# The co-evolution of strong AGN and central galaxies in different
environments

V. M. Sampaio,1,2 A. Aragón-Salamanca,1 M. R. Merrifield1, R. R. de Carvalho,2
S. Zhou,1 I. Ferreras3,4
1 School of Physics and Astronomy, University of Nottingham, University Park,
Nottingham NG7 2RD, UK
2 NAT - Universidade Cidade de São Paulo, 01506-000, SP, Brazil
3 Instituto de Astrofísica de Canarias, Calle Vía Láctea s/n, E38205, La
Laguna, Tenerife, Spain
4 Department of Physics and Astronomy, University College London, Gower
Street, London WC1E 6BT, UK E-mail<EMAIL_ADDRESS>
(Accepted 2023 July 18. Received 2023 July 11; in original form 2023 March 11)

###### Abstract

We exploit a sample of over 80,000 SDSS galaxies at the centre of their local
halo to investigate the effect of AGN feedback on their evolution. We trace
the demographics of optically-selected AGN (Seyferts) as a function of their
internal properties (stellar and halo mass, central velocity dispersion, star-
formation activity, morphology) and environment. We find that the preeminence
of AGN as the dominant ionising mechanism increases with stellar mass,
overtaking star-formation for galaxies with $M_{\text{stellar}}\geq
10^{11}M_{\odot}$. The AGN fraction changes systematically with the galaxies’
star-formation activity. Within the blue cloud, this fraction increases as
star-formation activity declines, reaching a maximum near the green valley
($\sim 17\pm 4\%$), followed by a subsequent decrease as the galaxies
transition into the red sequence. This systematic trend provides evidence that
AGN feedback plays a key role in regulating and suppressing star formation. In
general, Seyfert central galaxies achieve an early-type morphology while they
still host some residual star formation. This suggests that, in all
environments, the morphology of Seyfert galaxies evolves from late- to early-
type before their star formation is fully quenched. Stellar mass plays an
important role in this morphological transformation: while low mass systems
tend to emerge from the green valley with an elliptical morphology (T-Type
$\sim-2.5\pm 0.7$), their high-mass counterparts maintain a spiral morphology
deeper into the red sequence. In high-stellar-mass centrals, the fraction of
Seyferts increases from early- to late-type galaxies, indicating that AGN
feedback is linked with the morphology of these galaxies and, perhaps, its
transformation. Our analysis further suggests that AGN are fuelled by their
own host halo gas reservoir, but AGN at the centres of groups can also
increase their gas reservoir via interactions with satellite galaxies.

###### keywords:

galaxies: evolution – galaxies: Seyfert – galaxies: active – galaxies: ISM

††pubyear: 2023††pagerange: The co-evolution of strong AGN and central
galaxies in different environments–A

##  1 Introduction

The last few decades, astronomers have focused on understanding the different
mechanisms driving galaxy evolution across cosmic time. The persistent
bimodality observed in the distribution of several galaxy properties such as
their colours and star-formation rates (Strateva et al., 2001; Baldry et al.,
2006; Wetzel et al., 2012) provides not only a key piece of evidence, but also
a major challenge for any theory of galaxy formation and evolution that that
tries to explain it.

Galaxies divide between the blue cloud (BC) – blue star-forming galaxies
dominated by late-type morphologies (late-type galaxies, LTGs); the red
sequence (RS) – red galaxies with little or no star formation, populated
mainly by galaxies with early-type morphologies (early-type galaxies, ETGs);
and the green valley (GV) – an intermediate class comprising galaxies with
intermediate colours, reduced star formation, and a range of morphologies
(Schawinski et al., 2009; Masters et al., 2010a, b; Schawinski et al., 2014;
Angthopo et al., 2019). There have been many attempts at explaining the
transition from the BC through the GV to the RS invoking a variety of physical
mechanisms to reduce and quench the galaxies’ star formation and change their
morphology (e.g. Trussler et al., 2020; de Sá-Freitas et al., 2022), but a
definitive answer is still to be found.

A particularly interesting class of objects are the so-called ‘central
galaxies’. These are systems located at that the centre of dark matter
potential wells, and therefore at the focus of any possible gas accretion.
Because they are the dominant galaxy in their dark-matter halo, it is
reasonable to expect that the influence of external objects may be smaller
than for satellite galaxies. If this is the case, internal processes may be
relatively more dominant than external (environmental) ones, and therefore
easier to study.

A great deal is already known about central galaxies, providing a solid
framework to study their transformation. Their evolution has been show to
depend on the mass of their host dark-matter halo ($M_{\text{halo}}$), the
velocity dispersion of the cluster/group they inhabit
($\sigma_{\text{cluster}}$) and the number of its members
($N_{\text{members}}$) (Katayama et al., 2003; Wang et al., 2018; Zhang et
al., 2021; Guo et al., 2022). All these properties correlate with the depth of
the potential well at whose centre these galaxies live, linked with their
ability to accrete gas. The velocity dispersion and the number of members also
relate to the nature of their potential interactions with other galaxies and
the probability of merging with them (Chandrasekhar, 1943; White, 1976;
Binney, 1977). Furthermore, Behroozi et al. (2013) have shown that, in
general, star-formation efficiency peaks at $M_{\text{halo}}\sim
10^{11.7}\text{M}_{\odot}$. However, halo mass is not the only driver of star
formation in central galaxies; The detailed properties of their environment
also matter. For instance, La Barbera et al. (2014) find that central early-
type galaxies hosted by halos with $N_{\text{members}}\geq 3$ and
$M_{\text{halo}}\geq 10^{12.5}\text{M}_{\odot}$ have younger ages and longer
star-formation timescales (lower alpha enhancement, $\rm[\alpha/Fe]$) than
isolated centrals occupying less massive halos ($\leq
10^{12.5}\text{M}_{\odot}$). Younger ages and longer star-formation timescales
may be the result of gas-rich interactions with satellite galaxies (Jog &
Solomon, 1992), whose probability depends crucially on environment.

One of the main internal drivers of galaxy evolution is the presence of a
central super-massive black hole (SMBH). According to Dubois et al. (2013) and
Donahue & Voit (2022), the SMBH mass is one of the parameters that most
effectively predicts whether a galaxy is star-forming or quenched. It has been
suggested (e.g., Bourne et al., 2014) that the relation between SMBH mass and
star-formation suppression is due to the effect an active galactic nucleus
(AGN) has on the interstellar medium of the galaxy (often called ‘AGN
feedback’). The effect an AGN has will depend both on the mass of the SMBH at
its centre and the amount and rate of ‘fuel’ feeding it.

Empirically, Magorrian et al. (1998), Ferrarese & Merritt (2000), Gebhardt et
al. (2000), Tremaine et al. (2002) and Gültekin et al. (2009) have shown a
positive correlation between the SMBH mass and the central stellar velocity
dispersion of its host galaxy ($\sigma_{\text{galaxy}}$), while Bluck et al.
(2016) and Zhang et al. (2021) find an increasing fraction of quenched
galaxies with increasing $\sigma_{\text{galaxy}}$. Since cluster centrals are
generally the galaxies with the largest $\sigma_{\text{galaxy}}$ (Sheth et
al., 2003), we expect them to host the most massive SMBHs, and therefore show
signs of strong star-formation suppression.

A variety of models try to address the physics behind AGN feedback and its
effect on a galaxy’s interstellar medium and thus its star formation (Silk &
Rees, 1998; Fabian, 1999; King, 2003, 2010). High velocity AGN-driven winds
and radio jets have been shown to prevent the cooling of the available gas and
even to cause gas outflows (Morganti, 2017; Baron et al., 2018; Santoro et
al., 2020), therefore preventing this gas from forming stars. Wada (2012) also
show that radiation pressure around the AGN region can cause a vertical
circulation of gas, a phenomenon called a ‘galactic fountain’, which
constantly prevents the collapse of gas clouds. These are examples of
‘negative’ AGN feedback, where star formation is suppressed. On the other
hand, Begelman & Cioffi (1989) and Rees (1989) propose that the alignment of
radio and optical structures in high redshift galaxies is the result of
localised enhanced star formation due to the AGN radio jets themselves. This
would be a form of ‘positive’ AGN feedback, which enhances star formation
instead of suppressing it. Chokshi (1997) further suggests that the most
powerful jets are responsible for the formation of the most massive elliptical
galaxies, whereas less powerful ones are linked to smaller ellipsoids and
bulges. Gaibler et al. (2012) show that positive AGN feedback is also found in
simulations. The balance between positive and negative feedback is not fully
understood, and the possibility of a combination of both modes has also been
debated in the literature (Silk, 2013; Zinn et al., 2013; Zubovas et al.,
2013). In this paper we will try to use a relatively large sample of galaxies
to shed light on these issues.

One way to track the presence of AGN activity is through emission-line
diagnostic diagrams, which identify the main ionizing mechanism in the
interstellar gas by combining permitted and forbidden lines. Hydrogen
permitted lines are due mainly to high-energy photons generated by young
stars, thus serving as a proxy for star formation. The forbidden lines, mostly
from ionised metals, originate mainly in collisionally excited states, which
are usually related to the presence of AGN activity, traveling shocks, or the
effect of evolved stars during a short, yet very hot and energetic phase known
as post asymptotic giant branch (post-AGB, e.g. Cimatti et al., 2019). Several
diagnostic diagram have been proposed in the literature (e.g. Cid Fernandes et
al., 2010; Zhang & Hao, 2018), among which the Baldwin, Phillips & Terlevich
(BPT, Baldwin et al., 1981) diagram is the most commonly used.

Understanding the details of how AGN affect their host galaxies requires large
samples to be able to account separately for the external environment (e.g.,
mass and richness of host halo, local density) and internal properties (e.g.,
stellar mass $M_{\text{stellar}}$, galaxy velocity dispersion, morphology).
The Sloan Digital Sky Survey (SDSS) provides optical imaging and spectroscopic
data covering 14,555 squared degrees on the sky, providing a suitably large
galaxy sample in the local ($z\leq 0.1$) Universe. Environmental information
is available for SDSS galaxies (e.g. Yang et al., 2007; Wang et al., 2014),
providing the necessary data for extensive studies of the effects of the
environment on the properties of these galaxies (e.g. La Barbera et al., 2014;
Pasquali et al., 2019).

With such wealth of data we will be able to investigate the demographics of
optically-identified AGN in both isolated and group/cluster central galaxies.
We will study the interplay between internal and environmental properties
driving AGN and fueling. To this end, we will first separate galaxies
according to their environment and use the BPT diagram to investigate the
fraction of strong AGN (Seyfert galaxies) in different environments.
Additional factors such as galaxy mass, morphology, central velocity
dispersion, and host halo mass, will be considered and linked, together with
the environmental information, to the AGN and star-formation activity of the
galaxies. Our aim is to identify the physical processes fueling AGN and
driving star-formation activity, and causing both star-formation quenching and
morphological transition.

This paper is organized as follows: in §2 we present the galaxy sample
properties; in §3 we separate galaxies according to their environment and
stellar mass and compare their distribution on the BPT diagram; in §4 we
investigate the prevalence of strong AGN as a function of galaxy morphology
and environment; in §5 we directly trace the interplay between environment,
AGN activity, and the evolutionary state of central galaxies through the star-
formation rate versus stellar mass diagram; in §6 we present the main results
and our final conclusions. Throughout this paper we adopt a flat $\rm\Lambda
CDM$ cosmology with
$[\Omega_{\text{M}},\Omega_{\Lambda},H_{0}]=[0.27,0.73,72\,$km$\,\rm
s^{-1}Mpc^{-1}]$.

##  2 Data and sample selection

We use the single-fibre spectroscopy from the Sloan Digital Sky Survey
Sixteenth Data Release (SDSS–DR16, Abazajian et al. 2009). We limit our sample
to the redshift range $0.03\leq z\leq 0.1$; the lower limit minimises aperture
biases in the measured galaxy properties due to the fixed 3 arcsec fibre
diameter. To guarantee completeness, we only select galaxies with apparent
Petrosian magnitude in the $r$-band brighter than 17.78, which corresponds to
the spectroscopic completeness limit of the survey at $z=0.1$. We also impose
a signal-to-noise ratio (S/N)111Median signal-to-noise ratio of all good
pixels in the galaxy spectrum. threshold of 10 to ensure adequate spectral
quality.

###  2.1 Central galaxy selection and environment characterization

From these data, we select central galaxies using the Yang catalogue (Yang et
al., 2007). This catalogue was built by applying a halo finder algorithm (Yang
et al., 2005) to the New York University Value Added Galaxy Catalogue (Blanton
et al., 2005). Galaxies in the same halo are considered to be part of the same
group/cluster. This allows us to define different environments for central
galaxies: 1) isolated centrals – galaxies living in halos occupied by a single
galaxy ($N_{\text{members}}=1$); 2) binary system centrals – the most massive
galaxy of a pair hosted in the same halo ($N_{\text{members}}=2$); 3) group
centrals – central galaxies in halos occupied by at least 3 galaxies, but no
more than 10 ($3\leq N_{\text{members}}<10$); and 4) cluster centrals – the
central system in halos populated by more than 10 member galaxies
($N_{\text{members}}>10$). For halos hosting more than one galaxy, we define
the central system to be the most massive one, with stellar mass calculated
via equation (2) in Yang et al. (2007). We tested how the sample would change
if we selected the brightest cluster galaxy (BCG) instead; we find no
significant differences, since 98.2% of the most massive galaxies are also
BCGs. We further guarantee completeness regarding the halo mass estimate by
imposing the conservative threshold presented in Yang et al. (2009),

$\log(M_{\text{halo}}/M_{\odot})\geq 12+\frac{z_{\text{c}}-0.085}{0.069},$ (1)

where $z_{\text{c}}$ denotes the median redshift of a given system (halo), and
$M_{\text{halo}}$ is the halos mass estimated by Yang et al. (2007).

In our analysis we will need to take into account that, as a result of
separating central galaxies according to the number of satellites in their
host halo, each sub-sample has different magnitude (and therefore stellar
mass), and host halo-mass distributions, as shown in Fig. 1.

The four sub-samples of central galaxies we have defined contain 59,605
isolated centrals, 11,639 in binary systems, 7,586 in groups, and 1,291 in
clusters.

Figure 1: Distribution of the $r$-band absolute magnitude $M_{\text{r}}$
(left) and host-halo mass $M_{\text{halo}}$ (right) for the four sub-samples
of central galaxies: isolated centrals (blue line), centrals in binary system
(green), in groups (orange), and in clusters (red). The vertical dashed line
in the right panel show the lower halo-mass completeness limit from the Yang
Catalogue.

###  2.2 Galaxy properties

####  2.2.1 Stellar masses, star-formation rates, and velocity dispersions

Figure 2: Relation between host-halo mass and redshift. Galaxies are separated
into isolated centrals (top left), centrals in binary system (top right),
group centrals (bottom left), and cluster centrals (bottom right). The dashed
line in each panel indicates the halo mass completeness limit as a function of
redshift (Equation 1). Points are coloured according to the galaxies’ stellar
mass. Figure 3: Comparison of the SDSS images of pairs of galaxies with
different morphologies (T-Types) in three redshift bins (rows) for no-AGN
(left image in each pair) and AGN (Seyfert, right image) galaxies classified
using the BPT diagram. It is apparent that the presence of an AGN doesn’t
alter the morphology of the host galaxy significantly.

The galaxies’ stellar mass ($M_{\text{stellar}}$), star formation rate (SFR),
and velocity dispersion ($\sigma_{\text{galaxy}}$) are obtained from the Max
Planck Institut für Astrophysik – John Hopkins University catalogue (MPA–JHU,
Tremonti et al., 2004; Brinchmann et al., 2004). It provides reliable
measurements and their associated errors for galaxies in the SDSS–DR8 without
spectral anomalies. An important feature is the way they estimate the
galaxies’ SFR: it is first derived using the $\rm H\alpha$ emission-line flux
for galaxies classified as ‘star-forming’ in the BPT diagram (see Section
2.2.2), and then extrapolated to other galaxies using a calibration between
SFR and the 4000Å break. This is particularly important in our study since
this method prevents the SFR estimates being contaminated by possible AGN
contribution to the $\rm H\alpha$ flux. An indication of the typical
uncertainties in the galaxies’ properties is provided in Table 1,

Table 1: Median uncertainties in the $M_{\text{stellar}}$, SFR, and
$\sigma_{\text{galaxy}}$ estimates for galaxies in different stellar-mass
ranges. For the stellar masses and SFRs we calculate the relevant $1$-$\sigma$
uncertainty $\Delta(1\sigma)$ for each galaxy from the $\rm 86^{th}$ and $\rm
14^{th}$ percentiles $Q_{86}$ and $Q_{14}$ using
$\Delta(1\sigma)=0.5\times(Q_{86}-Q_{14})$. The velocity dispersion
uncertainties are provided by the MPA–JHU catalogues.

| $10\leq\log(M_{\text{stellar}}/M_{\odot})<10.5$ | $10.5\leq\log(M_{\text{stellar}}/M_{\odot})<11$ | $11\leq\log(M_{\text{stellar}}/M_{\odot})$
---|---|---|---
$\Delta\log(M_{\text{stellar}})$ [$M_{\odot}$] | 0.09 | 0.09 | 0.09
$\Delta\log(\text{SFR})$ [$M_{\odot}/yr$] | 0.31 | 0.99 | 1.02
$\Delta\sigma_{\text{galaxy}}$ [km/s] | 11.85 | 10.66 | 11.44

The galaxies in our sample have stellar masses in the range
$10^{10}M_{\odot}\leq M_{\text{stellar}}\leq 10^{11.5}M_{\odot}$. However,
Equation 1 implies that for some of the sub-samples we lose some of the less
massive systems at high redshift (see Fig. 2). This affects mostly isolated
centrals, for which we only reliably cover the full stellar mass range up to
$z\sim 0.06$. Since we only consider a relatively narrow redshift range, we do
not expect significant evolution with look-back time, and therefore the fact
that for some low-mass galaxies we don’t sample the full redshift range should
not affect our results.

Figure 4: Normalized Gaussian-kernel-smoothed distribution of central galaxies
in the BPT diagram for different environments (from left to right, and in
order of ‘environmental richness’, isolated centrals, centrals in binary
system, in groups, and in clusters) and in three mass bins (from top to
bottom, $10^{10}\leq M_{\text{stellar}}/M_{\odot}<10^{10.5}$; $10^{10.5}\leq
M_{\text{stellar}}/M_{\odot}<10^{11}$; and $M_{\text{stellar}}/M_{\odot}\geq
10^{11}$). The lines separating different regions of the diagram are described
in section 2.2.2. The number of galaxies in each sub-sample is indicated
towards the bottom left of each panel. Note that our sample does not contain
cluster centrals with log$(M_{\text{stellar}}/M_{\odot})<10.5$.

####  2.2.2 BPT classification

The BPT diagram uses the flux ratios of two pairs of emission lines,
$\rm[OIII]_{\lambda 5007}$ over $\rm H\beta$, and $\rm[NII]_{\lambda 6584}$
over $\rm H\alpha$ (Baldwin et al., 1981). The lines in each pair are close in
wavelength, minimising extinction effects. The MPA–JHU catalogues provide the
required emission-line fluxes. These are measured after the continuum and
stellar absorption lines have been subtracted222The stellar contribution to
the spectra is estimated through spectral fitting using single stellar
population models from Bruzual & Charlot (2003). See Brinchmann et al. (2004)
for more details. Table 2 shows the median uncertainties in the emission-line
flux measurements.

On a BPT diagram (see Fig. 4), the line demarcating the region where the
dominant ionisation mechanism is star formation can be derived theoretically
as the upper limit for the line ratios that can arise in gas ionised by an
starburst (Kewley et al., 2001). A second line is defined observationally by
Kauffmann et al. (2003) separating systems whose interstellar gas is mainly
collisionally ionized. The intermediate region enclosed by these two lines
contains galaxies with ‘composite’ spectra, such that their interstellar gas
is ionized by a combination of both radiative and collisional mechanisms.
Galaxies above and to the right of the Kewley et al. (2001) line are further
divided into two different classes, Seyferts and LINERs (Low Ionization
Nuclear Emission Regions), using another line defined by Kewley et al. (2001).
Fig. 4 presents BPT diagrams for several galaxy sub-samples, showing the lines
dividing the different regions.

Using emission-line data, the MPA–JHU catalogue classifies galaxies according
to their dominant ionising mechanism using the BPT diagram with the dividing
lines defined above. Galaxies are thus divided into six categories: 1) star
forming, 2) low S/N star forming, 3) composite, 4) Seyfert, 5) LINER, and 6)
unclassified. This last class comprises galaxies with no reliable
classification in the BPT diagram due to at least one of the four relevant
emission lines having S/N smaller than 3. Furthermore, in order to increase
the robustness of our results, we only accept the BPT classification for
galaxies with $\rm H\alpha$ equivalent width ($EW(\text{H}\alpha$)) greater
than 3Å, which is the threshold used in the WHAN diagram to separate LINERs
and Retired galaxies (Cid Fernandes et al., 2010). The flux of weaker lines
would be highly uncertain in the presence of underlying stellar absorption
lines even after correcting for them. This way we avoid contaminating our
sample with weak emission line galaxies that can be explained by the presence
of old stellar population. Hereafter we will refer to the joint sample of
‘unclassified’ galaxies and those with $EW(\text{H}\alpha)\leq 3$Å as
‘Passive+Retired’ (P+R) galaxies. As we will show below, these Passive+Retired
galaxies have negligible star formation, as expected.

It is important to point out that, while the emission lines of Seyfert
galaxies are well explained by the presence of a strong AGN, there is
considerable uncertainty – and some controversy – on the origin of the
emission lines observed in LINERs. However, it is now generally accepted that,
in addition to low-activity AGN, LINER emission may also be due to the
presence of an old stellar population (Cid Fernandes et al., 2010) containing
very hot low-mass stellar relics such as post-AGB stars. Since the object of
this work is to investigate the effect of AGN activity on their host galaxies,
we will not consider either composite-spectra galaxies, since we want to make
the cleanest possible separation between star-forming and Seyfert galaxies, or
LINERs, because it is very likely that these objects are not driven primarily
by a central SMBH engine, given that we use single fibre spectroscopy, so that
we cannot probe the spatial distribution of the nebular emission. In what
follows we will only consider galaxies in the Seyfert region of the BPT
diagram as unequivocal optically-selected AGN.

Table 2: Median uncertainties in line flux measurements for galaxies in
different stellar-mass ranges. The flux units are $10^{-17}\,{\rm
erg\,s^{-1}cm^{-2}}$.

| $\rm 10\leq log(M_{stellar}/M_{\odot})<10.5$ | $\rm 10.5\leq log(M_{stellar}/M_{\odot})<11$ | $\rm 11\leq log(M_{stellar}/M_{\odot})$
---|---|---|---
$\Delta\rm[NII]_{\lambda 6584}$ | 2.81 | 3.57 | 5.17
$\Delta\rm H\alpha$ | 3.53 | 3.86 | 5.59
$\Delta\rm[OIII]_{\lambda 5007}$ | 2.62 | 3.32 | 4.45
$\Delta\rm H\beta$ | 2.61 | 3.05 | 4.24

####  2.2.3 Morphologies

When the star-formation properties of galaxies change, their morphologies may
also change. Here we use the T-Type parameter, first introduced by de
Vaucouleurs (1963), to describe a galaxy’s morphology. To aid our analysis it
is convenient to use a revised T-Type parameter which varies continuously from
$-3$ to 6 (Meert et al., 2015) instead of the original discrete values. As
usual, a T-Type value $\leq 0$ indicates an early-type galaxy, while T-Type
values $>0$ correspond to late-type morphologies. We adopt the T-Type values
from the work of Domínguez Sánchez et al. (2018), which was based on the
application of a deep-learning convolutional neural network algorithm to
670,722 galaxies from the SDSS-DR7 database.

It is conceivable that the presence of a strong AGN may influence the
morphological classification of the host galaxy. To ensure that such effect is
not significant enough to alter the conclusions of this work, we examine the
images of a subset of randomly selected galaxies classified as Seyfert and
compare them with the images of non-Seyfert galaxies with similar
morphologies. Fig. 3 shows this comparison for a sample of galaxies, Seyfert
and non-Seyfert, for different morphologies and redshifts. Visual inspection
indicates that that the presence of an AGN does not alter the morphology
significantly, at least at optical wavelengths in these nearby galaxies.

Furthermore, in order to check that the results of our analysis do not depend
critically on the specific choice of morphological data, we repeated our
analysis using independent visual morphologies from the the Nair and Abraham
catalogue (Nair & Abraham, 2010). These morphologies do not rely on automated
algorithms, being based on human inspection of the galaxy images.
Notwithstanding the different sample sizes of both morphological catalogues,
the results obtained are completely compatible.

The results of both tests indicate that the morphological data we adopt are
suitable for this analysis.

##  3 Star formation and AGN activity as a function of stellar mass and
environment

Fig. 4 shows the distribution of central galaxies in the BPT diagram for the
different environments we are considering (isolated centrals, centrals in
binary system, in groups, and in clusters), in three stellar-mass bins
($10^{10}\leq M_{\text{stellar}}/M_{\odot}<10^{10.5}$; $10^{10.5}\leq
M_{\text{stellar}}/M_{\odot}<10^{11}$; and $M_{\text{stellar}}/M_{\odot}\geq
10^{11}$).

We observe a decreasing fraction of star-forming galaxies for increasing
stellar mass, irrespective of environment. This is in agreement with the so-
called ‘downsizing’ scenario, and suggests that, as star formation decreases,
other ionizing mechanisms become more relevant and prominent at high stellar
masses. In particular, the increasing fraction of massive galaxies where
collisionally driven ionisation dominates suggests that AGN activity may be
involved in quenching star formation (Combes, 2017; Bluck et al., 2020).
Within a given stellar mass bin, we find a decreasing fraction of star-forming
galaxies as ‘environmental richness’ increases. For instance, in the low
stellar-mass bin the fraction of star-forming galaxies decreases from 31% in
isolated centrals to 17% in cluster centrals.

Moreover, Fig. 4 indicates that AGN presence also depends on environment. For
instance, for low stellar mass centrals there is a higher Seyfert fraction in
group centrals (11%), compared with 6%, 8% and 7% for isolated, binary system
and cluster centrals, respectively. Although AGN are always a small minority
in each category, the change is sizeable. In more detail, Fig. 5 shows the
Seyfert fraction as a function of stellar mass, separating galaxies according
to their environment. We calculate the fraction in bins of 0.25 dex, from
$\log(M_{\rm stellar}/M_{\odot})=10$ to 12, limiting the calculation to bins
with at least 20 galaxies. We interpolate linearly between neighbouring bins.
Here and in subsequent figures we estimated the uncertainties using a standard
bootstrap technique with 1000 re-samplings. We find that the Seyfert fraction
increases with stellar mass for isolated, binary system and group centrals,
whereas cluster centrals show an almost constant fraction ($\sim 12.5\pm 4\%$
from $\rm 10^{11}$ to $\rm 10^{11.5}M_{\odot}$ followed by a steep decrease
towards $\rm 10^{11.75}M_{\odot}$ ($\rm 3\pm 6\%$ in the last bin).

Figure 5: Seyfert fraction as a function of stellar mass, separating galaxies
according to environment. Dashed lines and shaded areas represent medians and
1-sigma uncertainties, respectively.

Comparison between different environments shows an increasing Seyfert fraction
for increasing richness in the $\rm 10^{10.25}$ and $\rm 10^{11.25}M_{\odot}$
range. This suggests there may be a significant environmental effect on the
fueling of AGN activity, which supports that in order to understand AGN
feedback on central galaxies we need to analyse the complex interplay between
internal and external factors in detail.

##  4 The demographics of AGN as a function of the internal and environmental
properties of central galaxies

AGN activity depends on the availability of gas that can be accreted onto the
central SMBH. It is generally accepted that most galaxies in the mass range we
are considering contain a SMBH at their centre. The fact that only a small
fraction of galaxies contain a strong AGN (e.g., Seyfert galaxies) can be
attributed to the large amounts of gas required to fuel strong AGN (Coldwell
et al., 2014; Ellison et al., 2016). By tracing the fraction of Seyferts as a
function of the galaxies’ properties and environment we may be able to shed
light on the combination of internal and environmental factors needed to drive
AGN fueling in central galaxies, and consequently investigate the effect of
AGN activity on galaxy evolution.

###  4.1 The relation between AGN and the morphology of their host galaxies

In Fig. 6 we show the fraction of Seyferts as a function of the T-Type of
their host galaxies. To provide context, we also show the fraction of star-
forming and P+R galaxies. To guarantee reliable results, we also impose a
minimum of 20 galaxies per bin to calculate the relevant fractions. For
reference, we define three T-Type ranges: $-3\leq\text{T}<-0.75$ corresponds
to elliptical galaxies; $-0.75\leq\text{T}\leq 0.75$ to lenticular (S0)
galaxies; and $0.75<\text{T}\leq 6$ to spiral galaxies. These limits were
chosen to be consistent with the uncertainties in T-Type
($\Delta$T-Type$\,\sim 0.5$); changes in the bin boundaries of this size will
not significantly change our results. Elliptical and lenticulars are often
combined under the label ‘early-type galaxies’ (ETGs), while spirals are
‘late-type galaxies’ (LTGs). Overall, the decreasing fraction of star-forming
systems for decreasing T-type values (from LTGs to ETGs) simply reflects the
fact that most LTGs host significant star formation, whereas the opposite
trend observed for P+R galaxies indicates that most ETGs do not form many
stars. Although this basic picture is true for all galaxy masses and
environments, the actual fraction of galaxy type changes both with mass and
environment.

Figure 6: Fraction of star-forming (blue), Seyfert (green) and P+R (red)
galaxies as a function of morphological T-Type. As in Fig. 4, galaxies are
divided according to their environment (columns) and stellar mass (rows). The
red, gray and aqua colored backgrounds correspond to the T-Type ranges of
ellipticals, lenticulars, and spirals, respectively. Median error bars are
shown on centre right of each panel.

The fraction of Seyfert galaxies is always relatively small, increasing with
the galaxies’ stellar mass in all environments. In agreement with the results
of previous works, we find that low-mass galaxies are less likely to host an
AGN than massive ones (Wang & Kauffmann, 2008). This can be interpreted as an
indication that the fueling of an AGN depends on the amount of gas retained by
the galaxy’s host halo, which correlates with the halo mass. For the two
lowest stellar mass bins, we find an almost constant fraction of Seyferts for
morphologies in all environments, although the small numbers make this
invariance somewhat uncertain. This low fraction may indicate that, regardless
of their morphology, these systems are rarely able to hold a large enough gas
reservoir to both fuel star formation and AGN activity. In this case, as soon
any AGN feedback is triggered, all the neutral hydrogen gas is removed,
preventing any subsequent AGN activity (Guo et al., 2022).

For high stellar masses, the Seyfert fraction is significantly higher than in
low-mass galaxies. Quantitatively, the average over all environments for the
lower stellar mass bin gives a Seyfert fraction of $\rm 5\pm 3\%$, in
comparison with $\rm 13\pm 4\%$. In the most massive bin, Seyferts are more
abundant than star-forming galaxies in all environments for virtually all
morphologies. There are more than twice as many high-mass galaxies classified
as Seyferts than as star-forming even for late-type spirals. This could simply
suggest that, in the absence of star formation as an ionising mechanism, even
a relatively modest level of AGN activity becomes apparent. But it could also
mean that AGN activity is linked to (and perhaps the cause of) star-formation
suppression in massive galaxies.

Furthermore, the decreasing fraction of Seyferts when we transition from
spirals to ETGs provides some support to the idea that AGN feedback plays some
role in the morphological transition process, and in generating the
morphological diversity we observe in present-day galaxies (Rogers et al.,
2009; Dubois et al., 2016; Varglund et al., 2022). Our analysis further shows
that the slope of the relation between AGN activity and morphology depends on
environment, increasing with ‘environmental richness’: it is flatter for
isolated centrals and for those in binary systems than for group and cluster
centrals. The numerical values of the slopes of the relation between Seyfert
fraction and T-Type in Fig. 6 are $0.009\pm 0.003$, $0.015\pm 0.009$,
$0.022\pm 0.010$ and $0.042\pm 0.009$ for isolated, binary, group, and cluster
centrals respectively, showing that environment plays a role.

###  4.2 The relation between AGN, halo mass, and central velocity dispersion
of their host galaxies

The availability of gas and the mass of the central SMBH are both key factors
in AGN activity. The total gas mass is related, albeit in a complex way, to
the mass of the host galaxy halo ($M_{\text{halo}}$), while the mass of the
SMBH correlates with the central velocity dispersion of the galaxy
($\sigma_{\text{galaxy}}$; Tremaine et al. 2002; Gültekin et al. 2009). To
bring all these parameters together, we show in Fig. 7 the median fraction of
Seyferts in the $\sigma_{\text{galaxy}}$ vs. $M_{\text{halo}}$ plane for
central galaxies in different environments. For each pixel, we derive the
Seyfert fraction median and its uncertainty using a bootstrap technique, as
before. We will limit our analysis to galaxies with
$\sigma_{\text{galaxy}}>100\,$km/s, since below this value the galaxy velocity
dispersions provided by the MPA–JHU catalogue become unreliable due to the
resolution of SDSS spectra. In order to confirm the robustness of this trend,
we repeated this analysis using 50% larger bins to reduce the statistical
uncertainties. None of the trends described below changed. Furthermore, we
applied Gaussian smoothing to the density maps to enhance the visual
appearance of the observed overdensities. This also confirmed our conclusions
below. We decided to present the raw binned density maps without smoothing
since they provide a fairer representation of the data and their
uncertainties.

Figure 7: Seyfert fraction in the galaxies’ central velocity dispersion
($\sigma_{\text{galaxy}}$) versus Halo Mass ($M_{\text{halo}}$) diagram. We
separate central galaxies according to their environment into isolated
centrals (top left), centrals in binary system (top right), in groups (bottom
left) and in clusters (bottom right). The black dashed line shows the limit
below which $\sigma_{\text{galaxy}}$ values from the MPA–JHU catalogue become
unreliable. Note that galaxy stellar mass correlates reasonably well with
$M_{\text{halo}}$. Circles and ellipses indicate regions of special interest
(see text for details).

Panel (a) of Fig. 7 shows that the largest Seyfert fraction in isolated
centrals is found in galaxies residing in the largest mass halos
($M_{\text{halo}}\geq 10^{13}M_{\odot}$) and at intermediate velocity
dispersions ($100\leq\sigma_{\text{galaxy}}\leq 200\,$km s-1). A similar locus
with a relatively high fraction of Seyfert galaxies (highlighted by the red
circles) is also found in the other panels. Quantitatively, this region has
median Seyfert fractions of $\rm 17\pm 9\%$, $\rm 15\pm 7\%$, and $\rm 14\pm
3\%$ in isolated, binary system, and group centrals respectively. A high
$M_{\text{halo}}$ suggests a large reservoir of gas (Chen et al., 2014; Davies
et al., 2019), which may be used to fuel the AGN. However, a direct relation
between the size of the gas reservoir and AGN fueling still needs to be
verified by observations. The intermediate velocity dispersion range occupied
by these galaxies corresponds to the transition region between late- and
early-type morphologies, providing additional circumstantial evidence of the
effect strong AGN may have on the galaxies’ morphological transition.

Panel (c) of Fig. 7 shows, for group centrals, a second region with high
Seyfert fraction (indicated by the blue ellipse). These are galaxies with
relatively high velocity dispersion for their halo masses. The fraction of
Seyferts in the same location of the diagram decreases systematically when we
move to centrals in binary systems and isolated ones, with median values of
$2\pm 2\%$, $9\pm 4\%$ and $18\pm 7\%$ for isolated, binary system and group
centrals, respectively. Clearly, in this region of the diagram, the
environment affects AGN fuelling. For group centrals, at a given halo mass
Seyferts are mainly found in galaxies with high $\sigma_{\text{galaxy}}$,
indicating that, even if the gas reservoir is the same, a larger SMBH mass
increases the probability of AGN activity. These high velocity dispersion
galaxies tend to be ETGs. That this happens mostly in the group environment
may suggest that group centrals are more likely to have experienced a recent
interaction with other galaxies (their satellites) than isolated centrals and
centrals in binary systems. Such interactions can drive gas to the central
system, boosting its fuel reservoir. In support of this, La Barbera et al.
(2014) show that central galaxies in groups hosted a more recent star
formation episode in comparison to their isolated counterparts, indicating a
recent supply of gas. Additionally, Kollatschny et al. (2012) show and
increase in [OIII]5007Å when moving closer to the central galaxy. Finally,
Onoue et al. (2018) show an enhanced galaxy overdensity around quasar pairs,
which are more common in more massive halos. Together with our results, these
results provide evidence that the interaction between galaxies can enhance AGN
activity. Nevertheless, a more direct test to support this scenario would be
the observation of the gas component of a large sample of central galaxies
covering a wide range of halo masses, with enough resolution to detect inflows
and outflows.

Moving to cluster centrals, panel (d) of Fig. 7 shows the highest fraction of
Seyferts at the low-halo-mass end of the distribution ($\rm 20\pm 10\%$). The
innermost regions of the most massive clusters are already “fully developed”
(Butcher & Oemler, 1978; Capelato et al., 1980; Carlberg et al., 1997; Sampaio
et al., 2021), and the probability of satellite galaxies interacting with the
cluster central – and thus providing fuel – is lowest for the most massive
clusters due to the very high relative velocities of the satellite galaxies
(Chandrasekhar, 1943).

Figure 8: Gaussian kernel smoothed distribution of central galaxies in the
star formation rate versus stellar mass plane. The separating lines between
blue cloud, green valley, and red sequence regions are shown as yellow solid
lines. The white dashed lines have the same slope as the yellow lines, but
with varying intercept. Central galaxies are divided into isolated centrals
(upper left), centrals in binary systems (upper right), in groups (lower
left), and in clusters (lower right).

From the AGN demographics presented in this section, we have found that,
although stellar mass is the strongest statistical predictor of AGN activity
(c.f. Sections 3 and 4.1), other factors such as morphology, environment, SMBH
mass, and halos mass also play important roles. For massive galaxies, the
relatively high AGN fraction in LTGs and the dependence of AGN frequency on
T-Type suggests that feedback from the AGN is relevant in the morphological
transformation of the galaxies. The details of the distribution of Seyfert
fractions in the $M_{\text{halo}}$ versus $\sigma_{\text{galaxy}}$ plane
provides further insight into how the environment may drive the fueling of AGN
activity. For a given halo mass range, the high fraction of Seyferts in group
centrals is found at high velocity dispersion, suggests that interactions with
satellite group galaxies can enhance the gas reservoirs that fuel the AGN of
group central galaxies, which are predominantly ellipticals.

Figure 9: Fraction of central galaxies classified as star forming (blue),
Seyferts (green) and P+R galaxies (red) as a function of the vertical
distances $\rm\Delta SFMS$ from the star-formation main sequence (SFMS) for
galaxies in different environments (columns) and stellar-mass ranges (rows).
The blue, green, and red backgrounds represent the blue cloud, green valley,
and red sequence regions, as defined in Fig. 8. 1-sigma uncertainties are
presented as shaded regions. Positive $\rm\Delta SFMS$ values correspond to
galaxies with higher star-formation activity than galaxies in the SFMS, while
negative values indicate star-formation suppression relative to the SFMS.

##  5 The role of AGN on the star-formation activity of central galaxies

In this section we focus on how the interplay between AGN activity, stellar
mass, and environment drives the evolution of the star-formation activity of
central galaxies. We quantify the galaxies’ star-formation activity through
the the SFR vs. $M_{\text{\rm stellar}}$ diagram, shown in Fig. 8 for central
galaxies in different environments. The Blue Cloud (BC), Green Valley (GV),
and Red Sequence (RS) regions are defined by two dividing lines:
$\text{log(\rm SFR)}=0.7\log(M_{\text{\rm stellar}})-7.5$ separates the BC
from the GV, and $\text{log(\rm SFR)}=0.7\log(M_{\text{\rm stellar}})-8.0$
separates the GV from the RS (Trussler et al., 2020; Sampaio et al., 2022). To
avoid confusion, we refer to galaxies located in the BC region of this diagram
‘Blue-Cloud galaxies’, reserving the term ‘star-forming galaxies’ for those
classified as such in the BPT diagram.

Consistent with the results of previous sections, we find that the fraction of
galaxies in the BC, i.e. with significant star formation, decreases with
stellar mass and environmental richness, while the RS shows the opposite
trend.

In order to provide a more detailed continuous description of the transition
from the BC to the RS, we divide the SFR vs. $M_{\text{stellar}}$ plane into
12 zones separated by the white dashed lines in Fig. 8. The dividing lines
have the same slope as the lines separating the BC/GV/RS regions, but with
intercepts varying from $-6.5$ to $-9.5$ in steps $0.25$ wide. It is important
to highlight that by adopting a slicing procedure rather than using three
discrete zones, we largely remove the dependence of our results on the
specific boundaries chosen for the BC/GV/RS. Nevertheless, despite being a
somewhat arbitrary choice, the adopted boundary definition has proven to have
physical meaning, since it is shown to coincide with the regions where most of
the morphological transition happens (Sampaio et al., 2022). Each zone
corresponding to different vertical distances $\rm\Delta SFMS$ from the star-
formation main sequence (SFMS; Daddi et al. 2007; Noeske et al. 2007; Karim et
al. 2011) defined by the line $\text{log(\rm SFR)}=0.7\log(M_{\text{\rm
stellar}})-7.0$. The resulting variation in galaxy type fraction as a function
of the vertical distance to the star-forming main sequence is shown in Fig. 9
for different environments and stellar-mass ranges. As before, we limit our
analysis to bins with at least 20 galaxies.

###  5.1 Red but not dead: AGN in massive central red-sequence galaxies in
groups

ETGs are mainly found in the red sequence and are usually assumed to be
passively evolving, such that their star-formation has ceased and their
stellar populations simple age with time. They are often called “red and
dead”. However, by tracing the Seyfert fraction as a function of $\rm\Delta
SFMS$, we find that, depending on environment, not all central galaxies in the
red sequence are quite as dead as previously thought. In panel (h) of Fig. 9
we find that a relatively high fraction (about one third) of the most massive
group galaxies with the lowest star-formation activity are AGN (panel h). This
high AGN frequency is in agreement with our previous results, suggesting that
massive central galaxies in groups (usually ellipticals) can be fed with gas
via interactions with satellite galaxies, generating AGN activity.

Figure 10: Median T-Type as a function of $\rm\Delta SFMS$ for central
galaxies classified as Seyferts in the BPT diagram. We divide galaxies
according to stellar mass (different colours and line styles) and
environmental richness (different panels). Background colors correspond to the
BC, GV and RS regions, as in Fig. 9. 1-sigma errors are shown as shaded areas.

###  5.2 The AGN-driven transition from the blue cloud to the red sequence

The results shown in Fig. 9 provide a new perspective on the possible effect
of AGN activity on the evolution of central galaxies. The increasing Seyfert
fraction across the BC as we move away from the SFMS coincides with a
corresponding decrease in the star-forming fraction, providing evidence that,
despite representing only 10–20% of the central galaxy population, AGN
feedback could be extremely efficient at quenching star formation for all
stellar masses. In this scenario, the AGN is responsible for decreasing the
galaxies’ star formation, but there is a time delay between the triggering of
the AGN and its radiation becoming the main source of the ISM ionisation.
During this process, the AGN activity becomes ‘unmasked’ after the associated
decrease in star formation reduces the ionisisng effect of the high-mass
stars. High spatial resolution integral-field spectroscopic data from
instruments such as MUSE may provide the necessary evidence to test this
scenario.

These results are consistent with the idea that the transition from the BC to
the RS is caused by AGN-driven outflows (Trussler et al., 2020).
Interestingly, the peak of the Seyfert fraction occurs in the vicinity of the
GV, a region associated with both star-formation suppression and morphological
transition (Sampaio et al., 2022), suggesting, once again, that AGN activity
is linked with galaxy transition from spirals to early-type galaxies.

The subsequent decrease in Seyfert fraction from the GV to the RS may be due
to the combination of two processes, AGN feedback ejecting gas from central
galaxies, which depletes the gas fuel reservoir needed to feed the SMBH, and
the morphological transition from disks to spheroids, in which the gas is more
stable and less likely to be accreted by the SMBH (Martig et al., 2009). In
other words, the AGN itself is ultimately responsible for shutting down its
own activity.

###  5.3 Morphological Transition vs. Star Formation Quenching

By tracking the morphology of Seyfert galaxies as a function of their star-
formation activity, we are also be able to address the question of whether AGN
feedback changes the star formation activity of their host galaxies before or
after their morphology changes. The median T-Type of Seyfert galaxies as a
function $\rm\Delta SFMS$ is shown in Fig. 10, where the galaxies have been
separated according to stellar mass and environmental richness. For group and
cluster centrals, we show only the curves with a minimum number of 10 galaxies
per bin to ensure the statistical uncertainties are not too large.

This figure shows that, statistically, Seyfert galaxies reach elliptical
morphologies (median T-Type $\rm\sim-2$) before their star-formation is
completely suppressed (i.e., before they reach the core of the RS region,
$\rm\Delta SFMS\sim-2$). There is also a mass dependence in the morphological
transition of Seyfert galaxies: while low-mass galaxies typically emerge from
the GV with elliptical morphologies (irrespective of their environmental
richness), intermediate-mass systems emerge, on average, as S0s, and high mass
systems tend to retain spiral morphologies beyond the GV. This provides
evidence suggesting that the AGN activity is more relevant in the
morphological transition of low-mass galaxies, whilst more massive systems
hold their morphology “longer”.

In summary, our results show that morphological transition and star-formation
suppression happen at different pace, in agreement with Sampaio et al. (2022).
Although the detailed connection between AGN activity and the physical
processes by which it affects morphological transition are still not wholly
understood, it is noticeable that the sequencing we observe suggests that,
irrespective of stellar mass and environment, the morphology of Seyfert
galaxies evolves from late- to early-type before their star formation is fully
quenched.

##  6 Conclusions

With the aim of shedding light understanding how AGN affect the evolution of
their host galaxies, we have investigated the relationship between the
properties of central galaxies, their environment, and the presence or absence
of an AGN at their centres. We focus on central galaxies because, as the
dominant object in their dark-matter halo, external influences may be weaker
than for satellite galaxies, making them ideal candidates for studying the
effect of internal processes such as AGN feedback.

We have traced the effect of the environment by dividing the galaxies into
isolated centrals and centrals in pairs, groups, and clusters. SDSS
spectroscopy and the BPT diagram allow us to determine whether the dominant
ionising mechanism of the galaxies’ interstellar medium is star-formation or
AGN activity. We analyse this information as a function of internal galaxy
properties such as their stellar and dark-matter halo mass, morphology, and
central velocity dispersion (correlated with their SMBH mass). In doing so we
explore how the interplay between different combinations of internal and
external factors may be linked to the fueling of the central SMBH and thus AGN
activity, and how this activity may affect the properties and evolution of its
host galaxies. The main results of this analysis are:

  * •

In all environments, the preeminence of AGN activity as the dominant ionising
mechanism increases with stellar mass, overtaking star-formation for galaxies
with $\rm M_{\text{stellar}}\geq 10^{11}M_{\odot}$ (Figs. 5 and 6). It is
noticeable that, at these high masses, the fraction of LTGs with Seyfert
activity reaches $\rm 21\pm 4\%$ in group centrals, while only $\rm 7\pm 3\%$
of these galaxies have their interstellar medium ionised by star formation.

  * •

In high stellar mass central galaxies, the fraction of Seyferts increases with
T-Type from $\rm 5\pm 1\%$ at T-Type$\,\sim-2.5$ (ellipticals) to $\rm 18\pm
3\%$ at T-Type$\,\sim 4$ (late spirals). This increase in Seyfert fraction
with morphology suggest that AGN feedback is linked with the morphology of
these galaxies and, perhaps, its transformation. The low fraction of Seyfert
nuclei in low-mass galaxies, independent of morphology and environment,
results from the inability of these systems to fuel star-formation and AGN
simultaneously.

  * •

The separate variation of the Seyfert fraction with the galaxies’ velocity
dispersion and halo mass suggests two different ways to fuel AGN activity.
First, central galaxies can rely on their own host halo gas reservoir to fuel
their AGN, which is increasingly efficient with increasing halo mass; and
second, central galaxies can increase their gas reservoir via interactions
with satellite systems. We find that the second mechanism is most important
for the evolution of high-mass centrals in groups and low-mass clusters, where
such interactions will be more common.

  * •

The Seyfert fraction changes systematically as a function of star-formation
activity in their host galaxies (Fig. 9). Within the blue cloud this fraction
increases as star-formation activity declines, reaching a maximum when the
galaxies enter the green valley. The peak fraction depends on both stellar
mass and environmental richness. For instance, high mass group centrals show a
peak Seyfert fraction of $\rm 18\pm 4\%$ near the green valley. Subsequently,
the Seyfert fraction decreases as the galaxies transition into the red
sequence. This sequence strongly suggest that AGN feedback plays a key role in
regulating and suppressing star-formation.

  * •

Tracing the morphology of Seyfert central galaxies as a function of their
star-formation activity, we find that they typically achieve an early-type
morphology while they still host some residual star formation. This suggests
that, in all environments, the morphology of Seyfert galaxies evolves from
late- to early-type before their star formation is fully quenched. We
additionally show that stellar mass plays an important role in the
morphological evolution of Seyfert galaxies: low mass systems tend to emerge
from the green valley with an elliptical morphology, whereas their high-mass
counterparts maintain a spiral morphology deeper into the red sequence.

In summary, we have found strong evidence that AGN activity in central
galaxies is intimately linked with the morphology and star-formation of their
hosts, and that this link depends on both the internal properties of these
galaxies and their environment.

## Acknowledgements

VMS and RRdC acknowledge the support from FAPESP through the grants
2020/16243-3, 2020/15245-2 and 2021/13683-5. SZ, MRM, and AAS acknowledge
financial support from the UK Science and Technology Facilities Council (STFC;
grant ref: ST/T000171/1). IF acknowledges support from the Spanish Ministry of
Science, Innovation and Universities (MCIU), through grant
PID2019-104788GB-I00.

## Data Availability

The data underlying this paper were accessed from SDSS DR16 database
(https://skyserver.sdss.org/dr16/en/home). The data underlying this article
will be shared on request to the corresponding author.

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##  Appendix A Comparison using alternative diagnostic diagrams

Figure 11: Gaussian kernel smoothed distribution of galaxies in the NII-BPT
diagram. We divide systems according to stellar mass and environmental
richness.

The main underlying hypothesis of this work is that the BPT diagram we have
chosen is able to reliably identify the main mechanism ionizing the
insterstellar gas in central galaxies. However, the literature provides
alternative diagnostic diagrams to achieve the same goal using a variety of
emission-line ratios. Since the question “which diagnostic diagram is the best
for this purpose?” doesn’t have a simple answer (see Cid Fernandes et al. 2010
for a comprehensive comparative study of several diagnostic diagrams), we have
tested whether our findings depend on the specific diagnostic diagram we
choose. As an example, we show in Fig. 11 the distribution of galaxies in an
alternative BPT diagram that uses the [SII]/H$\alpha$ ratio instead of
[NII]/H$\alpha$, as we did in Fig. 4. Comparing both figures we find that the
galaxy distribution is similar using the alternative diagnostic. Therefore, we
are confident that our results do not depend significantly on the specific
diagnostic diagram adopted.