11institutetext: Departamento de Astrofísica, Universidad de La Laguna, 38206,
La Laguna, Tenerife, Spain
11email<EMAIL_ADDRESS>22institutetext: Instituto de Astrofísica de
Canarias, Calle Vía Láctea, s/n, 38205, La Laguna, Tenerife, Spain
33institutetext: Department of Physics & Astronomy, University of Sheffield,
S3 7RH Sheffield, UK

###### Abstract

Aims. We present a detailed study of the kinematics of 19 type 2 quasars
(QSO2s) with redshifts in the range 0.3$<$z$<$0.41 and [OIII] luminosities of
$L_{\rm[OIII]}>10^{8.5}$L⊙. We aim at advancing our understanding of the AGN
feedback phenomenon by correlating outflow properties with i) the presence of
young stellar populations (YSPs) with ages ¡100 Myr, ii) the optical
morphology and the environment of the galaxies, and iii) the radio luminosity.

Methods. We characterize the ionized gas kinematics using the
[OIII]$\lambda$5007 Å emission line profiles detected in intermediate spectral
resolution (R$\sim$1500-2500) optical spectra of the QSO2s. To do so we
employed three different outflow detection methods: multi-component
parametric, flux-weighted non-parametric, and peak-weighted non-parametric.

Results. We detect ionized outflows in 18 of the 19 QSO2s using the parametric
analysis, and in all of them using the non-parametric methods. We find higher
outflow masses using the parametric analysis (average log
MOF(M⊙)=6.47$\pm$0.50), and larger mass rates and kinetic powers with the
flux-weighted non-parametric method (ṀOF=4.0$\pm$4.4 M⊙ yr-1 and
Ėkin=41.9$\pm$0.6 erg s-1). However, it is when we use the parametric method
and the maximum outflow velocities (vmax) that we measure the highest outflow
mass rates and kinetic energies (ṀOF=23$\pm$35 M⊙ yr-1 and
log(Ėkin)=42.9$\pm$0.6 erg s-1). We do not find any significant correlation
between the outflow properties and the previously mentioned AGN and galaxy-
wide properties.

Conclusions. Four of the five QSO2s without a YSP of age ¡100 Myr show highly
disturbed kinematics, whereas only 5 out of the 14 QSO2s with YSPs show
similarly asymmetric [OIII] profiles. Despite the small sample size, this
might be indicative of negative feedback. The lack of correlation between the
outflow properties and the presence of mergers in different interaction stages
might be due to their different dynamical timescales (Myr in the case of the
outflows versus Gyr in the case of the mergers). Lastly, the small radio
luminosity range covered by our sample, log(L5GHz)=[22.1, 24.7] W Hz-1, may be
impeding the detection of any correlation between radio emission and outflow
properties.

###### Key Words.:

galaxies: nuclei – galaxies: evolution – galaxies: interactions – galaxies:
kinematics and dynamics – ISM: jets and outflows

##  1 Introduction

All galaxies, or at least the most massive ones, are thought to experience
short episodes of nuclear activity, of $\leq$100 Myr (Martini, 2004; Novak et
al., 2011; Schawinski et al., 2015). These nuclear activity phases are
considered key drivers of galaxy evolution because they can potentially
regulate black hole and galaxy growth (Di Matteo et al., 2005; Harrison,
2017).

Cosmological simulations require active galactic nuclei (AGN) feedback for
quenching star formation and preventing galaxies from becoming over-massive
(Di Matteo et al., 2005; Dubois et al., 2016), thereby correctly reproducing
the observed galaxy-halo mass relations (Silk & Rees, 1998; Croton et al.,
2006; Moster et al., 2010). Furthermore, observational studies have found
plenty of evidence of this feedback on different scales, from the central tens
to hundreds of parsecs (García-Burillo et al., 2021; Ramos Almeida et al.,
2022) to hundreds of kpc (Rupke et al., 2019; Martín-Navarro et al., 2021).

Multi-phase outflows of molecular, neutral, and ionized gas (Rupke & Veilleux,
2013; Cicone et al., 2018; Herrera-Camus et al., 2020; Fluetsch et al., 2021)
are one of the primary AGN feedback mechanisms that can quench star formation
by heating up, disrupting, and ultimately removing the surrounding gas
available to form stars. However, AGN-driven outflows have also been found to
have the opposite effect, often referred to as “positive feedback”, as they
can promote star formation by pressurizing the gas and enhancing fragmentation
(Klamer et al., 2004; Cresci et al., 2015; Cresci & Maiolino, 2018; Carniani
et al., 2016; Bessiere & Ramos Almeida, 2022). Hence, we still need to advance
in our understanding of their actual impact on star formation.

The drivers of these multi-phase outflows have also been a subject of study,
with radio jets or AGN-winds as the main potential candidates (Mukherjee et
al., 2018; Fischer et al., 2019). For example, jetted Seyfert galaxies
(Whittle, 1992; García-Burillo et al., 2014, 2019; Morganti et al., 2015) have
been found to show larger outflow velocities than those without jets,
suggesting an influence of these jets in launching and/or accelerating the
outflows (Wylezalek & Morganti, 2018; Jarvis et al., 2019). Furthermore, even
in the case of lower radio-power Seyferts and radio-quiet quasars, recent
studies have found evidence that compact and modest radio jets might induce
nuclear outflows (Aalto et al., 2016; Audibert et al., 2019; Fernández-
Ontiveros et al., 2020; García-Bernete et al., 2021; Speranza et al., 2022;
Audibert et al., 2023). The influence of jets on the ionized gas kinematics
has been also studied using low angular resolution data, as e.g., from the
Sloan Digital Sky Survey (SDSS): Mullaney et al. (2013) and Zakamska & Greene
(2014) found that the higher the radio luminosity, the more disrupted the
[OIII] kinematics. However, it has also been claimed that this correlation
disappears if the influence of the host galaxy gravitational potential is
taken into account (see Ayubinia et al. 2023 and references therein).

Mergers and interactions have long been known as an AGN triggering mechanism
(Canalizo & Stockton, 2001; Hopkins et al., 2008; Ramos Almeida et al., 2011,
2012; Bessiere et al., 2012; Satyapal et al., 2014; Goulding et al., 2018;
Pierce et al., 2023). Given that mergers can simultaneously enhance nuclear
star formation and nuclear activity (e.g., Satyapal et al. 2014), it might be
possible that outflow incidence and properties might show a dependence with
galaxy morphology and/or environment. For example, some of the most powerful
outflows in the local universe are found in ultra-luminous infrared galaxies
(ULIRGs; Cicone et al. 2014; Rose et al. 2018; Lamperti et al. 2022), which
are almost uniquely associated with major mergers. Apart from these, the
merger-induced gas flows may also provide a rich ISM with plenty of cool gas
for the radiation-driven winds and any jets to interact with, thus increasing
the coupling with the hosts and making the outflows easier to detect.

The properties of AGN-driven outflows have been shown to depend on AGN
luminosity, being faster and more powerful as the AGN luminosity increases
(Zakamska & Greene, 2014; Fiore et al., 2017). However, recent works showed
that other factors, including nuclear gas concentration and the coupling
between the winds/jets and the galaxy discs might also play a key role (Ramos
Almeida et al., 2012; Audibert et al., 2023). Type 2 quasars (QSO2s) in the
local universe are ideal laboratories to characterize outflows and study their
impact on the host galaxies. This is because the outflows are easier to
identify that the lower velocity outflows of Seyfert galaxies, and the high
obscuration (either nuclear or galaxy-wide; Ramos Almeida & Ricci 2017) blocks
the emission from the broad-line region and the AGN continuum, avoiding
dilution of the emission line and stellar absorption features.

The most widely studied gas outflow phase is the warm ionized (T$\sim$104 K),
since it emits strong forbidden emission lines in the infrared and optical
range, being the [OIII]$\lambda$5007 Å one of the strongest. QSO2s are
commonly found to present complex emission line profiles, showing large blue
asymmetries and deviations from Gaussianity (Greene et al., 2011; Liu et al.,
2013; Villar-Martín et al., 2011, 2014; Harrison et al., 2014; Ramos Almeida
et al., 2017, 2019), indicating highly-disrupted kinematics. The overall
majority of AGN outflow studies characterized the ionized gas kinematics
following a parametric approach (Holt et al., 2011; Greene et al., 2011;
Villar-Martín et al., 2011; Arribas et al., 2014), considering that each
gaseous component that contributes to the kinematics can be described by a
Gaussian distribution. They have the advantage of making it possible to
characterize the properties of different gas components, yet, for objects with
highly disrupted kinematics it becomes difficult to ascribe a physical meaning
to each component (Bessiere & Ramos Almeida, 2022). Hence, other studies
implemented a non-parametric analysis, based on measuring emission line
velocities at fixed fractions of the peak intensity or the cumulative line
flux function (Whittle, 1985; Harrison et al., 2014; Zakamska & Greene, 2014;
Speranza et al., 2021; Bessiere & Ramos Almeida, 2022). Non-parametric methods
are better for characterizing low signal-to-noise spectra with complex
emission line profiles. Although they do not allow us to separate different
gaseous contributions, they can easily identify high velocity gas in tail ends
of emission line wings. Despite all the recent works making use of both
parametric and non-parametric methods to characterize AGN-drive outflows in
the literature, to the best of our knowledge, no comparison between their
results has been performed for a common sample of objects.

Considering the previous, in this work we use three different outflow
detection methods (parametric, flux-weighted non-parametric, and the peak-
weighted non-parametric from Speranza et al. 2021) for characterizing the
ionized gas kinematics of 19 QSO2s with redshifts in the range 0.3$<$z$<$0.41
and [OIII] luminosities of $L_{\rm[OIII]}>10^{8.5}$L⊙. Furthermore, with the
aim of advancing in our understanding of the AGN feedback phenomenon, we study
potential correlations between the QSO2s outflow physical properties and
different AGN and host galaxy properties, including i) the presence of young
stellar populations (YSPs) with ages ¡100 Myr, ii) the optical morphology and
environment, and iii) the AGN and radio luminosity.

In Section 2 we describe the QSO2 sample and the spectroscopic data used here,
as well as the previously studied AGN and host galaxy properties. In Section 3
we explain the three different methods we used for analyzing the ionized gas
kinematic and present the results. Section 4 includes the physical outflow
properties derived through each of the three methods. In Section 5 we evaluate
the possible correlations between the outflow properties and different AGN and
host galaxy properties. In Section 6 we discuss the results, and finally in
Section 7 we summarize the findings of our work. Throughout this paper we
assumed a cosmology with H0=70 km s-1 Mpc-1, $\Omega_{\rm M}$=0.3 and
$\Omega_{\rm\Lambda}$=0.7.

##  2 Sample and data

Table 1: Main properties of the QSO2s

Name | RA | Dec | z | Seeing | Scale | log(L[OIII]/L⊙) | log(LBOL) | log(L5GHz) | YSP | Merger | Stage | Bgq
---|---|---|---|---|---|---|---|---|---|---|---|---
|  |  |  | (arcsec) | (kpc arcsec-1) |  | (erg s-1) | (W $Hz^{-1}$) | ¡ 100 Myr |  |  |
J0025-10 | 00:25:31.46 | -10:40:22.2 | 0.303 | 0.84 | 4.48 | 9.23(8.65) | 45.48 | 22.08 | yes | yes | 2,3 | -16
J0114+00 | 01:14:29.61 | 00:00:36.7 | 0.389 | - | 5.28 | 8.90(8.46) | 45.15 | 24.70 | no | yes | 2,3 | 254
J0123+00 | 01:23:41.47 | 00:44:35.9 | 0.399 | 1.12 | 5.36 | 9.53(9.14) | 45.78 | 23.27 | yes | yes | 1,2,3 | 676
J0142+14 | 01:42:37.49 | 14:41:17.9 | 0.389 | - | 5.28 | 9.40(8.87) | 45.65 | <22.58 | yes | no | 4 | 149
J0217-00 | 02:17:58.19 | -00:13:2.7 | 0.344 | 0.86 | 4.88 | 9.48(8.81) | 45.73 | 22.15 | yes | yes | 2 | 63
J0217-01 | 02:17:57.42 | -01:13:24.4 | 0.375 | 0.97 | 5.16 | 8.90(8.37) | 45.15 | 22.35 | yes | no | 4 | -153
J0218-00 | 02:18:34.42 | -00:46:10.3 | 0.372 | 1.11 | 5.13 | 9.07(8.62) | 45.32 | <22.13 | yes | yes | 1,2 | -49
J0227+01 | 02:27:1.23 | 01:07:12.3 | 0.363 | 0.53 | 5.05 | 9.13(8.70) | 45.38 | <22.11 | yes | yes | 2 | 159
J0234-07 | 02:34:11.77 | -7:45:38.4 | 0.31 | 0.78 | 4.55 | 9.81(8.78) | 45.06 | 22.35 | no | no | 4 | -115
J0249+00 | 02:49:46.09 | 00:10:3.22 | 0.408 | 0.73 | 5.44 | 9.25(8.75) | 45.50 | 22.14 | yes | yes | 1,2 | -177
J0320+00 | 03:20:29.78 | 00:31:53.5 | 0.384 | 0.75 | 5.23 | 8.63(8.40) | 44.88 | <22.17 | yes | yes | 2 | 1297
J0332-00 | 03:32:48.5 | -00:10:12.3 | 0.31 | 0.83 | 4.55 | 8.69(8.53) | 44.94 | 23.36 | no | yes | 2,3 | -19
J0334+00 | 03:34:35.47 | 00:37:24.9 | 0.407 | 1.13 | 5.43 | 9.26(8.75) | 45.51 | <22.23 | yes | yes | 2 | 36
J0848-01 | 08:48:56.58 | 01:36:47.8 | 0.35 | 0.72 | 4.95 | 8.90(8.46) | 45.15 | 24.00 | no | yes | 2 | 159
J0904-00 | 09:04:14.1 | -00:21:44.9 | 0.353 | 0.71 | 4.98 | 9.27(8.89) | 45.52 | 23.52 | yes | yes | 2 | 463
J0923+01 | 09:23:18.06 | 01:01:44.8 | 0.386 | 0.67 | 5.27 | 9.21(8.78) | 45.46 | 22.09 | yes | yes | 2 | 256
J0924+01 | 09:23:56.44 | 01:20:2.1 | 0.38 | 0.75 | 5.22 | 10.43(8.46) | 46.68 | 23.33 | yes | yes | 2 | -55
J0948+00 | 09:48:36.05 | 00:21:4.6 | 0.324 | 0.89 | 4.71 | 8.96(8.57) | 45.21 | 22.35 | no | no | 4 | -123
J2358-00 | 23:58:18.87 | -00:09:19.5 | 0.402 | 1.58 | 5.39 | 9.71(9.29) | 45.96 | <22.21 | yes | yes | 1,2 | 40

111Columns 1, 2, 3, and 4 correspond to the QSO2 identifier (full SDSS name
can be found in Bessiere et al. 2012), RA, Dec, and spectroscopic redshift
from SDSS. Columns 5 and 6 correspond to the seeing FWHM of the spectroscopic
observations used here, measured from stars in the acquisition images, and to
the spatial scale. Columns 7 and 8 list the extinction-corrected [OIII]
luminosities from Kong & Ho (2018), with the uncorrected [OIII] luminosities
from Reyes et al. (2008) within parenthesis, and the bolometric luminosities,
derived from the extinction-corrected [OIII] luminosities using the factor of
454 from Lamastra et al. (2009). Column 9 corresponds to the radio luminosity,
calculated using the integrated flux at 1.4 GHz from either the FIRST or NVSS
surveys, assuming a spectral index of $\alpha$ = -0.75 when unknown. When the
object is undetected in both surveys, an upper limit is given. Columns 10
indicates whether the inclusion of a young stellar population (YSP) with age
¡100 Myr was necessary for modelling the stellar spectral features, following
Bessiere et al. (2017). Columns 11 and 12 indicate whether there is evidence
of mergers/interactions in the optical images, and the different stages of
these interactions, as reported in Bessiere et al. (2012): (1) the quasar host
is part of a galaxy pair showing signatures of tidal interaction, (2) other
signs of morphological disturbance, (3) system with multiple nuclei (within 10
kpc between them), and (4) isolated galaxy. Column 13 lists the value of the
B${}_{\rm gq}^{\rm av}$ parameter from Ramos Almeida et al. (2013), that
measures the excess in the number of galaxies around the QSO2 as compared with
the average number of background galaxies.

Our QSO2 sample is based on the one studied by Bessiere et al. (2012), which
is a subset of the narrow-line AGN catalogue of Zakamska et al. (2003),
selected from SDSS (York et al., 2000) using emission line ratio diagnostic
diagrams. We specifically selected this QSO2 sample because several host
galaxy properties, including the stellar populations, optical morphologies,
and environments were already characterized (Bessiere et al., 2012, 2017;
Ramos Almeida et al., 2013), allowing us to investigate potential correlations
between them and the outflow properties that we report in this work.

Bessiere et al. (2012) selected the 20 QSO2s with right ascension (RA) in the
range 23¡RA¡10 h, declination ($\delta$) of $\delta$¡+20∘, redshifts in the
range 0.3¡z¡0.41, and emission line luminosities of L[OIII]¿108.5 L⊙. The
luminosity cut is equivalent to an absolute magnitude of MB ¡ -23 mag, which
is the classical definition of quasar. Subsequent updates to the [OIII]
luminosities were reported for these QSO2s in Reyes et al. (2008), which are
included in Table 1. These updated luminosities implied that six objects from
the original selection fall marginally below the quasar L[OIII] cut, but
Bessiere et al. (2012) chose to retain the original sample of 20 objects. In a
more recent work, Bessiere et al. (2017) reported deep optical spectroscopic
observations for 19 of the 20 QSO2s. SDSS J015911+143922 (J0159+1439) was
excluded from their analysis because they were unable to obtain spectroscopic
data of sufficient quality for modelling the stellar populations. This sample
of 19 QSO2s is then 95% complete and it constitutes our QSO2 sample. Table 1
includes the AGN bolometric luminosities of the QSO2s, which range from log
LBOL=44.9 to 46.7 erg s-1, with a median value of 45.5 erg s-1. These
luminosities were calculated from the extinction-corrected [OIII] luminosities
from Kong & Ho (2018) and using the correction factor of 454 from Lamastra et
al. (2009).

###  2.1 Spectroscopic data

The optical spectroscopic data used in this work, described in Bessiere et al.
(2017), were mainly obtained using the Gemini Multi-Object Spectrograph
(GMOS-S) mounted on the Gemini South telescope at Cerro Pachón, Chile. Long-
slit spectra were taken for 16 objects during semesters 2010B and 2011B using
a relatively wide slit of 1.5 arcsec, in both the B600 and the R400 gratings.
The observations consisted of 4$\times$675 s exposures using the B600 grating
and 3$\times$400 s exposures using the R400 grating. The average spectral
resolutions measured from the sky lines were 7.2 and 11.4 Å for the blue and
red wavelength ranges, respectively. However, since all the observations but
one (J2358-00) have a seeing full width at half maximum (FWHM) smaller than
the slit width, the actual spectral resolutions range from 4.0-8.2 Å for the
different spectra.

Different spectroscopic observations were compiled for the other three QSO2s
in the sample, either because no GMOS-S observations were obtained (J0217-00
and J0114+00) or because [OIII] was not covered by the GMOS-S spectrum
(J0142+00, for which only the blue range was observed). J0217-00 was observed
with the Gran Telescopio Canarias (GTC), at the Roque de los Muchachos
Observatory, La Palma, Spain. The Optical System for Imaging and low-
Intermediate-Resolution Integrated Spectroscopy (OSIRIS) instrument was used
in long-slit spectroscopy mode, using a slit of 1.23 arcsec width. The target
was observed with the R2000B and R2500R grisms for integration times of
3$\times$1800 s and 3$\times$1200 s, which lead to spectral resolutions of 4
and 5 Å, respectively. Finally, the spectra of J0114+00 and J0142+00 were
obtained from SDSS, which uses a standard 3 arcsec fiber covering an observed
wavelength range of 3800–9200 Å, with a spectral resolution (R) varying from
R$\sim$1500 at 3800 Å to R$\sim$2500 at 9000 Å. This spectral resolution
corresponds to a FWHM=2.78 Å at 7000 Å.

Here we used the reduced and flux-calibrated data from Bessiere et al. (2017),
where further details can be found. Large extraction apertures, of 1.5-2
arcsec ($\approx$8 kpc) were used there with the aim of performing stellar
population modelling of the QSO2s host galaxies. Here, since our goal is
studying the nuclear gas kinematics, we extracted the spectra using a diameter
determined by the size of the seeing of each observation. The seeing was
measured from the FWHM of the stars detected in the corresponding acquisition
images of the QSO2s (0.53-1.13 arcsec $\approx$ 2.7-6.1 kpc; see Table 1),
with the exception of J2358-00, for which we used an aperture of 8.5 kpc given
that the seeing of 1.58 arcsec is larger than the slit width. For extracting
these nuclear 1D spectra from the reduced and calibrated 2D spectra, we used
the task apall within the IRAF package twodspec. First, we summed the flux
contribution for the wavelengths centered around the ionized
[OIII]$\lambda$5007 emission line. Then, by plotting this flux against the
spatial axis we located the maximum of the emission, and extracted a seeing-
sized aperture centered at this position. In the case of the two QSO2s with
SDSS data, the spectra correspond to physical sizes 15.8 kpc, set by the size
of the fiber. We chose the [OIII] emission line to perform the kinematic
analysis of the ionized gas because it is intense and AGN-dominated in the
case of QSO2s, and it is not blended with other emission lines. In the case of
the targets for which the [OIII] line was detected in both the red and the
blue GMOS-S spectra, we used the blue because of its higher spectral
resolution.

###  2.2 Galaxy properties

The selected sample has been previously studied by Bessiere et al. (2012,
2017) and Ramos Almeida et al. (2013). From these works we can get information
about multiple properties of the QSO2s and their host galaxies, including the
presence of YSPs, optical morphologies, environments, and radio emission (see
Table 1). One of our goals is to search for correlations between these
AGN/galaxy properties and those of the ionized outflows that we characterize
here, for the first time in these QSO2s.

Bessiere et al. (2017) presented a detailed study of the stellar populations
of the host galaxies of the 19 QSO2s in our sample plus another two additional
QSO2s. That study is based on the modeling of the spectra described above and
extracted in a large aperture of $\sim$8 kpc, centred on the peak continuum
flux. For fitting the spectra, they used a combination of up to two stellar
population models that are representative of viable star formation histories,
and a power-law of varying spectral index, to account for the contribution
from scattered AGN light. Based on this analysis, Bessiere et al. (2017)
concluded that 71% of the 21 QSO2 host galaxies require the inclusion of a YSP
with an age¡100 Myr for correctly modelling the stellar features detected in
the optical range. From the sample of 19 QSO2s studied here, 14 host galaxies
(74%) need the inclusion of this YSP (see Table 1). In the following, we just
focus on the detection/non-detection of these YSPs in the QSO2s because their
ages are comparable with the current phase of quasar activity (Martini, 2004;
Hickox et al., 2014).

A full analysis of the optical morphologies of our QSO2 sample is presented in
Bessiere et al. (2012). They visually inspected deep optical broad-band
images, also observed with the GMOS-S instrument on the Gemini South
telescope. They claimed that 15 of the 19 QSO2s (79% of the sample) show signs
of galaxy interactions in the form of tails, shells, fans, irregular features,
amorphous haloes, and/or double nuclei. Based on the presence or absence of
these structures, Bessiere et al. (2012) classified the host galaxies in four
groups that correspond to different stages of the interaction between two
galaxies. These groups are the following.

(1) The QSO2 host is part of a galaxy pair in tidal interaction.

(2) The galaxy presents other signs of morphological disturbance such as fans,
shells, and/or tails.

(3) The system has multiple nuclei separated by $\leq$10 kpc.

(4) Isolated galaxy with no signs of morphological disturbance.

Bessiere et al. (2012) also reported the 5 GHz radio luminosities of the
QSO2s, which are listed in Table 1. They were calculated using the integrated
flux at 1.4 GHz, obtained either from the FIRST or NVSS surveys, assuming a
spectral index of $\alpha$=-0.75 when unknown. These 5 GHz luminosities range
from 22.1 to 24.7 W Hz-1, with a median value of 22.35 W Hz-1, excluding the
six QSO2s with upper limits (¡22.6 W Hz-1).

Lastly, Ramos Almeida et al. (2013) characterized and quantified the
environment of the QSO2s by means of the angular clustering amplitude, Bgq,
and using the deep GMOS-S optical imaging data from Bessiere et al. (2012).
The spatial clustering amplitude measures the excess in the number of galaxies
around the target as compared with the expected number of background galaxies,
assuming that the galaxy clustering is spherically symmetric around each
target. Both the neighbours and the background galaxies were counted as the
total number of galaxies surrounding the QSO2 (or its corresponding position
in the offset fields) within a projected distance of a 170 kpc radius and
having magnitudes between m-1 and m+2, with m being the magnitud of a generic
galaxy at the redshift of the target. More information about the procedure can
be found in Ramos Almeida et al. (2013). In Table 1 we show the values of
B${}_{gq}^{av}$, calculated using all the offset fields (i.e., not including
the QSO2) to determine the average number of background galaxies. Most of the
QSO2s have low values of B${}_{gq}^{av}$, corresponding to low-density
environments. The average value reported by Ramos Almeida et al. (2013) for
the QSO2s is 151$\pm$76, and for comparison, values of B${}_{gq}^{av}\geq$400
are typical of cluster environments. Indeed, Ramos Almeida et al. (2013)
compared the values of B${}_{gq}^{av}$ obtained for the QSO2s and for a
control sample of quiescent early-type galaxies and did not find significant
difference between them.

##  3 Kinematic analysis

Figure 1: Parametric fit of the [OIII] doublet for the QSO2 J0924+01. The left
panel shows the line-free regions, in blue, selected for fitting the
underlying continuum, in orange. The right panel shows the two kinematic
components fitted in the case of this QSO2, with the residuals included in the
inset at the bottom. The green shaded region in the residuals corresponds to
the region affected by atmospheric absorption.

We analyzed the nuclear [OIII]$\lambda\lambda$4959,5007 Å profiles in order to
investigate the kinematic properties of our sample, specially the possible
presence of outflows. As explained in Section 2.1, we extracted a nuclear
spectrum of each source by choosing an aperture comparable to the seeing of
each observation (see Table 1). These apertures correspond to physical sizes
of $\sim$3-6 kpc, except for J2358-00, which is 8.5 kpc. For the two QSO2s for
which only SDSS spectra are available, J0114+00 and J0142+00, the fiber size
corresponds to $\sim$15.8 kpc.

For characterising the ionized gas kinematics, the main methods applied in the
literature are based either on a parametric approach or a non-parametric one.
At every spatial location different gaseous components with different
kinematics can contribute to the flux and modify the shape of the line
profiles: gas in the narrow-line region (NLR), outflowing gas, contributions
from companion objects, etc. Parametric methods are based on the assumption
that the different kinematic components can be described as a Gaussian
distribution. They have the advantage of making it possible to characterize
the properties of the different kinematic components found, including density
and reddening (Holt et al., 2011; Villar-Martín et al., 2014; Arribas et al.,
2014). The challenge is that in some objects with disrupted kinematics, it is
difficult to ascribe a physical meaning to all the fitted kinematic components
(Bessiere & Ramos Almeida, 2022). On the other hand, the non-parametric
analysis consists of measuring emission line velocities at various fixed
fractions of the peak intensity (Speranza et al., 2021) or the line cumulative
flux function (Whittle, 1985; Harrison et al., 2014). This method is most
appropriate for characterizing gas properties in galaxies with multiple
kinematic components, as it permits to easily identify high velocity gas in
tail ends of emission line wings. However, non-parametric methods do not allow
us to characterize the relative contribution of the different gaseous
components at play.

Considering the previous, here we adopt both parametric and non-parametric
methods to characterize the ionized gas kinematics of the QSO2s. By doing this
we can investigate the dependence of the outflow properties, when present, on
the method employed to measure them. First, we modelled the
[OIII]$\lambda\lambda$4959,5007 Å emission line profiles using a parametric
method (i.e., fitting Gaussians to the line profiles). Second, taking
advantage of the parametric fit of the [OIII]$\lambda$5007 Å, we used both
flux-weighted and peak-weighted non-parametric methods to characterize the
line profile. In Section 4 we compare the results obtained with the different
methods that we describe below.

###  3.1 Parametric method

We fitted the [OIII]$\lambda$$\lambda$4959,5007 profiles with multiple
Gaussian components, using a Python program that we developed, based on the
Specutils and the Astropy packages.

Initially, before fitting the emission lines, the underlying continuum is
subtracted by linearly interpolating the spectrum between two line-free
regions close to the [OIII] doublet, redwards and bluewards (see the left
panel of Figure 1). To select the number of Gaussians fitted to each of the
QSO2s, we added new components until the increment of the reduced $\chi^{2}$
($\Delta\chi^{2}$) of the residuals is lower than 10%, following Bessiere &
Ramos Almeida (2022). We also imposed that any component must be broader than
the instrumental width (see Section 2.2), and its corresponding parameters
larger than their associated uncertainties. An example of fit including two
Gaussians is shown in the right panel of Figure 1.

Each kinematic component fitted to the [OIII] doublet corresponds to a set of
two Gaussians simultaneously fitted (i.e., sharing the same width and velocity
shift relative to systemic), with fixed wavelength separation (taking into
consideration the cosmological spread of the wavelength shift between the two
lines) and an amplitude ratio of [OIII]$\lambda$4959/[OIII]$\lambda$5007 = 1/3
(Dimitrijević et al., 2007). It is noteworthy that the GMOS-S spectra reduced
and analyzed by Bessiere et al. (2017) have residual atmospheric absorption
around the spectral region 6863-6913Å . When this residual absorption lies on
top or close to one of the emission lines, as it is the case of the QSO2s
J0114+00, J0142+14, J0217-01, J0218-00, J0320+00, and J0923+01, we first fit
just the unaffected [OIII] line, and then use the corresponding parameters to
force the fit of the affected line. In the case of J0924+01, where the
atmospheric absorption lies between the two emission lines, the affected
wavelength range is masked before fitting the emission line profiles (see
right panel of Figure 1).

All the fits and corresponding parameters derived from them (number of
Gaussians, flux, FWHM, velocity shift from systemic, luminosity, and
percentage luminosity of each component relative to the total luminosity of
the line) are shown in Figure 7 and Table 3 in Appendix A. We note that the
values of the FWHM have not been corrected from instrumental width, with the
aim of keeping them comparable with W80 (see Section 3.2). Nevertheless, the
individual instrumental FWHMs are listed in Table 3. The uncertainties of the
parameters were computed through a Monte Carlo simulation, creating 1000 mock
spectra by varying the flux at each wavelength adding random values from a
normal distribution with an amplitude given by the noise of the continuum. The
errors were then computed as the 1$\sigma$ of each parameter distribution
generated from the mock spectra.

Following the methodology described above, we fitted n Gaussian components to
the [OIII] profiles of the QSO2s and classified them as narrow, intermediate,
and broad depending on the FWHM.

  * •

Narrow (n): FWHM $<$ 800 km s-1.

  * •

Intermediate (i): 800 km s-1 $\leq$ FWHM $\leq$ 2000 km s-1.

  * •

Broad (b): FWHM $>$2000 km s-1.

We used these values trying to ascribe a physical meaning to the different
kinematic components. Here we assume that the narrow components are associated
with gas in the NLR, whose emission lines typically present FWHMs$\sim$400-600
km s-1 (Netzer, 1990; Groves, 2007). The intermediate components are broader
than the typical NLR FWHMs, but narrower than the broad components from the
broad-line region (BLR), which have FWHM$>$2000 km s-1. We note, however, that
the broad components that we are measuring here for the [OIII] emission lines
cannot be associated with the BLR because they are forbidden lines. Thus, the
intermediate and broad components would be most likely associated with
turbulent/outflowing ionized gas. With this is mind, the velocity shifts
reported in Table 3 were computed relative to the narrow component, or to the
centroid of the multiple narrow components when present. We consider these
velocity shifts as the outflow velocities, relative to the average kinematics
of the NLR. Since these are conservative estimates, we also calculate the
outflow maximum velocities as vmax=vs+2$\sigma$ (Rupke & Veilleux, 2013),
where $\sigma$ is FWHM/2.355.

In addition to the (n), (i), and (b) components, the fits of the QSO2s
J0217-01 and J0320+00 also include a narrow and redshifted (r) component (see
Table 3 in Appendix A) that, although do not meet all the criteria described
at the beginning of this Section, were necessary to successfully reproduce the
[OIII] profiles. However, these red components are not included in the outflow
analysis.

We found intermediate and broad components in 18 of the 19 QSO2s, which
implies an outflow incidence rate of $\sim$95%. The only QSO2 without
intermediate or broad components is J0218-00. The outflow components that we
measured for the other 18 QSO2s present an average FWHM of 1800 km s-1, with a
standard deviation of 1100 km s-1. They are mainly blueshifted, with an
average value of vs = -370 km s-1 and a standard deviation of 400 km s-1 (see
Table 2), and a maximum velocity of vmax = -1800$\pm$1400 km s-1.

Table 2: Average and median outflow properties from the parametric and non-
parametric methods.

Method | FWHM | vOF | log(MOF) | $\dot{M}_{\rm OF}$ | log($\dot{E}_{\rm kin}$)
---|---|---|---|---|---
| (km s-1) | (km s-1) | (M⊙) | (M⊙ yr-1) | (erg s-1)
| Mean | Median | Mean | Median | Mean | Median | Mean | Median | Mean | Median
Parametric (vs) | 1800$\pm$1100 | 1500 | -370$\pm$400 | -150 | 6.47$\pm$0.50 | 6.46 | 2.8$\pm$2.6 | 1.8 | 40.5$\pm$1.2 | 40.3
Parametric (vmax) | … | … | -1800$\pm$1400 | -1500 | 6.47$\pm$0.50 | 6.46 | 23$\pm$35 | 11 | 42.9$\pm$0.6 | 42.9
Flux-weighted | 940$\pm$280 | 890 | -1120$\pm$510/680$\pm$200 | -1040/690 | 6.03$\pm$0.30 | 5.93 | 4.0$\pm$4.4 | 2.5 | 41.9$\pm$0.6 | 41.9
Peak-weighted | - | - | -840$\pm$260 | -780 | 5.75$\pm$0.32 | 5.75 | 1.9$\pm$1.8 | 1.3 | 41.4$\pm$0.5 | 41.4

222In the case of the two non-parametric methods, W80 is listed instead of
FWHM, and the average values of the outflow velocity, vOF, are given for the
approaching and receding outflow sides for the flux-weighted method. In the
case of the peak-weighted non-parametric method, the value of vOF corresponds
to the average value of the 18 QSO2s with an asymmetric blue wing detected.
For J0227+01, which has an assymetric red wing instead, we measure
vOF=676$\pm$21 km s-1. The corresponding outflow physical quantities include
J0227+01.

We find that 14 of the QSO2s (74% of the sample) require the inclusion of more
than two Gaussian components (2 QSO2s with four and 12 with three Gaussians)
to correctly model the emission line profiles. The remaining 5 QSO2s (26% of
the sample) are well fitted with just two Gaussian components. Such diversity
of kinematic components detected in the [OIII] lines is common in QSO2s
(Villar-Martín et al., 2011, 2016; Harrison et al., 2014; McElroy et al.,
2015). However, the heterogeneous results from our parametric analysis make it
difficult to characterize the outflow properties of the sample. For this
reason, and taking advantage of the parametric analysis here described, we
performed a non-parametric analysis of the emission line profiles. This
analysis, described in Section 3.2, provides a more homogeneous set of
results, therefore allowing us to easily evaluate possible correlations
between the outflow and host galaxy properties (see Section 5).

###  3.2 Non-parametric analysis

Here we describe two different non-parametric methods to characterize the
[OIII]$\lambda$5007 Å emission line: flux-weighted and peak-weighted. The two
of them require of a noiseless isolated emission line profile, and hence we
use the models resulting from the parametric method described in Section 3.1
(i.e., the sum of the Gaussian components used to fit the [OIII]$\lambda$5007
Å emission line of each QSO2; see the right panel of Figure 1 for an example).

####  3.2.1 Flux-weighted non-parametric analysis

Figure 2: Example of the flux-weighted non-parametric method employed in this
work. The blue solid line is the parametric fit to the [OIII]$\lambda$5007 Å
emission line shown in Figure 1 for J0924+01, with the continuum subtracted.
The non-parametric velocity definitions included in this figure are the median
velocity (vmed), the velocities at the 5, 10, 90, and 95% points of the
normalized cumulative function of the emission line flux (v05, v10, v90, and
v95), and the width of the line containing 80% of the total flux
(W80=v90-v10). The grey region corresponds to the area containing 80% of the
total flux (i.e., between v10 and v90), and the blue and red regions
correspond to high-velocity gas, which we consider outflowing.

We first use a flux-weighted non-parametric approach (Heckman et al., 1981;
Harrison et al., 2014; Zakamska & Greene, 2014) to describe the kinematic
properties of the modelled [OIII]$\lambda$5007 Å emission line. The velocities
v05, v10, v90, and v95 are defined as the velocities at the 5th, 10th, 90th,
and 95th percentiles of the normalised cumulative function of the emission
line flux. Other quantities based on this analysis that we use hereafter are
the following.

  * •

The peak velocity, vp. It corresponds to the peak flux of the emission line,
and it is representative of the narrow component(s) fitted in Section 3.1
(i.e., of NLR gas).

  * •

The median velocity, vmed, corresponding to the 50th percentile of the
velocity, also representative of NLR gas.

  * •

The line width, W80, defined as the width of the line containing 80% the total
emission line flux, W80=v90-v10.

  * •

The velocity offset, $\Delta$v=($v_{05}$ \+ $v_{95}$)/2. It quantifies the
velocity offset of any blueshifted/redshifted component relative to systemic
(i.e., the peak velocity, vp).

  * •

The asymmetry, a=$\mid v_{90}-v_{med}\mid-\mid v_{10}-v_{med}\mid$. Negative
(positive) asymmetry values indicate the presence of a blue (red) tail in the
line profiles.

In the following, we consider that only the gas having velocities larger than
v05 and v95 is outflowing, and define the corresponding outflow velocities
(vOF) as the median velocity (v50) of the blueshifted and redshifted wings
(blue and red areas in Figure 2). In the example shown in Figure 2, the median
velocity of the blue wing is -1926 $\pm$ 37 km s-1, and 789 $\pm$ 21 km s-1
for the red wing. For the whole sample, we measure vOF=-1120$\pm$510 km s-1
for the blue wing, and 680$\pm$200 km s-1 for the red. All the parameters and
figures derived using this method can be seen in Appendix B. As in the case of
the parametric method, the uncertainties are computed as the 1$\sigma$ of each
parameter distribution generated with a Monte Carlo simulation of 1000 mock
spectra.

We find a wide range of emission line widths, with an average W80 = 940 $\pm$
280 km s-1. 12 of the 19 QSO2s present broad [OIII] line profiles, with
W${}_{80}>$800 km s-1. Regardless of this, here we consider that all the QSO2s
have outflows of ionized gas, since by definition, every emission line profile
will include velocities larger than v05 and v95. The average values of the
asymmetry, v05, and v95 are -120$\pm$130 km s-1, -820 $\pm$ 320 km s-1, and
530 $\pm$ 140 km s-1. All the QSO2s show negative asymmetry values except
J0227+01. These negative values are related to the presence of blue tails in
the profiles (see Figure 2 and Table 5 in Appendix B). Detecting blueshifted
wings is more common than redshifted wings because usually we see the bulk of
the outflowing gas that is coming toward us, whilst the receding side is
partly hidden behind the host galaxy. In cases where the outflows subtend a
small angle relative to the galaxy discs, it is possible to detect both the
blueshifted and redshifted outflow components, or depending on the galaxy
inclination, a dominant redshifted component. This might be the case of
J0227+01. Lastly, it should be mentioned that the quasar J0218-00, that did
not need the inclusion of an intermediate or broad component in the parametric
model, presents low values of the asymmetry and the velocity offset.

####  3.2.2 Peak-weighted non-parametric analysis

Figure 3: Same as in Figure 2, but using the peak-weighted non-parametric
method from Speranza et al. (2021). The black solid line in the blue side of
the emission line corresponds to the mirror image of the red side. The grey
area is the core of the line, defined as the region between the peak and 1/3
of the peak flux. The orange area is the result of subtracting the black from
the blue line outside the core region, which is what we consider outflowing
gas using this method. The black and grey vertical dashed lines are the peak
and outflow velocities (vp and vOF).

As we mentioned in Section 3.2.1, the flux-weighted non-parametric method
likely overestimates the outflow mass because by definition, a certain
proportion of the gas is outflowing, both blueshifted and redshifted. In
addition, Speranza et al. (2021) argued that $v_{05}$ might still be
representative of rotating gas, which generally constitutes most of the
emission line flux, and hence may not be fully representative of outflowing
gas. Consequently, Speranza et al. (2021) proposed a different non-parametric
analysis, based on the detection of asymmetries in the emission lines (see
Figure 3 for an example), to measure the outflow properties.

For this method we also use the model of the [OIII]$\lambda$5007 Å emission
line profile from the parametric method. The core of the emission line is
defined as the region between the peak of the line and one-third of the peak
(i.e., the region that corresponds to $\sim$90% of the total flux of the line
considering a Gaussian profile). By subtracting a mirror image of the less
prominent wing from the most prominent one, the symmetric component of the
emission line is removed, leaving just the asymmetric wing. Such residual is
what we associate with outflowing gas (orange area in Figure 3). For
characterizing the outflow we use two parameters: the median velocity of the
residual, vOF, (the 50th percentile of its total flux) and the flux of the
residual wing Fw. As in Section 3.2.1, the uncertainties were estimated as
1$\sigma$ of each parameter distribution from 1000 mock spectra. All the plots
and parameters derived from the peak-weighted non-parametric analysis can be
seen in Figure 2 and Table 7 of Appendix C.

Using this method we find that all the QSO2s in the sample show ionized
outflows in the form of asymmetric wings. 18/19 QSO2s, including those with
low values of W80, like J0218-00, present blue wings. J0227+01 presents a red
wing instead, in agreement with its positive asymmetry value. The average
value of the outflow velocity computed using this method, considering the 18
QSO2s having blue wings, is vOF=-840$\pm$260 km s-1, while for J0227+01 we
obtain a value of 676$\pm$21 km s-1 (see Tables 2 and 7).

##  4 Physical outflow properties

In Section 3 we described the three methods used here to characterize the
ionized outflows of the QSO2s, and the corresponding results. The parameters
derived from these fits are direct measurements (e.g., FWHM, W80, a, vmed),
but we can use them to derive physical properties, such as the outflow mass,
outflow mass rate, and kinetic power. These are key quantities for
investigating the outflow impact on the surrounding environment. First, we
calculated the mass of the ionized outflows using Eq. 1 (Osterbrock & Ferland,
2006; Carniani et al., 2015; Fiore et al., 2017).

$M_{\rm[OIII]}=4\times 10^{7}M_{\odot}\left(\frac{C}{10^{\rm
O/H}}\right)\left(\frac{L_{\rm[OIII]}}{10^{44}}\right)\left(\frac{10^{3}}{\langle
n_{e}\rangle}\right)$ (1)

where $n_{e}$ is the electronic gas density, C the condensation factor,
L[OIII] the outflowing gas luminosity and O/H = [O/H] - [O/H]⊙ is the oxygen
abundance ratio relative to solar, with [O/H]⊙ $\sim$ 8.86 (Centeno & Socas-
Navarro, 2008). For the whole sample, we assumed that the gas clouds have the
same electron density, leading to C = $<n_{e}^{2}>$ \- $<n_{e}>^{2}$ = 1, and
solar metallicity as in Bessiere et al. (2017), hence O/H = 0.

For ionized outflows, an important source of uncertainty is the electron
density (Harrison et al., 2018; Holden & Tadhunter, 2023). The outflow mass is
inversely proportional to the gas density, which can be estimated from the
ratio of the [SII]$\lambda\lambda$6716,6731 doublet, from the [OIII]/H$\beta$
and [NII]/H$\alpha$ ratios, or using the fainter trans-auroral lines. The
latter technique uses the flux ratios of the [SII]$\lambda\lambda$6716,6731
and [O II]$\lambda\lambda$3726,3729 doublets as well as of the trans-auroral
[O II]$\lambda\lambda$7319,7331 and [SII]$\lambda\lambda$4068,4076 lines. The
trans-auroral ratios have the advantage of being sensitive to higher density
gas than the classical [SII] ratio (Holt et al., 2011; Rose et al., 2018;
Ramos Almeida et al., 2019). Using [SII], Harrison et al. (2014) reported
densities in the range 200-1000 cm-3 for a sample of 16 QSO2s at z$<$0.2, and
Singha et al. (2022) measured outflow densities of $\sim$1900 for type-1 AGN
at 0.01¡z¡0.06. Using the trans-auroral lines, Rose et al. (2018) measured
outflow densities in the range 2500 ¡ ne (cm-3) ¡ 20000, for ULIRGS with 0.06
¡ z ¡ 0.15. Finally, using optical line ratios, Baron & Netzer (2019) reported
densities of $\sim$30000 cm-3 for a sample of 234 nearby type-2 AGN. For this
work, since our spectra do not cover either the [SII] doublet, the trans-
auroral lines, or the [NII] and H$\alpha$ emission lines, we adopted a gas
density of ne=200 cm-3 for all the QSO2s, as in Fiore et al. (2017) and
Speranza et al. (2021). Therefore, the derived outflow masses will most likely
be upper limits.

Since we are measuring only the [OIII] gas, we assume that the total ionized
gas mass of the outflows is three times the [OIII] outflow mass (MOF =
3$\times$M[OIII]; Fiore et al. 2017). The outflow mass rate represents the
instantaneous rate of outflowing gas at the edge of the wind. Assuming an
spherical sector (Fiore et al., 2017; Lutz et al., 2020), it can be defined as
three times the total [OIII] mass divided by the time required to push this
mass through a spherical surface of radius ROF.

$\dot{\rm M}_{\rm OF}=3\leavevmode\nobreak\ {\rm v}_{\rm
OF}\leavevmode\nobreak\ \frac{\rm M_{OF}}{\rm R_{OF}}$ (2)

As there are no integral field observations that we can use to constrain the
outflow radius (ROF), it might be possible to do it using averaged spatial
slices of the broad line wings detected in the long-slit spectra, as in Rose
et al. (2018) and Ramos Almeida et al. (2019). However, this procedure is not
straightforward in the case of the [OIII] lines, because the blueshifted wing
of [OIII]$\lambda$5007 is blended with [OIII]$\lambda$4959, and the
blueshifted wing of the latter is much fainter. Moreover, since for the GMOS-S
spectra used here we measured a median seeing of 0.83 arcsec ($\sim$3.8 kpc at
the average redshift of the sample, z$\sim$0.366), the ionized outflows will
most likely be unresolved, according to other studies of QSO2s at similar
redshifts (Villar-Martín et al., 2011, 2016; Karouzos et al., 2016; Ramos
Almeida et al., 2017, 2019; Speranza et al., 2021). Early studies of quasar-
driven outflows based on optical integral field observations of local QSO2s
reported ionized outflows extending up to $\sim$10-15 kpc (Liu et al., 2013;
Harrison et al., 2014; McElroy et al., 2015). However, later works claimed
that these sizes were overestimated due to seeing smearing effects (Husemann
et al., 2016; Karouzos et al., 2016; Harrison et al., 2018) or to selection
biases (Villar-Martín et al., 2016). More recent studies report ionized
outflows with sizes of $\sim$1-3.4 kpc for local QSO2s (Karouzos et al., 2016;
Ramos Almeida et al., 2017, 2019; Speranza et al., 2022). Hence, here we
assume an outflow radius of 1 kpc for all the QSO2s in our sample. If the
radii are larger than this value, our mass outflow rates will be upper limits,
although more compact outflows have been reported for nearby ULIRGs and AGN
(Tadhunter et al., 2018, 2021; Singha et al., 2022; Winkel et al., 2023).

The outflow velocity (vOF) that we used to compute the outflow mass rate
depends on the method: in the case of the parametric analysis we considered
both vs and vmax (see Table 3 in Appendix A). vs is the velocity of the
intermediate and/or broad components relative to the narrow component(s), and
vmax=vs+2$\sigma$ (see Section 3.1). We compute the outflow mass rate
associated with each of the intermediate and/or broad components and then
added them to compute the total outflow rate (see Table 4).

For the flux-weighted non-parametric analysis, we used as outflow velocities,
vOF, the v50 of the red and blue areas shown in Figures 2 and 2. Then, we
computed two separate outflow rates for each QSO2, red and blue, which we
finally added to compute the total outflow mass rate (see Table 6 in Appendix
B). Finally, for the peak-weighted non-parametric analysis we used 50th
velocity percentile of the residual wings (orange areas in Figures 3 and 2) to
calculate the outflow mass rates (see Table 7 in Appendix C).

Once we estimated the outflow mass rates using Eq. 2, we can calculate the
kinetic power as:

$\displaystyle\dot{\rm E}_{\rm kin}=\frac{1}{2}\leavevmode\nobreak\ \dot{\rm
M}_{\rm OF}\leavevmode\nobreak\ {\rm v}_{\rm OF}^{2}$ (3)

The outflow masses, outflow mass rates, and kinetic powers measured with the
three different methods are shown in Tables 4, 6, 7, and Figure 4. The
uncertainties were computed using propagation of errors.

Figure 4: Histograms of the outflow masses, mass rates, and kinetic powers
computed through the three different methods: parametric (considering either
vs or vmax as the outflow velocities), flux-weighted, and peak-weighted non-
parametric. For easier comparison of the values, in the outflow mass rate
histograms we omitted the largest values of 57 and 151 M⊙ yr-1, obtained for
J0923+01 and J0142+14 using vmax in the parametric method.

The outflow masses computed through the parametric, flux-weighted, and peak-
weighted non-parametric methods have average values of log(MOF)=6.47$\pm$0.50,
6.03$\pm$0.30, and 5.75$\pm$0.32 M⊙, and the medians are 6.46, 5.93, and 5.75
M⊙, respectively (see Table 2). From these results, and from the outflow mass
histograms shown in Figure 4, we conclude that using the parametric method we
derive the largest outflow masses. This is because this with this method we
consider the integrated flux of the intermediate and broad Gaussian components
as outflowing gas, whilst in the case of the non-parametric methods, we just
use the flux included in the tails of the emission lines.

The average outflow mass rates measured from the parametric, flux-weighted,
and peak-weighted non-parametric methods are 2.8$\pm$2.6, 4.0$\pm$4.4, and
1.9$\pm$1.8 M⊙ yr-1, and the medians are 1.8, 2.5, and 1.3 M⊙ yr-1 (see Table
2). The flux-weighted non-parametric method results in higher outflow mass
rates, as a consequence of always including blueshifted and redshifted gas
(see Section 3.2.1) with large velocities. However, all the values measured
from the three methods are between 0.2 and 9 M⊙ yr-1 except for J0142+14,
which has an outflow rate of 20 M⊙ yr-1 measured from the flux-weighted non-
parametric method. It is when we consider the parametric vmax values that we
get the largest outflow mass rates (average value of 23$\pm$35 M⊙ yr-1, with a
median value of 11 M⊙ yr-1; see middle panel of Fig. 4 and Table 2).

Focusing on the kinetic powers, we measure average values of
log($\rm\dot{E}_{kin}$) = 40.5$\pm$1.2, 41.9$\pm$0.6, and 41.4$\pm$0.5 erg s-1
using the three methods. The median values are 40.3, 41.9, and 41.4 erg s-1
(see Table 2). In this case, the lowest values of the kinetic power are those
measured with the parametric method. This is because of its dependency with
v${}^{2}_{\rm OF}$, which is higher in the case of the non-parametric methods
(see Tables 3, 6, and 7). By using the velocity shift of the broad and/or
intermediate components (vs) relative to the narrow component(s) as outflow
velocity, we are deriving lower kinetic powers than when considering the mean
velocities (v50) of the high-velocity tails considered in the non-parametric
methods. If instead of vs we use vmax, as commonly done in the literature
(McElroy et al., 2015; Fiore et al., 2017), the kinetic powers are larger than
the non-parametric ones (average of 42.9$\pm$0.6 erg s-1 and median of 42.9
erg s-1; see Table 2). Finally, the average values of the coupling
efficiencies ($\rm\dot{E}_{kin}$/$\rm L_{BOL}$) derived from for the
parametric, flux-weighted, and peak-weighted non-parametric methods are
(0.014$\pm$0.032)%, (0.080$\pm$0.16)%, and (0.020$\pm$0.025)%, with medians of
0.001%, 0.02%, and 0.01%. These values are one order of magnitude lower than
those reported by other studies of ionized outflows in AGN that have followed
similar considerations (Fiore et al., 2017; Baron & Netzer, 2019; Davies et
al., 2020; Speranza et al., 2021). However, in the case of the parametric
method using vmax (as in Fiore et al. 2017), we obtain much larger values,
with an average of (1.2$\pm$3.0)%, and median of 0.22%. The large value of the
average and its dispersion come from three QSO2s with coupling efficiencies
larger than one: J0142+14, J0332-00, and J0948+00 (see Table 4). In this case,
the median value is more representative of the whole sample.

Figure 5: Outflow mass rate and kinetic power as a function of the AGN
bolometric luminosity. Light and dark blue squares correspond to the values
derived from the parametric method using vs and vmax, respectively. Green and
orange circles are the values from the flux-weighted and peak-weighted non-
parametric methods. The values from Fiore et al. (2017) are shown as grey
triangles for comparison.

From this comparison we conclude that the three adopted methods provide
different physical outflow properties, as a result of the particular
considerations and procedure of each one. However, these differences are
consistent within the uncertainties considering that we are not accounting for
by those associated with the electron density and outflow radius. In Figure 5
we plotted the outflow mass rates and kinetic powers derived from each method
as a function of the bolometric luminosity. The values from the compilation of
Fiore et al. (2017) are also shown for comparison. They also considered a
fixed density of ne=200 cm-3, an outflow radius of ROF=1 kpc, and the same
outflow geometry that we are assuming here. We find that the flux-weighted
non-parametric results lie within the lower values of the outflow rates and
kinetic powers measured by Fiore et al. (2017) for AGN of similar
luminosities, while the peak-weighted and the parametric results are smaller.
However, the parametric results using vmax are the most similar to Fiore et
al. (2017), as expected since they also used vmax to calculate the outflow
physical properties.

##  5 Correlations between outflow properties and galaxy properties

Figure 6: Correlation matrix between the QSO2 outflow properties derived from
the [OIII] emission line and using the flux-weighted non-parametric method,
and their AGN and host galaxies properties. The Spearman’s rank correlation
coefficients ($\rho$) are shown in the top right half of the matrix (blue and
red colors) and the corresponding p-values in the bottom left half (grey
colors).

As previously mentioned, apart from determining the outflow demographics and
corresponding properties of our QSO2 sample, our goal is to evaluate possible
correlations with different AGN and galaxy properties. These properties,
available from Bessiere et al. (2012, 2017) and Ramos Almeida et al. (2013),
include: presence or not of stellar populations younger than 100 Myr (YSP), of
mergers (including interaction stage), density of large-scale environment
(Bgq), and radio luminosity (L5GHz).

To do so we evaluated the matrix correlation, shown in Figure 6, between the
outflow properties derived from the flux-weighted non-parametric analysis (see
Sections 3.2.1 and 4) and the AGN and host galaxy properties (see Section
2.2). From the outflow direct measurements we selected W80, v05, v95, vmed,
and $a$; and from the physical outflow properties, MOF, $\dot{M}_{\rm OF}$,
and $\dot{E}_{\rm kin}$.

In order to quantify the degree of correlation among all the properties, we
computed the Spearman’s rank correlation coefficient ($\rho$) for each
variable pair, which is a non-parametric measurement of the strength and
direction of the statistical dependence that exists between two variables.
Unlike the Pearson correlation coefficient (r), the Spearman’s rank
correlation coeffient does not assume that the data sets are normally
distributed and it assesses how well the relation between both can be
described using a monotonic function. Hence, values of $\rho$ equal to -1 or 1
imply an exact monotonic relationship, with positive values indicating that as
the X variable increases, Y also increases, while negative values imply that
as X increases, Y decreases. In general, absolute values of $\rho$ in the
range 0-0.39 are regarded as a weak or non-existent correlation, 0.40-0.59 as
moderate, 0.6-0.79 as strong, and 0.8-1 as very strong correlation. The $\rho$
values found for our sample are shown in the top right half of Figure 6, with
darker colors indicating stronger correlations.

We also performed a p-value test to verify the strength of the correlations,
which can be seen in the lower left half of the matrix shown in Figure 6. The
p-value measures the probability of observing a correlation coefficient as
extreme or more extreme than the one observed from two datasets of
uncorrelated properties, i.e., it quantifies the probability of observing such
correlation purely by chance. Seeking for a 90$\%$ confidence in our results,
we are setting a significance level of $\alpha$ = 0.1 (100%-confidence level).
This would imply that if p-value$\leq$0.1, we can be confident within a 90$\%$
level about a genuine correlation between two properties. On the contrary, if
p-value¿0.1, the correlation could have arisen by chance, and hence we cannot
conclude that it is significant.

As a sanity check, we first confirmed that correlations between certain
outflow properties exist. For example, $W_{80}$ shows strong correlations with
the outflow projected velocities, $v_{05}$ and $v_{95}$ ($\rho$=-0.91 and
$\rho$=0.81, respectively). This is a consequence of broader emission line
profiles having faster velocities associated with the wings. Similarly,
$v_{05}$ is also strongly correlated with the asymmetry, $a$, with
$\rho$=0.86. This is not the case for $v_{95}$ ($\rho$=-0.23), since most of
the asymmetries in our sample are associated with blueshifted gas. These
outflow parameters also show strong correlations with some of the outflow
physical properties, specially with the outflow mass rates and kinetics
powers.

Regarding the correlations between the outflow and the AGN and host galaxy
properties, we only find moderate correlations between the AGN bolometric
luminosity and the outflow mass and outflow mass rate, both with $\rho$=0.52,
respectively (p-values of 0.021 and 0.023). This implies that more luminous
AGN have more massive ionized outflows, and also higher outflow mass rates
(Cicone et al., 2014; Hainline et al., 2014; Fiore et al., 2017; Revalski et
al., 2018).

We did not find any significant correlations between the outflow properties
and the host galaxy properties. Regarding the presence or not of YSPs, 4 out
of the 5 quasars (80%; J0114+00, J0234-07, J0332-00, and J0948+00) that do not
require of the inclusion of a YSP ¡ 100 Myr to reproduce their optical spectra
show large values of the asymmetry: —a—¿100. On the contrary, only 5 of the 14
QSO2s with such YSPs (36%) have —a—¿100. Since larger asymmetries are
associated with more disrupted gas and faster outflows, this result, despite
the small sample size, might be indicating that recent star formation is being
supressed more efficiently in the QSO2s with the most disrupted kinematics.
Nevertheless, as we noted above, there are also QSO2s with disrupted
kinematics showing YSPs.

Regarding the optical morphologies of the QSO2s, 3 out of the 4 galaxies that
do not show any evidence for mergers/interactions (75%; J0332-00, J0234-07,
J0114+00, and J0948+00) show —a—¿100. Considering the merging QSO2s (15/19),
we do not find any trend between the outflow properties and the stage of the
interaction either (i.e., pre-coalescence or post-coalescence; Ramos Almeida
et al. 2011; Bessiere et al. 2012). This would imply that the presence of
outflowing gas and/or disrupted kinematics on the spatial scales that our
spectra are probing is related to the AGN and not to the mergers. Considering
this, it is not surprising that we do not find any correlation between the
outflow properties and the large scale environment either. In particular, we
looked at the spatial clustering amplitudes (B${}_{\rm gq}^{\rm av}$) from
Ramos Almeida et al. (2013). The QSO2s with most disrupted kinematics do not
show any preference for denser/sparser environments.

Finally, we also looked at possible correlations between the outflow
properties and the radio luminosity of the QSO2s. Indeed, Mullaney et al.
(2013) and Zakamska & Greene (2014) found a connection between the width of
the [OIII] profiles and L1.4GHz. The radio luminosity is a property that can
be associated with star formation and/or nuclear activity (Jarvis et al. 2021;
Bessiere et al. in prep.). For our QSO2s, we do not find any correlation
between L5GHz and any of the outflow properties here considered. Here we are
using the integrated luminosities at 5 GHz from Bessiere et al. (2012),
measured from 5 arcsec resolution FIRST data, and we also checked that the
results are the same when we use peak luminosities instead. The lack of
correlation might be due to the limited range of radio luminosities that our
sample is probing: 22.1 - 24.7 erg s-1, with an average value of
22.80$\pm$0.80 erg s-1 and median of 22.35 erg s-1 (see Table 1 and Section
6.2).

##  6 Discussion

In this work we characterized the ionized outflow properties of a sample of 19
QSO2s at redshift 0.3¡z¡0.41 using three different analysis methods. We
compared the results, and looked for correlations between the outflow
properties and various AGN and galaxy properties. Here we discuss these
results and put them in context with others from the literature.

###  6.1 Demographics and energetics of ionized outflows

We found signatures of ionized outflows in 18 of the 19 QSO2s using the
parametric method (Section 3.1), based on the presence of at least one
Gaussian component with FWHM¿800 km s-1 and generally blueshifted, as in
Villar-Martín et al. (2011, 2016). Using the peak-weighted non-parametric
method, we find that all the QSO2s have signatures of outflowing gas: 18 in
the form of blueshifted asymmetries, and one redshifted. This implies an
outflow incidence rate of $\sim$95-100%, similar to the results found in other
QSO2s studies (Villar-Martín et al., 2011, 2016; Fischer et al., 2018;
Dall’Agnol de Oliveira et al., 2021) and higher than those generally reported
for low-to-intermediate luminosity AGN (see e.g., Riffel et al. 2023 and
references therein).

Some of the QSO2s show extreme [OIII] kinematics, as for example J0924+01 (see
Figures 1-3). From the flux-weighted non-parametric analysis of all the QSO2s,
we find emission line widths ranging from 530 to 1645 km s-1 (average
W80=940$\pm$280 km s-1) and asymmetry values ranging from -235 to 50 km s-1
(average a=-120$\pm$130 km s-1). Regarding the outflow velocities, the fastest
that we measure come from the flux-weighted parametric method (average
vOF=-1120$\pm$510 km s-1) and from the parametric when we compute the maximum
velocity (average vmax=-1800$\pm$1400 km s-1). These velocities are typical of
AGN-driven ionized outflows detected in quasars with these bolometric
luminosities (Mullaney et al., 2013; Zakamska & Greene, 2014).

We computed outflow physical properties, such as the outflow mass, outflow
mass rate, and kinetic rates, from the direct outflow measurements derived
through each kinetic analysis method (see Section 3). This quantities are key
for investigating the outflow impact on the surrounding environment of their
hosts. From the definition of these quantities (see Section 4), it is clear
that both the electron density and the outflow radius play a critical role in
their determination, alongside with the outflow flux and velocity derived via
each method. Since with our data we cannot constrain either ne or ROF, we
assumed a gas density of ne=200 cm-3 and a radius of 1 kpc for all the QSO2s,
as in Fiore et al. (2017). By assuming these values, we can just focus on the
differences that are inherent to the method used to measure the outflow flux
and velocity.

From our analysis of the outflow energetics using the three different methods
we find that, on average, the parametric method results in the highest outflow
masses (log MOF(M⊙)=6.47$\pm$0.50), since it considers the integrated flux of
the broad and intermediate components. The flux-weighted non-parametric method
produces larger outflow mass rates and kinetic powers (ṀOF=4.0$\pm$4.4 M⊙ yr-1
and Ėkin=41.9$\pm$0.6 erg s-1) than the peak-weighted non-parametric method
and the parametric method using vs (see Figure 4 and Table 2). This happens
because by definition it always includes a contribution from both the blue and
red emission line wings. This effect is more pronounced in the kinetic powers,
because of its dependence on the outflow velocity, $\rm\dot{E}$kin $\propto$
$\rm\dot{M}$OFv${}_{\rm OF}^{2}$ $\propto$ v${}_{\rm OF}^{3}$. Nevertheless,
we find the highest values of the outflow mass rate and kinetic power when we
use the parametric method and vmax instead of vs (ṀOF=23$\pm$35 M⊙ yr-1 and
log(Ėkin)=42.9$\pm$0.6 erg s-1).

A comparison between the mass outflow rates and kinetic powers derived from
the three methods and the values reported by Fiore et al. (2017) for a sample
of 94 AGN is shown in Figure 5. The values derived from the parametric vmax
method are fully consistent with Fiore et al. (2017), as expected since they
used the same velocity definition to measure the outflow physical properties.
However, we argue that these maximum velocities are not representative of
outflowing gas, since they only trace the highest velocity gas instead of the
bulk of the outflowing gas mass. This bias the results towards large values of
the outflow physical properties. Other works using higher electron densities
for the winds and/or lower outflow velocities such as vs report outflow
properties that are from one to three orders of magnitude lower (Holt et al.,
2011; Villar-Martín et al., 2016; Rose et al., 2018; Spence et al., 2018;
Davies et al., 2020; Holden et al., 2023). Besides, Davies et al. (2020)
pointed out that the relatively low scatter find by Fiore et al. (2017) when
plotting the data shown in Figure 5, despite the wide range of luminosity, is
partly due to the adoption of common values of the outflow density and radius.

The median coupling efficiencies that we measure for the outflows using the
three methods, are 0.001%, 0.02%, and 0.01%, and when we use the parametric
method and vmax, it goes up to 0.22%. The former three values are lower than
those reported in recent literature (Fiore et al., 2017; Baron & Netzer, 2019;
Speranza et al., 2021), while the parametric vmax value is similar. For
example, both Fiore et al. (2017) and Speranza et al. (2021) reported a
coupling efficiency of $\sim$0.2% for a sample of AGN at z¡0.5 and
log(LBOL)$\sim$45.5 erg s-1, and of 3CR radio galaxies at z¡0.3 with
log(LBOL)=42-46 erg s-1, respectively. Again, this is a consequence of using
maximum outflow velocities and assuming a low value of the density.

###  6.2 Lack of correlations between the nuclear ionized outflow properties
and galaxy properties

To evaluate the outflow impact on star formation and their possible relation
with other AGN and/or host galaxy properties, in Section 5 we investigated the
correlation matrix using results from the flux-weighted non-parametric method.

We only found moderate correlations between the AGN bolometric luminosity and
the outflow masses and mass rates, both with a Spearman coefficient of $\rho$
= 0.52. More massive and powerful outflows are usually found in luminous AGN
galaxies (Hainline et al., 2014; Fiore et al., 2017; Revalski et al., 2018).
Indeed, since here we are considering AGN bolometric luminosities derived from
the extinction-corrected [OIII] luminosities, it is not surprising to find
correlations, albeit weak, with the outflow masses measured from the [OIII]
emission line. Likewise, high outflow mass rates are expected for luminous AGN
(Fiore et al., 2017), although here we only find a modest correlation. This
can be a consequence of the relatively small luminosity range probed by our
sample, of log(LBOL)=44.9-46.7 erg s-1.

We have not found any significant correlations between the outflow and the
host galaxies properties here considered. Since here we are assuming fixed
values of the outflow density and radius for all the targets, the outflow
physical quantities are not precise. Therefore, the different correlations
that we evaluate here might change if individual radii and densities would be
measured. This is not the case of the direct outflow measurements, such as the
velocity, W80, asymmetry, etc. The outflow density is one of the parameters
having the strongest impact in the derived outflow physical quantities. The
outflow mass rate and kinetic power vary by one order of magnitude when we
assume a density of 2000 cm-3 instead of 200 cm-3. However, we find the same
lack of correlation between the outflow properties derived from the flux-
weighted non-parametric method and different AGN and host galaxy properties
when precise density measurements are used for the individual targets in the
QSOFEED sample of QSO2s ( Bessiere et al. in prep.).

Regarding the impact of the outflows on recent star formation, we find that 4
of the 5 QSO2s lacking a YSP with age ¡100 Myr (Bessiere et al., 2017) present
disturbed kinematics with large asymmetry values (—a—¿100). On the other hand,
only 5 of the 14 QSO2s with a YSP present large asymmetry values. Despite the
small size of our sample, these results might be indicating that recent star
formation (i.e., the one having the same dynamical timescales as the outflows)
is being suppressed more efficiently in the QSO2s with most disrupted
kinematics. Nevertheless, there are also QSO2s with disrupted kinematics that
have YSPs. This could be due either to positive feedback (Klamer et al., 2004;
Gaibler et al., 2012; Zubovas et al., 2013; Cresci et al., 2015), to the
different spatial scales considered for the stellar population analysis
($\sim$8 kpc) and for the outflow measurements ($\sim$3.9 kpc), and/or to the
time that the winds might need to supress star formation. Using integral field
spectroscopic data of the QSO2 Mrk 34, Bessiere & Ramos Almeida (2022) showed
that both positive and negative feedback can simultaneously occur in different
parts of same galaxy, depending on the amount of energy and turbulence that
the outflows inject in the ISM. This illustrates the complexity of the
outflow-ISM interplay, and evidences the importance of using spatially
resolved studies of AGN to evaluate the impact of feedback.

Given that interactions between galaxies disrupt the stellar and gas content
of the galaxies involved, we could expect higher gas turbulence in mergers
than in undisturbed galaxies. However, we do not find any trend between the
[OIII] kinematics and the optical morphologies of the QSO2s or with their
environment. This is most likely due to the different timescales involved: 1-3
Gyr for the mergers (Conselice et al., 2003) and 1-100 Myr for the AGN-driven
outflows (Zubovas & King, 2016). A major or minor merger can efficiently
transport gas towards the center the galaxy during hundreds of Myr, and this
gas supply can be intermittent, leading to different phases of nuclear
activity (King & Nixon, 2015). This makes it challenging to look for
correlations between the large-scale galaxy morphology and the AGN-driven
outflows.

Finally, we investigated the role of jets in driving or contributing to drive
outflows in our QSO2s. We do not find any significant correlation between the
outflow properties and either the integrated or peak 5 GHz luminosities from
FIRST. Using spectra from SDSS, Mullaney et al. (2013) concluded that the
width of the [OIII]$\lambda$5007 line shows a maximum in AGN with radio
luminosities of log(L1.4GHz)=23-25 W Hz-1, i.e., moderate radio luminosities
as those of our QSO2s. The lack of correlation between these parameters is
probably due to the small radio luminosity range probed by our QSO2s, of
22.1-24.7 W Hz-1. However, the dominant origin of this radio emission is still
a matter of on-going debate (Zakamska & Greene, 2014), as it might be produced
by non-thermal AGN emission (Jarvis et al., 2019), star formation  (Bessiere
et al. in prep.), and/or shocks induced by the quasar winds/outflows (Fischer
et al., 2023).

##  7 Conclusions

We characterized the ionized gas kinematics and energetics of a sample of 19
QSO2s at 0.3¡z¡0.41, using three different methods, parametric and non-
parametric, to analyze the nuclear ($\sim$3.9 kpc) [OIII] emission-line
profiles. The main conclusions of the work are the following.

  * •

We detect ionized gas outflows in the form of asymmetric and broad emission
line profiles in 95-100% of the sample using the three methods. 18 of the 19
QSO2s show [OIII] profiles with blueshifted wings, whilst the other one shows
a redshifted wing.

  * •

The average physical outflow properties (e.g., outflow mass, mass rate, and
kinetic energy) that we derived from the three methods are consistent within
the errors. The parametric method results in the highest outflow masses, and
the flux-weighted non-parametric and specially the parametric method using
vmax provide the highest mass outflow rates and kinetic powers.

  * •

We measure outflow mass rates ranging between 0.2 and 20 M⊙ yr-1 and kinetic
powers between 38.3 and 42.9 erg s-1 for the QSO2s. For the parametric method
using vmax the highest values go up to 151 M⊙ yr-1 and 44.0 erg s-1. These
values are most likely upper limits, considering that we assumed fixed values
of 200 cm-3 and 1 kpc for the outflow density and radius, respectively.

  * •

We find a modest correlation between the AGN bolometric luminosity and the
outflow mass and mass rate, but we do not find any correlation with the host
galaxy properties here considered.

  * •

Four of the five QSO2s lacking a YSP with age ¡100 Myr present disturbed
kinematics with large asymmetry values (—a—¿100). On the other hand, only 5 of
the 14 QSO2s with a YSP present large asymmetry values. Despite the small
sample size, these results might be indicating that recent star formation is
being suppressed more efficiently in the QSO2s with most disrupted kinematics.

Here we showed for the first time a comparison between outflow measurements
using three different methods commonly used in the literature. By assuming a
fix outflow density and radius, we can focus on the differences introduced by
how the flux and velocity are calculated. We conclude that, although the
average physical outflow properties derived from the three methods are
consistent within the errors, the commonly adopted parametric measurements
using maximum outflow velocities provide the highest values, not
representative of the average outflow velocity. Finally, we argue that the
lack of correlations between the outflow and the AGN and galaxy properties
here considered is most likely due to the small luminosity ranges probed by
our sample, and to the different timescales of the outflows and galaxy-wide
properties.

###### Acknowledgements.

CRA and GS acknowledge financial support from the European Union’s Horizon
2020 research and innovation programme under Marie Skłodowska-Curie grant
agreement No 860744 (BiD4BESt). CRA, GS, JAP, and PSB acknowledge the project
“Feeding and feedback in active galaxies”, with reference
PID2019-106027GB-C42, funded by MICINN-AEI/10.13039/501100011033. CRA also
acknowledges the project “Quantifying the impact of quasar feedback on galaxy
evolution”, with reference EUR2020-112266, funded by MICINN-
AEI/10.13039/501100011033 and the European Union NextGenerationEU/PRTR. CRA
thanks the Kavli Institute for Cosmology of the University of Cambridge for
their hospitality while working on this paper, and the IAC Severo Ochoa
Program for the corresponding financial support. The authors thank the
anonymous referee for useful and constructive suggestions.

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##  Appendix A Parametric analysis

In Figure 7 we include all the fits performed using the parametric method
(except the one shown in Figure 1), which is described in full in Section 3.1.
The parameters of the kinematic components fitted to the [OIII] lines are
listed in Table 3, and the outflow physical properties in Table 4.

Figure 7: Parametric fits of the [OIII] doublet for the whole QSO2 sample.
Figures are identic al to the example case in Figure 1.

Figure 1: continued

Figure 1: continued Table 3: Results from the parametric fits of the
$[OIII]\lambda$5007 line.

Component | Fλ | FWHM | vs | L[OIII] | Luminosity
---|---|---|---|---|---
| (erg cm-2 s-1) | (km s-1) | (km s-1) | (erg s-1) | fraction
J0025-10
n1 | (3.76$\pm$0.12)$\cdot$10-15 | 700$\pm$11 (280) | -33.8$\pm$3.0 | (1.109$\pm$0.035)$\cdot$1042 | 0.655$\pm$0.020
n2 | (1.348$\pm$0.065)$\cdot$10-15 | 408.0$\pm$7.3 (280) | 54.9$\pm$2.5 | (3.98$\pm$0.19)$\cdot$1041 | 0.235$\pm$0.011
i | (6.3$\pm$1.4)$\cdot$10-16 | 1540$\pm$110 (280) | -73$\pm$25 | (1.87$\pm$0.42)$\cdot$1041 | 0.110$\pm$0.025
J0114+00
n1 | (4.30$\pm$0.25)$\cdot$10-15 | 606$\pm$22 (120) | 21.5$\pm$9.9 | (2.27$\pm$0.13)$\cdot$1042 | 0.680$\pm$0.040
n2 | (7.65$\pm$0.88)$\cdot$10-16 | 210$\pm$15 (120) | -41.8$\pm$6.5 | (4.05$\pm$0.47)$\cdot$1041 | 0.121$\pm$0.014
i | (1.25$\pm$0.39)$\cdot$10-15 | 1560$\pm$280 (120) | -477$\pm$180 | (6.6$\pm$2.0)$\cdot$1041 | 0.198$\pm$0.061
J0123+00
n1 | (2.29$\pm$0.19)$\cdot$10-15 | 437.0$\pm$7.7 (240) | 142.0$\pm$9.2 | (1.28$\pm$0.11)$\cdot$1042 | 0.404$\pm$0.033
n2 | (2.50$\pm$0.19)$\cdot$10-15 | 505$\pm$17 (240) | -150$\pm$16 | (1.40$\pm$0.11)$\cdot$1042 | 0.442$\pm$0.034
i | (8.74$\pm$1.3)$\cdot$10-16 | 1440$\pm$83 (240) | -94$\pm$19 | (4.90$\pm$0.75)$\cdot$1041 | 0.154$\pm$0.024
J0142+14
n | (7.36$\pm$0.30)$\cdot$10-15 | 493$\pm$15 (120) | 0.0$\pm$3.5 | (3.89$\pm$0.16)$\cdot$1042 | 0.405$\pm$0.016
i | (1.081$\pm$0.077)$\cdot$10-14 | 1590$\pm$56 (120) | -85$\pm$15 | (5.72$\pm$0.41)$\cdot$1042 | 0.595$\pm$0.042
J0217-00
n1 | (8.3$\pm$3.2)$\cdot$10-16 | 515$\pm$91 (310) | -170$\pm$58 | (3.3$\pm$1.3)$\cdot$1041 | 0.229$\pm$0.087
n2 | (7.3$\pm$3.0)$\cdot$10-16 | 581$\pm$110 (310) | 218$\pm$120 | (2.9$\pm$1.2)$\cdot$1041 | 0.202$\pm$0.084
i | (2.06$\pm$0.19)$\cdot$10-15 | 1530$\pm$40 (310) | -295$\pm$32 | (8.16$\pm$0.77)$\cdot$1041 | 0.569$\pm$0.053
J0217-01
n | (1.13$\pm$0.29)$\cdot$10-15 | 538$\pm$82 (280) | 0$\pm$19 | (5.5$\pm$1.4)$\cdot$1041 | 0.51$\pm$0.13
i | (9.47$\pm$5.7)$\cdot$10-16 | 1380$\pm$340 (280) | -100$\pm$180 | (4.6$\pm$2.7)$\cdot$1041 | 0.43$\pm$0.26
r | (1.3$\pm$2.1)$\cdot$10-16 | 460$\pm$200 (280) | 700$\pm$200 | (7$\pm$10)$\cdot$1040 | 0.061$\pm$0.094
J0218-00
n1 | (1.8$\pm$0.2)$\cdot$10-15 | 507$\pm$21 (280) | 51$\pm$16 | (8.54$\pm$0.95)$\cdot$1041 | 0.804$\pm$0.089
n2 | (4.4$\pm$2.1)$\cdot$10-16 | 611$\pm$58 (280) | -250$\pm$110 | (2.1$\pm$1.0)$\cdot$1041 | 0.196$\pm$0.096
J0227+01
n1 | (4.5$\pm$2.4)$\cdot$10-16 | 414$\pm$51 (220) | -14.2$\pm$8.0 | (2.0$\pm$1.1)$\cdot$1041 | 0.184$\pm$0.097
n2 | (1.43$\pm$0.32)$\cdot$10-15 | 593$\pm$30 (220) | 6.4$\pm$8.0 | (6.4$\pm$1.4)$\cdot$1041 | 0.59$\pm$0.13
i | (5.7$\pm$1.0)$\cdot$10-16 | 1160$\pm$55 (220) | 133$\pm$24 | (2.55$\pm$0.45)$\cdot$1041 | 0.231$\pm$0.041
J0234-07
n1 | (2.059$\pm$0.031)$\cdot$10-15 | 396.0$\pm$2.0 (320) | 63.68$\pm$0.87 | (6.4$\pm$0.095)$\cdot$1041 | 0.4570$\pm$0.0070
n2 | (8.55$\pm$0.33)$\cdot$10-16 | 590$\pm$13 (320) | -228$\pm$11 | (2.66$\pm$0.10)$\cdot$1041 | 0.1900$\pm$0.0070
i | (1.587$\pm$0.048)$\cdot$10-15 | 1500$\pm$18 (320) | -189.0$\pm$4.1 | (4.94$\pm$0.15)$\cdot$1041 | 0.353$\pm$0.011
J0249+00
n | (3.453$\pm$0.049)$\cdot$10-15 | 467.1$\pm$3.7 (240) | 0.00$\pm$0.59 | (2.043$\pm$0.029)$\cdot$1042 | 0.5700$\pm$0.0080
i | (2.18$\pm$0.11)$\cdot$10-15 | 1178$\pm$38 (240) | -77.2$\pm$9.2 | (1.289$\pm$0.065)$\cdot$1042 | 0.360$\pm$0.018
b | (4.23$\pm$0.96)$\cdot$10-16 | 3100$\pm$380 (240) | -950$\pm$180 | (2.50$\pm$0.57)$\cdot$1041 | 0.070$\pm$0.016
J0320+00
n1 | (2.8$\pm$2.4)$\cdot$10-16 | 710$\pm$110 (250) | -141$\pm$96 | (1.4$\pm$1.2)$\cdot$1041 | 0.22$\pm$0.19
n2 | (3.0$\pm$2.3)$\cdot$10-16 | 500$\pm$120 (250) | -116$\pm$54 | (1.53$\pm$1.2)$\cdot$1041 | 0.23$\pm$0.18
i1 | (3.4$\pm$2.4)$\cdot$10-16 | 840$\pm$110 (250) | -141$\pm$96 | (1.8$\pm$1.2)$\cdot$1041 | 0.27$\pm$0.19
i2 | (3.4$\pm$2.3)$\cdot$10-16 | 1150$\pm$120 (250) | -116$\pm$54 | (1.8$\pm$1.2)$\cdot$1041 | 0.27$\pm$0.18
r | (1.7$\pm$1.1)$\cdot$10-17 | 246.0$\pm$0.0 (250) | 1260$\pm$24 | (8.7$\pm$5.4)$\cdot$1039 | 0.0130$\pm$0.0080
J0332-00
n1 | (2.56$\pm$0.50)$\cdot$10-16 | 293$\pm$30 (170) | -70.2$\pm$6.8 | (8.0$\pm$1.5)$\cdot$1040 | 0.072$\pm$0.014
n2 | (1.22$\pm$0.22)$\cdot$10-15 | 604$\pm$26 (170) | 30$\pm$20 | (3.79$\pm$0.67)$\cdot$1041 | 0.343$\pm$0.061
i | (1.65$\pm$0.27)$\cdot$10-15 | 1050$\pm$46 (170) | -116$\pm$14 | (5.13$\pm$0.83)$\cdot$1041 | 0.464$\pm$0.075
b | (4.33$\pm$0.51)$\cdot$10-16 | 4750$\pm$300 (170) | -1140$\pm$150 | (1.35$\pm$0.16)$\cdot$1041 | 0.122$\pm$0.014
J0334+00
n1 | (1.06$\pm$0.17)$\cdot$10-15 | 645$\pm$28 (210) | -47$\pm$11 | (6.3$\pm$1.0)$\cdot$1041 | 0.234$\pm$0.038
n2 | (3.36$\pm$0.11)$\cdot$10-15 | 411.0$\pm$3.7 (210) | 9.47$\pm$0.94 | (1.974$\pm$0.064)$\cdot$1042 | 0.739$\pm$0.024
i | (1.22$\pm$0.44)$\cdot$10-16 | 1310$\pm$230 (210) | -490$\pm$210 | (7.16$\pm$2.6)$\cdot$1040 | 0.027$\pm$0.0
J0848-01
n | (8.37$\pm$0.83)$\cdot$10-16 | 426$\pm$21 (210) | 0.0$\pm$3.7 | (3.45$\pm$0.34)$\cdot$1041 | 0.414$\pm$0.041
i | (1.19$\pm$0.17)$\cdot$10-15 | 899$\pm$45 (210) | -41.0$\pm$8.6 | (4.89$\pm$0.70)$\cdot$1041 | 0.586$\pm$0.084
J0904-00
n1 | (4.43$\pm$0.13)$\cdot$10-15 | 376.0$\pm$5.3 (170) | 14.2$\pm$1.0 | (1.86$\pm$0.054)$\cdot$1042 | 0.652$\pm$0.019
n2 | (1.98$\pm$0.26)$\cdot$10-15 | 744$\pm$29 (170) | -63$\pm$13 | (8.3$\pm$1.1)$\cdot$1041 | 0.291$\pm$0.038
i | (3.86$\pm$0.81)$\cdot$10-16 | 940$\pm$180 (170) | -949$\pm$91 | (1.62$\pm$0.34)$\cdot$1041 | 0.057$\pm$0.012
J0923+01
n | (4.3$\pm$1.6)$\cdot$10-16 | 311$\pm$32 (220) | 0$\pm$11 | (2.26$\pm$0.84)$\cdot$1041 | 0.071$\pm$0.027
i1 | (4.20$\pm$0.97)$\cdot$10-15 | 890$\pm$27 (220) | -98.6$\pm$4.5 | (2.18$\pm$0.38)$\cdot$1042 | 0.69$\pm$0.12
i2 | (1.4$\pm$1.5)$\cdot$10-15 | 1890$\pm$250 (220) | -61$\pm$24 | (7.5$\pm$7.8)$\cdot$1041 | 0.24$\pm$0.25
J0924+01
n | (1.128$\pm$0.014)$\cdot$10-15 | 696.0$\pm$6.1 (290) | 0.0$\pm$2.1 | (5.64$\pm$0.07)$\cdot$1041 | 0.556$\pm$0.007
i | (8.99$\pm$0.29)$\cdot$10-16 | 2010$\pm$36 (290) | -593$\pm$26 | (4.50$\pm$0.14)$\cdot$1041 | 0.444$\pm$0.014
J0948+00
n1 | (7.32$\pm$0.97)$\cdot$10-16 | 489$\pm$26 (270) | 117.0$\pm$7.6 | (2.52$\pm$0.33)$\cdot$1041 | 0.245$\pm$0.032
n2 | (2.09$\pm$0.15)$\cdot$10-15 | 794$\pm$10 (270) | -67$\pm$11 | (7.20$\pm$0.50)$\cdot$1041 | 0.698$\pm$0.049
b | (1.70$\pm$0.29)$\cdot$10-16 | 4320$\pm$420 (270) | -980$\pm$270 | (5.86$\pm$0.98)$\cdot$1040 | 0.057$\pm$0.010
J2358-00
n | (5.127$\pm$0.039)$\cdot$10-15 | 567.0$\pm$2.7 (350) | 0.00$\pm$0.64 | (2.93$\pm$0.022)$\cdot$1042 | 0.7120$\pm$0.0050
i | (2.075$\pm$0.099)$\cdot$10-15 | 1440$\pm$26 (350) | -85.2$\pm$6.3 | (1.18$\pm$0.051)$\cdot$1042 | 0.288$\pm$0.012

333Column 1 indicates whether a component is narrow (n), intermediate (i),
broad (b), or red (r) according to the definition indicated in Section 3.1.
Columns 2, 3, 4, and 5 are the integrated flux, FWHM (with the instrumental
width indicated between parenthesis), velocity shift relative to systemic, and
integrated luminosity of each component. Column 6 indicates the fraction of
each component to the total luminosity of the line.

Table 4: Outflow physical properties resulting from the parametric method. |  |  | vs |  |  | vmax |
---|---|---|---|---|---|---|---
Name | Log(MOF) | $\dot{\rm\mathbb{M}}_{\rm OF}$ | Log($\dot{\rm\mathbb{E}}_{\rm kin}$) |  $\dot{\rm\mathbb{E}}_{\rm kin}$ / $\rm\mathbb{L}_{\rm BOL}$ | $\dot{\rm\mathbb{M}}_{\rm OF}$ | Log($\dot{\rm\mathbb{E}}_{\rm kin}$) |  $\dot{\rm\mathbb{E}}_{\rm kin}$ / $\rm\mathbb{L}_{\rm BOL}$
| (M⊙) | (M⊙ yr -1) | (erg s-1) | (%) | (M⊙ yr -1) | (erg s-1) | (%)
J0025-10 | 6.05$\pm$0.12 | 0.246$\pm$0.099 | 38.62$\pm$0.46 | (1.4$\pm$1.5)$\cdot$ 10-5 | 4.8$\pm$1.2 | 42.5$\pm$0.15 | (9.4$\pm$3.3)$\cdot$ 10-2
J0114+00 | 6.59$\pm$0.16 | 5.7$\pm$2.7 | 41.66$\pm$0.56 | (3.3$\pm$4.2)$\cdot$ 10-2 | 6.9$\pm$4.3 | 41.9$\pm$0.88 | (6$\pm$12)$\cdot$ 10-2
J0123+00 | 6.459$\pm$0.071 | 0.86$\pm$0.21 | 39.39$\pm$0.26 | (4.1$\pm$2.4)$\cdot$ 10-5 | 11.8$\pm$2.0 | 42.8$\pm$0.1 | (1.07$\pm$0.26)$\cdot$ 10-1
J0142+14 | 7.535$\pm$0.032 | 9.2$\pm$1.8 | 40.36$\pm$0.24 | (5.2$\pm$2.8)$\cdot$ 10-4 | 151.0$\pm$12.0 | 44.0$\pm$0.058 | (2.22$\pm$0.29)
J0217-00 | 6.688$\pm$0.039 | 4.49$\pm$0.64 | 41.11$\pm$0.15 | (2.42$\pm$0.84)$\cdot$ 10-3 | 23.9$\pm$2.3 | 43.3$\pm$0.056 | (3.69$\pm$0.46)$\cdot$ 10-1
J0217-01 | 6.46$\pm$0.33 | 0.9$\pm$1.4 | 39.7$\pm$1.4 | (4$\pm$13)$\cdot$ 10-4 | 9.8$\pm$7.6 | 42.67$\pm$0.54 | (3.4$\pm$4.2)$\cdot$ 10-1
J0227+01 | 6.187$\pm$0.082 | 0.62$\pm$0.16 | 39.53$\pm$0.26 | (1.43$\pm$0.85)$\cdot$ 10-4 | 5.19$\pm$0.98 | 42.3$\pm$0.1 | (8.5$\pm$2.0)$\cdot$ 10-2
J0234-07 | 6.472$\pm$0.013 | 1.719$\pm$0.063 | 40.286$\pm$0.030 | (1.70$\pm$0.12)$\cdot$ 10-3 | 13.32$\pm$0.42 | 42.956$\pm$0.019 | (7.92$\pm$0.34)$\cdot$ 10-1
J0249+00 | 6.965$\pm$0.024 | 6.1$\pm$1.3 | 42.07$\pm$0.27 | (3.8$\pm$2.3)$\cdot$ 10-2 | 25.5$\pm$1.5 | 43.967$\pm$0.044 | (2.95$\pm$0.30)$\cdot$ 10-1
J0320+00 | 6.33$\pm$0.26 | 0.80$\pm$0.59 | 39.80$\pm$0.62 | (6$\pm$10)$\cdot$ 10-4 | 6.3$\pm$3.2 | 42.31$\pm$0.32 | (2.7$\pm$2.0)$\cdot$ 10-1
J0332-00 | 6.588$\pm$0.058 | 3.90$\pm$0.53 | 42.06$\pm$0.17 | (1.34$\pm$0.51)$\cdot$ 10-1 | 22.4$\pm$2.5 | 44.045$\pm$0.095 | 12.8$\pm$2.8
J0334+00 | 5.63$\pm$0.22 | 0.58$\pm$0.36 | 40.61$\pm$0.77 | (1.3$\pm$2.2)10-3 | 2.10$\pm$0.84 | 42.22$\pm$0.30 | (5.2$\pm$3.6)10-2
J0848-01 | 6.464$\pm$0.062 | 0.36$\pm$0.09 | 38.27$\pm$0.29 | (1.34$\pm$0.90)$\cdot$ 10-5 | 7.24$\pm$1.1 | 42.169$\pm$0.086 | (1.05$\pm$0.21)$\cdot$ 10-1
J0904-00 | 5.99$\pm$0.10 | 2.84$\pm$0.70 | 41.91$\pm$0.16 | (2.47$\pm$0.93)$\cdot$ 10-2 | 5.2$\pm$1.3 | 42.69$\pm$0.18 | (1.49$\pm$0.63)$\cdot$ 10-1
J0923+01 | 7.24$\pm$0.14 | 4.7$\pm$1.2 | 40.12$\pm$0.11 | (4.7$\pm$1.2)$\cdot$ 10-4 | 57$\pm$24 | 43.46$\pm$0.39 | (10.0$\pm$9.0)$\cdot$ 10-4
J0924+01 | 6.432$\pm$0.014 | 4.89$\pm$0.29 | 41.733$\pm$0.065 | (1.14$\pm$0.17)$\cdot$ 10-3 | 19.04$\pm$0.71 | 43.502$\pm$0.027 | (6.68$\pm$0.42)$\cdot$ 10-2
J0948+00 | 5.544$\pm$0.075 | 1.03$\pm$0.34 | 41.50$\pm$0.44 | (1.9$\pm$2.0)$\cdot$ 10-2 | 4.94$\pm$0.99 | 43.524$\pm$0.15 | 2.08$\pm$0.72
J2358-00 | 6.851$\pm$0.020 | 1.84$\pm$0.16 | 39.617$\pm$0.099 | (4.6$\pm$1.0)$\cdot$ 10-5 | 28.5$\pm$1.3 | 43.184$\pm$0.029 | (1.68$\pm$0.11)$\cdot$ 10-1

##  Appendix B Flux-weighted non-parametric analysis

In Figure 2 we include all the fits performed using the flux-weighted non-
parametric method (except the one shown in Figure 2), which is described in
full in Section 3.2.1. The corresponding parameters from the fits of the
[OIII] line are listed in Table 5, and the outflow physical properties in
Table 6.

Figure 2: Flux-weighted non-parametric fits of the [OIII]$\lambda$5007 Å
emission line shown for the whole sample. Figures are identical to the example
in Figure 2.

Figure 1: continued Table 5: Results from the flux-weighted non-parametric fits of the $[OIII]\lambda$5007 line. Name | $\rm\mathbb{\lambda}_{c}$ | W80 |  $\rm\mathbb{\Delta}$V | V05 | V95 | Vmed | a
---|---|---|---|---|---|---|---
| (Å) | (km s-1) | (km s-1) | (km s-1) | (km s-1) | (km s-1) | (km s-1)
J0025-10 | 6528.139$\pm$0.014 | 770.4$\pm$2.8 | -66.0$\pm$3.3 | -589.3$\pm$4.9 | 457.2$\pm$3.0 | -30.43$\pm$0.83 | -51.0$\pm$2.2
J0114+00 | 6955.832$\pm$0.099 | 875$\pm$51 | -194$\pm$65 | -870$\pm$130 | 479$\pm$23 | -2.3$\pm$6.2 | -146$\pm$47
J0123+00 | 7002.574$\pm$0.043 | 742.5$\pm$3.4 | -85.5$\pm$4.2 | -581.3$\pm$6.5 | 410.7$\pm$4.2 | -45.2$\pm$1.8 | -48.7$\pm$2.4
J0142+14 | 6958.925$\pm$0.074 | 1303$\pm$28 | -85$\pm$16 | -1015$\pm$30 | 845$\pm$29 | -27.0$\pm$4.5 | -111$\pm$22
J0217-00 | 6724.11$\pm$0.27 | 1363$\pm$15 | -162$\pm$22 | -1069$\pm$29 | 746$\pm$22 | -21$\pm$12 | -188$\pm$15
J0217-01 | 6884.24$\pm$0.32 | 990$\pm$120 | -97$\pm$76 | -820$\pm$160 | 623$\pm$97 | -24$\pm$17 | -93$\pm$90
J0218-00 | 6868.18$\pm$0.11 | 642$\pm$11 | -67$\pm$11 | -486$\pm$18 | 352.1$\pm$9.7 | -26.5$\pm$4.1 | -47.5$\pm$8.8
J0227+01 | 6823.574$\pm$0.039 | 742.5$\pm$5.5 | 60.0$\pm$6.0 | -452.0$\pm$6.7 | 572$\pm$10 | 12.4$\pm$1.7 | 47.5$\pm$4.2
J0234-07 | 6560.469$\pm$0.010 | 950.9$\pm$2.8 | -229.0$\pm$3.4 | -925.5$\pm$5.1 | 466.6$\pm$4.1 | -69.96$\pm$0.57 | -234.9$\pm$2.9
J0249+00 | 7049.048$\pm$0.011 | 941$\pm$11 | -206$\pm$15 | -949$\pm$29 | 535.3$\pm$8.7 | -28.9$\pm$1.2 | -167$\pm$10
J0320+00 | 6924.11$\pm$0.16 | 961$\pm$12 | -97$\pm$13 | -734$\pm$18 | 540$\pm$20 | -64.9$\pm$6.3 | -65.6$\pm$8.9
J0332-00 | 6557.284$\pm$0.048 | 1197$\pm$16 | -433$\pm$54 | -1500$\pm$110 | 641$\pm$11 | -25.0$\pm$2.9 | -235$\pm$17
J0334+00 | 7044.5970$\pm$0.0090 | 526.4$\pm$2.2 | -39.3$\pm$2.5 | -392.8$\pm$4.6 | 314.2$\pm$2.0 | -12.3$\pm$0.5 | -24.3$\pm$1.5
J0848-01 | 6754.591$\pm$0.057 | 768$\pm$11 | -37.4$\pm$8.7 | -564$\pm$15 | 490$\pm$13 | -15.3$\pm$2.8 | -31.5$\pm$8.1
J0904-00 | 6771.839$\pm$0.014 | 627.7$\pm$7.5 | -188$\pm$11 | -685$\pm$22 | 308.9$\pm$3.3 | -27.96$\pm$0.88 | -117.8$\pm$7.1
J0923+01 | 6947.64$\pm$0.14 | 1153$\pm$16 | -56$\pm$12 | -854$\pm$13 | 742$\pm$28 | -50.4$\pm$5.4 | -25.2$\pm$8.4
J0924+01 | 6906.315$\pm$0.042 | 1645$\pm$25 | -509$\pm$18 | -1616$\pm$33 | 598$\pm$12 | -116.0$\pm$3.8 | -575$\pm$24
J0948+00 | 6629.820$\pm$0.071 | 894.9$\pm$9.0 | -154$\pm$15 | -767$\pm$26 | 458.2$\pm$8.3 | -59.0$\pm$3.3 | -103.2$\pm$7.9
J2358-00 | 7021.214$\pm$0.013 | 843.7$\pm$3.5 | -61.5$\pm$4.3 | -674.8$\pm$7.6 | 552.4$\pm$5.4 | -13.36$\pm$0.71 | -39.1$\pm$3.0
Table 6: Outflow physical properties resulting from the flux-weighted non-parametric method. Name | vOF | Log(MOF) | $\dot{\rm\mathbb{M}}_{\rm OF}$ | Log($\dot{\rm\mathbb{E}}_{\rm kin}$) |  $\dot{\rm\mathbb{E}}_{\rm kin}$ / $\rm\mathbb{L}_{\rm BOL}$
---|---|---|---|---|---
| (km s-1) | (M⊙) | (M⊙ yr -1) | (erg s-1) | (%)
J0025-10 | -751$\pm$13 / 589.6$\pm$7.9 | 5.9965$\pm$0.0040 | 2.030$\pm$0.028 | 41.472$\pm$0.016 | (9.89$\pm$0.37)$\cdot$10-3
J0114+00 | -1179$\pm$190 / 585$\pm$44 | 6.2994$\pm$0.0072 | 5.39$\pm$0.60 | 42.25$\pm$0.19 | (1.27$\pm$0.56)$\cdot$10-1
J0123+00 | -770$\pm$18 / 530$\pm$10 | 6.2709$\pm$0.0056 | 3.687$\pm$0.074 | 41.729$\pm$0.023 | (8.95$\pm$0.48)$\cdot$10-3
J0142+14 | -1256$\pm$38 / 1072$\pm$38 | 6.7538$\pm$0.0045 | 20.19$\pm$0.55 | 42.942$\pm$0.032 | (1.97$\pm$0.15)$\cdot$10-1
J0217-00 | -1305$\pm$35 / 917$\pm$33 | 5.9334$\pm$0.0044 | 2.913$\pm$0.065 | 42.088$\pm$0.028 | (2.29$\pm$0.15)$\cdot$10-2
J0217-01 | -1040$\pm$210 / 820$\pm$120 | 5.7720$\pm$0.0048 | 1.73$\pm$0.22 | 41.72$\pm$0.18 | (3.7$\pm$1.6)$\cdot$10-2
J0218-00 | -595$\pm$26 / 414$\pm$11 | 5.8001$\pm$0.0016 | 0.962$\pm$0.027 | 40.915$\pm$0.044 | (3.97$\pm$0.40)$\cdot$10-3
J0227+01 | -578$\pm$14 / 740$\pm$18 | 5.8061$\pm$0.0049 | 1.297$\pm$0.026 | 41.272$\pm$0.025 | (7.85$\pm$0.45)$\cdot$10-3
J0234-07 | -1179.0$\pm$7.1 / 692.5$\pm$7.1 | 5.9177$\pm$0.0026 | 2.356$\pm$0.018 | 41.8882$\pm$0.0072 | (6.78$\pm$0.11)$\cdot$10-2
J0249+00 | -1499$\pm$110 / 730$\pm$19 | 6.3289$\pm$0.0029 | 7.26$\pm$0.34 | 42.59$\pm$0.08 | (1.23$\pm$0.23)$\cdot$10-1
J0320+00 | -883$\pm$28 / 736$\pm$48 | 5.5796$\pm$0.0037 | 0.937$\pm$0.033 | 41.294$\pm$0.041 | (2.61$\pm$0.24)$\cdot$10-2
J0332-00 | -2660$\pm$130 / 863$\pm$35 | 5.8196$\pm$0.0029 | 3.54$\pm$0.13 | 42.79$\pm$0.06 | (7.06$\pm$0.98)$\cdot$10-1
J0334+00 | -525$\pm$13 / 379.5$\pm$2.4 | 6.1932$\pm$0.0083 | 2.152$\pm$0.054 | 41.169$\pm$0.026 | (4.59$\pm$0.27)$\cdot$10-5
J0848-01 | -704$\pm$22 / 610$\pm$18 | 5.6881$\pm$0.0067 | 0.979$\pm$0.025 | 41.129$\pm$0.029 | (9.59$\pm$0.63)$\cdot$10-3
J0904-00 | -1029$\pm$34 / 382.9$\pm$2.2 | 6.2328$\pm$0.0066 | 3.654$\pm$0.087 | 41.965$\pm$0.039 | (2.80$\pm$0.25)$\cdot$10-2
J0923+01 | -1102$\pm$23 / 987$\pm$62 | 6.2644$\pm$0.0031 | 6.5.86$\pm$0.19 | 42.304$\pm$0.038 | (7.02$\pm$0.62)$\cdot$10-2
J0924+01 | -1940$\pm$37 / 791$\pm$22 | 5.7792$\pm$0.0045 | 2.49$\pm$0.042 | 42.346$\pm$0.022 | (4.66$\pm$0.23)$\cdot$10-3
J0948+00 | -1360$\pm$260 / 576$\pm$18 | 5.7859$\pm$0.0054 | 1.76$\pm$0.22 | 41.87$\pm$0.22 | (4.6$\pm$2.3)$\cdot$10-2
J2358-00 | -923$\pm$13 / 740.6$\pm$9.7 | 6.3870$\pm$0.0050 | 6.199$\pm$0.086 | 42.142$\pm$0.014 | (1.530$\pm$0.049)$\cdot$10-2

##  Appendix C Peak-weighted non-parametric analysis

In Figure 2 we include all the fits performed using the peak-weighted non-
parametric method from Speranza et al. 2021 (except the one shown in Figure
3), which is described in full in Section 3.2.2. The corresponding outflow
velocities derived from the fits of the [OIII] line and the outflow physical
properties are listed in Table 7.

Figure 2: Peak-weighted non-parametric fits of the [OIII]$\lambda$5007 Å
emission line shown for the whole sample. Figures are identical to the example
in Figure 3.

Figure 1: continued Table 7: Outflow properties derived from the peak-weighted non-parametric fits of the $[OIII]\lambda$5007 line. Name | vOF | Log(MOF) | $\dot{\rm\mathbb{M}}_{\rm OF}$ | Log($\dot{\rm\mathbb{E}}_{\rm kin}$) |  $\dot{\rm\mathbb{E}}_{\rm kin}$ / $\rm\mathbb{L}_{\rm BOL}$
---|---|---|---|---|---
| (km s-1) | (M⊙) | (M⊙ yr -1) | (erg s-1) | (%)
J0025-10 | -594.4$\pm$7.6 | 5.652$\pm$0.015 | 0.815$\pm$0.031 | 40.959$\pm$0.023 | (3.03$\pm$0.16)$\cdot$10-3
J0114+00 | -1360$\pm$220 | 5.76$\pm$0.34 | 2.4$\pm$1.4 | 42.1$\pm$0.4 | (9.4$\pm$8.6)$\cdot$10-2
J0123+00 | -603.1$\pm$7.7 | 5.974$\pm$0.020 | 1.748$\pm$0.082 | 41.302$\pm$0.025 | (3.35$\pm$0.19)$\cdot$10-3
J0142+14 | -925$\pm$23 | 6.408$\pm$0.100 | 7.2$\pm$1.5 | 42.289$\pm$0.11 | (4.4$\pm$1.1)$\cdot$10-2
J0217-00 | -1110$\pm$29 | 5.734$\pm$0.063 | 1.88$\pm$0.27 | 41.864$\pm$0.072 | (1.37$\pm$0.23)$\cdot$10-2
J0217-01 | -840$\pm$860 | 5.410$\pm$0.082 | 0.63$\pm$0.58 | 41.2$\pm$1.6 | (1.1$\pm$4.0)$\cdot$10-2
J0218-00 | -551$\pm$21 | 5.508$\pm$0.025 | 0.541$\pm$0.036 | 40.716$\pm$0.054 | (2.50$\pm$0.31)$\cdot$10-3
J0227+01 | 676$\pm$21 | 5.412$\pm$0.030 | 0.534$\pm$0.040 | 40.887$\pm$0.050 | (3.24$\pm$0.37)$\cdot$10-3
J0234-07 | -709$\pm$4.1 | 6.0148$\pm$0.0046 | 2.254$\pm$0.026 | 41.5532$\pm$0.0086 | (3.130$\pm$0.062)$\cdot$10-2
J0249+00 | -951$\pm$32 | 6.103$\pm$0.019 | 3.7$\pm$0.2 | 42.018$\pm$0.050 | (3.32$\pm$0.38)$\cdot$10-2
J0320+00 | -730$\pm$15 | 5.258$\pm$0.048 | 0.401$\pm$0.046 | 40.829$\pm$0.056 | (9.0$\pm$1.1)$\cdot$10-3
J0332-00 | -1230$\pm$100 | 5.511$\pm$0.044 | 1.21$\pm$0.15 | 41.76$\pm$0.11 | (6.7$\pm$1.7)$\cdot$10-2
J0334+00 | -542$\pm$19 | 5.732$\pm$0.029 | 0.893$\pm$0.068 | 40.919$\pm$0.056 | (2.58$\pm$0.33)$\cdot$10-3
J0848-01 | -602$\pm$17 | 5.103$\pm$0.099 | 0.235$\pm$0.054 | 40.43$\pm$0.11 | (1.93$\pm$0.48)$\cdot$10-3
J0904-00 | -718$\pm$19 | 6.187$\pm$0.017 | 3.38$\pm$0.16 | 41.737$\pm$0.039 | (1.66$\pm$0.15)$\cdot$10-2
J0923+01 | -791$\pm$14 | 5.744$\pm$0.046 | 1.34$\pm$0.15 | 41.421$\pm$0.053 | (9.2$\pm$1.1)$\cdot$10-3
J0924+01 | -1240$\pm$16 | 6.032$\pm$0.014 | 4.11$\pm$0.14 | 42.302$\pm$0.021 | (4.22$\pm$0.21)$\cdot$10-3
J0948+00 | -732$\pm$17 | 5.622$\pm$0.026 | 0.943$\pm$0.059 | 41.197$\pm$0.039 | (9.77$\pm$0.88)$\cdot$10-3
J2358-00 | -827$\pm$33 | 5.793$\pm$0.088 | 1.58$\pm$0.28 | 41.534$\pm$0.097 | (3.77$\pm$0.85)$\cdot$10-3