy centre.

To fit each spectrum, we use the same procedure as for the integrated
spectrum, but the choice of SSP spectra is restricted only to the spectra that
had non-zero weight in the linear combination forming the best-fit aperture
spectrum.

Moreover, the selection of Gaussian templates representing nebular emission
and absorption is also simplified compared to what we used for the aperture
spectrum, reflecting the simpler kinematics of the spatially resolved spectra.
The first kinematic component consisting of the –series, the doublet, and the
three doublets , and . The second kinematic component consists of and , and
the third kinematic component consists of absorption. All doublets are fixed
or constrained, as described for the aperture kinematics. Example fits of
Voronoi bins are shown in Fig. 5 and 5.

Method II – Spaxel-by-spaxel data. To measure spaxel-by-spaxel kinematics, we
use a threshold $S/N>3~{}\mathrm{pixel}^{-1}$. In general, such a low value is
considered sub-optimal, but if the templates are carefully pre-selected, it is
still possible to obtain accurate measurements (vandesande+2017a, ). To
optimise the templates selection, we first create 11 annular-binned spectra
between 0 and 2.5 , spaced by 0.025 arcsec and with the same shape and
position angle as the observed stellar continuum. We then de-rotate the
spectrum in each spaxel according to the line-of-sight velocity measured in
the relevant Voronoi bins; this avoids the spectral broadening due to
rotation. The resulting bin spectra are fit with the same procedure as for the
Voronoi bins. From these fits we take the weights of the SSP templates and the
measured . We then proceed to fit the individual spaxels. Given a spaxel, we
identify the annular bins that the spaxel intersects and then also consider
two more bins (if they exist): the annulus adjacent to the innermost selected
annulus and the annulus adjacent to the outermost selected annulus. The
template selection is simply the union of all non-zero templates from the
best-fit annular spectra (typically 7–9 templates are selected). The velocity
dispersion is the average of the annular values, weighted by the fractional
overlap of the spaxel with the annuli. We fit the spaxel spectrum using this
restricted template selection and with fixed to the average . If the resulting
fit has $S/N<5$, the fit is concluded and we proceed to another spaxel. If the
resulting fit has $S/N>5$, we repeat the fit leaving free between $\pm 30$ per
cent from the input . The uncertainties are measured again using
bootstrapping. The resulting maps are shown in Fig. 9, where we compare them
with the Voronoi-binned maps. The resulting velocity values are quantitatively
different, but the results are qualitatively the same. shows higher values in
the central regions, likely due to a combination of lower average $S/N$ and
smaller template set compared to the Voronoi bins. Using this method, we
measure a spin parameter $\lambdar[\re]=0.40$, which rises to 0.60 after the
PSF correction; this latter value is consistent with the measurement from
Method I.

Figure 9: Comparison of the stellar kinematics between the fiducial method
(based on Voronoi bins, Method I; panels 9 and 9) and the alternative method
(based on individual spaxel with constrained templates, Method II; panels 9
and 9). The two measurements show good agreement, but the spaxel-by-spaxel
fits tend to find higher in the centre, possibly due to lower $S/N$ and
smaller set of input templates for the fit.

###  1.6 Emission-line measurements

To measure the line-of-sight velocity and velocity width of the nebular
emission lines, we used qubespec algorithm. We modelled simultaneously , and .
Each emission line was modelled with a single or a double Gaussian profile,
with the redshift and FWHM of each Gaussian component being the same between
the individual emission lines. We fixed the flux ratio of the and doublets as
described in $\mbox{\rm\bf S}_{~{}}$1.5. We estimate the posterior probability
distribution of both the single- and double-Gaussian models with the Markov-
Chain Monte-Carlo algorithm emcee (foreman-mackey+2013, ). We select the best
model (either one or two Gaussians per emission line) based on the Bayesian
Information Criterion (BIC; schwarz1978, ). For each spaxel, we took a median
spectrum of within the PSF ($\pm 2$ spaxel) to increase the $S/N$ of each
fitted spectrum, while maintaining the diffraction-limited spatial resolution.

For each fitted spaxel, we calculated the 10, 50, 90 and $\mbox{\rm\bf
w}_{8}$0 as velocities of 10th, 50th and 90th velocity percentiles of the
emission line and the velocity width of the line 80 per cent of the flux
(90-10). The systemic velocity of the galaxy (v0) was set to the systemic
velocity of the stellar component ($\mbox{\rm\bf S}_{~{}}$1.3). Despite each
of the Gaussian components fitted having the same redshift and FWHM, the final
kinematics can be different due to different flux ratios of the Gaussian
components in each emission line. The resulting flux and kinematic maps are
presented in Fig. 4.

###  1.7 Outflow measurements

To estimate the outflow rate of the ionised gas, we used the emission line.
Because is only seen in absorption, we calculated the mass of the outflowing
ionised gas from the line as follows (see e.g. (carniani+2015, ; kakkad+2021,
))

$\Mout[\OIII]=8\cdot
10^{7}\left(\frac{1}{10^{\mathrm{[O/H]-[O/H]_{\odot}}}}\right)\left(\frac{L_{\OIII}}{10^{44}~{}\mathrm{erg\,s^{-1}}}\right)\left(\frac{\nelec}{500~{}\mathrm{cm}^{-3}}\right)^{-1}M_{\odot}$
(5)

where $L_{\OIII}$ is the line luminosity, is the mean electron density, and
where we assumed that the electron temperature is 10,000 K, all the oxygen is
ionised to O2+, and the metallicity [O/H] of the outflowing material is equal
to the solar value [O/H]⊙. We further assume a uniformly filled biconical
outflow, and use the equation from (fiore+2017, ) as

$\Mdotout=3\cdot\vout\frac{\Mout}{\Rout}$ (6)

where is the velocity of the outflows (defined as =10 = 1,200 km s-1), is the
outflowing mass and is the radius of the outflow. The latter was estimated in
the $\mbox{\rm\bf w}_{8}$0 map as the radius of the region where $\mbox{\rm\bf
w}_{8}$0$>600$ (harrison+2016, ; kakkad+2021, ). This value corresponded to a
radius = 3.57 kpc. The largest source of uncertainty in this calculation is ,
which can range from 500 to 104 cm-3 (e.g., (baron+netzer2019, ; davies+2020,
)). Therefore, we estimated the outflow rate for the range of density values,
resulting in an outflow rate in ionised gas of 0.14–2.9 . This range is shown
as the range of the cyan errorbars in Fig. 2.

For the neutral gas outflows, we use the methods of (cazzoli+2016, ), based on
the absorption. These authors extend the methods of (rupke+2005, ) to
spatially resolved spectroscopy. We assume a thin-shell, conical geometry
orthogonal to the galaxy disc; (maiolino+2012, ) remark that assuming a
conical geometry with uniform density changes the outflow rate by a factor of
3. Our disc inclination is 66°, from the axis ratio of the best-fit Sérsic
model (vanderwel+2014, ). The outflow rate in the $k$th spaxel is

$\Mdotout[\NaI][,k]=11.5\,\left(\dfrac{\Rout}{10~{}\kpc}\right)\left(C_{f}\dfrac{\Omega_{k}}{0.4}\right)\left(\dfrac{N_{k}}{10^{21}\,\mathrm{cm}^{2}}\right)\left(\dfrac{v_{\mathrm{out},k}}{200\,\kms}\right)\,\MSun\,\peryr$
(7)

where is the extent of the outflow, $\Omega_{k}$ is the subtended solid angle,
$C_{f}=0.37$ is the cloud covering fraction (estimated from (rupke+2005, )),
$N_{k}$ is the gas column density, and $v_{\mathrm{out},k}$ is the outflow
physical velocity. The extent of the outflow is $\Rout=2.7~{}\kpc$, estimated
as the distance between the centre of the galaxy and the outermost detected
absorption, corrected for inclination. As noted by e.g., (cazzoli+2016, ),
this size measurement relies on the presence of a sufficiently bright
background illumination to detect foreground absorption, therefore we can
consider a lower limit to the true extent of the outflow. The solid angle
subtended by each spaxel is calculated from the spherical shell geometry.
$N_{k}$ is estimated from the equivalent width of using Eq. 1 from
(cazzoli+2016, ); our equivalent-width measurements are corrected for the
contribution due to the stellar atmospheric absorption. The outflow velocity
is taken from the ppxf fits, and is the (absolute value) of the centroid
Gaussian-line velocity, corrected for the outflow inclination by $\cos\,i$.

From this formula, summing over all spaxels where we detect blueshifted
absorption, we obtain $\Mdotout[\NaI]=100$ .

To estimate the escape velocity , we need the gravitational potential of the
galaxy, including its dark matter halo. Using the relation between stellar
mass and halo mass to infer the mass of the dark matter halo is impractical.
This is because – for the stellar mass of – the slope of the relation is
unfavourable for a precise inference. We adopt the alternative method of
assuming the gravitational potential of the galaxy is an isothermal sphere,
truncated at a radius $r_{\mathrm{max}}$ (veilleux+2005, ; arribas+2014, ;
uebler+2023, ). Using Eq 4 from (uebler+2023, ) with $r_{\mathrm{max}}=100$
kpc, we obtain an escape velocity $\vesc=1,200\pm 200$ . The uncertainties
were estimated with a simple Monte-Carlo analysis, where we have randomly
drawn the various observables that go into the equation of as follows.
Aperture velocity dispersion is drawn from the normal distribution
$\mathcal{N}(\mu,\sigma)$ with mean $\mu=356$ and standard deviation
$\sigma=36$ (ten per cent); is drawn from $\mathcal{N}(0.14,0.02)$ (units of
kpc); Sérsic index $n$ is from the truncated normal distribution
$\mathcal{T}(\mu,\sigma\mathchar 24635\relax\;\mu_{0},\mu_{1})$ with mean
$\mu=1.96$, $\sigma=0.4$ (twenty per cent), and truncated between $\mu_{0}=1$
and $\mu_{1}=4$; the $r_{\mathrm{out}}$ is from $\mathcal{T}(4.5,1,2.5,6)$
(units of spaxels); the galaxy intrinsic axis ratio $q_{0}$ is from
$\mathcal{T}(0.2,0.1,0.1,0.5)$, and the projected axis ratio $q$ is from
$\mathcal{T}(0.44,0.1,0.3,0.5)$, subject to $q\geq q_{0}$; $q$ and $q_{0}$ are
used to infer the inclination $i$.

Most of the uncertainty on is due to the outflow radius $r_{\mathrm{out}}$ (60
per cent), followed by (30 per cent) and (10 per cent); the other three
variables account for a few per cent each. Comparing our to the map of de-
projected velocities (Fig. 5), we find an average ratio
$\lvert\vnai\rvert/\vesc=0.8\pm 0.2$. Given the uncertainties on the outflow
geometry and escape velocity, we can conclude that at least part of the
neutral-gas outflows are able to escape the galaxy gravitational potential. At
the very least, the gas will be temporarily removed from the star-forming
region.

Comparing the ionised and neutral outflow phases, we conclude that the
ionised-gas outflow rate is negligible, being up to two orders of magnitude
lower than the neutral-gas outflow rate. The mass loading factor of the
neutral outflow is orders higher than the recent SFR, therefore this outflow
is sufficient to stop star formation. Similar events in the recent past of may
have caused the galaxy to become quiescent (see SFH in 2).

Data availability The data that support the findings of this study are
publicly available from the https://archive.stsci.edu/.

Code availability This work made extensive use of the freely available
http://www.debian.org operative system. We used the http://www.python.org
programming language (vanrossum1995, ), maintained and distributed by the
Python Software Foundation. We further acknowledge direct use of
https://pypi.org/project/astropy/ (astropyco+2013, ),
https://pypi.org/project/dynesty/ (speagle2020, ),
https://github.com/cconroy20/fsps (conroy+2009, ; conroy_gunn_2010, ),
https://pypi.org/project/matplotlib/ (hunter2007, ),
https://pypi.org/project/numpy/ (harris+2020, ),
https://github.com/bd-j/prospector (johnson+2021, )
https://pypi.org/project/dynesty/ (johnson_pyfsps_2023, ), and
https://pypi.org/project/scipy/ (jones+2001, ).

## Acknowledgements

FDE, TJL, RM and JS and acknowledge support by the Science and Technology
Facilities Council (STFC), by the ERC Advanced Grant 695671 “QUENCH”, and by
the UKRI Frontier Research grant RISEandFALL; RM is further supported by a
research professorship from the Royal Society. PGP-G acknowledges support
grants PGC2018-093499-B-I00 and PID2022-139567NB-I00 funded by Spanish
Ministerio de Ciencia e Innovación MCIN/AEI/10.13039/501100011033, FEDER, UE.
SA, BRP, and MP acknowledge support from the research project
PID2021-127718NB-I00 of the Spanish Ministry of Science and Innovation/State
Agency of Research (MICIN/AEI). MP is further supported by the Programa
Atracción de Talento de la Comunidad de Madrid via grant 2018-T2/TIC-11715. HÜ
gratefully acknowledges support by the Isaac Newton Trust and by the Kavli
Foundation through a Newton-Kavli Junior Fellowship. AJB, JC and GCJ
acknowledge funding from the “FirstGalaxies” Advanced Grant from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation programme (Grant agreement No. 789056). SC, EP and GV acknowledge
support by European Union’s HE ERC Starting Grant No. 101040227 - WINGS. GC
acknowledges the support of the INAF Large Grant 2022 “The metal circle: a new
sharp view of the baryon cycle up to Cosmic Dawn with the latest generation
IFU facilities” IL acknowledges support from PID2022-140483NB-C22 funded by
AEI 10.13039/501100011033 and BDC 20221289 funded by MCIN by the Recovery,
Transformation and Resilience Plan from the Spanish State, and by
NextGenerationEU from the European Union through the Recovery and Resilience
Facility. BER acknowledges support from the NIRCam Science Team contract to
the University of Arizona, NAS5-02015. The authors acknowledge use of the lux
supercomputer at UC Santa Cruz, funded by NSF MRI grant AST 1828315.

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