# The impact of ionised outflows from z$\sim$2.5 quasars is not through
instantaneous in-situ quenching: the evidence from ALMA and VLT/SINFONI

J. Scholtz$,^{\\!1,2}$ C.M. Harrison,${}^{\\!3}$ D.J. Rosario,${}^{\\!2}$ D.M.
Alexander,${}^{\\!2}$ K.K. Knudsen,1 F. Stanley,1 Chian-Chou Chen,4 D.
Kakkad,5 V. Mainieri,6 J. Mullaney7

1 Chalmers University of Technology, Department of Space, Earth and
Environment, Onsala Space Observatory, 439 92 Onsala, Sweden
2 Centre for Extragalactic Astronomy, Durham University, Department of
Physics, South Road, Durham, DH1 3LE, UK
3 School of Mathematics, Statistics and Physics, Newcastle University,
Newcastle upon Tyne, NE1 7RU, UK
4 Academia Sinica Institute of Astronomy and Astrophysics (ASIAA), No. 1, Sec.
4, Roosevelt Rd., Taipei 10617, Taiwan
5 European Southern Observatory, Alonso de Cordova 3107, Vitacura, Casilla
19001, Santiago de Chile, Chile
6 European Southern Observatory, Karl-Schwarzschild-Strasse 2, Garching bei
München, Germany
7 Department of Physics and Astronomy, University of Sheffield, Sheffield, S3
7RH, UK
E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>
(XYZ)

###### Abstract

We present high-resolution ($\sim$2.4 kpc) ALMA band 7 observations (rest-
frame $\lambda\sim 250\mu$m) of three powerful z$\sim$2.5 quasars ($L_{\rm
bol}=10^{47.3}$-$10^{47.5}$ ergs s-1). These targets have previously been
reported as showing evidence for suppressed star formation based on cavities
in the narrow H$\alpha$ emission at the location of outflows traced with [O
iii] emission. Here we combine the ALMA observations with a re-analysis of the
VLT/SINFONI data to map the rest-frame far-infrared emission, H$\alpha$
emission, and [O iii] emission. In all targets we observe high velocity [O
iii] gas (i.e., W80$\sim$1000–2000 km s-1) across the whole galaxy. We do not
identify any H$\alpha$ emission that is free from contamination from AGN-
related processes; however, based on SED analyses, we show that the ALMA data
contains a significant dust-obscured star formation component in two out of
the three systems. This dust emission is found to be extended over
$\approx$1.5–5.5 kpc in the nuclear regions, overlaps with the previously
reported H$\alpha$ cavities and is co-spatial with the peak in surface
brightness of the [O iii] outflows. In summary, within the resolution and
sensitivity limits of the data, we do not see any evidence for a instantaneous
shut down of in-situ star formation caused directly by the outflows. However,
similar to the conclusions of previous studies and based on our measured star
formation rates, we do not rule out that the global host galaxy star formation
could be suppressed on longer timescales by the cumulative effect of quasar
episodes during the growth of these massive black holes.

###### keywords:

galaxies: active; — galaxies: evolution; — X-rays: galaxies; — infrared:
galaxies

††pubyear: 2021††pagerange: The impact of ionised outflows from z$\sim$2.5
quasars is not through instantaneous in-situ quenching: the evidence from ALMA
and VLT/SINFONI–D

##  1 Introduction

It is now accepted that inside every massive galaxy resides a supermassive
black hole (Kormendy & Ho 2013). During the growth of these supermassive black
holes, via accretion events, these objects become visible as active galactic
nuclei (AGN; Soltan, 1982; Merloni et al., 2004). Current theoretical models
of galaxy evolution require AGN to inject significant energy into their host
galaxies in order to reproduce the basic properties of local galaxies and the
intergalactic medium (IGM), such as the steep mass function, the black
hole–spheroid relationships, increased width of specific star formation rate
distributions as a function of stellar mass, galaxy sizes, galaxy colour bi-
modality, AGN number densities and enrichment of the IGM by metals (e.g., Silk
& Rees, 1998; Di Matteo et al., 2005; Alexander & Hickox, 2012; Dubois et al.,
2013a, b; Vogelsberger et al., 2014; Hirschmann et al., 2014; Crain et al.,
2015; Segers et al., 2016; Beckmann et al., 2017; Harrison, 2017; Choi et al.,
2018; Scholtz et al., 2018). In these models, the AGN are required to regulate
the cooling of the interstellar medium (ISM) and/or intracluster medium (ICM)
or to eject gas out of the galaxy through galactic wide outflows. This process
is usually referred to as “AGN feedback” and it is believed to regulate the
rate at which stars can form. However, from an observational perspective, it
is still not clear what role AGN play in regulating star formation in the
overall galaxy population, especially at high redshift and for the most
radiatively powerful AGN called quasars (e.g., Harrison, 2017; Cresci &
Maiolino, 2018).

Over the past decade, many studies have focused on identifying and
characterising multiphase outflows in galaxies (see e.g., Fiore et al., 2017;
Harrison et al., 2018; Cicone et al., 2018; Veilleux et al., 2020). Indeed,
there is now significant evidence that energetic ionised, atomic and molecular
outflows are commonly found in AGN host galaxies across a wide range of cosmic
epochs (e.g. Veilleux et al., 2005; Morganti et al., 2005; Ganguly &
Brotherton, 2008; Sturm et al., 2011; Cicone et al., 2012; Harrison et al.,
2012; Cicone et al., 2014; Zakamska & Greene, 2014; Balmaverde & Capetti,
2015; Carniani et al., 2015; Brusa et al., 2015; Harrison et al., 2016a; Woo
et al., 2016; Leung et al., 2017; Brusa et al., 2018; Förster Schreiber et
al., 2018a; Lansbury et al., 2018; Fluetsch et al., 2019; Perna et al., 2019;
Ramos Almeida et al., 2019; Husemann et al., 2019). Furthermore, these AGN-
driven outflows have been identified on a large range of spatial scales
(between tens of parsecs to tens of kiloparsecs; e.g., Storchi-Bergmann et
al., 2010; Veilleux et al., 2013; Carniani et al., 2015; Cresci et al., 2015b;
Feruglio et al., 2015; Kakkad et al., 2016; McElroy et al., 2016; Rupke et
al., 2017; Jarvis et al., 2019; Kakkad et al., 2020). Given that these
outflows can be located on these scales, they may have the potential to impact
upon the ISM and, consequently, the star formation inside the host galaxies.

Despite observations showing that AGN outflows are common, and can extend over
large scales, the impact that they have on star formation is still open to
debate. For example, statistical, non spatially resolved, studies in the
literature provide contradictory conclusions on the relationship between
ionised outflows and the star formation rates of the host galaxies (Balmaverde
et al., 2016; Wylezalek & Zakamska, 2016; Woo et al., 2017, 2020). In many of
the spatially-resolved studies, the most powerful outflows are capable of
removing or destroying at least some of the star-forming material at a rate
faster than it can be formed into stars (e.g., see Fiore et al., 2017;
Harrison et al., 2018). However, in the majority of observations, there are
considerable uncertainties in these calculations due to uncertain spatial
extents and the many assumptions that have to be considered to convert
emission-line luminosities and velocities into mass outflow rates (e.g.
Karouzos et al., 2016; Villar-Martín et al., 2016; Husemann et al., 2016; Rose
et al., 2018; Harrison et al., 2018; Davies et al., 2020a). On the other hand,
measurements can be more accurate for more nearby sources (e.g. Baron et al.,
2018; Revalski et al., 2018; Venturi et al., 2018; Fluetsch et al., 2019;
Perna et al., 2020) and star formation has been detected inside outflows in
some local AGN host galaxies, which may be a form of ‘positive’ feedback
(Maiolino et al., 2017; Gallagher et al., 2019; Perna et al., 2020). However,
samples of nearby sources typically lack the most powerful AGN, which are more
common at high redshift (i.e., $z\gtrsim$1) and are thought to be most
important for influencing galaxy evolution (e.g., McCarthy et al., 2011).

At high redshift, observational evidence for a direct impact by AGN on star
formation is particularly scarce. Indirect evidence may have been found in
some AGN host galaxies with depleted molecular gas reservoirs; however, there
are contradictory claims on this topic in the literature (e.g. Kakkad et al.,
2017; Perna et al., 2018; Kirkpatrick et al., 2019; Fogasy et al., 2020). A
potentially powerful approach to determine the impact of AGN-driven outflows,
which has been applied to high-redshift AGN studies, has been to use integral
field units (IFUs) to map narrow H$\alpha$ emission to trace star formation
and to map [Oiii] emission to trace AGN outflows. Most relevant for this work
are the studies of four high-redshift AGN (presented in Cano-Díaz et al.,
2012; Cresci et al., 2015b; Carniani et al., 2016) where it was suggested that
there was no star formation at the location of the [O iii] outflows and
potentially increased star formation along the edges the outflows (see Vayner
et al., 2017, for similar conclusions based on a $z$=1.4 radio-loud quasar).

In Scholtz et al. (2020) we demonstrated some of the challenges in
interpreting the aforementioned results of suppressed H$\alpha$ at the
location of [O iii] outflows. For example, although narrow H$\alpha$ emission
can be used as star formation tracer, (e.g. Hao et al., 2011; Murphy et al.,
2011), it is sensitive to dust obscuration and can be contaminated by AGN
photo-ionisation. Indeed, most of the star formation in high-redshift galaxies
is obscured (Madau et al., 1996; Casey et al., 2014; Whitaker et al., 2014)
and, although obscuration corrections can help (Alaghband-Zadeh et al., 2016),
sometimes the H$\alpha$ emission can be completely hidden (e.g., Hodge et al.
2016; Chen et al. 2017, 2020). This dust absorbed emission is re-radiated at
far-infrared (8–1000 $\mu$m; FIR) wavelengths and, consequently, the FIR
emission is sensitive to on-going obscured star formation (for reviews see
Kennicutt & Evans, 2012; Calzetti, 2013). Importantly for this work, high-
redshift AGN and quasar host galaxies have been shown to host significant
levels of star-formation obscured by dust (e.g., Whitaker et al., 2012;
Burgarella et al., 2013; Stanley et al., 2015, 2018).

Using additional ALMA continuum observations, Scholtz et al. (2020) re-
analysed the source from Cresci et al. (2015b) with the addition of 7 other
moderate luminosity X-ray AGN at z=1.5-2.5 (LX=$10^{43}$–$10^{45.5}$ ergs
s-1). We found no direct evidence for [O iii]-traced outflows suppressing or
enhancing star formation. Nonetheless, the targets in that work were moderate
luminosity AGN (i.e., Lbol=$10^{44}$–$10^{46.5}$ ergs s-1, assuming an X-ray
to bolometric conversion factor of 10) and do not represent the most powerful
sources, or those with the most extreme outflows. Therefore, in this current
work we perform similar analyses, i.e., combining ALMA measurements of the
rest-frame far infrared emission with IFU data, on the very powerful
z$\sim$2.4 quasars (i.e., L${}_{\rm bol}\sim 10^{47.5}$ ergs s-1) presented in
Cano-Díaz et al. (2012) and Carniani et al. (2016). These objects were pre-
selected to be bolometrically luminous and host high velocity [O iii]
outflows. These studies reported cavities in narrow H$\alpha$ emission, that
they associated with star formation, at the same spatial location of the
extreme [O iii] outflows, interpreting these results as evidence of negative
AGN feedback in the location of the outflow and positive feedback on the edges
of the outflow.

In §2 we describe our targets, and the observations used in our study, §3
describes the data analyses of the ALMA and IFU observations, including
spectral fitting and constructing FIR, narrow H$\alpha$ emission and outflow
maps. In §4 we present and discuss our results and in §5 we draw our
conclusions. In all of our analyses we adopt the cosmological parameters of
$\rm H_{0}=67.3\ km\,s^{-1}$, $\rm\Omega_{M}=0.3$, $\rm\Omega_{\Lambda}=0.7$
(Planck Collaboration et al., 2014) and assume a Chabrier (2003) initial mass
function (IMF). We publish all the scripts for the data analyses here.

##  2 Target description and Data

The primary objective of this work is a study of three quasars in which
earlier studies have claimed that AGN-driven outflows suppress in-situ host
galaxy star formation. We use new ALMA band 7 observations to obtain FIR
continuum images which are compared to the distribution of narrow H$\alpha$
and [O iii] emission derived from archival VLT/SINFONI observations. In § 2.1
we describe the selection of our sample, in § 2.2 and § 2.3 we describe the
ALMA and IFU data we used in the analyses.

###  2.1 Target description

We selected three z$\sim$2.5 type 1 quasars for this work: 2QZJ002830.4-2817
from Cano-Díaz et al. (2012) and; LBQS0109+0213 and HB89 0329-385 from
Carniani et al. (2016). We note for the latter two objects the original [O
iii] analyses were presented in Carniani et al. (2015). We will refer to these
objects in this work as 2QZJ00, LBQS01 and HB8903, respectively. Originally,
2QZJ00, LBQS01 and HB8903 sources were selected as quasars with large [O iii]
equivalent widths ($>$ 10Å in the rest frame) and bright in $H$-band ($<$ 16.5
mag) from a sample of Netzer et al. (2004) and Shemmer et al. (2004) (for more
information see Carniani et al. 2015). These selection criteria were designed
to select the most bolometrically luminous quasars during the peak epoch of
galaxy and black hole growth (e.g., Madau & Dickinson, 2014) that could easily
have their [O iii] kinematics mapped with an IFU. Furthermore, the high
equivalent width [O iii] lines can be easily de-blended from the emission
associated with the broad line region (H$\beta$ and FeII emission; see §
3.3.1).

We compiled the black-hole masses and bolometric luminosities from Carniani et
al. (2015). The black-hole masses are in the range of $10^{9.9}-10^{10.1}$ M⊙,
with bolometric luminosities of $10^{47.3}$–$10^{47.5}$ ergs s-1, placing them
at the extreme end of the quasar population (these values are discussed
further in Section 4.5). The objects’ names, sky coordinates, redshifts,
black-hole masses and bolometric luminosities are summarised in Table 1.

Figure 1 places our targets within the context of the overall AGN and quasar
population in terms of their [O iii] luminosities and [O iii] line widths
(W80; velocity width containing 80% of the total flux; measured in § 3.3). We
compare our sources with: the parent sample of 104 $z$=1.5-3 quasars from
Shemmer et al. (2004) and Netzer et al. (2004); the $\approx$24,000 $z<0.4$
spectroscopically selected AGN from Mullaney et al. (2013), the 86 moderate
luminosity X-ray AGN with IFU observations from the KMOS Survey at High-$z$
(KASHz; Harrison et al., 2016a, and Harrison et al in prep.), and the 18
type-1 X-ray AGN with IFU observations from the SINFONI Survey for Unveiling
the Physics and Effect of Radiative feedback (SUPER; Circosta et al., 2018;
Kakkad et al., 2020) 111For QSOs from Shemmer et al. (2004), Netzer et al.
(2004) and Mullaney et al. (2013), we used reported emission line profile
parameters (FWHM of both Gaussian components and their velocity offset) to
recalculate the W80 values.. We also highlight the moderate luminosity X-ray
AGN from Scholtz et al. (2020), where we performed a similar experiment to
this one, combining ALMA data and IFU data. We note that the sources from that
study were less extreme in both luminosity and [O iii] emission-line width
than the three targets presented here. Indeed, the three quasars in our sample
have a [O iii] luminosity $\sim 2\times 10^{44.3}$ ergs s-1, a factor of
$\sim$ 100 larger than a typical AGN population at z = 1–2.5 (Harrison et al.,
2016a; Scholtz et al., 2020) and have extreme [O iii] W80 values of 1260–1980
kms-1.

Figure 1:  Plot of [O iii] emission-line width (W80) versus [O iii]
luminosity. We compare the quasars in this study (blue circles) with quasars
and AGN populations from the following works: the parent sample of these
quasars (green crosses; Shemmer et al. 2004 and Netzer et al. 2004),
spectroscopically identified $z<0.4$ AGN from Mullaney et al. (2013) (orange
contours), X-ray AGN from the KASHz survey (Harrison et al., 2016a, grey
crosses, z=1.2-2.5), Type-1 X-ray AGN from the SUPER survey (red circles,
Kakkad et al. 2020) and the X-ray AGN from Scholtz et al. (2020) (magenta
circles, z=1.4-2.6). The three quasars studied here represent the most extreme
objects in terms of bolometric power and [O iii] velocities. Table 1: A table
of the basic properties of our quasar sample. (1) Object name used in this
work; (2) Object ID from Cano-Díaz et al. (2012); Carniani et al. (2015);
(3,4) Optical coordinates of the objects; (5) Redshift measured from the peak
of the narrow emission lines (see § 3.3.1); (6) Bolometric luminosity from
Shemmer et al. (2004); (7) Star formation rates derived from total FIR
emission estimated in § 3.2; (8) Black hole masses compiled from Carniani et
al. (2015); (9) Original paper analysing the VLT/SINFONI data; (10) On-source
exposure time in the IFU $K$-band (H$\alpha$) observations. (10) On-source
exposure time in the IFU $H$-band ([O iii]) observations.

(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
---|---|---|---|---|---|---|---|---|---|---
ID | Full name | RA | DEC | z | log10 | SFR(FIR) | log10 | Original | IFU K-band exposure | IFU H-band exposure
|  | (optical) | (optical) |  | LBol/ergs s-1 | M⊙yr-1 | (MBH/M⊙) | work | time (ks) | time (ks)
HB8903 | HB89 0329-385 | 52.776542 | -38.401389 | 2.445 | 47.5 | $<59$ | 9.9$\pm$0.3 | (b) | 14.4 | 12.6
LBQS01 | LBQS0109+0213 | 18.070417 | 2.496389 | 2.352 | 47.5 | 69${}_{-31}^{+170}$ | 10.0$\pm$0.3 | (b) | 14.4 | 14.4
2QZJ00 | 2QZJ002830.4-281706 | 7.126833 | -28.284667 | 2.401 | 47.3 | 56${}_{-25}^{+196}$ | 10.1$\pm$0.3 | (a) | 2.4 | 12.6

(a) Cano-Díaz et al. (2012); (b) Carniani et al. (2016)

###  2.2 ALMA observations and imaging

To map the rest-frame FIR emission (i.e., $\approx$ 250 $\mu$m) for our quasar
host galaxies, we use ALMA band 7 data (870 $\mu$m, PI: Harrison, programme ID
2017.1.00112.S) with a native resolution of $\sim$0.3 arcseconds and a maximum
recoverable scales of $\sim$4.3 arcseconds. The observations were performed
using 45–49 antennae with a baselines range of 15–800 m. We discuss the origin
of this emission in § 3.2.

We calibrated all the data and created the measuring sets using standard ALMA
scripts using a version of Common Astronomy Software Application (CASA)
applicable to the Cycle of the observations (Cycle 5; CASA v5.1.2). We
performed additional checks (i.e. checking the flags, phase diagrams) to see
if all calibrations (such as phase corrections) and the pipeline flagging of
bad antennae pairs worked correctly and checked that none of the spectral
windows used to create the continuum image contains any visible strong
emission lines.

Since the ALMA band 7 observations were performed at a higher resolution than
the IFU observations (0.3 arcsec compared to $\sim$0.5–0.6 arcsec; see §2.3),
we chose natural weighting for the imaging of the ALMA data. This increases
sensitivity while decreasing the resolution. The final images had a resolution
of $\sim 0.5$ arcseconds, enabling a resolution-matched comparison to the IFU
data. The dirty images were consequently cleaned down to 3$\sigma$ by
estimating the noise (root-mean-square; RMS) in the dirty maps. We put
cleaning boxes around our primary science targets and any visible source in
the image. The final RMS of the maps of 2QZJ00, LBQS01 and HB8903 is 0.05,
0.06 and 0.10 mJy/beam, respectively. This was calculated by masking any
sources in the field and calculating the RMS in the primary beam. The sources
are all significantly detected with peak signal-to-noise ratios (SNRs) of
28–36. We show the ALMA band 7 continuum maps in Figure 2 and tabulate the
properties of the images in Table 2.

The targets in our study were also part of an ALMA follow up programme using
band 3 observations ($\lambda\sim$3 mm) to search for CO(3–2) emission lines
(Carniani et al., 2017). The corresponding 3 mm continuum measurements in
these data provide a valuable additional data point for assessing the
contamination to the ALMA band 7 data point from the radio synchrotron
emission during our SED analyses in § 3.2. These observations were taken as
part of programme 2013.0.00965.S and 2015.1.00407.S with a maximum baseline of
1.5 km. The data was calibrated using CASA software (version 4.5). Similarly
to our band 7 observations, we used natural weighting to maximise the
sensitivity of our final images; however, we only select spectral windows
without detected emission-lines. The final resolution of our images were
$\sim$ 0.6 arcseconds with a sensitivity of 12-18 $\mu$Jy/beam. The targets
were detected with peak SNRs of 11–350. We use the 3 mm continuum photometry
in § 3.2. For both band 3 and band 7 data, we assumed conservative flux
calibration errors of 10%.

###  2.3 IFU Data

Our targets were observed with the VLT/SINFONI integral field spectrograph, in
the $K$-band and $H$-band to map the H$\alpha$ and [O iii] emission lines,
respectively. The H$\alpha$ IFU data was first published in Cano-Díaz et al.
(2012) (2QZJ00)222We note that Williams et al. (2017) presented adaptive
optics assisted SINFONI IFU data for 2QZJ00. However, their study focuses on
the properties of the broad line region and they find that the star-forming
regions and diffuse spatially resolved [O iii] outflows are not detected in
these data. We, therefore, focus on the data presented in Cano-Díaz et al.
(2012) for our re-assessment of the relationship between outflows and star
formation in this quasar. and Carniani et al. (2016) (LBQS01 and HB8903) and
were observed through ESO programmes ID 077.B-0218(A) and 091.A-0261(A). The
H-band data we use were first presented in Carniani et al. (2015) and were
observed through ESO programme ID 086.B-0579(A). We note that initial results
from shorter exposure $H$-band VLT/SINFONI data were presented earlier in
Cano-Díaz et al. 2012.

Most of the observations were performed using the 8$\times$8 arcsec field of
view which is divided into 32 slices of width 0.25 arcsec with a pixel scale
of 0.125 arcsec. The exception is the $K$-band observations of 2QZJ00 that
were performed using the smaller field of view of 3$\times$3 arcsec which is
divided into 32 slices of width 0.10 arcsec with a pixel scale of 0.05 arcsec.
All observations were performed using the seeing limited mode. SINFONI has a
spectral resolution of R=4000 and 3000 in $K$-band and $H$-band, respectively.
We measured the width of the skylines (in the vicinity of the science emission
lines), and this width was subtracted in quadrature from the observed emission
line widths to account for spectral broadening. The on-source exposure time
for the $K$-band data varied between 14.4 ks for LBQS01 and HB8903 and 2.4 ks
for 2QZJ00. The short exposure for 2QZJ00 results in noticeably poorer quality
$K$-band data (see more in § 4.2). The on-source exposure time for the
$H$-band data was 14.4 ks for LBQS01, 12.6 ks for HB8903 and 12.6 ks for
2QZJ00.

For as much consistency as possible between our work and the previous work we
used the published $K$-band cubes from Carniani et al. (2016)333Available to
downloaded at http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=J/A+A/591/A28.
Nonetheless, the $K$-band and $H$-band IFU data for 2QZJ00 and the $H$-band
data for HB8903 and LBQS01 used in this work were reduced following the same
basic methods. Here, we briefly outline the procedure. The IFU data reduction
was carried out using the standard techniques within esorex (ESO Recipe
Execution Tool; Freudling et al., 2013). The individual exposures were stacked
on the centroids determined from white-light images from the datacubes. The
flux calibration solutions were derived using the iraf routines standard,
sensfunc and calibrate on the standard stars, which were observed on the same
night as the science observations444All our reduced data cube are available
here.

Following Scholtz et al. (2020) we use the spatial profile of the unresolved
H$\alpha$ and H$\beta$ broad line regions (BLR; see Appendix B.2) as a measure
of the point spread-function (PSF) in each cube, since it is a measure
directly from the observations (i.e., this method is preferred to using a non
simultaneously observed star observation). The final FWHM of the PSF measured
from the spatial profile of the unresolved BLR is 0.4 arcseconds for 2QZJ00
and 0.6 arcseconds for the LBQS01 and HB8903, for the $K$-band observations.
For the $H$-band data, the FWHM of the PSF is $\sim$0.5 arcseconds, for all
targets, consistent with reports by the original studies using the same data.

###  2.4 Astrometric alignment

The goal of this study is to compare the location of the rest-frame FIR
emission traced by ALMA band 7 with the rest-frame optical emission lines
traced by the VLT/SINFONI observations, and hence, we need to accurately align
the two astrometric frames. The nature of interferometric observations
requires accurate astrometry of the targets to reliably calculate the phase
differences from each of the antennae. The absolute astrometric accuracy of
ALMA depends on the baseline and frequency of the observations. For our setup
of baseline 800 m and 350 GHz, the accuracy of the astrometric frame is
$\approx$ 20–30 mas (ALMA Cycle 7 Technical
Handbook555https://almascience.eso.org/documents-and-tools/cycle7/alma-
technical-handbook).

For the astrometric calibration of the IFU data we follow the basic procedure
described in Scholtz et al. (2020) (also similar to Carniani et al., 2017, who
also align ALMA and SINFONI IFU data). For our reference astrometry in this
study, we use GAIA observations. Although there is a lack of sufficiently high
spatial resolution near infrared (NIR) imaging (see §3.2) of our targets, the
continuum emission is dominated by the point source quasar emission across all
optical-NIR wavelengths. Therefore we can benefit from using the high-quality
imaging available from GAIA to align our NIR cubes. Since our sources are
sufficiently bright ($H$-band magnitude $<$16.5) they are easily detected in
GAIA Data Release 2 (Gaia Collaboration et al., 2018) dataset.

To determine the central position of the quasar in the data cubes, we collapse
the cubes along the spectral channels to create a white-light (continuum)
image (i.e., by excluding wavelengths contaminated by emission lines). We then
proceeded with fitting a simple 2D Gaussian model to the resulting continuum
image. The final RA and Dec of the central continuum positions are then
determined from the corresponding GAIA positions. The NIR continuum is very
bright in our data cubes, and the uncertainties on the final position are
$\sim$0.1 arcsecond corresponding to $\sim$1 pixel (see Scholtz et al., 2020,
for more discussion). This astrometric alignment is sufficiently accurate for
the largely qualitative conclusions in this work that compares the location of
the [O iii], H$\alpha$ and rest-frame far infrared emission (§ 4.3).

##  3 Analyses

In this study, we investigate three powerful quasars with extreme [O iii]
emission-line widths (see Figure 1), that have previously been presented in
the literature to have cavities in the narrow H$\alpha$ emission at the
location of [O iii] outflows (Cano-Díaz et al., 2012; Carniani et al., 2016).
Specifically, we study the origin and spatial distribution of rest-frame FIR
emission and re-assess the origin and distribution of the narrow H$\alpha$ and
[O iii] outflows. In this section we present the data analyses of the ALMA
data in § 3.1 and assess the origin of the rest-frame FIR emission in § 3.2.
In § 3.3 we present our analyses of the $H$-band and $K$-band VLT/SINFONI
data.

###  3.1 ALMA Data Analyses

In this section, we describe how we measure the flux densities and sizes of
the rest-frame FIR emission traced by the ALMA band 7 observations. We note
that we use the rest-frame FIR flux densities to assist in establishing the
origin of this emission in § 3.2. Following the approaches described in
Scholtz et al. (2020) we measure these quantities in both the image- and the
uv-plane.

To measure the sizes and fluxes of the ALMA band 7 emission in the image
plane, we used the CASA IMFIT routine to fit a single elliptical Gaussian
model, convolved with the synthesised beam, to the images shown in the left
column of Figure 2. We used these models to measure the flux densities and the
sizes of FIR continuum. To do the uv-plane fitting, we use UVMultiFit (Martí-
Vidal et al., 2014), which simultaneously fits multiple objects in the field
thus allowing us to take into account the background sources that contaminate
the visibilities in the measurement sets. Using IMFIT on the images we found
that the primary sources and the background sources (one per field) are all
resolved. Therefore we fit all sources with a Gaussian profile and we used the
IMFIT results as the initial guesses on the parameters.

To visualise the visibilities, we investigated how the amplitude varies as a
function of uv-distance. To do this we first subtracted the background sources
from the visibility data by using the results from the UVMultiFit fitting
process described above. Using fixvis we then phase centred the data, now with
the background sources removed, to the targets’ positions. For each target, we
extracted the visibility amplitudes from the measurement sets, binning the
visibilities in bins of 50k$\lambda$. These are presented right column of
Figure 2. We fitted these amplitudes as a function of $uv$ distance with two
different functions, a constant, to represent an unresolved source (e.g.,
Rohlfs & Wilson, 1996), and a half Gaussian model centred on 0, to represent a
resolved source with a Gaussian morphology (see curves in Figure 2). For each
fit, we calculated the Bayesian Information Criterion (BIC).666The Bayesian
Information Criterion (Schwarz 1978) uses $\Delta\chi^{2}$ but also takes into
the account the number of free parameters, by penalising the fit for more free
parameters. BIC is defined as BIC=$\Delta\chi^{2}+k\log(N)$, where N is the
number of data points and k is the number of free parameters. The $\Delta$BIC
values between the point source and resolve source models are 230–1700,
strongly confirming that the rest-frame FIR emission is resolved in all three
objects.

We obtain very good consistency in the size and flux density measurements from
all our three methods across the targets (i.e., using UVMultiFit, IMFIT and
fitting the amplitudes as a function of uv-distance; see Table 2). We note
that the flux densities are $\approx$1–2 mJy and although they are not
formally consistent using the three different methods (because of the small
fitting uncertainties) they all agree within 3–22%, which is sufficient for
our purposes of using them to infer star formation rates and the dominant
physical source of the FIR emission (where systematics dominate the
uncertainties; see § 3.2). Furthermore the sizes across all methods yield
results of FWHM$\approx$2–5 kpc, and that agree within 1–2$\times$ of the
uncertainties across the three methods, which is sufficient for our primary
purpose of comparing to other galaxy populations at the same redshift (see §
3.2 & 4.3).

We use the results from the UVMultiFit method as the final, preferred,
measurement of flux densities and sizes. We summarise the flux densities, and
sizes (from our collapsed uv-data fit, IMFIT and UVMUltiFit) of the rest-frame
FIR emission in Table 2.

We repeated these same sets of analyses on the ALMA band 3 data (see § 2.2)
and we also use the results from UVMultiFit. Our measured band 3 continuum
(tracing rest-frame millimetre emission) flux densities are summarised in
Appendix Table 4 and they agree with those measured by Carniani et al. (2017)
within the errors.

Figure 2: Summary of our analyses on the ALMA data. Left column: ALMA band 7
continuum images mapping rest-frame FIR emission. The red solid contours
indicate 2, 3, 4, 5 $\sigma$ levels of the data, while the red dashed contours
show -1, -2 $\sigma$ levels of the data. The red shaded ellipses represent the
synthesised beams of the observations. Right column: The uv amplitude vs uv
distance binned per 50k$\lambda$, after subtracting any companion sources in
the field. The orange solid curves and black dashed curves show resolved and
unresolved model fits, respectively. In all cases, the rest-frame FIR emission
is resolved on 0.18–0.7 arcsec (i.e., $\approx$1.5–5.5 kpc) scales.  Table 2:
A table of the basic rest-frame FIR emission (i.e., the ALMA band 7 data)
properties of our quasar sample. (1) Object ID in this paper; (2) The FWHM
radii of the rest-frame FIR emission derived using UVMultiFit (see § 3.1); (3)
Flux density of the rest-frame FIR continuum measured using UVMultiFit (4) The
FWHM radii of the rest-frame FIR emission derived in the uv-plane (see § 3.1);
(5) Flux density of the rest-frame FIR continuum measured in the uv plane; (6)
The FWHM radii of the rest-frame FIR emission derived in the image-plane (see
§ 3.1); (7) Flux density of the rest-frame FIR continuum measured in the
image-plane; (8) SNR of the peak rest-frame FIR continuum measured from the
maps; (9) RMS of the rest-frame FIR maps; (10) Beam size of the final rest-
frame FIR maps.

(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
---|---|---|---|---|---|---|---|---|---
ID | FIR FWHM (UVMultiFit) | Flux FIR (UVMultiFit) | FIR FWHM (uv) | Flux FIR (uv) | FIR FWHM | Flux FIR | FIR | RMS | FIR Beam
| (kpc) | (mJy) | (kpc) | (mJy) |  IMFit (kpc) |  IMFit (mJy) | SNR | (mJy) | (arcsec)
HB8903 | $3.7\pm 0.5$ | $1.486\pm 0.079$ | $4.5\pm 0.7$ | 1.99$\pm$0.24 | $3.7\pm 0.5$ | $1.486\pm 0.079$ | 28 | 0.10 | $0.48\times 0.39$
LBQS01 | $5.5\pm 0.3$ |  $2.00\pm 0.16$. | $5.4\pm 0.7$ | 1.9$\pm$0.13 | $4.5\pm 0.7$ | $2.00\pm 0.16$ | 29 | 0.06 | $0.54\times 0.40$
2QZJ00 | $1.7\pm 0.3$ | $1.1\pm 0.04$ | $3.0\pm 0.5$ | 1.21$\pm$0.15 | $2.1\pm 0.3$ | $1.092\pm 0.027$ | 36 | 0.05 | $0.61\times 0.45$

###  3.2 SED fitting

Here we describe the de-composition the SEDs to establish the origin of the
870$\mu$m emission (rest-frame FIR) from the ALMA band 7 data and to estimate
star formation rates. There are potentially three main sources of the FIR
emission: (1) star-formation heated dust; (2) AGN-heated dust or (3) radio
synchrotron emission (Dicken et al., 2008; Mullaney et al., 2011; Falkendal et
al., 2019).

Our quasars were selected to be brighter than 16 mag in $H$-band (Carniani et
al., 2015) and, as a result, these quasars are bright enough to be detected in
several all-sky surveys. We used the optical–mid-infrared photometry from
2MASS (Skrutskie et al., 2006), PanSTARRS (Chambers et al., 2016), VST-ATLAS
(Shanks et al., 2015) and WISE (Mainzer et al., 2011). We also queried the 1.4
GHz radio sky surveys of FIRST (Helfand et al., 2015) and NVSS (Condon et al.,
1998). Additional radio photometry at 4–8 GHz was obtained from Hooper et al.
(1995) and Healey et al. (2007). We include the 870 $\mu$m and 3 mm data from
the ALMA band 7 and band 3 data described above. We present the compiled
photometry used for our SED analyses in the Appendix, in Table 4.

Figure 3: Results of our fitting to the optical to radio spectral energy
distributions. The black, blue, red, brown and green curves show the total
fit, accretion disk, dust heated by AGN (torus), dust heated by star formation
(obscured star formation) and the radio synchrotron emission, respectively.
Due to nature of the SED fitting, the template visualisation is sampled from a
coarse grid. The black filled points show the measured photometry, while the
red empty points indicate the modelled photometry by the SED code. The ALMA
band 7 photometry is highlighted by red square. The inset Figure in the top
panel shows individual spectral windows of the ALMA band 3 observations. In
this inset the blue dashed line shows the fit to these data that was used to
constrain the spectral slope in the overall SED fit. The rest-frame FIR
emission (250 $\mu$m) traces dust heated by star formation in LBQS01 and
2QZJ00, however, in HB8903 this emission is severally contaminated by radio
synchrotron emission.

The multi-wavelength SEDs of the targets were modelled using the Bayesian SED
code FortesFit (Rosario, 2019). Four SED components were used in the
modelling:

  * •

An AGN accretion disc with a range of spectral slopes (-1.1 to 0.75) as
prescribed by the models of Slone & Netzer (2012) with a variable extinction
following a Milky Way law ($B-V$ reddening up to 1 mag).

  * •

An AGN dust emission component with a range of shapes as prescribed by the
empirical templates from Mullaney et al. (2011) (short-wavelength slope: -3 to
0.8, long-wavelength slope: -1 to 0.5, turnover wavelength: 20 to 60 microns).

  * •

Dust emission heated by star-formation following the one-parameter template
sequence (0–4) from Dale et al. (2014).

  * •

Radio synchrotron emission described by a broken power law with two spectral
indices $\alpha_{\rm low}$ at low frequencies and $\alpha_{\rm high}$ at high
frequencies, and a variable break frequency. In the case of HB8903, we placed
a tight prior on $\alpha_{\rm high}$ in the range of 1.0-2.0 and allowed the
break frequency to vary in the GHz regime along with a variable $\alpha_{\rm
low}$ (see details below). For the other two sources, there are no constraints
on the power-law slopes or break frequency, so in order to derive an upper
limit, we assumed a fixed spectral slope across the radio bands ($\alpha_{\rm
low}$ = $\alpha_{\rm high}$ = 0.7).

The 1.4 GHz and 3 mm photometry of LBQS01 and 2QZJ00 indicate a very weak
potential radio synchrotron emission. For these objects, we used a tight prior
on radio spectral index of $\sim-0.7$, which is typical for extra-galactic
synchrotron-powered radio sources at low radio frequencies. However, these
photometric points indicate potentially strong radio synchrotron emission in
the case of HB8903. Indeed HB8903 is ‘radio loud’ with a radio luminosity of
$L_{\rm 8.4GHz}=10^{27.7}$ W Hz-1 (Healey et al., 2007). It was, therefore,
necessary to further constrain the SED in the sub-mm and mm regime for this
source. This exercise showed that is was necessary to use two power-law
components for this target. The 3 mm continuum observed in ALMA band 3 was
detected at $\sim 350\sigma$, allowing us to split the data into the different
spectral windows and obtain a flux density measurement in each one. Since the
CO(3-2) emission was not detected in any spectral window (also see Carniani et
al. 2017), we were able to use all four spectral windows. Consequently, we
were able to measure the spectral index ($\alpha$) to be 1.5 in this
wavelength region by fitting to these four data points (see the inset plot in
the top panel of Figure 3).

Probabilistic priors were used to constrain the luminosity of the accretion
disc and AGN dust emission components based on the bolometric luminosity (see
Rosario et al., 2019). FortesFit generates full marginalised posterior
distributions of FIR luminosity from star formation ($L_{\rm IR,SF}$; over
8–1000$\mu$m) and AGN, as well as other parameters that are not used in this
work. We present the individual SEDs and the resulting fits in Figure 3. Using
these FIR luminosities (i.e., with the AGN contribution subtracted), we
estimate star formation rates (SFR(FIR)) using the calibration from Kennicutt
& Evans (2012). The SFR(FIR) values are provided in Table 1, along with their
uncertainties. We note that the degeneracies of fitting the different model
components are fold in our uncertainties and are showed as coloured shaded
regions in Figure 3. They were calculated as 68% confidence posterior
distribution functions from the fitting shown in Figure 12, convolved with the
systematic uncertainties (0.3 dex, Kennicutt & Evans 2012) on the conversion
between $L_{\rm IR,SF}$ and SFR(FIR).

Our main concern here is to determine the dominant source of the ALMA band 7
photometric point: a) cold dust heated by star formation; hot dust heated by
the quasar or c) radio synchrotron emission from the radio jets. The SED
decomposition showed that the ALMA band 7 continuum observations have a
significant component tracing the cold dust heated by star formation in
objects LBQS01 and 2QZJ00. Based on the SED fitting, we estimated that the AGN
contamination to the ALMA band 7 continuum for LBQS01 an 2QZJ00 is
12${}^{+26}_{-11}$ and 14${}^{+24}_{-13}$ %, respectively, where the range
accounts for 1 $\sigma$ confidence interval. In Appendix A we further tested
that our SED de-composition procedure performs as expected. Specifically, we
show that the inferred infrared luminosity from the AGN component is
correlated with the UV luminosity of the AGN but the inferred far infrared
luminosity from star formation is not. There is a synchrotron contribution to
the band 7 ALMA photometric point of $\sim 3$ and $\sim 7$ %, for LBQS01 and
2QZJ00, respectively. In object HB8903, the ALMA band 7 continuum emission is
severally contaminated by the radio synchrotron emission from the AGN (over 99
%). We therefore only have an upper limit (3$\sigma$) on the infrared
luminosity due to star formation, and hence on the derived star formation
rate.

In Figure 4, we compare our sample in the FIR size versus FIR star formation
luminosity due to star formation with other high-redshift z$\sim 2$ galaxy
samples with equivalent measurements. This includes quasars, moderate
luminosity AGN and non-active galaxies. The quasars studied here fall within
the scatter of these other high-redshift galaxy populations. In particular
they have FIR sizes consistent with those seen in high-redshift star-forming
galaxies.

Overall, we conclude that for LBQS01 and 2QZJ00 the ALMA band 7 continuum has
a significant contribution from the cold dust, whilst for HB8903 is it
completely dominated by synchrotron emission.

Figure 4: Plot of the total infra-red luminosity due to star formation
(LIR,SF) as a function size of the FIR emission for our quasar sample (dark
blue squares), quasars from Schulze et al. (2019) (dark green squares), X-ray
AGN from Harrison et al. (2016b) (magenta squares), Scholtz et al. (2020)
(brown squares) and Lamperti et al (in prep; orange squares), XID 2028 (green
square, Brusa et al. 2018; Scholtz et al. 2020), submm galaxies from Simpson
et al. (2015) (light blue points) and stacked z$\sim$2 galaxies from Fujimoto
et al. (2018). Our objects FIR size to luminosity ratios consistent with other
quasars and star-forming galaxies.

###  3.3 IFU Data Analyses

For each of our targets, there are IFU $K$-band observations covering the
H$\alpha$ and [N ii]6548,6583 emission lines and $H$-band observations
covering the [O iii]4960,5008Å emission-line double and the H$\beta$ emission
lines (see § 2.3). In this section we provide information about the: (a)
modelling of the emission-line profiles (§ 3.3.1); (b) extraction of spectra
from a grid of spatial regions across the emission-line regions (§ 3.3.2); (c)
mapping of the narrow H$\alpha$ emission (see § 3.3.3); and (d) creation of [O
iii] velocity maps (§ 3.3.5).

####  3.3.1 Nuclear spectrum and emission-line modelling

We extracted an initial spectrum from the $K$-band and $H$-band cubes with the
primary goal of determining the H$\alpha$+[N ii] and H$\beta$+[O iii] spectrum
from the nuclear regions. We then used these to characterise the H$\alpha$ and
H$\beta$ emission associated with the central quasar. To do this, we first
determined the peak of the continuum emission (i.e., the central quasar
location) in the IFU data cubes by collapsing the datacube in the wavelength
direction, excluding any spectral channels contaminated by the emission lines
or sky-lines. We fitted a two-dimensional Gaussian to the continuum map to
find the centre of the continuum emission. Given that the continuum emission
is dominated by the emission coming from the quasar a two-dimensional Gaussian
is a sufficient model for this procedure.

Figure 5:  H$\alpha$ & [N ii] (left) and [O iii] & H$\beta$ (right) emission-
line profiles extracted from the nuclear spectra for the three quasars in our
sample. Light blue curves show the data and the grey curves show the masked
sky-line residuals. Left column: H$\alpha$ spectral region. Overlaid on the
H$\alpha$ profiles the yellow, magenta, green, black and red curves show the
narrow H$\alpha$ (dominated by NLR emission), broad line H$\alpha$, [N ii],
additional ”X” component and the total fit, respectively. The grey shaded
region shows the wavelength region of the [S ii] emission line. Right column:
[O iii] emission-line profiles. The green, dark blue and red dashed curves
show the narrow and broad [O iii] line components and the total fit,
respectively. The orange dashed and dotted lines show narrow and broad line
H$\beta$, respectively.

For each of the targets, we extracted a spectrum with circular aperture
centred on the continuum emission with a diameter of 0.5 arcsec (i.e., the
approximate size of the PSF) to determine the quasar spectrum. We present
these spectra in Figure 5. This choice of aperture was chosen to be dominated
by the central quasar emission whilst also maximising the signal to noise.
However, we note that our conclusions do not change if we use a different
aperture.

To model the emission-line profiles observed by the IFU, each emission line
was fitted with one or two Gaussian components (or modified Gaussian
components; see below) with the centroid, FWHM and normalisation (flux) as a
free parameter. In each case, the continuum is characterised by a linear
function.

To characterise the H$\alpha$ emission-line profile we simultaneously fitted
the following components: (a) broad line H$\alpha$ (to describe the emission
from the BLR); (b) narrow H$\alpha$ (which would include contributions from
the AGN narrow line region [NLR], any outflows, and any contribution from star
formation); and (c) [N ii]$6548$Å, [N ii]$6583$Å emission line doublet. At
this point we employ a simple model and do not attempt to decompose any star
formation, outflows and NLR components to the overall narrow H$\alpha$
emission. We will discuss this further in § 3.3.4 and Appendix B.4. To avoid
degeneracies in the fit, the central wavelength and FWHM of the narrow
H$\alpha$ and the [N ii]$6548$Å, [N ii]$6583$Å doublet were tied together,
with rest-frame wavelengths of 6549.86Å, 6564.61Å and 6585.27Å, respectively.
This method assumes that the H$\alpha$ and [N ii] originate from the same gas,
a commonly used assumption in high redshift observations (Förster Schreiber et
al., 2009; Genzel et al., 2014; Harrison et al., 2016a; Förster Schreiber et
al., 2018b). During the fitting, the H$\alpha$ and [N ii]6583Å fluxes were
free to vary but the [N ii]6548Å/[N ii]6583Å flux ratio was fixed to be 3.06
(based on the atomic transition probability; Osterbrock & Ferland 2006).

Following the approach by other studies, we modelled the broad line H$\alpha$
emission, originating from the BLR, as a Gaussian component multiplied by a
broken power-law (Netzer et al., 2004; Nagao et al., 2006; Cresci et al.,
2015b; Carniani et al., 2016; Kakkad et al., 2020; Vietri et al., 2020). This
model is a good description of the asymmetrical nature of these emission line
profiles in high luminosity sources such as our quasars. We also tested the
same BLR characterisation as done by the other authors, i.e., using one or two
Gaussians (Cano-Díaz et al. 2012, Scholtz et al. 2020), without any changes to
our conclusions on the spatial distribution of the narrow line emission.777We
note that Williams et al. (2017) characterise the broad line H$\beta$ with
both a positive and negative Gaussian component, the latter of which they
attribute to an ultra-dense fast outflow. This is an intriguing result;
however, this different approach does not affect our final conclusions In §4.2
& Appendix B.4 we discuss how more complex approaches to characterise the
narrow H$\alpha$ (to attempt to account for the relative contributions from an
AGN narrow line region, including possible outflow components, and from star
formation) do not provide robust results. Our primary approach is to model the
narrow H$\alpha$ emission as a single Gaussian component.

We note a small residual amount of emission above our fit over wavelengths
6300–6400 Å in Figure 5 and is likely attributed to a blend of multiple weak
emission lines over this region such as: [O I], [S iii] and [Si ii]. This was
treated as an additional broad and weak Gaussian component ”X” by Carniani et
al. (2016). We include this component in high SNR spectra such as the nuclear
aperture and regional spectra, but we did not include in the individual spaxel
spectra where the SNR is not high enough to detect it. Importantly, including
this additional component, or not, does not change the properties of the
narrow H$\alpha$ emission which is the focus of our analyses. The [S ii]
emission doublet is not detected with sufficiently high SNR to be reliably
modelled as both emission lines at once, and therefore we modelled this
emission line doublet as a single broad Gaussian, similarly to Carniani et al.
(2016). Again, this does not affect our mapping of the narrow H$\alpha$
emission.

For the $H$-band IFU observations, we simultaneously fit the [O iii]$4959$Å,
[O iii]$5007$Å and H$\beta$ emission lines, using the respective rest-frame
wavelengths of 4960.3Å and 5008.24Å and 4862.3Å. We tied the line widths and
central velocities of the [O iii] lines and fixed the [O iii]$\lambda$5008/[O
iii]$\lambda$4960 flux ratio to be 2.99 (Dimitrijević et al., 2007). Given the
complexity of the [O iii] line profile, and high SNRs, we found that a two
Gaussian component model was a good description for each of the [O iii]
emission lines.

Following the same approach as for H$\alpha$, for the H$\beta$ emission line,
we fitted a narrow and a broad line component (where the latter describing the
emission from the BLR). We fitted the narrow H$\beta$ component as a single
Gaussian component, while the broad line component was fitted as Gaussian
profile multiplied by broken power-law, similarly to the broad line component
of the H$\alpha$ emission line, described above. In agreement with Cano-Díaz
et al. (2012) (also see Williams et al. 2017) and Carniani et al. (2015) we do
not observe strong FeII emission in our targets and such a component is not
detected in our spatially-resolved fitting (see below) and consequently does
not impact upon our conclusions of the distribution of the high velocity [O
iii] gas.888Although Carniani et al. (2015) do include a weak FeII component
for fitting the $H$-band data of LBQS01, as discussed in § 4.1, we obtain a
qualitatively consistent kinematic [O iii] structure to that presented by
these authors in Carniani et al. (2016) (i.e., their Figure 3 compared to our
Figure 6). Therefore, our approach is sufficient for our primary purpose of
mapping the high velocity gas and for comparing to this previous work. Indeed,
this is not surprising as the targets were pre-selected to not have bright
FeII emission to make the [O iii] kinematic analyses easier (Carniani et al.,
2015).

The emission-line profiles were fit with the models described above using the
Python lmfit package, excluding spectral channels which were strongly affected
by the skylines. To construct a skyline residual mask we extracted a sky
spectrum from the object-free (sky only) spatial pixels in the cube and
identified the strongest skyline residuals by picking any spectral pixels
outside of 1$\sigma$. We note that our results do not change whether we use 1,
3, and 5 $\sigma$ threshold for masking the sky-line residuals. These are
shown as a grey spectrum in Figure 5. We estimated the errors using a Monte
Carlo approach. With this method, we added random noise (with the same RMS as
the noise in the spectra) to the best fit solution from the initial fit and
then we redid the fit. We repeated this 500 times to build a distribution of
all free parameters. The median of these distributions are consistent with our
original best fit parameters from lmfit. The final errors we quote are from
the 1$\sigma$ scatter of these distributions. The best fit parameters, and
their uncertainties, for the nuclear spectra are presented in Table 3. The
best fit models are shown on the emission-line profiles in Figure 5.

Table 3: A table of the basic properties of the H$\alpha$ and [O iii] emission
line profiles from the nuclear spectra. (1) Object ID in this paper; (2)
velocity FWHM of the narrow H$\alpha$ component; (3) velocity FWHM of the
broad line H$\alpha$ component; (4) Total [O iii] luminosity; (5) The W80
(velocity width containing 80% of the flux) of the [O iii] emission line; (6)
Velocity offset of the broad component of [O iii] to the systematic redshift.

(1) | (2) | (3) | (4) | (5) | (6)
---|---|---|---|---|---
ID | Narrow H$\alpha$ | Broad line H$\alpha$ | L${}_{\rm[O~{}{\sc III}]}$ | [O iii] W80 | vbroad
| FWHM (km s-1) | FWHM (km s-1) | ($\times 10^{44}$ ergs s-1) | (km s-1) | (km s-1)
HB8903 | $800\pm 78$ | $7490\pm 250$ | $3.2$ | $1260\pm 110$ | $-110\pm 80$
LBQS01 | $450\pm 65$ | $7690\pm 150$ | $2.0$ | $1900\pm 140$ | $-230\pm 120$
2QZJ00 | $620\pm 80$ | $6590\pm 200$ | $2.5$ | $1980\pm 150$ | $-580\pm 130$

Figure 6: Summary of [O iii] spectral line analyses to map AGN-driven outflows
in the quasar host galaxies. Left Column: Maps of the W80 of the [O iii]
emission line. The white contours show the velocities of 1200 and 1300 kms-1
for HB8903; 1800 and 1900 kms-1 for LBQS01 and; 1900 and 2000 kms-1 for
2QZJ00. The red star shows the continuum centre (i.e., quasar position).
Middle Column: Maps showing the velocity of the broad component, with respect
to the systemic. The contours show the velocity offsets of: -200 and -125
kms-1 for HB8903; -150,-100 and -50 kms-1 for LBQS01 and; -500 and 450 kms-1
for 2QZJ00. Again, the red star indicates continuum centre. The green and
orange rectangles show the regions from which we extracted the emission-line
profiles displayed in the right column. Right Column: Regional spectra
extracted from the green (top sub-panel) and orange (bottom sub-panel) regions
shown in the maps showing the [O iii]4960,5008 emission-line doublet. The dark
green and blue dashed curves show the narrow and broad components of the [O
iii] emission line. The total fit is showed in red (top panels) and blue
(bottom panels) as dotted curves. The grey vertical dashed line represents the
velocity of the quasar. We label the W80 width and velocity of the broad
component for each emission-line profile for an easier comparison with the
maps. The full set of regional spectra are shown in Figures 14, 15 and 16 in
the Appendix. Extreme velocities are observed across the whole emission-line
regions in all three targets.

####  3.3.2 Regional spectra across the emission-line regions

For a simple visual representation of the spatial variations of the emission-
line profiles, and to verify the results of our more complex analyses of
creating emission-line maps (derived below), we extracted spectra from nine
square regions across the quasar host galaxies. These regions were defined as
a 3$\times$3 grid of $0.5\times 0.5$ arcsecond squares (i.e., roughly
equivalent to the size of the PSF of our observations). The grids were centred
on the optical centre of the quasars. The entire grids sample a region of
1.5$\times$1.5 arcseconds and cover most of the emission from the quasar host
galaxies.

Spectral line fitting was performed on the spectra extracted from each region
using the same models as described in § 3.3.1. However, we fixed the central
wavelength and line-width of the H$\alpha$ and H$\beta$ broad line components
to be the same as obtained from the nuclear spectrum (see Figure 5), leaving
only the flux of these components as a free parameter. This is a reasonable
approach for such point source emission because only the flux in these broad
line components will vary with angular offset, following the PSF. This
approach also helps to avoid degeneracies in the fit, especially in the outer
regions where the SNR of the spectra is lower.

We present two examples of our regional spectra for each of the objects in
Figure 6 and Figure 7 and for the [O iii] and H$\alpha$ emisson-line profiles,
respectively. We discuss these key spatial regions in § 4.1 and § 4.2. The
full set of [O iii] regional spectra are presented in the Appendix in Figures
14, 15 & 16 and the full set of the H$\alpha$ regional spectra are presented
in Figures 17, 18 & 19.

Figure 7:  Left column: Narrow H$\alpha$ (dominated by NLR emission) surface
brightness (SB) map created by simultaneously modelling all of the spaxel’s
spectrum components (see § 3.3.3). The ALMA band 7 continuum data is displayed
as red contours (2.5, 3, 4, 5 $\sigma$ levels). The green shaded circles show
the $K$-band PSF measured from the H$\alpha$ broad-line region. The light
green and orange rectangles show the regions from which we extracted spectra
in the middle and right columns. Middle column: Spectra extracted from the
central region (light green square). Right column: Spectra extracted from the
region indicated by the orange square as indicated on the maps. We label the
narrow H$\alpha$ flux in each subplot. Overlaid on the H$\alpha$ profiles the
yellow and magenta, green dashed curves show the narrow H$\alpha$ (dominated
by NLR emission), broad line H$\alpha$, [N ii], respectively. The inset
spectrum in each spectral plot are the residual spectra -900 – 900 km/s around
the narrow H$\alpha$ component. We see no evidence for additional residual
emission. We find that there is a strong narrow H$\alpha$ emission at the
centres of all 3 quasars.

####  3.3.3 Mapping narrow H$\alpha$ emission

To achieve our goal of comparing the location of the rest-frame FIR emission
with the emission-line gas we produced two dimensional maps of the narrow
H$\alpha$ emission. That is, all of the remaining H$\alpha$ emission after
subtracting the broad-line region emission (see Section 3.3.1).

To map the narrow H$\alpha$ emission, the most relevant previous studies
(i.e., Cano-Díaz et al., 2012; Cresci et al., 2015b; Carniani et al., 2016,
and Scholtz et al. 2020) used two different approaches: (i) multi-component
fitting performed spaxel-by-spaxel and then visualising the distribution of
only the narrow H$\alpha$ emission-line component, here-after we call this
method “multi-fit”) ; (ii) subtracting the broad line emission and continuum
emission components from the cubes first and then creating a pseudo narrow
band image of the residual emission (i.e., an image of the narrow H$\alpha$
emission, as used in; here-after we call this method “BLR-subtraction”). In
principle, these two methods should yield emission-line maps with the same
flux and morphology and hence they are complementary methods to verify the
integrity of the procedures. In this work we will use the results from the
multi-fit method, however, we present the results of the BLR-subtraction
method in Appendix B.1 and the maps produced using both methods can be seen in
Figure 13. We obtain consistent conclusions with both methods.

To increase the SNR of the individual spectra during the production of the
maps, we binned the spectra by performing a running median of spaxels with a
radius of 0.2 arcseconds. This enhances the SNR while keeping the seeing
limited spatial resolution of $\approx$0.4–0.6 arcseconds. This method is
sufficient for our purposes of investigating the origin and morphology, on
$\gtrsim$4 kpc scales, of the narrow H$\alpha$ emission (e.g., following Cano-
Díaz et al., 2012; Carniani et al., 2016, § 4.2) and for comparing the spatial
distribution of the H$\alpha$ emission with the [O iii] outflows and FIR
emission (§ 4.3). The extracted spaxel-by-spaxel emission-line profiles were
fit following § 3.3.1. The final surface brightness maps of the narrow
H$\alpha$ component from the spatial fitting are shown in the left column of
Figure 7. In these maps, we only show values when the SNRs are $>$3.

We performed multiple checks to verify the spaxel-by-spaxel fitting. Firstly,
we compare the total narrow H$\alpha$ flux in the maps to the flux from the
total aperture spectra, and we find that the fluxes are consistent within
uncertainties on the respective measurements. Furthermore, the distribution
and flux measurements we obtain from these maps are consistent with what we
observe from visually inspecting the emission-line profiles that were
extracted from individual $\approx$0.5$\times$0.5 arcsecond spatial regions (§
3.3.2; Figure 7; also see Figures 17, 18 & 19). We also checked that the
surface brightness of the broad line H$\alpha$ emission is well fitted with a
2D Gaussian (as you would expect for the point source BLR emission following
the PSF).

We performed two final tests to assess if the H$\alpha$ emission is centrally
concentrated and if the emission is spatially resolved: (1) a curve-of-growth
analyses and (2) subtracting a model PSF from the narrow H$\alpha$ surface
brightness maps. These are described and presented in detail in Appendix B.2
and Appendix B.3. Both methods confirm that the narrow H$\alpha$ emission is
centrally concentrated in all three targets. Furthermore, for LBQS01 and
2QZJ00 this emission is consistent with the PSF, i.e., it is spatially
unresolved. However, we note that in LBQS01, we detect a faint region of
H$\alpha$ emission one arcsecond north of the quasar location. However, given
that the bulk of the emission is unresolved, we still designate this target as
unresolved for this work. For HB8903 these tests demonstrate that narrow
H$\alpha$ emission is spatially resolved, but is still consistent with being
centrally concentrated.

####  3.3.4 Interpreting the narrow H$\alpha$ components

As presented in Section 3.3.1, we have so-far only considered a single
component to the H$\alpha$ emission that is not part of the broad-line region
(i.e., the component we call “narrow”). However, for this work it is important
to establish the relative contribution from AGN NLRs, outflowing gas, and star
formation to the total narrow H$\alpha$ flux.

Carniani et al. (2016) produced maps of residual narrow H$\alpha$ emission
after subtracting a contribution for an AGN NLR (including any possible
outflows). They considered any residual emission beyond these components to be
attributed to star formation. To search for such residual emission, we created
a residual cube (i.e., by subtracting the modelled spectra from the data) and
inspected it for any residual emission left by the fitting. We collapse these
residual cubes along the spectral regions reported in Cano-Díaz et al. (2012)
and Carniani et al. (2016) and show them in Figures 17, 18 & 19. We did not
detect any significant residual narrow H$\alpha$ emission hence forward
refereed to as a narrow star formation component anywhere in the cube.

Similarly to Carniani et al. (2016), we also extracted a residual ring
aperture spectra of $0.5<r<0.8$ arcsecond around the nucleus. We present these
residual spectra in Figure 8, showing $\pm$1000 km s-1 around the redshifted
H$\alpha$ emission line. We do not detect any additional emission in these
residual spectra. We further show the residuals for the individual spatial
regions in Figures 17, 18 & 19.

Figure 8: Residual spectra from the K-band H$\alpha$ fitting using the "multi-
fit" method. The spectrum is extracted from the same ring shaped region
($0.5<r<0.8$ arcsecond) as done in Carniani et al. (2016). The black dashed
line indicates the expected location of the residual "star formation"
H$\alpha$ component from Cano-Díaz et al. (2012) and Carniani et al. (2016).
The red dashed line shows the zero point of the spectra. We do not detect any
additional narrow H$\alpha$ residual emission that could be associated with
star formation.

We note that any residual narrow H$\alpha$ emission, beyond the modelled line,
will be sensitive to the choice of how to model the emission line. Therefore
we investigated multiple approaches into the decomposition of the narrow
H$\alpha$ emission line into multiple components associated with an outflow,
an AGN NLR and star formation components (see Appendix B.4). We found that
fitting additional components to our spectra resulted in fits that were not
statistically improved and/or they resulted in nonphysical results.

Based upon all of these tests, we feel confident that our narrow H$\alpha$
maps presented in Figure 7 are a fair representation of the true morphology of
the total narrow H$\alpha$ emission. At the resolution of our observations,
all sources are consistent with centrally concentrated narrow H$\alpha$
emission, with only HB8903 being spatially resolved. However, we can only
reliably identify a single component to describe the total narrow H$\alpha$
emission dominated by the NLR and we do not identify any residual narrow
H$\alpha$ emission that could be associated with star formation. We discuss
the implications of this in Section 4.2. We stressed that despite not
detecting the residual narrow "star formation" component as previous studies,
we do not claim that there is no unobscured star formation in these objects as
it is most likely sub-dominant compared with the NLR H$\alpha$ emission.

####  3.3.5 Mapping the ionised outflows traced by [O iii] emission line

Following Cano-Díaz et al. (2012), Carniani et al. (2015) and Carniani et al.
(2016) we performed spaxel-by-spaxel fitting of the $H$-band IFU data to
spatially map the kinematics of the [O iii] emission line. The aim is to
establish where the highest velocity [O iii] emitting gas is located.
Similarly to the method used to map the narrow H$\alpha$ emission, described
above, we binned the spectra by the calculating the running nearby of the
nearby spaxels within a radius of 0.2 arcseconds, to enhance the SNR, while
keeping the seeing limited spatial resolution of 0.4–0.6 arcseconds.

We fitted the [O iii]+H$\beta$ spaxel spectra using the same models as for the
nuclear spectra (see § 3.3.1). However, following the same procedure that we
employed for the broad line H$\alpha$ (see § 3.3.3), we fixed the line-width
and the central wavelength of the broad line H$\beta$ component with only the
flux as a free parameter.

The results from the spaxel-by-spaxel fitting were used to spatially map the
distribution and kinematics of the [O iii] emission. We focus on maps of: (1)
surface brightness; (2) W80 and (3) the velocity offset of the broad component
from the systemic. The systematic is defined as the redshift of the narrow [O
iii] emission-line component in the nuclear spectra (§ 3.3.1). For these maps,
we only show values when the SNRs were $>$3\. All of these maps are presented
in Figures 14, 15 and 16, alongside the grids of [O iii] emission-line
profiles and their fits (see § 3.3.2). The velocity maps are also shown in
Figure 6. Reassuringly, a comparison between the emission-line profiles
extracted from the spatial grids and these maps demonstrates that the maps are
a good description of the data. Similarly to the H$\alpha$ maps, we also
inspected the map of the H$\beta$ broad line component to verify that it
symmetrically fell off in flux (i.e., it was well described by a 2D Gaussian
profile) to provide confidence that the fitting procedures were effective.
Again, we also created the residual cube and similarly to the H$\alpha$
fitting, we did not detect any significant residual emission in these cubes.

For the rest of this work we focus on the maps of W80 (i.e., the overall
velocity width of the [O iii] emission line) and the velocity offset (from
systemic) of the broad [O iii] emission-line component. This is to broadly
follow the previous works of Cano-Díaz et al. (2012) and Carniani et al.
(2016), respectively. Although Cano-Díaz et al. (2012) used a second moment
map, instead of W80, to define the emission-line width we verified that the
spatial distribution of the high velocity width emission is the same using
either definition. We present these maps, alongside example regional spectra
in Figure 6. We find extreme velocities (i.e., W80$\gtrsim$1000 km s-1) across
the entirety of the emission-line regions in all three targets, although with
spatially-varying kinematic structure. We discuss the interpretation of these
maps, and a comparison to the results of the previous works in Section 4.1..

##  4 Results and Discussion

In this study, we are re-assessing the impact of powerful ionised outflows on
the host galaxy star formation in three $z\sim 2.5$ quasars that have received
a lot of attention in the literature because IFU data was used to provide
evidence for depleted star formation at the location of [O iii] outflows
(Cano-Díaz et al., 2012; Carniani et al., 2016). In the previous section, we
re-analysed the IFU data that was presented in this earlier work and we added
new information from our ALMA band 7 observations to trace the rest-frame FIR
emission. In § 4.1, we discuss the spatial distribution of ionised outflows.
In § 4.2 we discuss the morphology and interpretation of the narrow H$\alpha$
emission. In § 4.3 we compare the location of the narrow H$\alpha$ emission,
rest-frame FIR emission and AGN-driven outflows. In § 4.4 we investigate the
evidence for suppressed galaxy-wide star formation. Finally, in § 4.5 we
discussed the implications of our results.

###  4.1 Mapping of the ionised outflows

We present our [O iii] kinematic maps in Figure 6 that were constructed using
the [O iii] emission-line profile models described in §3.3.1. There are many
different definitions of “outflow velocity” used throughout the literature
(see review in Harrison et al., 2018). Therefore great care should be taken
when interpreting outflow maps across different studies. Here we investigate
different approaches to mapping the location of outflows. We were initially
motivated to reproduce the broad approaches taken in Cano-Díaz et al. (2012)
and Carniani et al. (2016) who chose to plot contours of the highest [O iii]
emission-line widths and highest velocity offsets of a broad [O iii]
component, respectively (see § 3.3.5).

The maps of [O iii] W80, i.e., to characterise the total emission-line widths,
are shown in the first column of Figure 6. Based on these maps it can be seen
that all three objects show extremely broad [O iii] emission-line profiles
throughout the whole emission-line regions with W80 velocities of 900–1500 km
s-1, 1300–2000 km s-1 and 1600–2000 km s-1 for HB8903, LBQS01 and 2QZJ00,
respectively. These extreme velocities of W80$\gtrsim$1000 km s-1, indicate
ionised outflows are present across the full extent of the observed emission-
line regions (e.g., Liu et al., 2013; Harrison et al., 2014; Kakkad et al.,
2020).

In Figure 6 we have used white dashed contours to highlight the regions with
the highest [O iii] emission-line widths, defined as the top $\approx$10% of
the W80 values. For HB8903 these highest velocities are found to be moderately
offset by $\approx$0.3 arcsecond (i.e., $\approx$2.4 kpc) to the south-east of
the quasar position, for LBQS01 these are found to be $\approx$0.6 arcsecond
(i.e., $\approx$4.8 kpc) to the west of the quasar position and for 2QZJ00 to
be $\approx$0.3 arcsecond (i.e., $\approx$2.4 kpc) to the south-east of the
quasar position. We find good agreement with our results and those presented
in Cano-Díaz et al. (2012) and Carniani et al. (2015) for the location of
these highest velocity widths. Following the approach of Carniani et al.
(2016) (who presented results for LBQS01 and HB8903) we also present maps of
the velocity offset (from the systemic) of the broad component of the [O iii]
emission line in the second column of Figure 6. Similarly as we did for W80,
we show the top $\approx$10% of (blue-shifted) velocities as contours to
represent the spatial location of the highest velocities. We find good
agreement with Carniani et al. (2016) on the location of the highest velocity
offsets.

In Figure 6 it can already be seen that different conclusions would be drawn
on the location of the highest velocities outflows if using W80 compared to
broad component velocity offset. This is particularly noticeable for HB8903
where the broadest emission is towards the centre but the highest velocity
offsets are to the very east of the emission-line region. Therefore this
already highlights that caution should be taken when interpreting such
contours as tracing the outflow location; for example, to compare to maps of
star formation tracers (see Section 4.3).

Another approach to map the ionised outflows is to look at the surface
brightness distribution of the broad [O iii] emission-line components,
assuming that these trace outflowing gas (e.g., Rose et al., 2018; Tadhunter
et al., 2018; Tadhunter et al., 2019). This approach traces where the
outflowing component has the greatest luminosity and, consequently, is likely
to correspond to the majority of the ionised gas mass in the outflow (although
using emission lines to trace outflow mass is subject to several challenges;
Harrison et al., 2018). In Figure 9 we show solid white contours of the
surface brightness distribution of the broad [O iii] emission-line components,
derived from our spaxel-by-spaxel fitting (see Section 3.3.5). It can
immediately be seen that these contours are centred around the nuclear
regions. These results are in agreement with Figure 3 of Carniani et al.
(2017) who show that the high velocity blue wing of the [O iii] emission of
LBQS01 is brightest in the nuclear regions. The same is also observed by Cano-
Díaz et al. (2012) for 2QJZ00 where they find that their broad [O iii]
emission-line component (i.e., the one tracing the outflow) is brightest in
the central regions (see their Figure A.1), even though the highest velocities
are located to the south. In summary, an agreement is found across our studies
that the broad [O iii] emission-line components peak in the center.

In Figure 6 and Figure 9 we have shown that different choices to define the
spatial distribution of ionised outflow can give very different conclusions on
the peak spatial location of these outflows. This has important ramifications
for when comparing an outflow location to the spatial distribution of star
formation. Figure 9 shows that for the three quasars in this study the high
velocity [O iii] emission-line components are most prominent in the centre (in
terms of surface brightness), even though the highest velocity widths and
highest velocity offsets can be off-centre. We chose to plot contours of the
most extreme $\approx$10% of velocities in Figure 9, following the broad
approach taken by the previous work on these targets (Cano-Díaz et al., 2012;
Carniani et al., 2016). However, we re-iterate that high velocity gas is found
across the entirety of the emission line regions (see maps in Figure 6) and
the high velocity gas is not only confined to the locations inferred by these
contours.

###  4.2 Interpretation of the narrow H$\alpha$ emission

Previous works on the three quasars explored in our study presented cavities
in residual H$\alpha$ emission (i.e., after subtracting components related to
the AGN: BLR+NLR), located at the same location of the highest velocities of
the AGN-driven outflows. This was interpreted as evidence that outflows
rapidly suppress star formation in the vicinity of the outflows and,
potentially, enhancing star formation along the edges of the outflow (Cano-
Díaz et al., 2012; Carniani et al., 2016). Using the analysis from Section
3.3, we re-examined the H$\alpha$ emission in these targets.

We created narrow H$\alpha$ maps and we present these in the left column of
Figure 7. However, as discussed in §3.3.4, the major source of the emission in
our narrow H$\alpha$ maps is the NLR; hence our labelling of this emission as
dominated by NLR emission). In all three cases, we see a smooth distribution
of the narrow H$\alpha$ emission around the quasars. As discussed at length in
§ 3.3.3 we performed numerous tests to establish that these maps were a fair
representation of the data. We found that the emission is consistent with
being centrally compact, and is only spatially resolved in the case of HB8903.

Our tests described in § 3.3.3 showed that only HB8903 has spatially-resolved
narrow H$\alpha$ emission (§ B.2 & B.3) and that we were unable to identify
residual emission that could be associated with star formation either in the
central regions or outer regions of any of the sources (see Figure 7 and
Figure 8). Indeed, the signal-to-noise ratios of the narrow H$\alpha$
components are low (see Figure 7) and therefore it is extremely challenging to
reliably de-compose these into three components (i.e., an outflow, an AGN
narrow line region and star formation emission). This is especially
challenging for these Type 1 quasars because the broad-line H$\alpha$
components are so dominant and the narrow components so weak. Although
possibilities explored to help with this included tying the properties of the
H$\alpha$ emission-line profile to the [O iii] emission-line profile, this
still resulted in degenerate and solutions with extreme/unrealistic emission
line ratios. It is possible that such degeneracies may be the cause of the
non-physical negative surface brightness values seen in the cavities of the
H$\alpha$ emission maps used to represent the distribution of star formation
in Figure 8 of Carniani et al. (2016).

We further note the challenges in confidently establishing the dominant
ionisation mechanism of the H$\alpha$ emission. Local IFU studies demonstrate
it is possible to produce AGN un-contaminated maps of star formation by using
emission-line ratio diagnostics to spatially decompose the contributions from
star formation, shocks and AGN to individual kinematic components when there
is sufficient signal-to-noise ratios in multiple lines and with sufficient
spatial resolution. However such approaches are not feasible with these
data.999We note that the adaptive optics assisted IFU observations of 2QZJ00
in Williams et al. 2017 find that the overall emission-line ratios are
consistent with AGN ionization across most of the sampled regions in their
data; however, they note that most extended, diffuse, emission associated with
star formation is likely to be missed due to the use of adaptive optics.

In summary, within the limits of these data we find that it is not possible to
identify H$\alpha$ emission that can be confidently associated with star
formation and free from AGN contamination. Therefore, the surface brightness
maps of the overall narrow H$\alpha$ emission are likely to be dominated by
AGN-related processes.

###  4.3 Comparison of the H$\alpha$, FIR continuum and AGN-driven outflows

In Figure 9 we compare the spatial distribution of the narrow H$\alpha$
(dominated by NLR emission) emission (background map) and rest-frame FIR
emission (red contours). As demonstrated in § 3.2 the rest-frame FIR emission
is tracing dust heated by star formation in LBQS01 and 2QZJ00 (indicated as
red dashed contours in the figure), and AGN radio synchrotron emission in
HB8903 (indicated as red dotted contours in the figure). The H$\alpha$
emission is most likely dominated by AGN-related processes in all three
targets (see § 4.2). The red and blue points show the location of the peak of
H$\alpha$ and rest-frame FIR emission, while the red star indicates the
location of the quasar. The rest-frame FIR emission is centrally concentrated
and we find that the peaks of the H$\alpha$ and rest-frame FIR emission are
co-spatial in all three quasars.

Figure 9: A comparison of the spatial distribution of FIR emission (red
contours; levels of 2.5, 3, 4, 5$\sigma$), surface brightness of narrow
H$\alpha$ (dominated by NLR emission) emission (background maps; see § 3.3.3)
and AGN-driven outflows (white contours; § 3.3.5) for: HB8903 (top); LBQS01
(middle) and; 2QZJ00 (bottom). The FIR is attributed to star formation (dashed
red contours) for LBQS01 and 2QZJ00, and to AGN radio synchrotron for HB8903
(dotted red contours; § 3.2). The white dashed contours show [O iii] W80
velocities with values of: 1200 and 1300 km s-1 for HB8903; 1800 and 1900 km
s-1 for LBQS01 and; 1900 and 2000 km s-1 for 2QZJ00. The white solid contours
represent the distribution of the broad [O iii] “outflow” component (levels of
0.68, 0.9 and 0.95 of the peak). The outflows peak in the centre, co-spatial
with the FIR emission, but the highest velocities are found off centre.

At least for LBQS01 and 2QZJ00, we have shown that there are significant
levels of dust in the central $\approx$1.5-5.5 kpc (§ 3.1). This is consistent
with previous ALMA studies of sub–mm and star-forming galaxies, with and
without an AGN, at high redshift which show dust emission extended over a
$\approx$1–5 kpc (e.g., Ikarashi et al., 2015; Simpson et al., 2015; Harrison
et al., 2016b; Hodge et al., 2016; Spilker et al., 2016; Tadaki et al., 2017;
Fujimoto et al., 2018; Brusa et al., 2018; Lang et al., 2019; Schulze et al.,
2019; Chen et al., 2020; Chang et al., 2020; Scholtz et al., 2020, Lamperti et
al. in prep; see Figure 4). Furthermore, Carniani et al. (2017) find centrally
concentrated CO(3-2) emission for LBQS01, i.e., co-spatial with the rest-frame
FIR emission that we trace here. This would be consistent with obscured star
formation at the same location as the molecular gas reservoir. Due to the
strong radio emission in HB8903, we are not able to reliably map the
distribution of dust with our observations.

We find that the rest-frame FIR emission overlaps with the H$\alpha$ emission
cavities that were presented in Cano-Díaz et al. (2012) and Carniani et al.
(2016). Therefore, without reliable obscuration corrections, observed maps of
H$\alpha$ emission are likely to miss a significant fraction of the total
intrinsic emission. Along with the several other complications discussed in §
4.2 we suggest that the narrow H$\alpha$ maps presented here and in Cano-Díaz
et al. (2012) and Carniani et al. (2016) are not reliable for mapping the on-
going star formation in the host galaxies.

We discussed different definitions for mapping the the [O iii] outflows in §
4.1 and we present these as white contours on Figure 9, compared to the
obscured star formation distribution. With either outflow definition (i.e.,
using velocity contours or surface brightness contours) we see no evidence
that the outflows have had any significant impact on the distribution of star
formation. In particular, by mapping the AGN-driven outflows in terms of the
surface brightness of the broad component of the [O iii] emission line, shows
that the outflow is spatially located at the same location as the obscured
star formation. We do see an offset between this obscured star formation and
the highest velocities of the [O iii] emission but this could be just an
indication of how the outflows are escaping from the host galaxies (e.g.,
Gabor & Bournaud, 2014, also see § 4.5).

In summary, we find no evidence that the ionised outflows have had an
instantaneous impact on the distribution of the in-situ star formation. We
discuss the limitations and implications of these conclusions in § 4.5

###  4.4 Global star formation rates of our quasars

In the previous section, we saw no evidence that star formation is disturbed
at the location of the [O iii] outflows in the three quasars of this study.
Nonetheless, high velocity outflows are found across the observed emission-
line regions (Figure 6). Therefore, it is appropriate to assess if there is
any evidence that the global (i.e., galaxy wide) star formation rates of our
quasar host galaxies have been suppressed, potentially by the outflows
observed.

Figure 10: Plot of the total infra-red luminosity due to star formation
(LIR,SF) as a function of black hole mass of the quasars. The dark blue filled
and green hollow points show quasars investigated in this work and quasars
from Schulze et al. (2019) (z$\sim$ 2), respectively. The red shaded region
shows the measured averages and 68 % confidence interval of quasars for
redshift range of 1.5–2.5 from Stanley et al. (2017). The green and blue
dashed lines show the expected LIR,SF of main-sequence galaxies (Schreiber et
al., 2015) (recalculated for black-hole mass rather than stellar mass) for z=2
and z=2.4, respectively. There is some evidence that the most powerful quasars
scatter to lower SFRs

In Figure 10 we present the star formation rates (see § 3.2) as a function of
black hole masses (see § 2.1) for the three quasars. In this figure, we
compare our sample to the results of Stanley et al. (2017), who measured the
mean star formation rate (also using far-infrared luminosity as their star
formation tracer) of $z=$1.5–2.5 quasars as a function of black hole mass; we
show the 68 % confidence interval around the mean values from this study as a
red shaded region. To allow for a comparison between our quasar host galaxies
and the overall star-forming galaxy population, we also show tracks of the
average star-formation rate from Schreiber et al. (2015) for star-forming
galaxies. To produce these tracks we converted black hole mass to stellar mass
following Bennert et al. 2011 and then we calculated the star-formation rate
for a given mass at both $z=2.0$ and $z=2.4$ following Schreiber et al.
(2015). We note that our comparison to these tracks are dominated by the
systematic uncertainties in star formation rates and, because the tracks are
almost flat over the mass range of interest, the uncertainties in black hole
masses or the conversions to stellar masses have no impact upon our
conclusions.

In Figure 10 it can be seen that the average star formation rates of quasars,
taken from Stanley et al. (2017), follow the main sequence of star forming
galaxies (in agreement with their conclusions). However, their black hole
masses are limited to $<10^{9.7}$ $\mathrel{\rm M_{\odot}}$, compared to the
$\approx 10^{10}$ $\mathrel{\rm M_{\odot}}$ of three quasars in this study.
Extrapolating the main sequence into the predicted mass range of our targets
would suggest that the quasars in this study have star formation rates a
factor of $\approx$10 below the main sequence.

In Figure 10 we also compare our targets to the quasars from Schulze et al.
(2019). Their study observed a sample of 20 very luminous type 1 quasars at
$z\sim 2$ (log10 L${}_{\rm Bol}>46.9$ ergs s-1) with ALMA band 7, making them
an ideal comparison sample to our study. To make a robust comparison between
our studies, we refitted the optical to sub-mm SEDs of the Schulze et al.
(2019) quasars using the FortesFit code described in § 3.2. We plot the
results of this re-analyses as green hollow points in Figure 10 where it can
be seen that the quasars from Schulze et al. (2019) lie on or below the main
sequence. Previous work has shown that even if the mean star formation rates
of AGN host galaxies follow the main sequence, the distributions can scatter
to lower values (Mullaney et al., 2015; Bernhard et al., 2019). However,
recent work by Grimmett et al. (2020) implies that the distribution of the
more powerful AGN (such as the quasars in this study) tend towards following
the same distribution as main sequence star-forming galaxies. Broadly
speaking, the powerful quasars presented here would not follow this trend as
they appear to fall below the main sequence galaxies.

Although caution should be taken when using global star formation rate
measurements as evidence for AGN feedback, especially in the absence of
specific model predictions (e.g., Harrison, 2017; Scholtz et al., 2018, also
see § 4.5), based on the results presented in Figure 10 we can not rule out
that the host galaxies of the bolometrically luminous (i.e., $L_{\rm
bol}\approx 10^{47.5}$ ergs s-1) high black hole mass (i.e., $M_{\rm
BH}\approx 10^{10}$ M⊙) quasars in this study are “on the path” to becoming
quenched with lower star formation rates than you would expect for the black
hole masses. This can also be in agreement with Carniani et al. (2017) who
find that all three quasars appear to have low molecular gas content compared
to main-sequence galaxies at the same redshift using observations of the
CO(3-2) emission line.

###  4.5 Implications of our results

We have shown that there is no strong evidence that the powerful ionised
outflows in the three quasars in this study have a localised “in-situ” rapid
impact on the star formation inside their host galaxies (§ 4.3). Nonetheless,
we could not rule out global star formation rate suppression in the host
galaxies (see Carniani et al., 2016).

Our conclusions are consistent with most IFU observations (with or without
adaptive optics) and inteferometric observations of high redshift AGN that do
not find strong evidence that outflows are instantaneously shutting down in-
situ star formation in the host galaxies (e.g., Scholtz et al., 2020; Davies
et al., 2020b, Lamperti et al., in prep). Our study extends this previous work
to more powerful quasars with extreme outflows where the impact might be
expected to be most dramatic (Figure 1). However, we caution that our results
are only for three powerful quasars and there are samples in the literature
which include sources that are even more powerful, and exhibit even more
extreme outflows, than those investigated here (Zakamska et al., 2016;
Bischetti et al., 2017; Perrotta et al., 2019). It would now be interesting to
assess if the outflows in these systems have any impact on the in-situ star
formation.

The star formation tracer that we have been able to use in this study is far-
infrared emission that has a mean stellar population age contribution to the
emission from $\approx$5 Myr, up to $\approx$100 Myr Kennicutt & Evans (2012).
Unfortunately, we lack a reliable tracer of star formation that is dominated
by recent star formation episodes (i.e., $\lesssim$10 Myr), which may be
helpful for searching for more immediate changes in star formation. However,
with current facilities, it is not clear how to reliably overcome this problem
for the most powerful high-redshift quasars where the challenges of removal of
AGN contamination to tracers such as H$\alpha$ and ultraviolet are severe, to
impossible (see § 4.2). Future studies of Type 2 quasars (as opposed to Type 1
quasars) would at least reduce the challenges of subtracting the broad line
region contribution to the H$\alpha$ emission and the ultra-violet continuum
emission associated with the accretion disk but would still suffer from many
of the other challenges we outlined in § 4.2.

When searching for observational evidence of feedback by AGN, it is also
important to ask if the results are actually in conflict with specific
theoretical predictions (e.g., Harrison, 2017; Scholtz et al., 2018).
Simulations of individual galaxies show the reality of how outflows would
impact upon their host galaxies is complex. For example, simulations show that
the level of any negative or positive impact on the host galaxy star formation
rates will depend on many factors such as: the relative orientation of an
outflow (or jet) with a disk; the gas fraction and distribution of the ISM;
and the luminosity of the AGN itself (e.g., Wagner et al., 2013; Pontzen et
al., 2017; Zubovas & Bourne, 2017; Mukherjee et al., 2018; Costa et al.,
2020). Furthermore, whilst simulations suggest that some level of rapid
suppression in the star formation rate could be caused by AGN-driven outflows
this may typically be by modest factors and only in the central regions even
in the case of the powerful quasars (e.g., Gabor & Bournaud, 2014; Costa et
al., 2018; Costa et al., 2020). These simulations show complete destruction of
the gas disc is extremely unlikely since outflows tend to become collimated
and escape through paths of least resistance.

In agreement with the aforementioned simulations, using the greater spatial
resolution possible for integral field spectroscopy and mm-inteferometry
observations of local galaxies, some evidence for modest positive and negative
feedback on small scales has been observed (e.g., Croft et al., 2006; Alatalo
et al., 2015; Cresci et al., 2015a; Querejeta et al., 2016; Rosario et al.,
2019; Shin et al., 2019; Husemann et al., 2019; Perna et al., 2020). These
effects are out of reach of what can be observed with the lower (i.e.,
$\sim$2–5 kpc) resolution and sensitivity of IFU observations of high-redshift
galaxies. However, even from these impressive observations of local galaxies,
it is not clear if the global, long-term impact of these effects will be
significant.

As discussed in Costa et al. (2020), quasars may be able to cause feedback
effects without the removal of dense star-forming material. For example,
through the ejection of gas from the gaseous halo, which would accelerate the
decline of gas inflow from the halo. Such a process would operate on longer
$\sim$100 Myr timescales. Observations of the Sunyaev-Zeldovich effect have
provided tantalising evidence that quasars are effective at depositing energy
into the circumgalactic environment (e.g., Crichton et al., 2016; Lacy et al.,
2019). Our observations would be consistent with such a mode of AGN feedback
that has an impact on star formation over a longer timescale, perhaps through
the cumulative effect of quasar episodes (also see McCarthy et al., 2011;
Zubovas & King, 2012; Gabor & Bournaud, 2014; Scholtz et al., 2018; Costa et
al., 2020).

##  5 Conclusions

We have presented new high-resolution ALMA band 7 continuum observations
(rest-frame $\lambda\sim 250\mu$m) of three quasars at $z\sim 2.5$ that have
previously been presented as showing evidence for suppressed star formation
based on cavities in the narrow H$\alpha$ emission at the location of the
quasar-driven outflows (traced with [O iii] emission; Cano-Díaz et al. 2012;
Carniani et al. 2016). All three quasars are significantly detected by ALMA
(SNR$>$25) and we exploited these observations to trace the dust-obscured star
formation. Furthermore, we re-analysed the $H$-band and $K$-band archival IFU
data. Based on our analyses we find:

  1. 1.

FIR emission contains a significant dust-obscured star formation component in
two of the three quasars. This result is based on: (a) the observation that
the FIR emission traced by ALMA band 7 observations is spatially extended on
scales typical for high-redshift star-forming galaxies (i.e., $\approx$1.5–5.5
kpc; see Figure 2 & 4) and; (b) our SED decomposition shows that the FIR
emission contains a significant star formation heated dust component ($\sim
86\%$) (see § 3.2 and Figure 3); therefore, we conclude that we can use the
spatially-resolved maps to trace the obscured star formation in LBQS01 and
2QZJ00 and this star formation is located in the regions of the previously
reported cavities in the narrow H$\alpha$ emission (Figure 9). In the third
quasar (HB8903), the FIR emission is dominated by AGN synchrotron emission.

  2. 2.

High velocity ionised gas is found across the whole emission-line regions as
traced by the [O iii] emission line (W80$\gtrsim$1000 km s-1). This is based
on our [O iii] velocity maps (Figure 6). Following the approach of the
previous work, when the outflow locations are defined based on the top
$\approx$10% of emission-line velocities, they are offset by $\approx$2–5 kpc
from the central quasar. However, based on the surface brightness distribution
of the broad component of the [O iii] emission line, the outflows peak in the
centre (see Figure 9). Consequently, the relative spatial distribution of an
outflow and star formation is sensitive to the choice of outflow definition.

  3. 3.

We do not identify any H$\alpha$ emission that is a reliable tracer of
spatially-resolved star formation despite testing a variety approaches to
isolate such emission. This is because we are unable to reliably identify any
residual H$\alpha$ emission beyond that associated with the AGN narrow line
region and/or outflow in the galaxy-integrated or spatially-resolved spectra
(see Figure 7 and Figure 8). Furthermore, the H$\alpha$ emission is only
spatially resolved in one of the three targets.

  4. 4.

We do not observe any localised instantaneous suppression of star formation by
the ionised outflows. Specifically, we do not find any evidence for suppressed
star formation co-spatial with the location of the bulk of the ionised
outflows, at least for the two targets for which we have been able to trace
the star formation with the ALMA data (see Figure 9).

  5. 5.

We cannot rule out global star formation suppression caused by the quasars.
Based on the infrared luminosities we find that the inferred galaxy-wide SFRs
of the three quasars are 50–170 $\mathrel{\rm M_{\odot}yr^{-1}}$. Assuming a
black hole to stellar mass conversion from Bennert et al. (2011), these are an
order of magnitude lower than mass-matched main sequence galaxies at the same
redshift. This could also be in agreement with the findings of Carniani et al.
(2017), who reported low molecular gas content in these same objects.

Using the FIR emission as a tracer of star formation, we see no direct
evidence that ionised outflows instantaneously suppress in-situ star formation
in the nuclear regions of these extreme quasars on $\sim 4$ kpc scales. Any
instantaneous impact by these outflows must be subtle, occurring beyond that
which can be detected within the resolution and sensitivity limits of these
observations. This is consistent with Scholtz et al. (2018) which showed a
good agreement between ALMA observations of X-ray AGN and the predictions from
EAGLE hydrodynamical simulation. To search for more subtle effects will
require deep observations with future high-resolution IFU facilities such as
with VLT/ERIS, JWST/NIRSpec and ELT/HARMONI. We suggest that any impact on
star formation from a single outflow event must be limited. However, our
results could still be consistent with a more long term impact of the central
quasars resulting in a more gradual global suppression; for example, the
cumulative effect of outflow episodes could accelerate the decline of gas
inflow onto the host galaxy (also see e.g., Cano-Díaz et al., 2012; Gabor &
Bournaud, 2014; Carniani et al., 2016; Costa et al., 2020).

## Data Availability

The raw IFU and ALMA data is available at VLT/SINFONI and ALMA archive
services. The reduced data and main analyses code underlying this article are
available on Github here.

## Acknowledgements

We thank the referee for useful comments that improved the quality of this
work. We thank Sebastien Muller from Nordic ARC Node for helping with
UVMultiFit. JS acknowledges support from the Nordic ALMA Regional Centre (ARC)
node based at Onsala Space Observatory. The Nordic ARC node is funded through
Swedish Research Council grant No 2017-00648. We gratefully acknowledge
support from the Science and Technology Facilities Council (JS through
ST/N50404X/1; DJR and DMA through grant ST/L00075X/1). JS and KK acknowledge
support from the Knut and Alice Wallenberg Foundation. C.C.C. acknowledges
support from the Ministry of Science and Technology of Taiwan (MOST
109-2112-M-001-016-MY3). This paper makes use of ALMA data: 2017.00112.S,
2013.0.00965.S and 2015.1.00407.S. ALMA is a partnership of ESO (representing
its member states), NSF (USA) and NINS (Japan), together with NRC (Canada) and
NSC and ASIAA (Taiwan), in cooperation with the Republic of Chile. The Joint
ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. We thank the authors
of Carniani et al. (2016) for making their K-band cubes public. This work uses
data from VLT/SINFONI that were part of programmes ID 077.B-0218(A),
086.B-0579(A) and 091.A-0261(A). This work has made use of data from the
European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia),
processed by the Gaia Data Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

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##  Appendix A Verifying SED fitting procedure

To further verify the validity of our SED fitting we have explored the derived
correlation between FIR luminosity from star formation ($L_{\rm IR,SF}$), FIR
in luminosity from AGN ($L_{\rm IR,AGN}$ and UV luminosity from AGN ($L_{\rm
UV,AGN}$) in Figure 11. To provide a larger sample we additionally fitted the
photometry of a sample of 20 quasars from Schulze et al. (2019) as they are in
a similar redshift and bolometric luminosity range as our targets and include
ALMA band 7 observations (see §4.4 for a discussion on the derived star-
formation rates). We find a strong correlation between $L_{\rm IR,AGN}$ and
$L_{\rm UV,AGN}$ while a very weak correlation between $L_{\rm IR,SF}$ and
$L_{\rm UV,AGN}$. This gives confidence that the star formation component is
independent of the AGN luminosity and we are not attributing emission from the
AGN to the star formation component at infra-red bands.

We show the posterior density functions (PDFs) for the $L_{\rm IR,SF}$ and
$L_{\rm IR,AGN}$ in Figure 12 for 2QZJ00 and LBQS01. With the mid-IR and ALMA
band 7 and 3 photometry we are able to constrain the $L_{\rm IR,SF}$ to 0.5
dex. However, we stress that these PDFs show uncertainties on the $L_{\rm
IR,SF}$ and $L_{\rm IR,AGN}$ and not on the hot dust contamination to ALMA
band 7 photometry, as described in § 3.2.

Figure 11: Top panel: Comparison of infra-red luminosity due to AGN
($\mathrel{\rm L_{IR,AGN}}$) versus UV luminosity due to AGN ($L_{\rm
UV,AGN}$). Bottom Panel: Comparison of infra-red luminosity due to SF
($\mathrel{\rm L_{IR,SF}}$) versus UV luminosity due to AGN ($L_{\rm
UV,AGN}$). The black and blue points represent quasars from Schulze et al.
(2019) and this work, respectively. The dotted black line in both panels
indicate 1:1 ratio. We re-fitted the quasars from Schulze et al. (2019) using
method described in §3.2. While there is a strong correlation between $L_{\rm
UV,AGN}$ and $\mathrel{\rm L_{IR,AGN}}$, we see no correlation between
$\mathrel{\rm L_{IR,SF}}$ and $L_{\rm UV,AGN}$. This indicates that our SED
code correctly removes AGN contribution to the infra-red luminosity.  Figure
12: Posterior distribution for $\mathrel{\rm L_{IR,SF}}$ and $\mathrel{\rm
L_{IR,AGN}}$ for LBQS01 (top panel) and 2QZJ00 (bottom panel). The dashed
lines indicate 16th, 50th and 84th for the $\mathrel{\rm L_{IR,SF}}$
parameter. The contours indicate 1, 2 and 3 $\sigma$ values. With the
available photometry we are able to constrain the $\mathrel{\rm L_{IR,SF}}$
within 0.5 dex.

##  Appendix B A detailed assessment of the narrow H$\alpha$ emission

In this Appendix we perform a series of additional analyses to those already
presented in § 3.3 to assess the distribution of the narrow H$\alpha$ emission
in the IFU data cubes and then compare our results to the previous work that
presented these same IFU data. Firstly we consider the total narrow H$\alpha$
emission, i.e., all of the emission after subtracting the broad-line region
(see Section 3.3.1) and assess how reliably we can map this emission (Sections
B1–B3). We then assess if it is possible to de-compose the narrow H$\alpha$
emission into multiple components associated with an AGN NLR, any outflows and
any star formation emission (Section B4).

###  B.1 BLR-subtraction method for mapping narrow H$\alpha$ emission

Although the multi-component fit of the spatial spectra is our preferred
method of creating the surface brightness maps of the narrow H$\alpha$
emission (§ 3.3), we repeat with the alternative method of first subtracting
the broad-line region and looking for residuals (e.g., Cresci et al., 2015b,
see § 3.3.3). We refer to this method as the BLR-subtraction method. This
method consists of subtracting the BLR and continuum emission from the data
cube first, followed by creating a pseudo narrow-band image of the (residual)
narrow H$\alpha$ emission.

Before we fit and subtract the broad line H$\alpha$ emission, we masked the
spectral regions containing the narrow H$\alpha$, [N ii] and [S ii] doublets,
determined from the spectra show in Figure 5 (§ 3.3.1). This ensures that the
narrow H$\alpha$ and [N ii] line-emission do not artificially boost the broad
line H$\alpha$ fit, which would eventually lead to over-subtracting the broad-
line H$\alpha$ emission from the cube. We perform the spaxel-by-spaxel
fitting, by only fitting the broad line and continuum models (see § 3.3.1 for
more details). We fix the central wavelength and line-width to the same values
as obtained in the nuclear spectrum. We then subtract the model broad line
H$\alpha$ emission and continuum model, spaxel by spaxel, from the cube to
create a residual cube, only containing the narrow emission lines (i.e., the
narrow H$\alpha$, [N ii] doublet and [S ii] doublet).

From this residual cube we created a nuclear spectrum from following §3.3.1
and fitted this residual total spectrum with models describing only the narrow
emission lines. We note that the fluxes of the narrow H$\alpha$ from the
nuclear spectra using the original and the residual cubes are consistent
within 10%, showing that our BLR and continuum subtraction performed
correctly. We then collapsed the cube along the spectral channels centred on
the peak wavelength of the narrow H$\alpha$ emission with a width equivalent
to the FWHM of the emission-line profile. We present this pseudo narrow band
H$\alpha$ image in the second column of Figure 13. The observed morphology of
the narrow H$\alpha$ emission, which is dominated by AGN emission (see Section
3.3.4), is consistent with that seen in our primary ‘multi-fit’ method (§
3.3.3).

###  B.2 Modelling the curves-of-growth of narrow H$\alpha$ emission

Figure 13: Summary of our analyses on the H$\alpha$ data and modelling the COG
for different narrow H$\alpha$ morphologies. Columns from left to right:
Column 1: The narrow H$\alpha$ maps from the multi-fit method (see § 3.3.3).
Column 2: The narrow H$\alpha$ maps from the BLR-subtraction method (see §
3.3.3). The scaling for the maps is set between 3$\sigma$ and maximum of the
map. Column 3: The curves of growth for the H$\alpha$ emission. The solid red
curve shows the COG for the narrow H$\alpha$ with the shaded region indicating
the 1 $\sigma$ uncertainty. The dashed blue curves indicate the COG of the
broad line region (BLR). We spatially resolve the narrow H$\alpha$ emission in
HB8903. Column 4: PSF subtracted narrow H$\alpha$ images. HB8903 shows bright
residual emission indicating that this object is resolved in narrow H$\alpha$
emission. The central parts of LBQS01 and 2QZJ00 are unresolved. The scaling
of the maps is set between 3-5 $\sigma$.

In this section, we used curve-of-growth (COG) analyses (see e.g., Chen et
al., 2017, 2020; Scholtz et al., 2020) as an additional test of the
distribution of the total narrow H$\alpha$ emission. The COG method consists
of measuring the total enclosed flux in a series of increasingly large
apertures, centred on the central quasar position. We fitted the emission-line
profiles with the models described in § 3.3.1. Similarly to the creation of
the emission line maps (see § 3.3.3), we lock the central wavelength and line-
width of the broad line H$\alpha$ component. We measure both the narrow and
broad line H$\alpha$ flux in each aperture. This provides another method for
assessing the spatial distribution of the H$\alpha$ emission with higher SNRs
than the spaxel-by-spaxel fitting described in § 3.3.3, albeit resulting in a
one-dimensional analysis. The COG of the broad line H$\alpha$ is also used to
measure the PSF of the observations. The measured fluxes in the individual
curves-of-growth are normalised to the maximum flux measured, for both the
narrow and BLR component. As a result if the normalised emission flux grows
slower than the normalized flux of the PSF (BLR in this case), the emission is
resolved.

The third column of Figure 13 shows the comparison of the COG for the narrow
H$\alpha$ emission (solid red curves) and broad line H$\alpha$ emission (blue
dotted curves). To interpolate between the data points, we used linear splines
and we then estimated the half-light radii, i.e., the radius containing 50 %
of the total flux. We calculated the objects intrinsic sizes of the emission
line regions ($r_{e}$), by subtracting off the size of the PSF (measured from
the broad line emission) in quadrature. Uncertainties on the final H$\alpha$
sizes are calculated by considering the full range of possible radii for the
1$\sigma$ range of fluxes at each radii. We spatially resolved narrow
H$\alpha$ in only one of the quasars (HB8903; i.e., the PSF subtracted size
was not consistent with zero for this target) with a size of $r_{e}=1.9\pm
0.8$ kpc (FWHM $4.3\pm 1.8$ kpc).

###  B.3 Subtraction of a PSF model from the narrow H$\alpha$ maps

As a final investigation into the distribution of the total narrow H$\alpha$
emission, we test if the observed surface brightness maps (Figure 7) are
spatially resolved by subtracting a PSF model. This compliments the one-
dimensional COG analyses presented in the previous section by performing a
similar test in two dimensions.

We used the 2D Gaussian profile to the broad line region H$\alpha$ emission to
characterise the PSF (see § 3.3.3). We then subtract the PSF normalised to the
peak surface brightness of the narrow H$\alpha$ map. We present these PSF
subtracted narrow H$\alpha$ maps in fourth column of Figure 13. For LBQS01, we
see a small patch of residual emission to the north region, however, the
centre (majority) part of the emission is not resolved. In 2QZJ00, we do not
see any significant residual emission, confirming that the narrow H$\alpha$
emission for this target is not resolved. In contrast, we do see significant
residual emission in the HB8903. This confirms our COG analyses (§ B.2) that
the narrow H$\alpha$ emission is spatially resolved for this one target. We
note that the zero surface brightness emission at the centre of the residual
map in Figure 13, is due to normalising the PSF to the peak of the narrow
H$\alpha$ emission. This map should not be interpreted as an intrinsic
distribution of the narrow H$\alpha$ emission, it merely demonstrates there is
residual emission beyond that expected for a PSF.

We note that in LBQS01 there is faint, but well detected ($>5\sigma$) residual
emission 1 arcsecond north from the quasars location. However, the bulk of the
emission is still unresolved, hence are classification of this objects as
unresolved.

###  B.4 Exploring more complex models for the narrow H$\alpha$ emission line
profiles

He we investigate more detailed modelling of the narrow H$\alpha$ emission-
line profiles. So far in this Appendix we have treated the narrow H$\alpha$
emission as a single component and have not attempted to decompose for
contributions from AGN and star formation. This is relevant when looking to
physically interpret any H$\alpha$ emission as associated with star formation
(see § 3.3.3). We attempted variety of different models to both the nuclear
and ring spectra (see § 3.3.1 and § 3.3.3) to try to decompose the AGN narrow
line region, outflow and star formation components (see Cano-Díaz et al. 2012;
Carniani et al. 2016). In each case we calculated BIC to assess if additional
components were required (see §3.1). We fitted the following models to the
narrow H$\alpha$ emission-line profiles:

  1. 1.

Two Gaussian components, where the second component is forced to be narrow
H$\alpha$ (FWHM$<500$ km s-1) to describe the potential star formation
component proposed in the previous studies (see Cano-Díaz et al. 2012;
Carniani et al. 2016). The fitted additional narrow component had negligible
fluxes (i.e., $\sim 10^{-23}$ ergs s-1 cm-2 compared to the rms of $\sim
5^{-19}$ ergs s-1 cm-2) and are essentially not detected.

  2. 2.

We fitted an additional Gaussian component to each of H$\alpha$ and [N ii] to
represent an outflow (as seen in [O iii]). The resulting AGN-driven outflow
component had an unrealistic H$\alpha$/[N ii] ratio of 1000. We still obtained