11institutetext: Dipartimento di Fisica e Astronomia ’Augusto Righi’, Alma
Mater Studiorum - Università di Bologna, Via Gobetti 93/2, 40129 Bologna,
Italy 22institutetext: INAF-Osservatorio di Astrofisica e Scienza dello Spazio
via Gobetti 93/3, 40129 Bologna, Italy 33institutetext: Max-Planck-Institut
für extraterrestrische Physik, Giessenbachstraße 1, D-85748 Garching bei
München, Germany 44institutetext: Institute for Astronomy and Astrophysics,
National Observatory of Athens, V. Paulou and I. Metaxa, 11532, Greece
55institutetext: Leibniz-Institut für Astrophysik Potsdam, An der Sternwarte
16, 14482 Potsdam, Germany 66institutetext: Department of Astronomy, Kyoto
University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
77institutetext: Academia Sinica Institute of Astronomy and Astrophysics, 11F
of Astronomy-Mathematics Building, AS/NTU, No. 1, Section 4, Roosevelt Road,
Taipei 10617, Taiwan 88institutetext: Research Center for Space and Cosmic
Evolution, Ehime University, 2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan
99institutetext: Graduate School of Science and Engineering, Ehime University,
2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan 1010institutetext: SISSA, Via
Bonomea 265, 34136 Trieste, Italy 1111institutetext: Instituto de Astrofísica
de Canarias, Calle Vía Láctea, s/n, 38205 La Laguna, Tenerife, Spain
1212institutetext: Departamento de Astrofísica, Universidad de La Laguna,
38206 La Laguna, Tenerife, Spain 1313institutetext: Centre for Extragalactic
Astronomy, Department of Physics, Durham University, South Road, Durham, DH1
3LE, UK 1414institutetext: School of Physics and Astronomy, University of
Southampton, Highfield, SO17 1BJ, UK 1515institutetext: Kavli Institute for
the Physics and Mathematics of the Universe, The University of Tokyo, Kashiwa
277-8583 (Kavli IPMU, WPI), Japan 1616institutetext: School of Astronomy and
Space Science, University of Science and Technology of China, Hefei 230026,
People’s Republic of China 1717institutetext: Department of Astronomy,
University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
1818institutetext: National Center for Supercomputing Applications, University
of Illinois at Urbana-Champaign, Urbana, IL 61801, USA 1919institutetext:
Center for AstroPhysical Surveys, National Center for Supercomputing
Applications, University of Illinois at Urbana-Champaign, Urbana, IL 61801,
USA 2020institutetext: National Center for Supercomputing Applications,
University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

# A new discovery space opened by eROSITA:

Ionised AGN outflows from X–ray selected samples

B. Musiimenta 1122 M. Brusa 1122 T. Liu 33 M. Salvato 33 J. Buchner 33 Z. Igo
33 S. Waddell 33 Y. Toba 667788 R. Arcodia 33 J. Comparat 33 D. Alexander 1313
F. Shankar 1414 A. Lapi 1010 C. Ramos Almeida 11111212 A. Georgakakis 44 A.
Merloni 33 T. Urrutia 55 J. Li 151516161717 Y. Terashima 99 Y. Shen 18181919
Q. Wu 18182020 T. Dwelly 33 K. Nandra 33 J. Wolf 33

(Received 28 November 2022; accepted 12 September 2023)

###### Abstract

Context.  In the context of an evolutionary model, the outflow phase of an
active galactic nucleus (AGN) occurs at the peak of its activity, once the
central supermassive black hole (SMBH) is massive enough to generate
sufficient power to counterbalance the potential well of the host galaxy. This
outflow feedback phase plays a vital role in galaxy evolution.

Aims. Our aim in this paper is to apply various selection methods to isolate
powerful AGNs in the feedback phase, trace and characterise outflows in these
AGNs, and explore the link between AGN luminosity and outflow properties.

Methods. We applied a combination of methods to the Spectrum Roentgen Gamma
(SRG) eROSITA Final Equatorial Depth survey (eFEDS) catalogue and isolated
$\sim$1400 candidates at z$>$0.5 out of $\sim 11750$ AGNs ($\sim 12$%).
Furthermore, we narrowed down our selection to 427 sources that have
0.5$<$z$<$1\. We tested the robustness of our selection on the small subsample
of 50 sources with available good quality SDSS spectra at 0.5$<$z$<$1 and, for
which we fitted the [OIII] emission line complex and searched for the presence
of ionised gas outflow signatures.

Results.  Out of the 50 good quality SDSS spectra, we identified 23 quasars
($\sim 45$%) with evidence of ionised outflows based on the presence of
significant broad and/or shifted components in [OIII]$\lambda 5007\text{\AA}$.
They are on average more luminous ($\mathrm{logL_{bol}\sim\leavevmode\nobreak\
45.2\leavevmode\nobreak\ erg\leavevmode\nobreak\ s^{-1}}$) and more obscured
($\mathrm{N_{H}}$ $\mathrm{\sim 10^{22}\leavevmode\nobreak\ cm^{-2}}$) than
the parent sample of $\sim$427 candidates, although this may be ascribed to
selection effects affecting the good quality SDSS spectra sample. By adding
118 quasars at 0.5$<$z$<$3.5 with evidence of outflows reported in the
literature, we find a weak correlation between the maximum outflow velocity
and the AGN bolometric luminosity. On the contrary, we recovered strong
correlations between the mass outflow rate and outflow kinetic power with the
AGN bolometric luminosity.

Conclusions. About 30% of our sample have kinetic coupling efficiencies,
$\dot{E}/L_{bol}\\!>\\!1$%, suggesting that the outflows could have a
significant effect on their host galaxies. We find that the majority of the
outflows have momentum flux ratios lower than 20 which rules out an energy-
conserving nature. Our present work points to the unequivocal existence of a
rather short AGN outflow phase, paving the way towards a new avenue to dissect
AGN outflows in large samples within eROSITA and beyond.

###### Key Words.:

galaxies: active –high-redshift –feedback –X–rays: surveys

##  1 Introduction

Active galactic nuclei (AGNs) are central nuclei of massive galaxies that are
powered by the accretion of matter towards the central supermassive black
holes (SMBHs) (Soltan, 1982; Rees, 1984). The energy produced during the
accretion episodes by AGNs in the form of winds, radiation or jets is argued
to have a great impact on the interstellar medium (ISM) (Alexander & Hickox,
2012; Fabian, 2012; Harrison, 2017). The link between the energy produced by
the AGNs and the surrounding ISM is called AGN feedback (Silk & Rees, 1998; Di
Matteo et al., 2005; Hopkins & Elvis, 2009), and it is considered a key
element in galaxy evolution models and simulations (e.g. Schaye et al. 2015).

To better understand galaxy evolution, it is crucial to determine how SMBHs
form and evolve. Various processes have been proposed to trigger the formation
and evolution of SMBHs, including internal processes such as disc or bar
instabilities and external processes such as mergers, among others (Hopkins et
al., 2008). In the merger scenario, the black hole grows within a dust-
enshrouded and star-forming environment, followed by high accretion close to
the Eddington limit. This in turn releases a tremendous amount of energy (the
blow-out phase) through radiation pressure-driven winds or outflows to the
surrounding environment.

These AGN-driven outflows may provide the mechanism needed to remove the gas
and thus quench star formation (SF) (Costa et al., 2018b), limiting the
further growth of the galaxy and the SMBHs as well (e.g. Di Matteo et al.,
2005). As discussed in Harrison et al. (2018), an alternative mechanism is the
injection of energy in the ISM or intergalactic medium (IGM), which indirectly
heats the halo and prevents future in-fall of matter onto the galaxy. Referred
to as the maintenance mode of feedback, this phenomenon is primarily caused by
jet-driven outflows at large scales. When these outflows collide, they
introduce turbulence and generate shocks in their vicinity, effectively
preventing cooling and impeding star formation (Croton et al., 2006; Ciotti et
al., 2010; Nelson et al., 2019). The outflows influence further fueling the
AGN activity affects the fueling of star formation and regulates its duty
cycle.

According to hydrodynamical simulations, during the key ’blow-out phase’, the
AGN is characterised by high nuclear obscuration with column densities
($\mathrm{N_{H}}$) $\mathrm{>10^{22}cm^{-2}}$, high AGN bolometric
luminosities, and accretion close to the Eddington limit (Hopkins et al.,
2005; Di Matteo et al., 2005; Blecha et al., 2018). As discussed in the recent
study by Blecha et al. (2018) with simulations of AGN evolution through galaxy
mergers, the AGN luminosity and column densities are enhanced during the late
stages of galaxy mergers where the blow-out phase is also expected to occur.
Surveys that are robust to obscuration are needed to study these kinds of
objects.

In addition, this phase is expected to be short, and possibly even shorter
than the AGN lifetime of $\sim 10^{5}$ years (Schawinski et al., 2015; King &
Nixon, 2015), hence the need for large-area surveys. AGN outflows may occur
during the early phases of SMBH and galaxy evolution according to some models
(e.g. Lapi et al., 2014, 2018), and could occur on relatively short timescales
depending on the exact modelling of the light curve.

AGN outflows at all gas phases (ionised or neutral, molecular or atomic) and
all scales (from the launching region to host galaxy scale) have been revealed
and studied in sources detected both in the local (Tombesi et al., 2010;
Gofford et al., 2013; Feruglio et al., 2013a, b; Rupke & Veilleux, 2013;
Harrison et al., 2014; Aalto et al., 2015; Morganti et al., 2016; Toba et al.,
2017a, b; Igo et al., 2020; Ramos Almeida et al., 2022; Speranza et al., 2022)
and distant universe (Cano-Díaz et al., 2012; Maiolino et al., 2012; Cresci et
al., 2015b, a; Cicone et al., 2015; Perna et al., 2015b; Carniani et al.,
2016; Brusa et al., 2015, 2016; Harrison et al., 2016; Kakkad et al., 2016;
Bischetti et al., 2017; Perrotta et al., 2019; Scholtz et al., 2020; Kakkad et
al., 2020; Ishikawa et al., 2021; Vayner et al., 2021; Brusa et al., 2022)
through integrated or spatially resolved spectroscopy (see also Cicone et al.,
2018, for a review).

We note that to quantify and characterise AGN outflows, assumptions on
different parameters such as electron density, velocity, radius, geometry,
etc., are made when it is not possible to measure them. This makes it
challenging to determine the correlations between the outflow properties, the
AGN properties and the host galaxy properties (e.g. Fiore et al., 2017).
Moreover, due to their multi-phase nature, we can only access and characterise
the gas motions by emission line tracers that highlight different and
incomplete gas phases. This complexity makes it more difficult to compare
observations with theoretical predictions (Harrison et al., 2018). Whether
these AGN outflows affect their host galaxies and how is still a puzzling
question.

Although exploring individual systems with outflows is important, from the
observational point of view it is also paramount to study large samples and
explore efficient selection techniques to 1) better provide constraints for
models and simulations; and 2) isolate the best targets for multiwavelength
follow-up with current and future facilities. As discussed in detail in the
next sections, several studies have investigated the properties of AGN
outflows. They have pre-selected these AGNs with outflows using different
observational techniques in the X-ray, UV, optical, infrared and radio (e.g.
Zakamska et al., 2016; Perrotta et al., 2019; Brusa et al., 2022, among
others). The different selection methods used in these studies, which are
still prone to incompleteness, are an indication that there is no unique way
of selecting AGNs in the feedback phase. This calls for the need for more
studies to explore different multi-wavelength approaches to pre-select these
kinds of objects. Moreover, AGNs in this key evolutionary phase are more
sensitive to obscuration in the optical and soft X-rays than IR and hard
X-rays (Alexander & Hickox, 2012; Blecha et al., 2018).

This study aims to apply a combination of different methods that have been
used to select this class of AGNs to sources detected in a new large X–ray
survey field, imaged by the extended Roentgen Survey with an Imaging Telescope
Array (eROSITA), and explore the scaling relations between AGN properties and
outflow properties combining results from this work with literature samples
published so far. This paper is organised as follows. Section 2 describes the
different selection criteria of AGN outflows from eFEDS. Section 3 describes
the properties of our selected candidates, spectral analysis and outflow
properties. Discussions of the results and our conclusions are presented in
Sect. 4 and 5, respectively. Throughout the paper, we adopt the cosmological
parameters $\rm{H_{0}=70kms^{-1}Mpc^{-1}}$, $\rm{\Omega_{m}=0.3}$ and
$\rm{\Omega_{\Lambda}=0.7}$ (Spergel et al., 2003). We use the AB magnitudes
system unless otherwise stated.

##  2 Selection of AGNs in the feedback phase

###  2.1 The eFEDS sample

eROSITA is an X–ray imaging telescope aboard the Spectrum Roentgen Gamma (SRG,
Sunyaev et al. 2021) observing within 0.2 – 10 keV band and it is expected to
detect millions of AGNs over the all-sky at the end of a 4 years survey
(Merloni et al., 2012; Predehl et al., 2021). A large ($\sim$140 deg²)
extragalactic area, the eROSITA Final Equatorial Depth survey (eFEDS), rich in
photometric and spectroscopic multi-wavelength coverage, was observed for four
days during eROSITA’s performance and verification phase. One of the main
purposes of the eFEDS survey is to allow eROSITA scientists to test their
techniques on this smaller sample to prepare for the future all-sky larger
samples and explore the possible science that can emerge from the eROSITA
X–ray sources population.

The eFEDS X-ray catalogue consists of 27369 point-like X–ray sources detected
in the 0.2-2.3 keV band (Main catalogue; Brunner et al., 2022). The optical
and IR counterparts are presented in Salvato et al. (2022), along with multi-
band photometric (from Galex FUV to Wise W4) and redshift (spectroscopic
redshifts when available, and photometric redshifts otherwise) information.
From this catalogue, Liu et al. (2022) presents, the X–ray spectral properties
along with monochromatic luminosities at 5100Å and 2500Å, for the AGN
subsample (22097 objects). While only 1% of these sources are significantly
detected in the 2.3-5 keV band (Hard catalogue, Nandra et al. in prep), Liu et
al. (2022) analysed the 0.2-8 keV X-ray spectra of all AGNs in the main
catalogue, and estimated 2-10 keV X-ray fluxes (absorption corrected in the
rest-frame band). The next step is to isolate AGNs with a high chance of being
in the feedback phase. To do so, we have adopted the criteria discussed in
detail in Sects. 2.2 and 2.3, as follows.

###  2.2 Colour selection in eFEDS (Sample A)

During the blow-out phase, enhanced obscuration is expected, evidenced by red
colours in the optical to infrared bands. Previous studies (e.g. Urrutia et
al., 2008; Banerji et al., 2012) have studied colour-based pre-selection of
red quasars at z$>$0.5 based on the colour cut

$\mathrm{r-W1}>4$ (1)

and

$\mathrm{i-W3}>4.6,$ (2)

where i is the magnitude in the i band, r is the magnitude in the r band, and
W1 and W3 are the magnitudes in the WISE W1 and W3 bands, respectively.

These criteria have also been utilised in prior investigations (e.g. Ross et
al., 2015; Hamann et al., 2016; Zakamska et al., 2016; Perrotta et al., 2019)
to select targets for spectroscopic follow-up. Specifically, Eq. 2 has been
employed to identify extreme red quasars (ERQs; e.g. Hamann et al., 2016;
Perrotta et al., 2019; Vayner et al., 2021) characterised by their reddish
hues, indicative of outflow phenomena.

In other investigations instead, the red colours have been coupled with a
selection involving also a high hard X–ray to optical flux ratio given by

$\rm{log\left(\frac{F_{2-10keV}}{F_{opt}}\right)}>1,$ (3)

where $\mathrm{F_{2-10keV}}$ is the X–ray flux in 2-10 keV band and
$\rm{F_{opt}}$ is the flux in the optical r-band (Brusa et al., 2010, 2015;
Perna et al., 2015b; LaMassa et al., 2016). As a pilot study, Brusa et al.
(2022) applied the combination of Eq.1 and Eq.3 to the eFEDS Hard sample
($\sim$250 sources). This method isolated three sources. The only one with an
available optical spectrum from SDSS (XID 439, hereafter ID 608 from the main
sample) turned out to be an obscured source with N${}_{H}>10^{22}$ cm-2, and
X–ray luminous, with L${}_{\rm X}>10^{44}$ erg s-1. The analysis of the
optical spectrum revealed the presence of a broad and red-shifted [OIII] line,
with associated mass outflow rates of $\sim$1.4 $\mathrm{M_{\odot}yr^{-1}}$
(Brusa et al., 2022). This is the first outflowing quasar isolated from
eROSITA data.

We now extend this approach to the larger eFEDS AGN sample (Liu et al., 2022).
From a sample of 22,097 extragalactic sources, 14930 have reliable
spectroscopic or photometric redshift (redshift grade 4 or 5 – see Salvato et
al. 2022). We select AGNs with redshift z$>$0.5, and we isolate 11754 AGNs as
our starting sub-sample. The redshift of 0.5 is chosen to encompass the range
in which high luminous AGNs peak and the fact that AGN radiative feedback is
relevant or common at these high redshift ranges.

We now apply the different criteria to select AGNs in the feedback phase by
colour and flux ratios described above to the eFEDS AGN sample. First, we
apply a combination of Eq. 1 and Eq.3 (Eq. 1 $\land$ Eq.3) to the eFEDS main
sample as illustrated in Figure 1. This selection retrieved 274 sources.
Figure 1 shows, on the upper left panel, the eFEDS Main catalogue sources
populated in this selection plane (contours) and as empty circles the selected
candidates.

Because at z$>$1 the soft X-ray band partially samples the rest-frame hard
X-ray emission, allowing us to use the large Main sample, we consider also the
soft X-ray to optical flux ratio. The upper right panel of Fig. 1 shows the
soft X–ray to optical flux ratio coupled with the r-W1 selection, that is,

$\rm{\left(r-W1>4\right)\land\left(log\frac{F_{0.2-2.3keV}}{F_{opt}}>0.5\right)},$
(4)

where $\mathrm{F_{0.2-2.3keV}}$ is the X–ray flux in 0.2-2.3 keV band and
$\mathrm{F_{opt}}$ is the optical flux in r band. From this method, 516 AGNs
are isolated.

Finally, because IR brightness is also an indicator of obscuration, the MIR to
optical flux ratio (see also Brusa et al. 2015; Perna et al. 2015a) is
combined with the optical to NIR red colour as

$\mathrm{\left(r-W1>4\right)\land(i-W4}>7).$ (5)

We present this plane, in the bottom right panel of Fig. 1. This criterion
selects 203 candidates.

Unlike the other colour selection criteria, used as combinations, Eq. 2
criterion is applied independently as in the previous studies and because AGNs
that satisfy this criterion have already demonstrated a correlation between
colour and [O III] line properties (Perrotta et al., 2019). As stated in
Perrotta et al. (2019), a redder colour corresponds to a broader [O III] line
profile. Additionally, previous studies by Perrotta et al. (2019); Vayner et
al. (2021) have identified outflows in 100% of their samples that were
previously selected with Eq. 2. With the i-W3 colour cut (Eq. 2, Hamann et al.
(2016); Perrotta et al. (2019)), 539 candidates are selected. These are shown
in the lower left panel of Fig. 1. The number of candidates is comparable to
the r-W1 selection.

Altogether, the above colour selection methods result in a sample of 853
unique candidates which are most likely luminous and obscured and hence, with
high chances of containing AGNs in the feedback phase. We refer to these 853
candidates as ’sample A’, hereafter. Of these, 352 have redshift of
0.5$<$z$<$1.

In Fig. 14, all the colour selection methods that resulted in sample A are
plotted in the selection diagnostics together. In this Figure, the selected
candidates are scattered in almost all the regions of the planes defined by
the main eFEDS AGN sample. This shows that we are selecting these candidates
AGNs with strong winds homogeneously, which means minimal bias in our
selection methods. It tells us how complicated it is to select these
candidates since they do not fall into a defined region. This implies that the
complete and pure way to pre-select AGNs with strong winds is by applying a
combination of methods as we have done in this study.

###  2.3 Selection based on X–ray and optical spectral properties (Sample B)

To exert powerful radiative feedback, AGNs in the feedback phase are expected
to experience high mass accretion rates and high Eddington ratios (e.g.
Hopkins et al., 2005; Di Matteo et al., 2005). This may drive outflows of gas.

The gas along the line-of-sight is unstable to (Thompson) radiation pressure
if the column density is low and the Eddington ratio is high. The wedge is
computed by Fabian et al. (2008, 2009) considering dusty media, with an
enhanced cross-section. Fabian et al. (2008, 2009) defined a plane of column
density ($\mathrm{N_{H}}$) vs. Eddington ratio ($\mathrm{\lambda_{Edd}}$) in
which such kinds of sources are expected to appear that is, the region where
$\mathrm{N_{H}>10^{21.5}cm^{-2}}$ and $\mathrm{\lambda_{Edd}}$ is greater than
the effective Eddington limit for different values of $\mathrm{N_{H}}$. This
position in the $\mathrm{N_{H}}$-$\mathrm{\lambda_{Edd}}$ plane has been used
to select AGNs in the feedback phase in previous studies (e.g. Kakkad et al.,
2016; Ricci et al., 2017; Lansbury et al., 2020; Alonso-Herrero et al., 2021).
We applied the same selection to the eFEDS sample.

We derive $\mathrm{\lambda_{Edd}}$ for a sub-sample of eFEDS sources with
optical spectroscopic observations. It is possible to derive virial black hole
masses (MBH) using broad line region (BLR) and the velocity dispersion of the
BLR gas from single epoch spectra and line widths (e.g. Peterson et al., 2004;
Vestergaard & Peterson, 2006; Shen et al., 2011; Woo et al., 2015). Following
the approach by Wu & Shen (2022), BH masses are available for all the sources
included on the SDSS DR16 and SDSS DR17 quasar catalogue (DR16Q and DR17Q), by
applying PyQSOFit (Guo et al., 2018; Shen et al., 2019) to their optical
spectra. 4931 sources in eFEDS have BH masses estimated in this way, with 3813
at z$>$0.5.

To obtain $\mathrm{\lambda_{Edd}}$ which is defined as
$\mathrm{L_{bol}/L_{Edd}(MBH)}$, we computed the Eddington luminosity from the
BH masses. The AGN bolometric luminosity was obtained from the catalogued
X–ray luminosity (Liu et al., 2022), applying the bolometric corrections using
Eq. 3 in Duras et al. (2020). We populated our sources in the
$\mathrm{N_{H}}$-$\mathrm{\lambda_{Edd}}$ plane and we isolated a sample of
528 candidates which show $\mathrm{N_{H}}>10^{21.5}$ cm -2 and
$\mathrm{\lambda_{Edd}>\lambda_{eff}^{limit}}$. We use the column density
values in (Liu et al., 2022) that were obtained using a single power law
model. The selected sources are shown as red circles in Fig. 2. We refer to
these 528 candidates as ’sample B’, hereafter. Of these, 78 have a redshift of
0.5$<$z$<$1.

In Fig. 14, our sample B selected by $\mathrm{N_{H}}$ and
$\mathrm{\lambda_{Edd}}$ appear in the blue region of the colour selection
planes used to construct sample A (see previous subsection). This is due to
the fact that these obscured and highly accreting sources are likely being
observed immediately before the blow-out phase, or to the fact that the
obscuration is inhomogeneous (see Appendix A for details).

##  3 Results

|
---|---
|
Figure 1:  Plots showing the colour selections to isolate AGNs in the feedback
phase. Top left panel: The $2-10$ keV to optical flux ratio versus r-W1
colour. The black thick dashed lines represent Eq. 3 and 1 selection locus.
Top right panel: The $0.2-2.3$ keV to optical flux ratio versus r-W1 colour.
The black thick dashed lines represent Eq. 4 and 1 selection locus. Bottom
left panel: Distribution of i-W3 selected sample. Red distribution are
selected candidates with Eq. 2. Bottom right panel: i-W4 versus r-W1 selection
method. The black thick dashed lines represent the Equations 5 and 1 selection
locus. In all panels, the red circles are the selected candidates. Brown
contours are sources in the complementary locus. Solid grey contours or
distribution indicate the eFEDS AGN sample after applying the cut on redshift
(z$>$0.5) and dashed grey contours or distribution show the full eFEDS AGN
sample. XID 439 or ID 608 Brusa et al. (2022) is shown as a blue star.  Figure
2:  $\mathrm{N_{H}}$ plotted against Eddington ratio. Sources marked in red
are the selected candidates. Solid grey contours are eFEDS sample after
applying the cut on redshift (z$>$0.5) and dashed grey contours show the full
eFEDS sample. ID 608 (Brusa et al., 2022) (blue star) and the sources isolated
from Sect. 2.2 are shown with violet circles. The black thick dashed line and
curve represent the region $\mathrm{N_{H}>10^{21.5}cm^{-2}}$ and
$\mathrm{\lambda_{Edd}>}$ effective Eddington limit. The dotted curve (thick
and thin) is the effective Eddington limit for different values of
$\mathrm{N_{H}}$ (Fabian et al., 2009).

The results from the selections presented in Sect. 2.2 and 2.3 are summarised
in the flow chart shown in Fig. 3, with the final Sample A and B and the
relevant numbers highlighted in the red and blue boxes, respectively. In
total, we isolated 1376 ($\sim$1400) unique candidates ($\sim 12$% of the
z$>0.5$ eFEDS AGN population).

Figure 3:  Flow chart summarising our selection criteria used to isolate
candidates from the eFEDS AGN sample. Each box contains a selection method
with the cuts applied and the number of sources obtained in the bottom right
corner of each box. In brackets, we indicate the number of sources for z less
than one (0.5$<$z$<$1) which we apply later on for SDSS spectra analysis. By
reliable spectroscopic or photometric redshift, we only consider redshift
grade 4 or 5 –see Salvato et al. 2022. $\rm{F_{opt}}$ refers to flux in the
optical r-band. The box highlighted in red is sample A obtained after applying
the colour selections in the top right of Fig. 1. The box highlighted in blue
is the $\mathrm{N_{H}>10^{21.5}cm^{-2}}$ and
$\mathrm{\lambda_{Edd}>\lambda_{eff}^{limit}}$ selection or sample B in Fig. 2

To clearly visualise how many of our selected candidates from different
selection methods overlap, we represent all our samples on the Venn diagram as
shown in Fig. 4. 950 (69% of our selected sources) candidates are uniquely
selected in an individual selection method. This shows how unique each method
is and why using this strategy of applying different methods to isolate
candidate AGNs in the feedback phase minimises the chances of missing
potential candidates. Only one source satisfies all the selection criteria,
and this is ID 608, the archetypal outflowing quasar already presented in
Brusa et al. (2022).

Figure 4:  Venn diagram showing how many sources overlap from our selection
criteria. The source that is common in all the four selection method is ID 608
(Brusa et al., 2022). $\rm{F_{opt}}$ refers to flux in the optical r-band. The
selection methods are indicated by different colours. The Venn diagram was
drawn using bioinformatics and evolutionary genomics webtool at
https://bioinformatics.psb.ugent.be/webtools/Venn/

###  3.1 Properties of eFEDS outflowing quasar candidates

We present the X–ray luminosity and redshift distribution for Sample A and
Sample B in Fig. 5, compared with the full eFEDS sample at z$>0.5$. Sample A
(in red) populates mainly the low redshift and with lower X–ray luminosities
range, while Sample B spans a wider range of both luminosities and redshift.

Figure 6 presents the $\mathrm{N_{H}}$ distributions of all the candidates
outflowing quasars from sample A and sample B. Given that objects in sample B
have been selected on the basis of N${}_{\rm H}>10^{21.5}$ cm-2, their
histogram is reported for completeness. The objects in sample A appear more
obscured than the general eFEDS AGN population. In particular, about 11% of
the eFEDS z$>0.5$ AGN sub-sample have
$\mathrm{N_{H}}\mathrm{>10^{22}\leavevmode\nobreak\ cm^{-2}}$ while our
candidate AGNs in the feedback phase from Sample A show a 3 times higher
obscured fraction (30% have
$\mathrm{N_{H}}\mathrm{>10^{22}\leavevmode\nobreak\ cm^{-2}}$). This confirms
that the colour selection methods are efficient in isolating more obscured
sources than the overall AGN population.

Figure 7 shows the position of the sources in Sample A and B in the
$\mathrm{\rm{L_{5100\text{\AA}}}}$-$\rm{L_{2500\text{\AA}}}$ plane111The rest
frame luminosities at 2500Å and 5100Å have been derived and catalogued in (Liu
et al., 2022). The dividing line at
$\mathrm{\rm{L_{5100\text{\AA}}}}$-$\rm{L_{2500\text{\AA}}}$=0.2 can be used
to divide the sample in ’blue’ and ’red’ on the basis of their relative fluxes
in the rest frame optical and UV band (Liu et al., 2022): sources above the
dividing line are expected to be reddened. In this figure, we also show all
the AGNs in eFEDS with significant X–ray obscuration (N${}_{\rm H}>10^{21.5}$
cm-2), colour coded according to their position with respect to the dividing
line. We refer to sources above the dividing line as ’red X-ray obscured’ and
those below the dividing line as ’blue X-ray obscured’.

The vast majority of the sources in Sample A lie above the dividing line (see
Fig. 7), overlapping the locus of the ’red obscured’ sources, as expected. Our
Sample B instead correlates well with the orange points (’blue obscured’), in
agreement with the fact that they show broad lines in the optical spectra and
therefore exhibit less attenuation in the $\rm{L_{2500\text{\AA}}}$. A few
sources in our Sample B, however, appear in the region of red obscured
sources.

Figure 5: X–ray luminosity and redshift distributions of our two main
candidate samples. The grey points indicate the eFEDS AGN sample at z$>$0.5.
The red circles indicate sample A obtained after applying the colour
selections described in Sect. 2.2 while blue circles indicate Sample B
selected as detailed in 2.3. Figure 6: $\mathrm{N_{H}}$ distribution of our
selected candidates from the different methods compared with the overall eFEDS
AGN sample and subsample at z$>$0.5. Our isolated candidates appear more
obscured than the overall eFEDS AGN population and subsample at z$>$0.5.

Figure 7: Luminosity at 5100 Å($\rm{L_{5100\text{\AA}}}$) versus Luminosity at
2500 Å($\rm{L_{2500\text{\AA}}}$) for sources in Sample A and B.
Representation of the selected samples with the X–ray obscured sources
($\mathrm{N_{H}>10^{21.5}cm^{-2}}$: red obscured and blue obscured based on
the line $\rm{L_{5100\text{\AA}}}$-$\rm{L_{2500\text{\AA}}}$=0.2; see Text for
details). Candidates in sample B appear in the blue side (selects mostly type
1 AGN). It also correlates well with
$\rm{L_{5100\text{\AA}}}$-$\rm{L_{2500\text{\AA}}}$=0.2 relation which
indicates their type 1 nature. Sample A indeed appear in the red side (selects
mostly type 2 AGN). We indicate in black stars the 23 ionised outflows from
the eFEDS sample (see Sect. 3.2 for the discussion of these 23 sources )

.

###  3.2  $\rm{[OIII]}$ line SDSS spectral analysis of eFEDS outflowing quasar
candidates at 0.5$<$z$<$1 and outflow properties

Outflowing gas can give rise to asymmetric and/or broad optical line profiles.
The presence of ionised outflowing gas is assessed by spectral fitting of the
[OIII]4959,5007 forbidden line complex, in the rest-frame optical spectra.
This line has been extensively used in the literature for ionised outflow
search and characterisation (see e.g. Fiore et al. 2017 and Leung et al. 2019
for recent compilations)

For the spectral analysis, we exploit the Sloan Digital Sky Survey (SDSS I-II-
III and IV; York et al. (2000); Gunn et al. (2006); Smee et al. (2013);
Ahumada et al. (2020)). In particular, we use the SDSS public spectra mainly
from SDSS-IV (Blanton et al., 2017) from SDSS data release 16 (DR16) and 17
(DR17) (Lyke et al., 2020; Abdurro’uf et al., 2022). The SDSS spectral range
is such that the [OIII]4959,5007 line complex is sampled only up to z$\sim$1\.
Therefore, in order to confirm the nature of our candidates, we isolated from
Samples A and B all AGNs with spectroscopic redshift of 0.5$<$z$<$1.

Only 78 AGNs from Sample B (out of 528) have 0.5$<$z$<$1, all with spectra. On
the other hand, from sample A, only 352 out of the 853 candidates have
0.5$<$z$<$1 and only 6 out of 352 have their spectra available.Two of these 6
sources also appear in sample B (ID608 and ID13349). Therefore, given that 2
sources appear in both samples A and B, in total, we retrieved 82 spectra at
0.5$<$z$<$1 for further spectral analysis.

We then fit our spectra with the python fitting code (PyQSOFit)222This is a
python fitting code used to measure spectral properties of quasars which is
also used to decompose different components of the quasar spectra (Guo et al.,
2018; Shen et al., 2019). PyQSOFit takes the spectrum, redshift, and line
fitting parameters specifying the range and fitting constraints as inputs
parameter, performs a continuum modelling and host galaxy subtraction and a
multi-component fit of the emission lines. The line best-fit parameters are
then returned as outputs (Guo et al., 2018; Shen et al., 2019).

We fit the $\mathrm{[OIII]\lambda 5007}$ line complex with two Gaussian
functions: one is included to model the systemic component, tracing the NLR
and the second one is included to model any additional broad component,
possibly indicating the presence of outflowing gas. In both cases, the flux
ratios between $\mathrm{[OIII]\lambda{4959}}$ and
$\mathrm{[OIII]\lambda{5007}}$ were fixed at 1:2.99 (Osterbrock, 1981). The
FWHM of the narrow component was fixed to be less than 550 km s-1. The
velocity shifts were obtained from the velocity peak of either the broad or
narrow emission lines and the systemic velocity.

We ran PyQSOFit and visually inspected all 82 spectra. We discarded 32 of them
either because of a very noisy continuum around the [OIII] region or bad
residuals after the continuum and host galaxy subtraction. Two out of 32
sources are from sample A.

We then considered the remaining 50 sources. From the spectral fitting of the
$\mathrm{[OIII]\lambda{5007}}$ and $\mathrm{[OIII]\lambda{4959}}$ line
complex, we found that 21 sources are significantly best fit with two Gaussian
components (e.g. the additional broad component has a flux to flux error ratio
$>$2.5), showing a blue or red shifted broad $\mathrm{[OIII]\lambda{5007}}$
with FWHM $\mathrm{\sim 600-2800\leavevmode\nobreak\ km\leavevmode\nobreak\
s^{-1}}$. Another 17 spectra are best fitted with two Gaussian components.
Here the broad component is less significant, with a flux to flux error ratio
$<$2.5. The remaining 12 sources are instead fitted with a single Gaussian
component. Two of them have FWHM$\mathrm{>800\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}}$. Our outflow sample is composed of 21 sources
with significant broad component detection and the 2 sources with a single
component fit, but FWHM$\mathrm{>800\leavevmode\nobreak\
km\leavevmode\nobreak\ s^{-1}}$. This approach follows previous works (e.g.
Bischetti et al., 2017; Perrotta et al., 2019; Brusa et al., 2022).

In total, we retrieved 23 sources with outflows. Only one of the [OIII]
spectral fit of these candidates is shown in the main text in Fig. 8, while
all the other fits (22 sources) are presented in the Appendix (see Appendix B
for details). We started with a sample of $\sim 11750$ AGN, from which we
selected $\sim$1400 which are AGN feedback candidates. Out of these, 427
sources have 0.5$<$z$<$1\. To test the robustness of our selection, we
selected the 50 AGN feedback candidates with best quality SDSS spectra. We
found evidence for outflowing gas in $\sim$45% of the sample (23/50), with a
higher fraction if we consider sample A only (3/4).

Figure 8: SDSS emission line profiles fit of the H$\beta$+[OIII] line
continuum subtracted complex for one of our candidates. The blue dashed line
indicated the broad component, the green fit indicates the narrow component.
The red dashed line indicates the total fit. The vertical dotted lines
indicate the peaks at 4862.68, 4960.30, and 5008.24 for Hβ and [OIII] rest-
frame wavelength.

In order to investigate the limitations and biases arising from our small
sample sizes, we check how they accurately represent the original samples. We
focus on parameters such as column density (N${\rm H}$), bolometric luminosity
(L${\rm bol}$), X-ray luminosity (Lx), and redshift (z). Figure 9 illustrates
this representation using various samples which include: The eFEDS sources at
0.5$<$z$<$1, Sample A and Sample B at 0.5$<$z$<$1 (consisting of 427 sources;
’parent sample’), Sample A and Sample B with good quality spectra (comprising
50 sources), and 23 sources identified with outflows.

From the left panel of this Figure, we observe that the sources with good-
quality SDSS spectra (indicated by purple stars) are clustered towards high
column densities and slightly high bolometric luminosities with respect to
their parent sample (indicated by blue stars). On the other hand, the sources
with clear outflow signatures (indicated by red stars) cover the same
parameter space as those with good-quality SDSS spectra. The fact that the
sources with outflows have on average N${}_{\rm H}\sim 10^{22}$ cm-2 and high
bolometric luminosities $\mathrm{logL_{bol}\sim\leavevmode\nobreak\
45.2\leavevmode\nobreak\ erg\leavevmode\nobreak\ s^{-1}}$ than the parent
sample may be ascribed to a selection bias affecting the sample with good
quality SDSS spectra, which is dominated by Sample B. Since NH is a direct
parameter in one of our selection methods, we plot the X–ray luminosity and
redshift distributions again (right panel) but only for three samples to asses
their representation. We find that our samples are generally consistent with
each other in terms of redshift, but we do tend to pick up sources with
slightly higher X–ray luminosities.

We refer the reader to Appendix C for comprehensive details regarding the
number of sources identified with outflows from individual selection methods.
Having in mind that the sources with detected outflows may be a genuine
representation only of the most obscured and luminous sources in the parent
sample, we use our small samples to discuss the reliability and validity of
the statistical analyses conducted in the study.

|
---|---
Figure 9: Comparisons of the different samples. Left panel: $\mathrm{N_{H}}$
and AGN bolometric representation of our isolated candidates. Open grey
circles represent eFEDS sources at 0.5$<$z$<$1, blue-filled stars represent
sample A and sample B at 0.5$<$z$<$1, purple-filled stars represent sample A
and sample B with good quality SDSS spectra and the red-filled stars represent
the 23 candidates confirmed with outflows. The colours used in the histograms
are identical to the colours used in the legend of the scatter plot for the
same samples. The dotted lines represent the means of the respective
distributions. Right panel: The X–ray luminosity and redshift distributions of
three samples; sample A and sample B at 0.5$<$z$<$1, sample A and sample B
with good quality SDSS spectra and 23 candidates confirmed with outflows. The
colours used in the histograms are identical to the colours used in the legend
of the scatter plot for the same samples.

The number of sources with outflows has narrowed down to less than half of the
candidates with the best quality SDSS spectra. This study primarily relies on
SDSS spectra, which are prone to poor signal-to-noise conditions, consequently
imposing limitations on the accuracy of our results. Furthermore, our ability
to trace outflows is constrained by the wavelength range available, thereby
restricting our study to a single phase (ionised). Our relatively small sample
size can be attributed to these inherent limitations. However, we note that
the identification of these outflows, despite their limited numbers, could
potentially be linked to the duty cycle of outflows and the blow-out phase
being rather short (Schawinski et al., 2015; King & Nixon, 2015) compared to
the average AGN timescales in evolutionary models. This means that only a few
fractions of AGNs can be detected in the blow-out phase.

We list in Table 4 the fitting results for these 23 sources, that is the
narrow and broad FWHM, the broad [OIII] flux (and its significance) and the
corresponding luminosity with their uncertainties as estimated using a Monte
Carlo approach that is already included in PyQSOFit package (Guo et al., 2018;
Shen et al., 2019). For each source, we defined a maximum outflow velocity
(Vmax) as

$\rm{V_{max}=|\Delta{V}|+2\sigma_{[OIII]}^{broad}},$ (6)

where $\Delta{V}$ is the velocity shift between the velocity peak of the broad
emission line and the systemic velocity and $\sigma$ is the velocity
dispersion (see Appendix E for a detailed discussion on the computation of
outflow velocities in the literature). This quantity is also listed in Table
4, along with $\Delta{V}$ and $\sigma$. Other properties of these 23 sources
(NH, LX, Lbol and M∗) are reported in the first part of Table 1.

Table 1:  X-ray properties, stellar mass and outflow properties of our
candidates with outflows

EROID | $\mathrm{log\>N_{H}}$ | log $\rm{L_{x}}$ | log $\mathrm{L_{bol}}$ | log ${M_{*}}$ | $\rm{R_{out}}$ | $\rm{M_{out}}$ | ${\dot{M}}$ | ${\dot{E}}$ | ${\dot{P}_{OF}}$
---|---|---|---|---|---|---|---|---|---
| $\mathrm{cm^{-2}}$ | $\mathrm{erg\leavevmode\nobreak\ s^{-1}}$ | $\mathrm{erg\leavevmode\nobreak\ s^{-1}}$ | $\mathrm{{M}_{\odot}}$ | kpc |  $\mathrm{{M}_{\odot}}$ ($10^{6}$) | $\mathrm{{M}_{\odot}{yr}^{-1}}$ |  $\mathrm{erg\leavevmode\nobreak\ s^{-1}}$ ($10^{41}$) |  $\mathrm{dyne}$ ($10^{34}$)
25592 | 20.3 | 42.7 | 43.9 | 11.2 | 5.4 | 10.7$\pm$0.1 | 17.1$\pm$0.3 | 241.9$\pm$8.4E-6 | 22.9
6743 | 23.0 | 44.2 | 45.5 | 10.8 | 6.5 | 0.8$\pm$0.03 | 0.6$\pm$0.06 | 2.6$\pm$9.4E-5 | 0.4
608 | 22.3 | 44.8 | 46.2 | -99.0 | 10.0 | 4.4$\pm$0.2 | 2.6$\pm$0.1 | 17.2$\pm$8.4E-5 | 2.4
19520 | 22.1 | 44.0 | 45.3 | 9.8 | 4.5 | 13.0$\pm$0.9 | 22.6$\pm$2.2 | 260.6$\pm$0.005 | 27.3
18777 | 21.5 | 43.7 | 44.9 | 10.9 | 9.0 | 1.8$\pm$0.1 | 2.7$\pm$0.3 | 94.7$\pm$0.005 | 5.7
21835∗ | 21.8 | 44.3 | 45.6 | 10.9 | 9.3 | 6.3$\pm$0.5 | 2.1$\pm$0.3 | 4.2$\pm$6.2E-4 | 1.1
12686 | 22.4 | 44.3 | 45.6 | 10.9 | 6.0 | 4.1$\pm$0.3 | 3.1$\pm$0.6 | 12.0$\pm$0.006 | 2.2
31136 | 21.7 | 43.1 | 44.3 | -99.0 | 10.0 | 4.5$\pm$0.4 | 2.9$\pm$0.3 | 24.0$\pm$8.7E-4 | 3.0
5896∗ | 22.3 | 44.4 | 45.7 | -99.0 | 10.0 | 9.1$\pm$0.9 | 3.4$\pm$0.5 | 8.9$\pm$0.001 | 2.0
16271 | 21.7 | 43.5 | 44.7 | 10.3 | 2.0 | 0.6$\pm$0.09 | 1.5$\pm$0.3 | 7.3$\pm$0.007 | 1.2
14896 | 21.5 | 43.9 | 45.2 | 11.2 | 3.5 | 1.7$\pm$0.2 | 2.5$\pm$0.5 | 13.9$\pm$0.008 | 2.1
10152 | 20.7 | 43.8 | 45.1 | -99.0 | 10.0 | 2.2$\pm$0.3 | 1.9$\pm$0.9 | 27.4$\pm$0.4 | 2.6
11596 | 21.6 | 44.2 | 45.5 | 10.9 | 3.9 | 7.3$\pm$1.3 | 20.2$\pm$4.0 | 452.4$\pm$0.04 | 34.0
14390 | 21.7 | 43.5 | 44.7 | 10.2 | 3.0 | 5.7$\pm$1.1 | 6.4$\pm$1.3 | 13.7$\pm$5.4E-4 | 3.3
16050 | 21.6 | 43.5 | 44.8 | 11.1 | 7.7 | 2.8$\pm$0.6 | 1.4$\pm$0.6 | 3.9$\pm$0.04 | 0.8
19964 | 21.7 | 43.5 | 44.8 | 10.5 | 5.7 | 0.4$\pm$0.1 | 0.1$\pm$0.06 | 0.1$\pm$4.7E-4 | 0.1
14541 | 21.5 | 43.8 | 45.1 | 10.0 | 4.6 | 2.1$\pm$0.6 | 6.8$\pm$2.9 | 274.6$\pm$2.5 | 15.4
19174 | 22.9 | 44.4 | 45.7 | 11.0 | 5.7 | 12.3$\pm$3.9 | 11.9$\pm$8.7 | 70.1$\pm$6.3 | 10.3
28337 | 21.9 | 43.9 | 45.2 | -99.0 | 2.9 | 1.0$\pm$0.3 | 0.7$\pm$0.5 | 0.7$\pm$0.04 | 0.3
16799 | 21.6 | 43.3 | 44.5 | 10.8 | 7.8 | 0.6$\pm$0.2 | 0.1$\pm$0.2 | 0.1$\pm$0.1 | 0.04
19841 | 21.5 | 43.6 | 44.9 | -99.0 | 10.0 | 1.5$\pm$0.5 | 0.4$\pm$0.1 | 0.9$\pm$7.1E-4 | 0.2
17754 | 21.7 | 44.1 | 45.3 | 10.9 | 6.3 | 0.5$\pm$0.1 | 0.2$\pm$0.1 | 0.6$\pm$0.004 | 0.1
15417 | 22.1 | 44.1 | 45.4 | 10.3 | 7.8 | 9.9$\pm$3.5 | 6.2$\pm$2.3 | 28.1$\pm$0.02 | 4.7

  * •

Notes: The columns (left-right) are eROSITA ID (EROID ) of our candidates with
outflows, column density ($\mathrm{log\>N_{H}}$), X–ray luminosity (
$\rm{L_{x}}$; 2-10 keV), AGN bolometric luminosity (AGN $\mathrm{L_{bol}}$)
and stellar mass (${M_{*}}$). Column density and X–ray luminosity are obtained
from (Liu et al., 2022), AGN bolometric luminosity calculated from X–ray
luminosity and the bolometric corrections using Eq. 3 in Duras et al. (2020)
relation. Followed by outflow properties; radius ($\rm{R_{out}}$), outflow
mass ($\rm{M_{out}}$), mass outflow rate (${\dot{M}}$), outflow kinetic power
(${\dot{E}}$) and momentum flux of the outflow(${\dot{P}_{OF}}$) as estimated
in this study. -99.0 is used to indicate missing values. Sources marked with ∗
have single Gaussian components.

###  3.3 Ionised AGN outflow properties

From the spectral analysis, quantities such as the measured velocities, and
the emission line luminosities can be derived. Outflow physical properties
such as mass outflow, mass outflow rate and kinetic power, can then be
constrained by applying a set of standardised assumptions.

As far as the $\mathrm{[OIII]}5007$ line is concerned, and adopting the
approach proposed by Cano-Díaz et al. (2012) and Carniani et al. (2015), the
ionised mass outflow is given by:

$\mathrm{M_{out}^{ion}}=\rm{5.33\times{10^{7}}M_{\odot}\left(\frac{C}{10^{[O/H]}}\right)\left(\frac{L_{[OIII]}}{10^{44}ergs^{-1}}\right)\left(\frac{<n_{e}>}{10^{3}cm^{-3}}\right)^{-1}},$
(7)

where $\rm{L_{44}([OIII])}$ is the luminosity of the broad component of the
$\mathrm{[OIII]}$ line in units of $\mathrm{10^{44}\leavevmode\nobreak\
erg\leavevmode\nobreak\ s^{-1}}$, $\mathrm{n_{e}}$ is the outflowing gas
electron density in units of $\mathrm{10^{3}cm^{-3}}$, $\mathrm{10^{[O/H]}}$
is the oxygen abundance in solar units and C is a factor that encodes the
condensation factor of the gas clouds (see Cano-Díaz et al. 2012, for details.
The ionising gas clouds are always assumed to have the same density thus the
condensation factor C is approximated to 1, and the metallicity of the
outflowing material is always assumed solar.

From Eq. 7, the mass outflow rate can be calculated either assuming spherical
or shell$-$like geometry. In the case of spherical mass outflow rate, from the
fluid field continuity equation,
$\mathrm{\rho=\frac{3M_{out}}{\Omega{\pi}R^{3}}}$ is the mean density of an
outflow, while $\mathrm{\Omega{\pi}}$ is the solid angle covered by the
outflow. The mass outflow rate can thus be written as;

${\dot{\textrm{M}}_{\mathrm{{out}}}^{\rm{ion}}}=\rm{\Omega{\pi}R^{2}\rho{\nu}=3\frac{M_{out}^{ion}V_{out}}{R_{out}}},$
(8)

where $\rm{V_{out}}$ is the outflow velocity, and $\rm{R_{out}}$ (in kpc) is
the radius at which the outflow is computed333For an outflow assumed to
propagate in a thin shell of thickness $\rm{\Delta{R}}$, the mass outflow rate
is given by
${\dot{\textrm{M}}_{\mathrm{{out}}}^{\rm{ion}}}=\rm{\frac{M_{out}^{ion}V_{out}}{\Delta{R}}}.$
(9) .

By substituting Eq. 7 in 8, and assuming solar metallicity and a condensation
factor C$=$1, the mass outflow rate in units of $\rm{M_{\odot}yr^{-1}}$ can be
rewritten as;

$\begin{split}{\dot{\textrm{M}}_{\mathrm{{out}}}^{\rm{ion}}}=\rm{164\left(\frac{kpc}{R_{out}}\right)\left(\frac{L_{[OIII]}}{10^{44}erg\leavevmode\nobreak\
s^{-1}}\right)}\\\
{\left(\frac{\rm{V_{out}}}{1000\;\rm{kms^{-1}}}\right)\left(\frac{<\rm{n_{e}}>}{10^{3}\;\rm{cm^{-3}}}\right)^{-1}}.\end{split}$
(10)

The momentum flux of the outflow can then be computed as,

${\dot{\textrm{P}}}={\dot{\textrm{M}}_{\mathrm{{out}}}^{\rm{ion}}}\times{\rm{V_{out}}}.$
(11)

Finally, the kinetic luminosity can be deduced as,

${\dot{\textrm{E}}_{\mathrm{{kin}}}}={\frac{1}{2}\times{{\dot{\textrm{M}}_{\mathrm{{out}}}^{\rm{ion}}}\times{\rm{V^{2}_{out}}}}}.$
(12)

For all the sources in Table 1, we calculated the outflow properties using Eq.
10, 11 and 12. Given that for our eFEDS sources we do not have spatially
resolved data, we assumed as outflow radius (Rout) the galaxy half-light
radius as estimated from AGN-host galaxy image decomposition (Li et al. (2023)
following the method described in Li et al. 2021) on deep i-band data obtained
in the footprint of the Hyper Suprime Cam (HSC, Miyazaki et al. 2018) Subaru
Strategic Program (HSC-SSP: Aihara et al. 2018, 2017, 2019). Most likely, the
outflow will be contained within the host galaxy therefore the assumed radius
will provide conservative estimates of the mass outflow rates. As outflow
velocity Vout, we used the maximum velocity calculated from our fit parameters
using Eq. 6, while to compute the [OIII] line luminosity we considered the
flux associated with the detected broad component.

Finally, our data do not permit a direct estimate of the gas electron density.
Therefore, we assumed for ne a value of 200 $\mathrm{cm^{-3}}$, that is the
one used in Fiore et al. (2017) and within the range of the measured values of
other high-redshift targets (Nesvadba et al., 2006; Perna et al., 2015b; Brusa
et al., 2015, 2016, among others).

We measure mass outflow rates in the range $\mathrm{\sim
0.2-23\leavevmode\nobreak\ M_{\odot}\leavevmode\nobreak\ yr^{-1}}$, kinetic
powers in the range ${log(\dot{E})\leavevmode\nobreak\
\sim\leavevmode\nobreak\ 40-44}$ erg s-1 and outflow momentum rates in the
range $\rm{4.8\leavevmode\nobreak\ \times\leavevmode\nobreak\
10^{32}\leavevmode\nobreak\ dyne}$ \- $\rm{3.4\leavevmode\nobreak\
\times\leavevmode\nobreak\ 10^{35}\leavevmode\nobreak\ dyne}$. When compared
to the radiative momentum flux from the central black hole
(${\dot{\textrm{P}}_{\mathrm{{AGN}}}=\mathrm{L_{bol}/c}}$), we obtain momentum
flux ratios in ranges of $\sim$0.02 - 75 with only one source having
${\dot{\textrm{P}}_{\mathrm{{OF}}}}/\dot{\textrm{P}}_{\mathrm{{AGN}}}$ above
20. All these values are listed in the second part of Table 1. The several
assumptions on different parameters such as geometry, electron density,
temperature, and in some cases, the velocity of the outflowing gas and radius
introduce at least 2-3 orders of magnitude uncertainties in the final
estimated values of the outflow properties (see Appendix E for details).

##  4 Discussion

###  4.1 Selection of quasars in the feedback phase

Any single selection criterion may be incomplete and biased for the
identification of the blow-out candidates. This is especially problematic when
the sub-population of interest constitutes a small minority with uncertain and
potentially diverse observational signatures. This is the case for AGNs in the
blow-out phase, where we expect different observed and physical properties
depending on the exact coupling of the AGN feedback with the ISM and the level
of the obscuration, and where everything is further complicated by redshift
effects. This work merges several complementary selection criteria to enable a
more complete selection and minimise the selection biases of individual
selections.

In Sect. 2, we applied a variety of methods used in previous studies (Brusa et
al., 2015; Kakkad et al., 2016; Perrotta et al., 2019; Vayner et al., 2021;
Brusa et al., 2022) to a large, homogenous sample of X–ray selected AGNs in
the eFEDS field (Liu et al., 2022). We constructed two samples of candidate
AGNs with outflows, highly complementary in terms of luminosity and redshift
distribution. The two samples were defined based on the combination of colour-
selection methods targeting mostly sources where reddening, extinction or
obscuration are important (Sample A) and on the $\mathrm{N_{H}}$-$\lambda_{\rm
Edd}$ diagnostic (Sample B). This resulted in a total of $\sim$1400 unique
sources.

We tested the efficiency of the selection via spectroscopic analysis of SDSS
optical spectra, looking for unsettled gas motions in the [OIII] line
emission. We can conduct this experiment only for the $\sim 430$ sources at
0.5$<$z$<$1\. All sources in Sample B have available spectra, but only
$\sim\\!15$% are at 0.5$<$z$<$1\. On the other hand, despite $\sim\\!40$% of
sources in Sample A having 0.5$<$z$<$1, optical spectra exist only for 6 of
them. This implies that we are able to validate the efficiency of the
selection only on limited samples, for example, 20% of the 0.5$<$z$<$1 sample
and $\sim$6% of the overall candidates. Although incompleteness and selection
biases may still affect our subsample of outflowing sources, our work still
enables us to increase the overall number of outflowing AGNs so far detected
and thus provides additional validation tests for the scaling relations
previously published in the literature.

We report that $\sim$45% of the sources with available good quality spectra
from the combined sample (Sample A + B) have clear signatures of outflows (see
Sect. 3.2) and this may be as high as 80% if we consider sources for which a
broad component can be accommodated in the fit, but at a lower significance.
This is a striking confirmation of the efficiency of the combined selection to
recover this rare population, at least at 0.5$<$z$<$1, and among the most
obscured and luminous sources.

When only sources from Sample A are considered, the fraction of significant
broad line detections rises from 45% to 75%. In particular, strong winds in
red sources are expected in the very initial stages of models in which AGN
feedback is radiatively driven and launched by trapped IR radiation (e.g.
Costa et al., 2018c, a). In these same models, the optical depth in the UV and
IR is initially very high along all lines of sight (Costa, private
communication). Based on the limited and very small but satisfactory data
obtained from the colour selection (3/4 sources), it appears that our combined
colour selection method could potentially be the most effective approach for
isolating sources in the initial phases of the outflow.

The column density versus Eddington ratio-based selection (’forbidden region’
in the $\lambda_{Edd}$-NH plane which defines Sample B) may still trace
radiatively driven outflows episodes launched by trapped IR radiation. The
adopted selection diagnostic returned, however, mostly AGNs with blue
optical/IR colours. This is largely due to a selection bias: BH masses are
hardly measurable in optical spectra for red and/or Type 2 AGN, for which
instead dedicated deep or NIR follow-up is needed (see e.g. Bongiorno et al.,
2014). In most hydrodynamical simulations the timescale for the blow-out phase
is predicted to be very short ($<$ few$\times 10$-100 Myr; (see e.g. Hopkins
et al., 2008; Yutani et al., 2022)) and the average value of the optical depth
also decreases very rapidly. After 10 Myr, the average line of sight UV and IR
depth may be already diminished by a factor of $\sim 100$, facilitating the
leaking of blue continuum radiation from the inner regions of the accretion
disc.

###  4.2 AGN and outflow properties correlations

Figure 10:  AGN bolometric luminosity as a function of outflow velocity.
Different shapes represent different samples from literature, as labelled. The
solid grey line is the scaling relation obtained from fitting between the two
variables including our AGN outflows from eFEDS (see Table 2). The grey region
indicates the 95% confidence interval and the shaded filled region between two
dashed black lines is the 1 $\sigma$. The red dashed line is the scaling
relation from Fiore et al. (2017), obtained for a sample of $\sim 55$ ionised
outflows without imposing a redshift cut z$>0.5$. The blue dashed line is the
scaling relation obtained from fitting the two variables excluding our eFEDS
sources. The relation still appears flattish as compared to Fiore et al.
(2017). It is important to note that we maintain the same legend for QWO and
eFEDS sources in the following figures.  Figure 11: Ionised mass outflow rate
as a function of AGN bolometric luminosity. Different shapes represent
different literature samples (as labelled). The filled circles are colour-
coded with redshift. The blue dashed line is the best-fit relation obtained
for ionised outflows in Bischetti et al. (2019). The solid grey line is the
scaling relation obtained in this work, from fitting between the two variables
(see Table 2). The grey region indicates the 95% confidence interval and the
shaded filled region between two dashed black lines is the 1 $\sigma$. The red
dashed line is the scaling relation from Fiore et al. (2017), obtained for a
sample of $\sim 55$ ionised outflows without imposing a redshift cut z$>0.5$.
The error bars on mass outflow rate values were obtained by extrapolating the
errors on FWHM or $\rm{\delta{V}}$ whenever available. These values may have
2-3 orders of magnitude uncertainties due to the different assumptions
applied.

AGN feedback is one of the suggested mechanisms which contributes to SF
quenching. If it happens, how it happens, on which scale does it affect the SF
(impact on nuclear regions or the whole galaxy) and how much it contributes to
the quenching are all still open questions. A way to address this topic, at
least statistically, is to look at correlations between outflow properties and
properties of AGNs and host galaxies. From an observational point of view,
several studies in the past reported correlations between the physical
properties of outflows at all scales and AGNs and/or host galaxies properties
(e.g. Fiore et al., 2017; Bischetti et al., 2017; Matzeu et al., 2023, among
others), the most striking being the correlation between mass outflow rate and
AGN bolometric luminosity. The mutually inconsistent recipes used to compute
the outflow properties in the literature, not considering different scenarios
such as multi-phase nature, multi-scale and environment (the wind that may
have escaped in the least resistance media or more resistance) can contribute
to diluting the correlation between these properties.

In the following, we explore the correlations between outflow properties and
AGN luminosity for a large sample of sources with ionised gas outflows. More
specifically, our newly detected 23 sources with ionised outflows are
presented in Sect. 3.3. We add a sample of AGN with outflows compiled from the
literature and including previously confirmed AGNs with outflows at z$>$0.5
and for which the physical properties have been derived, with a focus on
ionised outflows traced by [OIII], $\rm{H_{\alpha}}$ or $\rm{H_{\beta}}$
emission lines. We refer to this sample as the Quasar With Outflows (QWO)
sample hereafter.

The QWO sample contains 118 sources at z$>$0.5, compiled from Brusa et al.
(2015); Kakkad et al. (2016); Fiore et al. (2017); Leung et al. (2019);
Perrotta et al. (2019); Kakkad et al. (2020); Vayner et al. (2021); Brusa et
al. (2022). Fiore et al. (2017) contains ionised outflows detections and an
estimate of their main physical parameters from a number of references which
include: Nesvadba et al. (2008); Harrison et al. (2012); Maiolino et al.
(2012); Rupke & Veilleux (2013); Liu et al. (2013); Harrison et al. (2014);
Genzel et al. (2014); Cresci et al. (2015a); Perna et al. (2015b, a); Carniani
et al. (2015); Cicone et al. (2015); Brusa et al. (2016); Bischetti et al.
(2017). For all these sources AGN bolometric luminosity is available, although
derived in a heterogeneous way: the bolometric luminosity in Leung et al.
(2019) is obtained from $\mathrm{[OIII]}$ line luminosity (L[OIII]) by
applying a bolometric correction of 600 (Kauffmann & Heckman, 2009), Kakkad et
al. (2020) obtain an estimate of Lbol by SED fitting, Fiore et al. (2017) and
the rest from either SED fitting or bolometric correction from different
wavebands. The uncertainty that may arise due to bolometric luminosity
obtained from different approaches is assumed negligible. Finally, we note
that the several assumptions on different parameters such as geometry,
electron density, temperature, and in some cases, the velocity of the
outflowing gas and radius introduce at least one order of magnitudes
uncertainties in the estimated values of the outflow properties, and this
could contribute to increasing the scatter in the correlations.

|
---|---
Figure 12: Ionised kinetic power and kinetic coupling efficiency as a function
of AGN bolometric luminosity. Left panel: Ionised kinetic power as a function
of AGN bolometric luminosity. The red dashed line is the best scaling relation
obtained in Fiore et al. (2017). The solid grey line in both panels is our
scaling relation obtained from OLS fitting between the two variables. The grey
region indicates the 95% confidence interval and the faded filled region
between two dashed black lines is the 1 $\sigma$. Right panel: Kinetic
coupling efficiency (${\dot{E}/L_{bol}}$) versus AGN bolometric luminosity.
The black dashed line represents ${\dot{E}=0.1L_{bol}}$, red dashed line
represents ${\dot{E}=0.01L_{bol}}$ and green dashed line represents
${\dot{E}=0.001L_{bol}}$. 30% of the candidates appear above
${\dot{E}/L_{bol}}$=0.01 or 1% . These values have 2-3 orders of magnitude
uncertainties due to the different assumptions applied.

For the QWO sample, we collected all the parameters as measured from spectral
fitting ($\rm{[OIII]}$ or line luminosity, FWHM, $\sigma$ and $\mathrm{n_{e}}$
if reported, the quoted outflow velocities otherwise) and from observations
(outflow radius if available). We computed mass outflow, mass outflow rate,
and outflow kinetic power following the same receipt used for our eFEDS
sources444In case of parameters derived from H$\alpha$ or H$\beta$ spectral
fit, the outflow parameters can be derived following an approach similar to
the one presented in Sect.3.3, with prescriptions changed accordingly to
convert hydrogen flux to mass, (see e.g. Nesvadba et al., 2017; Leung et al.,
2019; Riffel et al., 2023) . We maintain the reported outflow properties for
sources in Fiore et al. (2017). The limited spatial resolution of the
available observations required several assumptions to estimate outflow
properties (see Appendix E for the details of the properties we re-computed
and the assumptions applied).

We investigate several scaling relations between outflow properties and AGN
bolometric luminosities, for a total of 141 sources in the distant Universe
(z$>0.5$; QWO+eFEDS sample). This is the largest sample of AGNs with ionised
outflows at z$>$0.5 and it is $\sim$3 times larger than the previous
compilations (e.g. Fiore et al. 2017; Leung et al. 2019). Adopting the linear
regression fitting procedure that uses the ordinary least square (OLS) model
between $\mathrm{V_{max}}$ and bolometric luminosity, we obtain a best-fit
scaling relation as $\mathrm{L_{bol}\propto{V_{max}}^{1.78\pm 0.2}}$ which
significantly differs from $\mathrm{L_{bol}\propto{V_{max}}^{6.1\pm 4.4}}$
reported in Fiore et al. (2017). The QWO+eFEDS sample in the Lbol-Vmax plane
is shown in Fig. 10 along with the best-fit relation (grey shaded region) and
the Fiore et al. (2017) relation (red dashed line). There is still a
significant difference with the Fiore et al. (2017) correlation when the
fitting is done on the QWO sample, excluding our confirmed outflows from
eFEDS. In this case we obtain a scaling relation of
$\mathrm{L_{bol}\propto{V_{max}}^{1.87\pm 0.21}}$, shown as a blue dashed line
in Fig. 10555When fitting our sample in the $\mathrm{V_{max}}\propto{L_{bol}}$
plane, we find $\mathrm{V_{max}}\propto{L_{bol}^{0.15\pm 0.02}}$, and
$\mathrm{V_{max}}\propto{L_{bol}^{0.22\pm 0.03}}$ when eFEDS sources are
excluded. This value is consistent with the slope of 0.27 reported by Leung et
al. (2019).. We note that the much steeper Fiore et al. (2017) correlation has
been derived on a factor of $\sim 3$ smaller sample, and more heterogeneous in
terms of redshift. Indeed, the Fiore et al. (2017) sample includes 51 sources
detected at all redshifts, with about 35% at z$<$0.5. This is also reflected
in the relatively large error associated with the measured slope reported in
their work. The main reason for a flatter trend is due to the fact that
sources in the QWO+eEFEDS sample have on average lower bolometric luminosities
($\sim 1dex$) than the original Fiore et al. (2017) sample, despite having
high outflow velocities. This points once again to the importance of the
sample selections for correlation studies. In particular, the primary
selection of our eFEDS sample is the presence of bright X-ray emission,
whereas this is not the case for the majority of the sources from the QWO (and
in the Fiore et al. 2017 sample). Our thesis is that the X-ray active,
obscured phase may be the best tracer of the fastest phase of the winds, and
their velocity may not necessarily depend on the AGN bolometric luminosity
(see e.g. Brusa et al. 2015). Even though 23 sources from eFEDS may be a
relatively small sample detected with outflows, they occupy a region of
parameter space never explored before in the
$\mathrm{L_{bol}}$-$\mathrm{V_{max}}$ plane. This points, when looking at the
data at face value in their entirety, to a non-existent correlation between
these two variables.

In Fig. 11, we show that for our combined sample the ionised mass outflow
rate, ${\dot{\textrm{M}}_{\textrm{{ion}}}}$ (computed on the basis of
standardised and homogenised assumptions) correlates well with the AGN
bolometric luminosity. We obtain the scaling relation as
${\dot{\textrm{M}}_{\textrm{{ion}}}\propto\mathrm{{L_{bol}}}^{1.16\pm 0.07}}$
with Spearman rank correlation coefficient of 0.64. The more luminous the AGN,
the more prevalent the outflows (see also Mullaney et al., 2013; Zakamska &
Greene, 2014). Our scaling relations of mass outflow rate with AGN bolometric
luminosity are only slightly flatter than what has been published in previous
studies on smaller samples, which reported scaling relations of
${\dot{\textrm{M}}_{\textrm{{ion}}}\propto\mathrm{{L_{bol}}}^{1.29\pm 0.38}}$
(Fiore et al., 2017) and
${\dot{\textrm{M}}_{\textrm{{ion}}}\propto\mathrm{{L_{bol}}}^{1.34\pm 0.37}}$
(Leung et al., 2019). We have increased the degrees of freedom threefold than
those in Fiore et al. (2017). Our correlation is also consistent with the
best-fit relation obtained for ionised outflows in Bischetti et al. (2019),
shown with a blue curve in Fig. 11.

The colour bar in Fig. 11 highlights that there is a slight trend in redshift
with AGN bolometric luminosity (and therefore mass outflow rate). We also
found correlation trends between the mass outflow rates, black hole mass, and
Eddington ratio. These trends are reported in the Appendix F, contrary to the
weak correlation between these properties found in Kakkad et al. (2022) for
low redshift quasars. This may imply that there is a single mechanism dominant
in driving the outflows for the sources in our compilation. The scatter
observed in the AGN bolometric luminosity and mass outflow rate scaling
relation indicates that outflow power depends not only on $\mathrm{L_{bol}}$
but also on other factors such as the coupling between outflows and host and
amount or geometry of dense gas in the nuclear regions (as discussed in e.g.
Ramos Almeida et al. 2022)

We computed the kinetic power from the above mass outflow rates, using
standardised assumptions for both the QWO sample and our eFEDS targets. As
shown in the left panel of Fig. 12, by applying linear regression fitting
procedure that uses the ordinary least square (OLS) model, we obtained a best-
fit scaling relation of
${\dot{\textrm{E}}_{\textrm{{ion}}}\propto\mathrm{{L_{bol}}}^{1.47\pm 0.09}}$.
Fiore et al. (2017) and Leung et al. (2019) reported
${\dot{\textrm{E}}_{\textrm{{ion}}}\propto\mathrm{{L_{bol}}}^{1.48\pm 0.37}}$
and ${\dot{\textrm{E}}_{\textrm{{ion}}}\propto\mathrm{{L_{bol}}}^{1.87\pm
0.51}}$, respectively with slopes that are comparably similar to our scaling
relation obtained from our sample. The results from all our fittings are
represented in Table 2 which shows the slope, Spearman rank correlation
coefficient and the constant with their respective errors.

Mass outflow rates and kinetic powers are the quantities that, on the basis of
theoretical models, are expected to correlate with the AGN bolometric
luminosity and depends both on the outflow velocity and the total entrained
mass. For a given bolometric luminosity the same mass outflow rate can be
observed in sources with fast winds and low entrained mass (for instance,
winds caught at an early stage of the feedback phase), or with massive but
slower winds (for instance, winds caught at a later stage of feedback phase).
Overall, combining our results shown in Fig.10, 11 and 12 we can conclude that
our eFEDS selection preferentially isolates obscured QSO in the fastest phase
of the wind (see also Costa et al. 2018c).

The right panel of Fig. 12 shows the ratio between the kinetic power and the
AGN bolometric luminosity
(${\dot{\textrm{E}}_{\mathrm{{ion}}}/\mathrm{L_{bol}}}$) as a function of the
AGN bolometric luminosity. A larger fraction of ionised outflows occupy the
1$\%\\!<\\!{\dot{\textrm{E}}_{\mathrm{{ion}}}/\mathrm{L_{bol}}}\\!<$10% as
compared to Fiore et al. (2017), and $\sim$30% of the ionised winds have
${\dot{\textrm{E}}_{\mathrm{{ion}}}/\mathrm{L_{bol}}}$ in the range 1$-$100%.
Overall, more than half of the sample has
${\dot{\textrm{E}}_{\mathrm{{ion}}}/\mathrm{L_{bol}}}$ within one dex of the
theoretical predictions (Di Matteo et al. 2005; Hopkins & Elvis 2010; Schaye
et al. 2015, see also Fig. 2 in Harrison et al. 2018 for more theoretical
predictions as compared to observations). However, we note that taking
measurements at face value, 70% have
${\dot{\textrm{E}}_{\mathrm{{ion}}}/\mathrm{L_{bol}}}\\!<\\!1$%. As discussed
in Harrison et al. (2018), as the wind traverses in the surrounding ISM, some
part of the original nuclear wind energy is used to do work against other
forces. As a consequence, the final outflow kinetic energy is expected to be
considerably lower than the original ejected energy. Some models (e.g. Hopkins
& Elvis (2010) and as reviewed in Harrison et al. 2018 ) predict that even
with ${\dot{\textrm{E}}_{\mathrm{{ion}}}/\mathrm{L_{bol}}}\\!<\\!$1%
radiatively driven winds are capable of having a significant effect on the
host galaxy.

Table 2: Results from AGN and outflow properties correlations.  Correlation |  Slope |  Constant |  R$-$value |  P$-$value
---|---|---|---|---
$\mathrm{L_{bol}}$ Vs. $\mathrm{V_{max}}$ |  1.78$\pm$0.2 |  40.7$\pm$0.8 |  0.27 |  $<10^{-5}$
${\dot{M}}$ Vs. $\mathrm{L_{bol}}$ |  1.16$\pm$0.07 |  -51.7$\pm$3.3 |  0.67 |  $<10^{-5}$
${\dot{E}}$ Vs. $\mathrm{L_{bol}}$ |  1.47$\pm$0.09 |  -24.3$\pm$4.2 |  0.66 |  $<10^{-5}$
Figure 13: We plot the outflow momentum rate (momentum flux of the outflow
divided by the radiation momentum flux from the central black hole) against
the maximum outflow velocity and colour-coded with the AGN bolometric
luminosity. The black solid lines show the
${\mathrm{{\dot{P}_{OF}/\dot{P}_{AGN}}}}\\!=\\!20$ and =1 as indicated in the
plot. The majority of our sources have momentum flux ratios of less than 20.

The comparison between outflow momentum rates
($\dot{\textrm{P}}_{\mathrm{{OF}}}$) and the radiative momentum flux from the
central black hole (Lbol/c) has been proposed to be key to understanding
whether the detected outflows are energy or momentum conserving. Indeed,
models predict that energy-driven winds on large-scale outflows have momentum
fluxes ${\dot{\textrm{P}}_{\mathrm{{OF}}}\\!\sim\\!\mathrm{20L_{bol}/c}}$
(e.g. Zubovas & King, 2012). On the contrary, momentum-driven winds would show
${\dot{\textrm{P}}_{\mathrm{{OF}}}\\!\sim\\!1\mathrm{L_{bol}/c}}$. Figure 13
shows the momentum flux versus the outflow velocity for our QWO+eFEDS
homogenised sample. For the outflows confirmed for the first time in this work
(red stars in Fig. 13), a bigger fraction have momentum flux ratios lower than
20 which in principle rules out their energy-conserving nature. This indicates
that our probed outflows could be either momentum-driven or energy-driven with
momentum being carried in other gas phases. These results are consistent with
the momentum flux ratios found in the previous studies for ionised outflows,
for example Perna et al. (2015b); Leung et al. (2019) and Tozzi, G. et al.
(2021) for outflow momentum rates $<10\rm{L_{bol}/c}$ and in Carniani et al.
(2015); Kakkad et al. (2016) and Marasco et al. (2020) for ionised outflows
below the momentum flux ratio of 1. Considering the full new compilation (QWO
and eFEDS targets) shown in Fig. 13, we obtain median outflow momentum rates
$\sim$1 times the momentum flux from the AGN.

##  5 Conclusions

This paper focused on the selection and characterisation of z$>0.5$ AGNs in
the feedback phase. We applied a combination of various selection methods
previously proposed in the literature to the eFEDS main AGN sample (Sect. 2),
to maximise the completeness (of the selection) and reduce the chances of a
biased selection. We then investigated the presence of ionised gas outflows in
the 0.5$<$z$<$1 subsample population via spectral fitting of the [OIII]
emission line profile (Sect. 3.2). Finally, we explored the scaling relations
between AGN luminosity and outflow properties of a large sample of 141 sources
at z$>\\!0.5$ (Sect. 4.2).

We summarise our results from this study as follows:

  * •

By applying a combination of selection methods to eFEDS, we isolated 853
candidates AGNs in the outflow phase from flux ratios and colour selection
diagnostics. Similarly, we isolated 528 candidates applying the NH versus
Eddington ratio diagnostic, to the subsample of sources with BH mass measured
in SDSS-IV data (see Sect. 2.3). In total, we isolated a sample of $\sim$1400
obscured and/or red quasars expected to be in the feedback phase, which
corresponds to $\sim$12% of the z$>0.5$ AGN population ($\sim$9% of the
0.5$<$z$<$1) in eFEDS, with a sky number density of $\sim$10/deg2.

  * •

We analysed the [OIII] line fitting of 50 candidates in our study. These
candidates were selected based on having good quality SDSS spectra and being
at 0.5$<$z$<$1\. Among these candidates, we identified 23 sources that
displayed evidence of a broad component with FWHM $\sim$600–2800
$\mathrm{km\leavevmode\nobreak\ s^{-1}}$, signalling the presence of unsettled
gas motions and confirming their nature as outflowing QSOs. This corresponds
to $\sim$45% of the spectroscopic sample and this may increase to 80% if we
consider an additional 17 sources (see Sect. 3.2) for which a broad component
can be accommodated in the fit, but at a lower significance. It is worth
noting that our sample may be biased towards sources with high bolometric
luminosity ($\mathrm{logL_{bol}}$ between $\mathrm{\sim\leavevmode\nobreak\
44-46.2\leavevmode\nobreak\ erg\leavevmode\nobreak\ s^{-1}}$ ) and column
densities ($\mathrm{N_{H}}$ $\mathrm{\sim 10^{22}\leavevmode\nobreak\
cm^{-2}}$), due to the selection effects affecting our sample of candidates
with good quality spectra, which is dominated by sources from sample B. The
average [O III] luminosity, $\mathrm{L[OIII]}$ is $\sim\leavevmode\nobreak\
10^{42}\leavevmode\nobreak\ \mathrm{ergs^{-1}}$ and by assuming the outflow
radius as the half-light radius of the galaxy as measured from deep HSC data
(from $\sim 2-10$ kpc), we obtain mass outflow rates in the range of
$\mathrm{\sim 0.2-23\leavevmode\nobreak\ M_{\odot}\leavevmode\nobreak\
yr^{-1}}$ and ${\log(\dot{\textrm{E}})\leavevmode\nobreak\
\sim\leavevmode\nobreak\ 40-44\leavevmode\nobreak\ erg\leavevmode\nobreak\
s^{-1}}$.

  * •

We complemented these 23 sources with an additional 118 sources at z$>0.5$
reported in the literature, for which we recomputed in a standardised and
homogenised way the outflow properties. This constitutes the largest sample of
AGNs with detected ionised outflows. From this compilation, we find a
correlation between the maximum velocity of the outflow and the AGN bolometric
luminosity ($\mathrm{L_{bol}\propto{V_{max}}^{1.78\pm 0.2}}$) with a slope
considerably flatter than the scaling relation presented in previous studies
and a much larger scatter (see Sect. 4.2)

  * •

The mass outflow rate and the kinetic power of the outflow instead correlate
well with the AGN bolometric luminosity
(${\dot{\textrm{M}}_{\mathrm{{ion}}}\propto\rm{{L_{bol}}}^{1.16\pm 0.07}}$ and
${\dot{\textrm{E}}_{\mathrm{{ion}}}\propto\rm{{L_{bol}}}^{1.47\pm 0.09}}$).
Both trends are in agreement with the relations derived in previous studies
(see Sect. 4.2), despite the considerable difference in the maximum velocity
and AGN bolometric luminosity correlation. This can be explained if our X–ray
based, eFEDS selection preferentially isolates obscured QSO in the fastest
phase of the wind.

  * •

More than half of our sample have $\dot{\textrm{E}}/\rm{L_{bol}}$ close to the
theoretical predictions (see discussion in Sect. 4.2). About 30% of ionised
outflows have the
$1\%\\!<\\!{\dot{\textrm{E}}_{\mathrm{{ion}}}}/\rm{L_{bol}}\\!<\\!10$%. This
is an indication that the outflows present in these sources could have a
significant impact on their host galaxies. We are comparing outflows in a
single phase (ionised) with the theoretical predictions that consider multi-
phase outflows.

  * •

The majority of the sources show outflows with momentum flux ratios lower than
20, which rules out an energy-conserving nature since models predict that
energy-driven winds on large-scale outflows have momentum rates that are 20
times the momentum rates from the central black hole,
${\dot{\textrm{P}}_{\mathrm{{OF}}}\\!\sim\\!\rm{20L_{bol}/c}}$.

Overall, this study provides an improved approach to isolate quasars in the
feedback phase, suggesting that the best way to select AGNs with strong winds
is by applying a combination of selection methods, minimising the selection
biases that result from using incomplete and single selection methods. Of the
50 objects with good quality optical spectra for which we performed spectral
fitting, we have significantly detected the presence of ionised outflows in
$\sim$45%. This is a strong confirmation of the reliability of our strategy.
Even though 23 sources ($\sim$45%) may be a relatively small sample, we will
be able to validate our selection techniques on larger scales with eROSITA.

From our methods, we selected $\sim$1400 sources ($\sim$12% of the AGN
subsample at z$>0.5$) from the eFEDS area of $\sim$140 deg2. We, therefore,
expect $\sim$140000 such candidates will exist in the eROSITA all-sky
catalogue (area factor of $\sim$100 considering the best extra-galactic sky).
We predict that following a similar strategy and with the extended
spectroscopic coverage provided by dedicated and sensitive AGN surveys within
4MOST (Merloni et al., 2019) and SDSS-V (Kollmeier et al., 2019) we will be
able to fully uncover and characterise this rare population bringing the total
number of confirmed objects from a single X–ray survey to $>2500$.

This study finally provides an observational benchmark for the investigation
of the correlations between AGN and outflow properties, being the largest
compiled sample (141 objects, including the eFEDS sources) of ionised outflows
available at z$>$0.5 and with properties derived with standardised
assumptions. This study can be extended by also including the molecular
outflows and follow-up studies for the candidates with higher redshift.

###### Acknowledgements.

This work is based on data from eROSITA, the soft X-ray instrument aboard SRG,
a joint Russian-German science mission supported by the Russian Space Agency
(Roskosmos), in the interests of the Russian Academy of Sciences represented
by its Space Research Institute (IKI), and the Deutsches Zentrum für Luft- und
Raumfahrt (DLR). The SRG spacecraft was built by Lavochkin Association (NPOL)
and its subcontractors and is operated by NPOL with support from the Max
Planck Institute for Extraterrestrial Physics (MPE). The development and
construction of the eROSITA X-ray instrument was led by MPE, with
contributions from the Dr. Karl Remeis Observatory Bamberg & ECAP (FAU
Erlangen-Nuernberg), the University of Hamburg Observatory, the Leibniz
Institute for Astrophysics Potsdam (AIP), and the Institute for Astronomy and
Astrophysics of the University of Tübingen, with the support of DLR and the
Max Planck Society. The Argelander Institute for Astronomy of the University
of Bonn and the Ludwig Maximilians Universität Munich also participated in the
science preparation for eROSITA. The eROSITA data shown here were processed
using the eSASS or NRTA software system developed by the German eROSITA
consortium. The Hyper Suprime-Cam (HSC) collaboration includes the
astronomical communities of Japan and Taiwan, and Princeton University. The
HSC instrumentation and software were developed by the National Astronomical
Observatory of Japan(NAOJ), the Kavli Institute for the Physics and
Mathematics of the Universe (Kavli IPMU), the University of Tokyo, the High
Energy Accelerator Research Organisation (KEK), the Academia Sinica Institute
for Astronomy and Astrophysics in Taiwan (ASIAA), and Princeton University.
Funding was contributed by the FIRST program from Japanese Cabinet Office, the
Ministry of Education, Culture, Sports, Science and Technology (MEXT), the
Japan Society for the Promotion of Science (JSPS), Japan Science and
Technology Agency (JST),the Toray Science Foundation, NAOJ, Kavli IPMU,
KEK,ASIAA, and Princeton University. Funding for the Sloan Digital Sky Survey
IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of
Energy Office of Science, and the Participating Institutions. SDSS
acknowledges support and resources from the Center for High-Performance
Computing at the University of Utah. The SDSS web site is www.sdss.org SDSS is
managed by the Astrophysical Research Consortium for the Participating
Institutions of the SDSS Collaboration including the Brazilian Participation
Group, the Carnegie Institution for Science, Carnegie Mellon University,
Center for Astrophysics — Harvard & Smithsonian (CfA), the Chilean
Participation Group, the French Participation Group, Instituto de Astrofísica
de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and
Mathematics of the Universe (IPMU) or University of Tokyo, the Korean
Participation Group, Lawrence Berkeley National Laboratory, Leibniz Institut
für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA
Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-
Institut für Extraterrestrische Physik (MPE), National Astronomical
Observatories of China, New Mexico State University, New York University,
University of Notre Dame, Observatório Nacional or MCTI, The Ohio State
University, Pennsylvania State University, Shanghai Astronomical Observatory,
United Kingdom Participation Group, Universidad Nacional Autónoma de México,
University of Arizona, University of Colorado Boulder, University of Oxford,
University of Portsmouth, University of Utah, University of Virginia,
University of Washington, University of Wisconsin, Vanderbilt University, and
Yale University. BM is supported by the European Union’s Innovative Training
Network (ITN) funded by the Marie Sklodowska-Curie Actions in Horizon 2020 No
860744 (BiD4BEST). MB and CRA acknowledge support from BiD4BEST. MB
acknowledges support from PRINMIUR 2017PH3WAT (’Black hole winds and the
baryon life cycle of galaxies’). BM and MB warmly thank Tiago Costa for the
insightful discussion. CRA acknowledges support from the projects ’Feeding and
feedback in active galaxies’, with reference PID2019-106027GB-C42, funded by
MICINN-AEI/10.13039/501100011033, and ’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.

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##  Appendix A More of the eFEDS selected samples represented in same
selection planes

In this appendix, for each selection method, we represent our samples isolated
from Sect. 2. As seen in Fig. 14, our isolated samples populate all the
regions of the plane. This shows the complexity of isolating AGNs in the
feedback phase since they do not occupy a specific region but also shows how
our strategy can be used to minimise the chances of leaving out potential
candidates.

The sample selected by $\mathrm{N_{H}}$ and $\mathrm{\lambda_{Edd}}$ appear in
the blue region of the colour selection planes. This means that, with this
method, we are selecting obscured AGNs with blue colours. This can also be
attributed to the blow-out phase being short. Therefore, these sources have
bluer colours because they are being observed in the growing phase
(immediately before the blow-out phase) or due to contamination from star
formation or their host galaxy. The other possibility could be that the blue
colours are due to the obscuration being inhomogeneous.

|
---|---
|
Figure 14:  All selected candidates plotted in different planes. Top left
panel: i-W3 distribution of candidates selected by different methods. Top
right panel: Candidates selected by different methods plotted in $2-10$ keV to
optical flux ratio vs. r-W1 colour plane. Bottom left panel: $0.2-2.3$ keV to
optical flux ratio vs. r-W1 colour. The sources from different selection
methods are indicated with different colours or shapes as shown in the legend.
Bottom right panel: All selected candidates plotted in i-W4 vs. r-W1. The
sources from different selection methods are indicated with different colours
as shown in the legend.

##  Appendix B The rest of the spectra.

Here we present the rest of the spectra as obtained in Sect. 3.2 for more 22
quasars with ionised outflows (in Fig. 15). One example of the 10 single
components fits with FWHM$\rm{>800kms^{-1}}$ (in the left panel of Fig. 16)
and an example of the 17 two-component fits with flux to flux error ratio less
than 2.5 (in the right panel of Fig. 16). In Fig. 17, we show an example of
the spectra that we classified as bad due to a very noisy continuum around the
[OIII] region or bad residuals after the continuum and host galaxy
subtraction.

|
---|---
|
|
|
Figure 15: SDSS emission line profiles fit for our candidates with outflows. The blue line indicates the broad component and the green fit indicates the narrow component. The red line indicates the total fit. The vertical dotted lines indicate the peaks at 4862.68, 4960.30, and 5008.24 for $H_{\beta}$ and [OIII] rest-frame wavelength. |
---|---
|
|
|
Fig. 15 continued |
---|---
|
|
Fig. 15 continued |
---|---
Figure 16: Examples of spectra from two component fit but with poor spectra
and single component fit. Left panel: An example of the spectra with single
component fit (ID 8813) and FWHM$\rm{<800kms^{-1}}$. Right panel: An example
of the spectra with two component fit (ID 5185) but whose flux-to-flux error
ratio is less than 2.5. These sources were excluded from our final candidates
with outflows because the additional broad component is not significant. In
both panels, the red line indicates the total fit. The vertical dotted lines
indicate the peaks at 4862.68, 4960.30, and 5008.24 for $H_{\beta}$ and [OIII]
rest-frame wavelength. Figure 17: An example of the spectra that we classified
as bad due to a very noisy continuum around the [OIII] region or bad residuals
after the continuum and host galaxy subtraction. The red line indicates the
total fit. The vertical dotted lines indicate the peaks at 4862.68, 4960.30,
and 5008.24 for $H_{\beta}$ and [OIII] rest-frame wavelength.

##  Appendix C Summary of the results from each selection method.

We have employed various selection techniques to identify AGNs in the feedback
phase, aiming to evaluate our methods completeness and reliability through
spectroscopic analysis. Unfortunately, the lack of available spectra for our
candidates limits our analysis. Furthermore, the few spectra that are
accessible exhibit poor quality, adding to our limitations. Consequently, in
order to derive meaningful statistics from our reduced number of final
subsamples relative to the original samples, we have grouped these subsamples
into Sample A and Sample B instead of examining each method individually.
Nevertheless, in order to demonstrate the efficacy of the individual methods,
we present the performance results for different subsamples after applying
various criteria in Table 3. This table effectively showcases the outcomes of
our selection techniques which include; 1) r - W1 $>$ 4 and
$\mathrm{F_{0.2-2.3keV}/F_{opt}>}$1: selects 516 sources, 171 have z $<$ 1, 2
have SDSS spectra available (ID 608 and ID 4744) and only 1 source has good
quality spectra and with outflows (ID 608). 2) r - W1$>$ 4 and
$\mathrm{F_{2-10keV}/F_{opt}>}$0.5: selects 274 sources, 77 have z $<$ 1, 2
have SDSS spectra available (ID 608 and ID 4744) and only 1 source has good
quality spectra and with outflows (ID 608). 3)i - W4 $>$ 7 and r - W1$>$4:
selects 203 sources, 66 have z $<$ 1, 1 have SDSS spectra available with good
quality spectra and shows outflows (ID 608). 4) i - W3 $>$ 4.6: selects 539
sources, 231 have z $<$ 1, 6 have SDSS spectra available, 4 have good quality
spectra (ID 608, ID 10152, ID 13349, ID 25592) and 3 sources show outflows (ID
608, ID 10152, ID 25592). 5) $\mathrm{log(N_{H})}>21.5$ and
$\mathrm{\lambda_{Edd}}$: selects 528 sources, 78 have z $<$ 1,78 have SDSS
spectra available, 47 have good quality spectra (these includes ID 608 and ID
13349 in colour selection ) and 21 sources show outflows (which include ID
608).

Table 3: Summary of the results from each selection method. To accurately convey the numerical data presented in this table, refer directly to the text.  Selection method |  Total |  0.5$<$ z $<$ 1 |  available spectra |  reliable spectra |  confirmed outflows
---|---|---|---|---|---
r - W1 $>$ 4 and $\mathrm{F_{2-10keV}/F_{opt}>}$1 |  516 |  171 |  2 |  1 |  1
r - W1 $>$ 4 and $\mathrm{F_{0.2-2.3keV}/F_{opt}>}$0.5 |  274 |  77 |  2 |  1 |  1
i - W4 $>$ 7 and r - W1$>$4 |  203 |  66 |  1 |  1 |  1
i - W3 $>$ 4.6 |  539 |  231 |  6 |  4 |  3
$\mathrm{log(N_{H})}>21.5$ and $\mathrm{\lambda_{Edd}}$ |  528 |  78 |  78 |  47 |  21
Total (sample A + sample B) |  1400 |  427 |  82 |  50 |  23

Except ID 608 which is selected by all the colour criteria, 2/3 of sources
with outflows in Sample B are only selected by Eq. 2. As already discussed in
Hamann et al. (2016); Perrotta et al. (2019), this colour cut is reliable in
isolating ERQs whose red colours are related to outflows.

##  Appendix D Additional table

Table 4: Fit results from the broad and narrow components of [OIII] line are
represented in the table below.

ERO ID | z | FWHMn | FWHMb |  $\mathrm{\Delta}$V | $\mathrm{\sigma}$ | $\rm{V_{max}}$ | flux | flux/fluxerr | L[OIII]b | sample
---|---|---|---|---|---|---|---|---|---|---
|  | $\mathrm{km\leavevmode\nobreak\ s^{-1}}$ | $\mathrm{km\leavevmode\nobreak\ s^{-1}}$ | $\mathrm{km\leavevmode\nobreak\ s^{-1}}$ | $\mathrm{km\leavevmode\nobreak\ s^{-1}}$ | $\mathrm{km\leavevmode\nobreak\ s^{-1}}$ |  $\mathrm{erg\leavevmode\nobreak\ cm^{-2}\leavevmode\nobreak\ s^{-1}}$ ($10^{-17}$) |  |  $\mathrm{erg\leavevmode\nobreak\ s^{-1}}$ ($10^{42}$) |
25592 | 0.660 | 554.2$\pm$12.9 | 1732.2$\pm$19.0 | 667.7$\pm$22.4 | 725.1$\pm$8.1 | 2118.0$\pm$27.6 | 284.5$\pm$4.4 | 64.1 | 5.3$\pm$0.08 | A
6743 | 0.652 | 394.4$\pm$29.7 | 773.1$\pm$112.0 | 526.3$\pm$60.6 | 322.3$\pm$47.6 | 1171.1$\pm$112.9 | 22.4$\pm$0.9 | 24.8 | 0.4$\pm$0.01 | B
608 | 0.602 | 501.4$\pm$46.4 | 1514.0$\pm$79.1 | 171.1$\pm$9.0 | 634.2$\pm$33.6 | 1439.6$\pm$67.9 | 148.1$\pm$6.9 | 21.4 | 2.2$\pm$0.10 | A & B
19520 | 0.937 | 554.3$\pm$-99.0 | 1794.3$\pm$133.5 | 407.9$\pm$52.9 | 751.1$\pm$56.8 | 1910.2$\pm$125.4 | 146.6$\pm$10.5 | 13.8 | 6.5$\pm$0.4 | B
18777 | 0.852 | 554.0$\pm$1.1 | 2684.0$\pm$60.3 | 1053.4$\pm$306.3 | 1124.4$\pm$25.6 | 3302.4$\pm$310.5 | 26.2$\pm$1.9 | 13.4 | 0.9$\pm$0.06 | B
21835∗ | 0.981 | -99.0 | 884.6$\pm$36.8 | 44.6$\pm$90.6 | 369.2$\pm$15.7 | 783.2$\pm$95.9 | 64.0$\pm$5.1 | 12.3 | 3.1$\pm$0.2 | B
12686 | 0.768 | 349.3$\pm$7.2 | 1174.1$\pm$228.0 | 119.4$\pm$77.7 | 491.8$\pm$97.0 | 1103.0$\pm$209.0 | 76.4$\pm$6.4 | 11.8 | 2.0$\pm$0.1 | B
31136 | 0.655 | 412.0$\pm$21.5 | 1580.5$\pm$112.3 | 275.1$\pm$66.0 | 661.4$\pm$47.8 | 1598.0$\pm$116.2 | 123.3$\pm$11.6 | 10.5 | 2.2$\pm$0.2 | B
5896∗ | 0.699 | -99.0 | 1009.1$\pm$97.7 | 67.4$\pm$62.4 | 422.6$\pm$41.6 | 912.8$\pm$104.0 | 209.9$\pm$21.4 | 9.7 | 4.5$\pm$0.4 | B
16271 | 0.508 | 496.4$\pm$25.1 | 1270.0$\pm$257.8 | 155.4$\pm$48.6 | 531.1$\pm$109.7 | 1217.7$\pm$224.7 | 32.1$\pm$4.9 | 6.4 | 0.3$\pm$0.04 | B
14896 | 0.819 | 317.8$\pm$114.9 | 1382.3$\pm$190.1 | 145.7$\pm$126.7 | 579.0$\pm$80.9 | 1303.9$\pm$205.5 | 26.5$\pm$4.2 | 6.1 | 0.8$\pm$0.1 | B
10152 | 0.923 | 554.1$\pm$178.2 | 1727.0$\pm$921.4 | 671.7$\pm$492.4 | 723.5$\pm$392.1 | 2118.7$\pm$926.0 | 26.0$\pm$4.5 | 5.6 | 1.1$\pm$0.1 | A
11596 | 0.956 | 323.9$\pm$84.6 | 2315.4$\pm$147.4 | 723.9$\pm$174.4 | 970.0$\pm$62.7 | 2664.1$\pm$214.9 | 78.6$\pm$14.4 | 5.4 | 3.6$\pm$0.6 | B
14390 | 0.608 | 462.5$\pm$8.7 | 916.5$\pm$48.9 | 55.8$\pm$24.6 | 383.9$\pm$20.8 | 823.6$\pm$48.4 | 187.3$\pm$36.7 | 5.0 | 2.8$\pm$0.5 | B
16050 | 0.615 | 554.2$\pm$117.0 | 1019.2$\pm$413.8 | 83.0$\pm$51.6 | 426.9$\pm$176.1 | 936.8$\pm$355.9 | 91.2$\pm$20.2 | 4.5 | 1.4$\pm$0.3 | B
19964 | 0.670 | 358.4$\pm$189.6 | 551.4$\pm$55.2 | 104.6$\pm$110.1 | 228.8$\pm$23.5 | 562.3$\pm$119.7 | 10.7$\pm$3.1 | 3.4 | 0.2$\pm$0.06 | B
14541 | 0.906 | 554.3$\pm$73.2 | 2813.6$\pm$782.9 | 1210.2$\pm$909.3 | 1178.4$\pm$333.1 | 3567.1$\pm$1127.3 | 26.4$\pm$7.8 | 3.3 | 1.0$\pm$0.3 | B
19174 | 0.707 | 450.4$\pm$49.3 | 1570.7$\pm$1032.9 | 47.4$\pm$158.6 | 658.0$\pm$439.5 | 1363.5$\pm$893.3 | 275.9$\pm$88.6 | 3.1 | 6.1$\pm$1.9 | B
28337 | 0.706 | 199.8$\pm$116.7 | 639.1$\pm$234.1 | 3.5$\pm$243.3 | 267.6$\pm$99.6 | 538.7$\pm$314.4 | 23.9$\pm$7.8 | 3.0 | 0.5$\pm$0.1 | B
16799 | 0.546 | 306.2$\pm$117.6 | 581.5$\pm$894.5 | 2.9$\pm$268.8 | 243.5$\pm$380.6 | 489.9$\pm$807.4 | 25.4$\pm$8.4 | 3.0 | 0.3$\pm$0.1 | B
19841 | 0.854 | 368.9$\pm$79.1 | 898.6$\pm$102.8 | 43.7$\pm$52.4 | 376.3$\pm$43.7 | 796.5$\pm$102.0 | 21.1$\pm$7.3 | 2.8 | 0.7$\pm$0.2 | B
17754 | 0.667 | 374.7$\pm$19.3 | 854.7$\pm$219.6 | 135.5$\pm$131.3 | 358.0$\pm$93.4 | 851.5$\pm$228.5 | 12.9$\pm$4.5 | 2.8 | 0.2$\pm$0.08 | B
15417 | 0.983 | 554.1$\pm$6.2 | 725.8$\pm$138.9 | 593.2$\pm$119.5 | 302.4$\pm$59.1 | 1198.0$\pm$168.1 | 99.2$\pm$35.3 | 2.8 | 4.9$\pm$1.7 | B

  * •

Notes: The superscript b and n stand for broad and narrow components,
respectively. The columns (left-right) are eROSITA ID (ERO ID ), redshift (z),
the narrow and broad FWHM with their respective errors, change in velocity
($\mathrm{\Delta}$V), velocity dispersion ($\mathrm{\sigma}$), maximum
velocity ($\rm{V_{max}}$), [OIII] flux, [OIII] luminosity (L[OIII]b ) and the
sample in which the source was selected. -99.0 is used to indicate missing
values. Sources marked with ∗ have single Gaussian components.

##  Appendix E Assumptions on different parameters in the computation of
outflow properties

The computations of outflow properties are based on several assumptions on
different parameters which include; geometry, electron density, temperature,
metallicity, in some cases, the velocity of the outflowing gas and radius.
These assumptions introduce several uncertainties in the properties of the
final values estimated. Below, we summarise some of the assumptions made in
computing the outflow properties of QWO from the literature that is Brusa et
al. (2015); Kakkad et al. (2016); Fiore et al. (2017); Perrotta et al. (2019);
Leung et al. (2019); Kakkad et al. (2020); Vayner et al. (2021); Brusa et al.
(2022).

Different proxies of velocities are used to compute AGN outflow rates. In the
literature, non parametric line width that contains 80% of the total flux
(W80) (Kakkad et al. 2016, 2020), V10 (Kakkad et al. 2016; Vayner et al.
2021), V98 (Perrotta et al. 2019), mean radial velocity (Vr) (Perrotta et al.
2019), V50 and maximum velocity ($V_{max}$ ) (Brusa et al. 2015; Fiore et al.
2017; Leung et al. 2019; Brusa et al. 2015) have been used. Maximum velocity
has been calculated as;

$\rm{V_{max}=|\Delta{V}|+2\sigma_{[OIII]}^{broad}},$ (13)

where $\Delta{V}$ is the velocity shift between the velocity peak of the broad
emission line and the systemic velocity and $\sigma$ is the velocity
dispersion. Another definition of maximum velocity is used in Rupke et al.
(2005); Fluetsch et al. (2019) ($\rm{V_{max}=|\Delta{V}|+FWHM/2}$). W80 is
close to the FWHM of the line and relates to the typical velocity of the
outflow gas for a Gaussian profile. V10 gives an estimate of the velocity the
gas is moving towards us at the high-velocity end. This implies that W80 gives
higher velocity values than v10 (Kakkad et al. 2016). W80 is highly correlated
with $V_{max}$ as W80 $\sim 0.9\leavevmode\nobreak\ \times\leavevmode\nobreak\
V_{max}$ (Fiore et al. 2017; Leung et al. 2019). W80 can be a factor of
1.3-1.8 smaller than $V_{max}$ (Bischetti et al. 2017).

Since the mass of the outflow is inversely related to the gas electron
density, the assumptions made whenever $n_{e}$ is not measured have direct
uncertainties in the outflow mass which indirectly contributes to the mass
outflow rate value. As compared to Fiore et al. (2017), Vayner et al. (2021);
Kakkad et al. (2020); Brusa et al. (2022) will have outflow energies lower by
a factor of $\sim$2.5 while Brusa et al. (2015) and Kakkad et al. (2016) will
be higher by a factor of $\sim$2\. Although $n_{e}$ has been assumed in most
of the previous studies, it has been measured in a few such as Nesvadba et al.
(2006, among others); Perna et al. (2015b, among others); Brusa et al. (2015,
2016, among others) from the line flux ratios of
[SII]$\lambda\lambda$6717,6731 line doublet using the formula;

$n_{e}=10^{2}T^{0.5}\left(\frac{r-1.49}{5.62-12.8r}\right),$ (14)

where r is the [SII] flux ratio. Some of the measured values of $n_{e}$
include among others; $780\pm 300\leavevmode\nobreak\ cm^{-3}$ (Brusa et al.
2016), $1000-3000\leavevmode\nobreak\ cm^{-3}$ (Brusa et al. 2015),
$120\leavevmode\nobreak\ cm^{-3}$ (Perna et al. 2015b) ,
$240-570\leavevmode\nobreak\ cm^{-3}$ (Nesvadba et al. 2006). In addition to
the commonly used method of using [SII] doublet flux ratios to estimate
electron densities, there are alternative approaches in the field. These
include the auroral and transauroral line method and the ionisation parameter
method. A comprehensive comparison of these various methods can be found in
the study conducted by Davies et al. (2020). The aforementioned study by
Davies et al. (2020) highlights certain limitations associated with the [SII]
doublet method, particularly for electron densities $\sim 10^{3}$ cm-3. The
researchers caution against relying solely on this method as it tends to
predominantly trace low electron density regions, potentially leading to a
biased perspective of the ionised gas. Similar caution is also echoed in other
studies (e.g. Baron & Netzer 2019; Davies et al. 2020). Furthermore, ongoing
research by Speranza et al. (in preparation) emphasises similar concerns.
Collectively, they have found electron densities estimated by [SII] doublet
method to be lower as compared to other methods and hence giving much higher
values of mass outflow rates and even much higher values if you consider
electron density of 200 cm-3 as assumed in Fiore et al. (2017) and our study.

Outflow rates computed by assuming shell$-$like geometry give higher values by
a factor of $\sim$3 than biconical or spherical geometry (Maiolino et al.
2012; Cicone et al. 2014; Kakkad et al. 2016). The use of different electron
temperatures (e.g. 10000 or 25000 K) would change the normalisation factor in
Eq. 10 by a certain factor since the emissivity depends on the temperature
Kakkad et al. (2020).

The radius of the outflow can be measured but it is always assumed if the
outflow is unresolved. Mass outflow rates and outflow energies computed by
assuming higher values of the radius will be times lower than those computed
with lower values of radius.

Using different lines to derive the outflow properties, different assumptions,
not taking into account the multi-phase nature of outflows, etc., makes it
challenging to characterise AGNs in the feedback phase and comparison of these
outflow properties to theoretical prediction. The assumption made in previous
studies is summarised in Table 5.

Table 5: Assumed parameters in computing mass outflow rates and energetics.

Outflow properties assumptions
---
Reference |  Geometry |  Temperature $T_{e}$ |  Electron density ($n_{e}$) (cm${}^{-}3$) |  Radius (Kpc) |  Velocity
1 |  spherical |  - |  500 |  10 |  Eq. 6, V90
2 |  conical |  - |  500 |  - |  V10
3 |  biconical & thin shell |  104 |  500 |  2 |  W80
4 |  biconical |  - |  200 |  1 |  V98 &Vr
5 |  thin shell |  104 |  150 |  r10 |  Eq. 6
5 |  spherical |  104 |  200 |  - |  Eq. 6
6 |  conical |  104 |  100 |  - |  v10 & W80
7 |  spherical |  - |  100 |  5 |  Eq. 6

  * •

Notes: We show the reference(1.Brusa et al. (2022), 2.Vayner et al. (2021),
3.Kakkad et al. (2020), 4.Perrotta et al. (2019), 5.Leung et al. (2019),
6.Kakkad et al. (2016), 7.Brusa et al. (2015)), geometry is the assumed
geometry whether conical, biconical, spherical or thin shell, Te is the
electron temperature, $n_{e}$ is the gas electron density, the radius at which
the outflow was computed (assumed or measured), the outflow velocity used.

By carefully considering the uncertainties that arise from the different
assumptions made, we re-computed the outflow properties of the QWO sample with
the best-homogenised assumptions. We have computed mass outflow, mass outflow
rate and kinetic power for Kakkad et al. (2020); Perrotta et al. (2019); Leung
et al. (2019); Brusa et al. (2022) assuming a spherical outflow geometry and
electron density of 200 cm-3. We used radius as provided in the literature.
For the case of velocity, we used V$\rm{max}$ or outflow velocity when
provided, otherwise, we computed using
$\rm{V_{max}=|\Delta{V}|+2\times{FWHM/2.355}}$. The final values will have 2-3
orders of magnitude uncertainties due to the different assumptions applied.

##  Appendix F The X–ray properties of our eFEDS candidates with outflows.

In this section, we present the correlations between the mass outflow rate and
AGN bolometric luminosity with the best-fit relation obtained in Sect. 4.2. In
Fig. 18, left panel, the data is colour-coded with the Eddington ratio while
in the right panel, the data is colour-coded with the black hole mass. We see
a trend between these quantities as discussed already in Sect. 4.2.

---
Figure 18: Ionised mass outflow rate as a function of AGN bolometric
luminosity. Different shapes represent the literature of the sources. The
black dashed line is the scaling relation obtained in Fig. 11. In the left
panel of Fig. 18, the sources are colour coded with the Eddington ratio. In
the left panel, the sources are colour-coded with the black hole mass. Among
the sources with black hole masses, we observe a correlation trend in the
sense that AGNs with high black hole masses also appear to have high
bolometric luminosity and higher mass outflow rates. In the right panel, the
sources are colour-coded with the Eddington ratio. AGNs with high Eddington
ratio values appear to have high mass outflow rates and bolometric luminosity.
The error bars on mass outflow rate values were obtained by extrapolating the
errors on FWHM or $\rm{\delta{V}}$ whenever available.