# The Relationship between the Incidence of X-ray selected AGN in Nearby
Galaxies & Star-formation Rate

Keir L. Birchall1, M. G. Watson1, J. Aird1,2, and R. L. C. Starling1
1School of Physics & Astronomy, University of Leicester, University Road,
Leicester LE1 7RH, UK
2Institute for Astronomy, University of Edinburgh, Royal Observatory,
Edinburgh EH9 3HJ, UK
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present the identification and analysis of an X-ray selected AGN sample
that lie within the local ($z<0.35$) galaxy population. From a parent sample
of 22,079 MPA-JHU (based on SDSS DR8) galaxies, we identified 917 galaxies
with central, excess X-ray emission (from 3XMM-DR7) likely originating from an
AGN. We measured the host galaxies’ star formation rates and classified them
as either star-forming or quiescent based on their position relative to main
sequence of star formation. Only 72% of the X-ray selected sample were
identified as AGN using BPT selection; this technique is much less effective
in quiescent hosts, only identifying 50% of the X-ray AGN. We also calculated
the growth rates of the black holes powering these AGN in terms of their
specific accretion rate ($\propto\mathrm{L_{X}/M_{*}}$) and found quiescent
galaxies, on average, accrete at a lower rate than star-forming galaxies.
Finally, we measured the sensitivity function of 3XMM so we could correct for
observational bias and construct probability distributions as a function of
accretion rate. AGN were found in galaxies across the full range of star
formation rates ($\log_{10}\mathrm{SFR/M_{\odot}\ yr^{-1}}=-3\ \mathrm{to}\
2$) in both star-forming and quiescent galaxies. The incidence of AGN was
enhanced by a factor 2 (at a 3.5$\sigma$ significance) in star-forming
galaxies compared to quiescent galaxies of equivalent stellar mass and
redshift, but we also found a significant population of AGN hosted by
quiescent galaxies.

###### keywords:

galaxies:active – galaxies:evolution – black hole physics – X-rays:galaxies

††pubyear: 2023††pagerange: The Relationship between the Incidence of X-ray
selected AGN in Nearby Galaxies & Star-formation Rate–10

##  1 Introduction

Galaxies grow by forming stars, a process driven by the availability of cold
gas. This material is also thought to fuel the growth of SMBHs (Alexander &
Hickox, 2012). However, a lot of uncertainty remains over exactly how the
growth of galaxies and their central SMBHs co-evolve over cosmic time. Large
scale surveys of AGN activity across the electromagnetic spectrum have been
employed to shed light on the nature of this relationship (e.g. Aird et al.,
2018; Mullaney et al., 2012a; Rosario et al., 2013; Smolčić et al., 2017;
Reines et al., 2013, and many others). By exploring how the incidence of AGN
changes with the SFR of its host galaxy several key pieces of evidence have
been uncovered that suggest the growth of SMBHs and their host galaxies are
connected.

One of the most well-constrained correlations highlighting the relationship
between SMBH and galaxy growth was discovered through including SMBH mass
measurements from the nearby Universe. Using a mixture of ground and space-
based observations, Magorrian et al. (1998) measured the dynamical masses of a
sample of 32 SMBHs and uncovered a relationship between a SMBH’s mass and the
luminosity of the host galaxy’s classical bulge. Soon after, similarly strong
correlations between related bulge quantities like mass and velocity
dispersion (e.g. Ferrarese & Merritt, 2000; Gebhardt et al., 2000; Kormendy &
Ho, 2013; Greene et al., 2020) were found. These results imply the existence
of historic, correlated SMBH-galaxy growth.

Further compelling evidence for this relationship has been found by comparing
the average properties from large samples. For example, Madau & Dickinson
(2014) compiled IR and UV measurements from dozens of previous studies. With
this data they measured the cosmic star formation history (SFH) out to $z\sim
6$. They found that, from $z=6$, the density of star formation in the Universe
increased as galactic structures concentrated gas allowing stars to form
rapidly. It then peaked at around $z=1.5$ \- $2$, before declining to about a
tenth of the peak in the present-day Universe. They then compared this to
several measurements of black hole accretion rate density (BHARD), derived
from luminosity functions measured in hard X-rays (Aird et al., 2010) and the
infrared (Shankar et al., 2009; Delvecchio et al., 2014). They found a strong
agreement between the SFH and BHARD distributions. Thus, it became
increasingly clear that there exists a strong connection between star
formation and SMBH growth.

When directly attempting to connect the AGN activity with the host galaxy’s
SFR, however, the results are not clear. On the one hand, numerous studies
found that the average SFR of AGN-hosting galaxies increased out to at least
$z\approx 3$ (e.g. Harrison et al., 2012; Mullaney et al., 2012b; Rosario et
al., 2012, 2013), and that the SFR is found to tightly correlate with the
average AGN luminosity (e.g. Mullaney et al., 2012a; Chen et al., 2013). On
the other hand, it was found that AGN at a fixed X-ray luminosity can have a
broad range of SFRs (e.g. Alexander et al., 2005; Mullaney et al., 2010) \- in
some cases covering up to 5 orders of magnitude (Rafferty et al., 2011).

As the galaxy population evolves through cosmic time, there is a significant
change in the star-forming composition of the overall galaxy population. Since
$z=2$, there has been a significant build up of the quiescent galaxy
population, particularly in higher mass galaxies (Brammer et al., 2011;
Tomczak et al., 2014; Barro et al., 2017), which highlights a significant
amount of star-formation quenching in this period. This decline in the density
of star formation across recent cosmic time is thought to be driven by a
decreasing density of molecular gas (Popping et al., 2012; Maeda et al.,
2017). A concurrent decline in the AGN activity of star-forming galaxies could
imply a relationship between star-forming activity and black hole fuelling.
Kauffmann & Heckman (2009) described this kind of activity through their
"feast and famine" fuelling model. By analysing the Eddington ratio
distributions of a sample of optically-selected SDSS AGN they were able to
demonstrate the existence of two distinct populations of AGN implying there
were different regimes of black holes growth. The "feast" mode is associated
with galaxies containing significant amounts of star formation in their
central regions. The large amounts of cold gas required for star formation
fuels black hole growth. The "famine" mode is associated with galaxies hosting
older stellar populations. In this case, black hole growth is regulated by the
rate at which stars lose their mass.

Whilst the optical selection method used in Kauffmann & Heckman (2009)
produced an incomplete sample (Jones et al., 2016), this relationship between
star formation and black hole accretion has been observed in more recent
studies with more complete samples. For example, Aird et al. (2019) explores
the effect of star formation on a sample of AGN from the CANDELS survey
($0.1\leq z\leq 4$), selected using Chandra X-ray data. After applying
observational corrections to this sample, they find evidence of an SFR-
dependent fuelling mechanism reflective of the model proposed in Kauffmann &
Heckman (2009). On the other hand, Torbaniuk et al. (2021) explored this
relationship on a sample on AGN at $z<0.33$ using data from SDSS DR8 and 3XMM
DR8. They found twice as many AGN in star-forming galaxies compared to
quiescent hosts. They then corrected their sample for observational
incompleteness using 3XMM upper limits to study the intrinsic accretion rate
distribution in this region. They found systematically larger accretion rates
in star-forming galaxies across all stellar masses. Their results imply that
both black hole accretion and star formation are fuelled by a common source.

In this paper, we explore the star-forming properties of galaxies in the
nearby Universe ($z<0.35$) and investigate how this affects the likelihood of
finding an X-ray selected AGN. For this analysis, we use techniques developed
in our previous work (Birchall et al., 2020, 2022). In these papers we
investigated the relationship between host galaxy properties and the incidence
of X-ray selected AGN in dwarf galaxies, and then in the full galaxy
population. Our galaxies were taken from the MPA-JHU (based on SDSS DR8) and
X-ray information from 3XMM DR7. We used upper limits to correct our sample
for observational incompleteness and used this to measure the probability of
finding AGN activity in a galaxy of a given mass and redshift.

This paper is structured as follows. First, we describe how our AGN sample was
constructed (§2). Second, we present our approach to classifying the star-
forming properties of the galaxies in our sample, making sure to account for
the effect of changing stellar mass and redshift (§3). Then we assess the
agreement between our X-ray selected sample and BPT selection, and how star-
forming activity affects that classification (§4). After that, we investigate
the rate at which the black holes powering our AGN are accreting material and
explore how this changes with its star formation classification (§5). With
this data we then measure the probability of finding AGN activity as a
function of accretion rate distributions (§6) and use them to calculate how
the fraction of galaxies that host AGN varies with stellar mass, redshift and
star formation rate (§7). Throughout, we assume Friedmann-Robertson-Walker
cosmology: $\Omega=0.3$, $\Lambda=0.7$ and $H_{0}=70\ \mathrm{km\ s^{-1}\
Mpc^{-1}}$.

##  2 Data & Sample Selection

To define a parent sample of local galaxies for this study we used the MPA-JHU
catalogue111Available at http://www.mpa-garching.mpg.de/SDSS/DR7/. This
catalogue is based on the Sloan Digital Sky Survey Data Release 8 (SDSS DR8),
and includes stellar masses, star formation rates (SFRs) and emission line
fluxes for 1,472,583 objects classified as galaxies by the SDSS pipeline.
Whilst the MPA-JHU catalogue is formally deprecated by the SDSS, we found the
alternatives (Wisconsin, Portsmouth and Granada222For more information about
these catalogues, visit the SDSS galaxy properties page) to be insufficient
for our purposes. See Birchall et al. (2022) for more details on this
analysis.

The X-ray data comes from the 3XMM DR7 catalogue (Rosen et al., 2016). It is
based on 9,710 pointed observations with the _XMM-Newton_ EPIC cameras in the
$\sim 0.2-12\ \mathrm{keV}$ energy range. We use fluxes in the $2-12\
\mathrm{keV}$ range, by summing the $2-4.5\ \mathrm{keV}$ and $4.5-12\
\mathrm{keV}$ bands, then converted them to luminosities using the MPA-JHU
redshifts, assuming $\Gamma=1.7$. We used this catalogue, instead of 4XMM,
because this was the data used in Birchall et al. (2022) and the analysis
required the use of comprehensive upper limits data from Flix333Found at
https://www.ledas.ac.uk/flix/flix_dr7.html (Carrera et al., 2007). At the time
of performing this analysis, 3XMM DR7 was the most recent version of the
serendipitous sky survey available with this infrastructure. See Birchall et
al. (2020) for a more detailed description of both these catalogues.

We use the ARCHES cross-correlation tool, xmatch (Pineau et al., 2017) to
match these catalogues. It is an astronomical matching tool which can identify
the counterparts of one catalogue to multiple others and compute the
probabilities of associations using background sources and positional errors.
We broke down the data into individual XMM fields and matched SDSS and X-ray
object therein. Using a 90% probability of association as the matching
threshold left us with a well-matched sample of 1,559 X-ray emitting galaxies.
See Birchall et al. (2022) for more details on the matching process.

Our AGN X-ray selection technique was developed in Birchall et al. (2020).
First, we modelled the combined emission coming from other X-ray emitting
sources - X-ray binary stars ($L_{\mathrm{Gas}}$, based on the Mineo et al.
(2012) model) and hot gas emission ($L_{\mathrm{XRB}}$, based on the Lehmer et
al. (2016) model) - and compared it to the observed X-ray luminosity. After we
calculated these contributions, we summed them and compared this quantity to
the observed X-ray luminosity, $L_{X,Obs}$. Any object that met or exceeded
the following criterion was considered to be an AGN,

$\frac{L_{\mathrm{X,Obs}}}{L_{\mathrm{XRB}}+L_{\mathrm{Gas}}}\geq 3$ (1)

Using this criterion, 949 X-ray emitting galaxies were classified as AGN. For
the purposes of measuring an accurate AGN fraction we had to ensure we had a
statistically complete sample of galaxies above a given stellar mass limit. As
in our previous work, we adopt a redshift-dependent stellar mass limit for our
sample corresponding the mass above which 90% of galaxies lie in narrow
redshift bins ($\Delta z\sim 0.05$). This results in the removal of 32
objects. See Birchall et al. (2022) for full details.

##  3 Star-forming Classification

The galaxy population in the nearby Universe is strongly bimodal: there are
star-forming galaxies that lie close to or above the main sequence (Noeske et
al., 2007; Elbaz et al., 2011) and quiescent galaxies that lie below. Salim et
al. (2007) found that for a large sample of star-forming SDSS galaxies, the
main sequence of star formation at a given redshift is described by a power
law, $\mathrm{SFR}\propto\mathrm{Mass}^{0.65}$. However, given the relative
amount of star formation has changed dramatically through cosmic time (See
Madau & Dickinson, 2014, among many others) the exact form of the main
sequence relation will evolve with redshift. In this section, we outline the
process by which we classify galaxies as star-forming or quiescent using their
SFRs relative to this evolving main sequence relation.

###  3.1 Star-forming or Quiescent

Our method for splitting the sample into different star-forming classes is
based on Moustakas et al. (2013). They calculate a quantity referred to as the
"rotated SFR", $\mathrm{SFR_{rot}}$, which attempts to account for the effect
of changing stellar mass on SFR. Thus $\mathrm{SFR_{rot}}$ has the form,

$\log_{10}(\mathrm{SFR_{rot}})=\log_{10}(\mathrm{SFR})-0.65(\log_{10}M_{\mathrm{*}}-10)$
(2)

where SFR is in units of $\mathrm{M_{\odot}\ yr^{-1}}$ and stellar mass
($M_{\mathrm{*}}$) is in units of $\mathrm{M_{\odot}}$. We plotted histograms
of $\mathrm{SFR_{rot}}$ binned by redshift to produce distributions of this
mass-independent SFR for the underlying galaxy population. This then allowed
us to identify the $\mathrm{SFR_{rot}}$ corresponding to the local minimum
between the star-forming and quiescent peaks in each redshift bin. Fitting a
straight line to the change of $\mathrm{SFR_{rot}}$ minima with redshift
produced an appropriately normalised equation which could be used to split the
whole galaxy population into star-forming and quiescent,
$\mathrm{SFR_{SF/Q}}$. It took the form,

$\log_{10}(\mathrm{SFR_{SF/Q}})=\log_{10}(\mathrm{SFR})-0.65(\log_{10}M_{\mathrm{*}}-10)+\frac{z-0.79}{0.77}$
(3)

Figure 1 shows the results of this analysis. Our AGN sample is plotted as
large, coloured points on the mass and SFR plane and contrasted with the
underlying MPA-JHU galaxy population. Each panel contains a green line,
described by equation (3), which is used to split these AGN into star-forming
(blue stars) and quiescent (red circles). Any objects that lie above the line
are classified as star-forming, those below it are quiescent.

Figure 1: The AGN sample contrasted with the underlying galaxy population
(black contours, containing 90%, 70%, 50%, 30%, and 10% of the population).
The green dashed line describes the changing minimum of the bimodal SFR
distribution for this galaxy population and is used to determine whether an
AGN is "star-forming" (blue stars) or "quiescent" (red circles). See section
3.1 for more information on how this was calculated.

###  3.2 SFR relative to the Main Sequence

Dividing the sample into star-forming and quiescent galaxies is useful to
compare the general effect of star-formation on AGN activity. However, to
understand this effect in greater detail we extended the above analysis to
further divide the galaxy sample by its changing level of star-formation. For
this quantity we shifted equation (3) up to the galactic main sequence of star
formation at a given redshift (See Aird et al., 2019). It has the form,

$\log_{10}(\mathrm{SFR_{MS}})=\log_{10}(\mathrm{SFR})-0.65(\log_{10}M_{\mathrm{*}}-10)+\frac{z-0.05}{0.77}$
(4)

With this equation we could establish 5 bins of
$\log_{10}(\mathrm{SFR/SFR_{MS}})$ to track the changing level of star-
formation in the sample:

  * •

Starburst: Star-forming galaxies with excess star-formation relative to the
main sequence ($\log_{10}(\mathrm{SFR/SFR_{MS}})>0.3$)

  * •

Main Sequence: Star-forming galaxies with SFRs consistent with the main
sequence ($-0.3\leq\log_{10}(\mathrm{SFR/SFR_{MS}})\leq 0.3$) corresponding to
50% of the total star-forming galaxy population

  * •

Sub-Main Sequence: Galaxies with SFRs lower than the bulk of the main sequence
($-0.965\leq\log_{10}(\mathrm{SFR/SFR_{MS}})<-0.3$) consisting of weak star-
forming galaxies

  * •

Quiescent (High): Quiescent galaxies with SFRs in the top 50% of this
population ($-1.8\leq\log_{10}(\mathrm{SFR/SFR_{MS}})<-0.965$)

  * •

Quiescent (Low): Quiescent galaxies with SFRs in weakest 50% of that
population ($\log_{10}(\mathrm{SFR/SFR_{MS}})<-1.8$)

Figure 2 shows how each bin maps onto the AGN sample. By taking this approach
we have ensured there are sufficient numbers of observed AGN in each bin and
that, for a fixed redshift, an increase in the
$\log_{10}(\mathrm{SFR/SFR_{MS}})$ tracks only the effects of SFR.

Figure 2: Defining the of $\log_{10}(\mathrm{SFR/SFR_{MS}})$ groups for the
AGN sample. Overlaid are black, dashed lines describing bins of
$\log_{10}(\mathrm{SFR/SFR_{MS}})$ calculated based on the underlying galaxy
population. Star-forming AGN are shown as blue stars, and quiescent AGN are
red circles. Section 3.2 provides an explanation of how these limits were
chosen.

##  4 BPT Classification

AGN activity impacts the host galaxy’s emission across the electromagnetic
spectrum. The BPT diagnostic (Baldwin et al., 1981) is a commonly used
technique which can identify the dominant source of ionising radiation in the
optical part of the spectrum. It compares the ratios of various emission lines
to determine whether star formation, AGN or a composite of both processes are
the likely dominant source of ionisation in any given galaxy. Birchall et al.
(2020) found that this diagnostic missed around 85% of our X-ray selected AGN
in dwarf galaxies. Birchall et al. (2022) found that BPT selection missed a
similar proportion of AGN in low mass galaxies but that its accuracy increased
towards higher stellar masses. In this section, we investigate how star
formation affects the accuracy of this diagnostic.

Figure 3: BPT diagram for the 658 AGN with significant detections in all four
emission lines overlaid onto the underlying galaxy population in grey. Star-
forming AGN are shown as blue stars, and quiescent AGN are red circles. The
inset figure shows the fraction of AGN that have sufficiently strong emission
lines to be detected by the BPT diagnostic, split up star-forming category and
as a function of stellar mass. Black lines separate the AGN hosts into
different classifications: star-formation-dominated sources lie in the bottom-
left, AGN-dominated sources in the top-right, and those with composite spectra
are in the central region (Kewley et al., 2001; Kauffmann et al., 2003).

Of the 917 AGN hosts we identified in section 2, 658 had strong detections
($\frac{\mathrm{Line\ Flux}}{\mathrm{Line\ Flux\ Error}}>3$) in the required
emission lines. These were used in our BPT analysis. In figure 3, we show the
BPT and X-ray-selected AGN on the BPT plane, with star-forming AGN as blue
stars, and their quiescent counterparts as red circles. Black lines separate
the AGN hosts into different classifications: objects with ionisation
signatures predominately from star formation lie in the bottom-left, those
dominated by AGN emission lie in the top-right, and those with composite
spectra are in the central region (Kewley et al., 2001; Kauffmann et al.,
2003). A subset of the MPA-JHU galaxies are shown underneath these points, in
grey, to illustrate the underlying BPT distribution.

The vast majority of the X-ray selected star-forming AGN have significant
enough detections in all the BPT emission lines to make it the BPT diagram.
This population can be clearly seen across the full extent of the diagnostic.
However, under half of the X-ray selected quiescent AGN have significant
enough detections to make it onto the BPT diagram. This population is
concentrated largely in the AGN region.

By requiring a significant detection in each BPT emission line, objects with
relatively large amounts of optical ionisation are much more likely to make it
onto figure 3, regardless of its source. However, this is not reflected in the
X-ray luminosities. There is no systematic difference in the X-ray luminosity
distributions of BPT-detected and non-detected sources for either the full AGN
population or just the quiescent AGN.

By definition, star-forming AGN produce significant amounts of optical
emission from both forming stars and AGN activity. Thus, these objects will
have higher levels of optical emission on average. This results in a higher
fraction of these objects having significant enough emission lines to make it
onto the BPT diagram. It also means that these objects can appear across all
classifications, although, a BPT classification of ’composite’ or ’star-
formation-dominated’ does not exclude the presence of AGN activity (Birchall
et al., 2020, 2022).

Quiescent galaxies, on the other hand, are defined by their reduced levels of
star formation. This means that the only route by which they can appear on the
BPT diagram is through significant AGN activity. This explains why these
objects are concentrated in the AGN region. It could also explain why these
objects are disproportionately missing from the BPT diagnostic: if there is
little star formation and the AGN activity is optically quiet, then there is
no source to produce strong enough emission lines to make it onto the BPT
diagnostic.

To investigate this, we first analysed the individual emission lines and found
that H$\beta$ most frequently missed the significance threshold. Cid Fernandes
et al. (2010) also found a significant population of SDSS galaxies were missed
out from the BPT diagram due to lack of significant H$\beta$ line detections.
In addition, it was galaxies that would have been classified as AGN (should
the significance criterion not have been required) that were most affected.

We then looked at how the fraction of BPT-detected AGN changes with stellar
mass and star-forming classification. The results are inset in figure 3. The
blue, star-forming distribution shows high proportions of BPT-detected AGN,
reaching $94\%$ in the $10.5\leq\log_{10}\
(M_{\mathrm{*}}/M_{\mathrm{\odot}})\leq 11$ bin and never dropping below
$67\%$. However, the red, quiescent distribution peaks at 77% in the
$10\leq\log_{10}\ (M_{\mathrm{*}}/M_{\mathrm{\odot}})\leq 11$, before rapidly
dropping to $17\%$ in the highest mass bin. There was only one quiescent AGN
detected in the lowest mass bin which was missed, hence the $0\%$ detection
rate.

Since, by definition, quiescent AGN are not forming as many new stars as their
star-forming counterparts, stellar absorption lines, like H$\beta$, could
dominate their spectra. These absorption lines will be most pronounced in the
spectra of the highest mass galaxies as they contain the largest amount of
stellar material. Thus, weak AGN emission lines could be dominated by strong
absorption lines and produce the significant drop in the fraction of high
mass, quiescent AGN shown on the BPT diagram in figure 3. This suggests that
the BPT diagnostic is not effective at identifying optically-weak emission
from AGN, especially in quiescent galaxies.

##  5 Specific Black Hole Accretion Rate

AGN are powered by the accretion of matter onto a central supermassive black
hole. Measuring the accretion rate is important as observing only the absolute
X-ray luminosity can provide a biased picture, especially when examining the
AGN content of galaxies that span a broad mass range. Consider two black
holes, one black hole is growing at a higher accretion rate in a lower mass
galaxy, another black hole with a lower accretion rate in a high mass galaxy.
It is possible that these two galaxies could emit the same X-ray luminosity,
obscuring the activity occurring at the central black hole. Thus, to break
this degeneracy, we need to investigate the specific black hole accretion rate
(sBHAR), $\lambda_{\mathrm{sBHAR}}$. This quantity compares the bolometric AGN
luminosity with an estimate of the black hole’s Eddington luminosity to
provide an estimate of how efficiently material is being accreted. It has the
following form,

$\lambda_{\mathrm{sBHAR}}=\frac{25L_{\mathrm{2-10keV}}}{1.26\times
10^{38}\times 0.002M_{*}}\approx\frac{L_{\mathrm{bol}}}{L_{\mathrm{Edd}}}$ (5)

and is taken from Aird et al. (2012). Using $0.002M_{*}$ implies a perfectly
constant correlation between the masses of the SMBH and stellar bulge which,
in reality, is dependent on galaxy morphology, among other properties (e.g.
Blanton & Moustakas, 2009; Jahnke et al., 2009). However, our intention when
using this correlation is to present an Eddington-scaled accretion rate
quantity rather than accurately recreate an Eddington ratio. By using this
scaling to calculate sBHAR - a tracer of the rate of black hole growth
relative to the host galaxy’s stellar mass - it allows for ease of comparison
with the literature.

Figure 4: Stellar mass against the observed X-ray luminosity for the 917 AGN
detected in section 2. Star-forming AGN are shown as blue stars, and quiescent
AGN are red circles. Several grey lines of constant sBHAR have also been
plotted for reference. The inset panel shows how the AGN population is
distributed along the sBHAR axis when split by star-forming classification.
This distribution has not been corrected to account for X-ray sensitivity
limits, for more information on this see section 6.

Figure 4 shows the observed AGN sample distributed on a stellar mass and X-ray
luminosity plane, and coloured based on their star-forming classification.
Star-forming AGN are shown as blue stars, and quiescent AGN are red circles.
Lines of constant sBHAR are shown to indicate its approximate value for
different masses and luminosities. The clearest difference between star-
forming and quiescent AGN is in the highest mass galaxies
($\log_{10}\mathrm{M_{*}/M_{\odot}}\gtrsim 11$). Here the brightest, most
actively accreting AGN are in star-forming galaxies, and the dimmer, weakly
accreting AGN are in quiescent hosts. This effect is repeated across the
stellar mass range to a lesser degree, with star-forming AGN generally having
higher values of sBHAR. This is evident in the inset panel, where we plotted
the sBHAR distributions split by star-forming classification. It is clear that
quiescent AGN are dominated by relatively low accretion rates, whereas star-
forming AGN are much more evenly spread and peak at much higher rates. In
fact, for quiescent AGN, the mean $\log_{10}\lambda_{\mathrm{sBHAR}}\sim-3.1$,
whereas for star-forming AGN, the mean
$\log_{10}\lambda_{\mathrm{sBHAR}}\sim-2.7$. Whilst this sample is subject to
a selection bias, it clearly shows there is an increased level of accretion
activity in star-forming galaxies. This result has been seen in numerous
samples at similar (Torbaniuk et al., 2021) and higher redshifts (e.g. Chen et
al., 2013; Yang et al., 2017).

##  6 Completeness-corrected Probability Distributions

No AGN selection technique is perfect. Our approach, briefly described in
section 2, aimed to overcome the preference that a flat luminosity threshold
has towards selecting higher mass galaxies (which typically have higher X-ray
luminosities) by modifying the threshold value based on the host galaxy
properties. However, figure 4 shows that despite our efforts the sample is
still dominated by higher mass galaxies. Birchall et al. (2020) outlines, in
detail, the method we developed to reduce the effects of this bias. By
correcting for 3XMM’s varying detection sensitivity, this method allows us to
investigate how the underlying distribution of AGN varies with changes in host
galaxy properties. Birchall et al. (2022) showed that the X-ray luminosity
probability distributions were still subject to an apparent observational
bias, despite the completeness corrections applied. So, we only consider the
sBHAR-based probability distributions. In this section, we will briefly
describe how the completeness corrections are calculated, how they are applied
to the observational data to create these distributions, and what they tell us
about the effect of star formation on the incidence of AGN in the nearby
Universe. See Birchall et al. (2020, 2022) for a more comprehensive
description of this process.

###  6.1 Creating the Probability Distributions

The detection sensitivity of 3XMM varies significantly across its observed sky
area. This variation brings the possibility that lower luminosity AGN in this
region may have been missed because 3XMM is insufficiently sensitive to detect
them. To correct for this, we used Flix, 3XMM’s upper limit service, to
measure the $0.2-12\ \mathrm{keV}$ upper limit at the centres of the 22,079
MPA-JHU galaxies in the 3XMM footprint. We restricted detections to the PN8
band which reduced our AGN sample from 917 to 739. Using the Flix upper limit
and the MPA-JHU redshift and stellar mass, we calculated the X-ray luminosity
upper limit and $\lambda_{\mathrm{sBHAR}}$ for each galaxy. With these
properties, we could construct a cumulative histogram normalised by the total
number of galaxies in the current mass and redshift range. These luminosity
sensitivity functions allowed us to determine the fraction of galaxies where
an AGN accreting above a given rate could be detected.

Using these sensitivity functions, we can, for example, calculate the
probability of finding an AGN in a given galaxy as a function of specific
black hole accretion rate, in bins of increasing stellar mass. To construct
this distribution, we first split up the AGN sample into a series of stellar
mass bins. These are then further broken as a function of
$\lambda_{\mathrm{sBHAR}}$. This gives us an observed AGN count distribution.
We also created a bespoke sensitivity function for each of these stellar mass
bins. From this, we constructed a binned probability distribution by dividing
the number of AGN in a given galaxy sub-sample and sBHAR bin,
$N_{\mathrm{AGN},\ i}$, by the number of galaxies where such an sBHAR would be
detectable, $N_{\mathrm{gal}}$. Thus,

$p(\lambda_{\mathrm{sBHAR},\ i})=\frac{N_{\mathrm{AGN},\
i}}{N_{\mathrm{gal}}(\lambda_{\mathrm{sBHAR},\ lim}>\lambda_{\mathrm{sBHAR},\
i})}$ (6)

where $p(\lambda_{\mathrm{sBHAR},\ i})$ is the probability of observing an AGN
in a given galaxy sub-sample, accreting above the limiting accretion rate
$\lambda_{\mathrm{sBHAR},\ lim}$. The results of this process are shown in
figure 5, the probability of finding an AGN as a function of sBHAR in bins of
increasing mass. Reference information is also printed on each panel including
the size of each AGN population and the stellar mass range of the galaxies
included therein.

By applying correction fractions, extracted from the
$\lambda_{\mathrm{sBHAR}}$ sensitivity function, to the observed AGN counts we
were able to provide robust measurements of the true incidence of AGN within
the nearby galaxy population. Figure 5 shows the results of this calculation.
It is clear that AGN exist across the stellar mass range despite the favouring
of higher mass AGN seen in figure 4. In addition, we see that AGN populations
are well described by power law distributions, as found in Birchall et al.
(2020) and Birchall et al. (2022), with AGN being found predominantly at lower
$\lambda_{\mathrm{sBHAR}}$ (see also Aird et al., 2012, and others).

Errors on the data points are found using the confidence limits equations
presented in Gehrels (1986) so the size of the error is proportional to the
number of detected AGN in a given bin.

Power laws were fit to the data in each of these panels with the following
form,

$p(\lambda)=A\left(\frac{\lambda}{\lambda^{\prime}}\right)^{k}d\log_{10}\lambda$
(7)

where $p(\lambda)$ is the probability of observing an AGN as a function of
$\lambda_{\mathrm{sBHAR}}$ and centred on a value $\lambda\textquoteright$.
Each power law is centred on the median accretion rate for the sample,
$\log_{10}\lambda^{\prime}=-2.55$. The star-forming AGN population are shown
as blue stars, and the quiescent AGN population are red circles The power laws
are shown as dashed lines, indicating how the probability of finding an AGN
changes as a function of $\lambda_{\mathrm{sBHAR}}$. The error regions
surrounds each power law and was calculated by performing a $\chi^{2}$ fit
with equation (7) to the data points and errors in each bin. Fit parameter
errors were estimated by taking the square-root of the covariance matrix’s
diagonal. With this we could outline the extent of the uncertainty in each
fit. Encouragingly, the power law provides a good fit in nearly all of the
bins.

Figure 5: Probability of finding an AGN in the nearby Universe, using the
completeness-corrected AGN samples, as a function of
$\mathrm{\lambda_{sBHAR}}$ and stellar mass. The star-forming AGN population
are shown as blue stars, and the quiescent AGN population are red circles.
Power laws (dashed lines) have been fit to the data in each panel and
displayed alongside their $1\sigma$ uncertainty (pale region). Information
about the number of PN-8-detected AGN and parent galaxies in the each mass
range are printed on the panels. See section 6.1 for more details on how these
plots were constructed. Table A lists the coefficients required for equation
(7) to recreate these distributions.

###  6.2 Probability Distribution Comparison

Using the method described above we have created a series of probability
distributions investigating how other host galaxy properties might affect the
incidence of AGN in the nearby Universe. Figure 6 adds probability
distributions for redshift and $\log_{10}\mathrm{(SFR/SFR_{MS})}$, split up
into quiescent (left-hand column) and star-forming (right-hand column) AGN.
Each panel contains numerous probability distributions, represented by dashed
lines, which are coloured to indicate the respective stellar mass (top row),
redshift (middle row) or $\log_{10}(\mathrm{SFR/SFR_{MS}})$ (bottom row) bin.
The best-fit coefficients and associated errors used to calculate these
distributions are presented in appendix A. The error regions were all fit to
data points but were not included on figure 6 to aid clarity. The redshift and
$\log_{10}\mathrm{(SFR/SFR_{MS})}$ distributions with data points are
presented in appendix B.

####  6.2.1 Normalisation

The normalisation of the distributions in figure 6 do not change
significantly. There is some evidence of increase in the overall probability
of finding AGN in star-forming galaxies as we shift towards higher redshifts
and star formation rates, but the magnitude of this effect appears to be
fairly small.

Not all of these distributions cover the full extent of
$\log_{10}\lambda_{\mathrm{sBHAR}}$ axis. This can be seen most clearly in the
stellar mass row, with the distributions describing the lowest mass, quiescent
AGN and highest mass, star-forming AGN. In addition, the star-forming column
of both the redshift and $\log_{10}\mathrm{(SFR/SFR_{MS})}$ rows show a slight
shift towards higher accretion rates at higher values of the respective
property. These changes are due to the limited number of observations in these
bins. However, this does highlight changes in galaxy population across the
star-forming classifications. In the stellar mass row, we see that star-
forming galaxies dominate at lower stellar masses and quiescent at higher
masses. And in the redshift and $\log_{10}\mathrm{(SFR/SFR_{MS})}$ rows, a
slight favouring of higher accretion rate galaxies.

####  6.2.2 Slope

The clearest changes in slope can be seen in the redshift row of figure 6. The
quiescent distributions are much steeper than those composed of star-forming
AGN. There is also a distinct steepening between the quiescent distributions,
showing that lower accretion rates are favoured with increasing redshift. The
star-forming distributions, however, do not show this trend. In fact, the
highest redshift, star-forming distributions appear significantly flatter than
their quiescent counterparts, suggesting that star formation facilitates
higher accretion rates at higher redshifts.

There is not much change in slope in the $\log_{10}(\mathrm{SFR/SFR_{MS}})$
row. Given the nature of this quantity the quiescent/star-forming division
occurs along the $\log_{10}(\mathrm{SFR/SFR_{MS}})$ axis, so there are only
two bins in the left panel and three on the right.

There does not appear to be any consistent trend within the stellar mass row,
nor any clear effect when comparing the quiescent and star-forming
populations. Whilst the highest mass, star-forming bin has a distinctly flat
gradient, it is poorly constrained and is consistent with the lower mass bin
within the errors.

Figure 6: Comparison of the full range of sBHAR-dependent probability
distributions. The left-hand column plots the distributions of quiescent AGN,
the right-hand column plots the distributions of the star-forming AGN. The
distributions are binned as a function of stellar mass (top row), redshift
(middle row) and $\log_{10}(\mathrm{SFR/SFR_{MS}})$ (bottom row). See section
6.1 for more details on how these plots were constructed. Table A lists the
coefficients required for equation (7) to recreate these distributions.

##  7 AGN Fractions

Integrating under the probability distributions shown in figure 6, allowed us
to further analyse how star formation affects the AGN population in the nearby
Universe. Figure 7 shows the AGN fraction as function of each property, split
up into star-forming and quiescent populations. As before we are only
considering the sBHAR-derived fractions; the corresponding integration limits
are shown in the bottom-left corner of each panel. These limits were chosen
because they represent the bulk of the measured activity for our AGN sample.
In this section, we will outline the results of this calculation and explain
their significance.

It is encouraging to see that the top and middle panels, exploring the AGN
fraction with stellar mass and redshift respectively, highlight similar trends
shown in Birchall et al. (2022). In that work we found little change in AGN
fraction with stellar mass, averaging around 1%. In the top panel of figure 7
there is a similarly flat AGN fraction with stellar mass, averaging about 1%
for the quiescent galaxies, and 2% for star-forming galaxies. Birchall et al.
(2022) also showed that AGN fraction with redshift increased from around 1% to
10%. In the middle panel of figure 7 there is also a clear increase in AGN
fraction with redshift. Between $z=0$ and $0.35$, AGN fraction rises from 0.5%
to 4.5% for quiescent galaxies, and from 1.5% to 7% for star-forming objects.

Splitting the AGN sample by star-forming classification shows that star-
forming galaxies have slightly enhanced AGN fractions. However, this
enhancement does not appear statistically significant. To check its
significance, we calculated the overall fraction of AGN found in star-forming
galaxies and compared it to the fraction in quiescent galaxies. The star-
forming AGN fraction was found to be enhanced by a factor of 2 at a
$>3.5\sigma$ significance. Thus there does appear to be a real increase in the
incidence of AGN in star-forming galaxies. Azadi et al. (2015) observed a
similarly sized star-formation-driven enhancement in a different X-ray
selected AGN sample out to $z\approx 1.2$.

This enhancement of AGN fraction in star-forming galaxies is also reflected in
the bottom panel of figure 7. The AGN fraction rises from 0.7% to 3.8% with
increasing $\log_{10}(\mathrm{SFR/SFR_{MS}})$. A similar positive correlation
has been observed between average black hole accretion rate and SFR in samples
at higher redshifts (e.g. Chen et al., 2013; Yang et al., 2017; Pouliasis et
al., 2022).

Figure 7: AGN fraction as a function of stellar mass (top), redshift (middle)
and $\log_{10}(\mathrm{SFR/SFR_{MS}})$ (bottom). In each panel star-forming
AGN fractions are shown as blue stars, and quiescent AGN fractions are red
circles. The sBHAR ($\lambda_{\mathrm{sBHAR}}$) integration limits are also
displayed in the bottom-left corner.

Both redshift and $\log_{10}(\mathrm{SFR/SFR_{MS}})$ appear to drive strong
increases in AGN fraction. To disentangle these effects, we divided the galaxy
and AGN populations and re-plotted the AGN fractions as a function of
$\log_{10}(\mathrm{SFR/SFR_{MS}})$ for these new samples. It is clear from
figure 8, that AGN fraction increases with SFR throughout the sample. Whether
split at the median mass ($\log_{10}(M_{*}/M_{\odot})=10.89$) in the top row
or redshift ($z=0.11$) in the bottom row, both trends show a systematic
increase in fraction and a steepening gradient between the low and high value
bins.

The systematic increase between the low and high redshift bins is expected
given the observed trend in figure 7. Similarly, splitting the sample by mass
will shift the average redshift of each bin. So, we would expect an increase
in the average fraction in the higher mass driven by the increased redshift.
To confirm this, we consolidated each set of fractions from the low and high
mass bins into quiescent and star-forming classifications at each panel’s
median redshift (0.08 for lower mass galaxies, 0.15 for higher mass galaxies).
We found that the increase between these consolidated fractions was consistent
with the overall AGN fraction increase with redshift.

We also see a steepening gradient between low and high value bins which is
likely due to changing combinations of star-forming and quiescent hosts. As
outlined previously, star formation is known to change with both stellar mass
and redshift. So, increasing the average redshift of the bin will change the
sample’s star-forming properties: the proportion of AGN in star-forming
galaxies will increase, those in quiescent galaxies will decrease and produce
the observed steeper increase.

Whilst this has not been able to precisely disentangle the effects of redshift
and $\log_{10}(\mathrm{SFR/SFR_{MS}})$, we have confirmed the effects seen
previously. Stellar mass has little effect on the AGN fraction in the nearby
Universe, and anything we might see is consistent with a redshift-driven
increase. In addition, we have shown that the star-formation-driven
enhancement is present at fixed stellar masses and redshifts throughout the
nearby Universe.

With this analysis, we have shown that the incidence of AGN activity within
given accretion limits in the nearby Universe is driven both by the host
galaxy’s redshift and $\log_{10}(\mathrm{SFR/SFR_{MS}})$. What connects these
quantities is the availability of cold gas: the level of star formation is
strongly correlated to its availability in a given galaxy, and its abundance
is thought to increase at earlier cosmic times (Mullaney et al., 2012b;
Popping et al., 2012; Vito et al., 2014). Thus, our results highlight a strong
connection between the availability of cold gas and the level of AGN activity.
However, there is still a significant population of AGN within quiescent
galaxies. Whilst diminished relative to star-forming galaxies, this population
of quiescent AGN implies that another fuelling mechanism is possible, perhaps
fuelled by stellar mass loss, as theorised in Kauffmann & Heckman (2009).

Figure 8: AGN fraction as a function of $\log_{10}(\mathrm{SFR/SFR_{MS}})$
split at the median stellar mass (top row) and redshift (bottom row) of the
sample. In each panel star-forming AGN fractions are shown as blue stars, and
quiescent AGN fractions are red circles. The sBHAR
($\lambda_{\mathrm{sBHAR}}$) integration limits are also displayed in the
bottom-left corner.

##  8 Summary & Conclusions

We have investigated how star formation influences the distribution of AGN in
the nearby Universe. For this analysis, we created two sets of definitions
designed to track changing rates of star formation whilst accounting for
redshift and mass driven enhancements. The first definition split the sample
into star-forming and quiescent populations; the second, split the sample into
even more refined bins of star formation relative to the galactic main
sequence.

We then applied these star-forming classifications to the BPT-selected AGN
sample. Only 72% of the X-ray selected sample were identified as AGN using the
BPT diagnostic. In particular, it is much less effective in quiescent hosts:
identifying near all star-forming AGN compared to only 50% of the X-ray AGN.
The other half of the quiescent sample was made up of higher mass galaxies
which did not have sufficiently significant emission line activity to make it
onto the BPT diagnostic. We believe this is may be due to stellar absorption
lines hiding the weaker optical emission lines from low levels of AGN
activity. This is further evidence to suggest that the BPT diagram is not
effective at identifying weakly accreting AGN, especially in quiescent host
galaxies.

Next, we investigated how star-forming classification affects the rate at
which black holes accrete material. We found that across stellar mass, AGN in
star-forming galaxies generally have much higher accretion rates than their
quiescent counterparts with a mean difference between star-forming
classifications of $\log_{10}\lambda_{\mathrm{sBHAR}}\sim 0.5$. This effect
was most pronounced at the very highest stellar masses
($\log_{10}\mathrm{M_{*}/M_{\odot}}\gtrsim 11$).

We built on the probability distribution analysis from Birchall et al. (2020,
2022) by applying the star-forming classifications to highlight how they
affect the AGN population in the nearby Universe. The strongest star-
formation-driven changes were seen in the redshift-binned distributions.
Quiescent AGN showed a significant steepening with redshift, appearing to
favour much lower accretion rate activity. Star-forming galaxies appeared to
show the opposite trend with flatter distributions at higher redshifts. This
implies star formation facilitates more active accretion at higher redshifts.

Finally, by integrating under these distributions we could calculate the
fraction of galaxies in the nearby Universe hosting AGN and determine the
effect of star formation. Reassuringly, both AGN fraction trends with stellar
mass and redshift seen in Birchall et al. (2022) are recreated when split by
star-forming classification. There is little change in AGN fraction with
stellar mass, and a noticeable increase with redshift. We found that star
formation increases the incidence of AGN by a factor of 2 at a $>3.5\sigma$
significance. This enhancement is also seen when binning the AGN fraction as a
function of $\log_{10}(\mathrm{SFR/SFR_{MS}})$. However there is still a
significant population of AGN in quiescent galaxies in the nearby Universe.

In conclusion, we have shown that star formation has an effect on the AGN
distribution in the nearby Universe by facilitating higher black hole
accretion rates and increasing the probability of finding AGN activity in a
given galaxy. However, AGN are still prevalent in quiescent galaxies
suggesting additional fuelling mechanisms, such as from stellar mass loss, can
also facilitate AGN activity.

## Acknowledgements

The authors would like to the reviewer for their helpful comments. KB
acknowledges funding from a Horizon 2020 grant (XMM2Athena). JA acknowledges
support from an STFC Ernest Rutherford Fellowship (grant code: ST/P004172/1)
and a UKRI Future Leaders Fellowship (grant code: MR/T020989/1).

This research has made use of data obtained from the 3XMM XMM-Newton
serendipitous source catalogue compiled by the 10 institutes of the XMM-Newton
Survey Science Centre selected by ESA.

In addition, this research made use of Astropy,444http://www.astropy.org a
community-developed core Python package for Astronomy (Astropy Collaboration
et al., 2013, 2018).

Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the
Participating Institutions, the National Science Foundation, and the U.S.
Department of Energy Office of Science. The SDSS-III web site is
http://www.sdss3.org/.

KB would also like to thank F-X Pineau for his help with constructing the
xmatch scripts, and Duncan Law-Green for the help accessing the Flix archive.

## Data Availability Statement

The data underlying this article has been derived from publicly available
datasets: the MPA-JHU Catalogue (based on SDSS DR8) & 3XMM DR7. Section 2
outlines where these catalogues are available and how the final sample was
derived. The underlying data will also be shared on request to the
corresponding author.

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##  Appendix A Probability Distribution Fit Coefficients

Table A1 outlines the best-fit coefficients, and associated errors, for
equation (7) to create every probability distribution shown in figure 6.

$\log_{10}x^{\prime}=-2.55$ | Quiescent AGN | Star-forming AGN
---|---|---
$\log_{10}$ Stellar Mass ($\mathrm{M_{\odot}}$) | $\log_{10}\ A$ | $k$ | $\log_{10}\ A$ | $k$
8.00 - 9.00 | $-2.44\pm 1.27$ | $-0.52\pm 0.04$ | $-2.36\pm 0.33$ | $-0.98\pm 0.58$
9.50 - 10.00 | $-2.77\pm 0.80$ | $-0.91\pm 0.25$ | $-2.33\pm 0.31$ | $-0.93\pm 0.37$
10.00 - 10.50 | $-2.60\pm 0.23$ | $-0.55\pm 0.36$ | $-2.36\pm 0.14$ | $-0.57\pm 0.19$
10.50 - 11.00 | $-2.50\pm 0.11$ | $-0.68\pm 0.15$ | $-2.03\pm 0.07$ | $-0.48\pm 0.11$
11.00 - 11.50 | $-2.62\pm 0.14$ | $-1.04\pm 0.15$ | $-2.14\pm 0.15$ | $-0.90\pm 0.21$
11.50 - 12.00 | $-2.53\pm 0.00$ | $-1.28\pm 0.02$ | $-1.82\pm 0.14$ |  $0.00\pm 1.36$
z | $\log_{10}\ A$ | $k$ | $\log_{10}\ A$ | $k$
0 - 0.05 | $-2.64\pm 0.27$ | $-0.59\pm 0.27$ | $-2.29\pm 0.13$ | $-0.66\pm 0.17$
0.05 - 0.10 | $-2.63\pm 0.15$ | $-0.79\pm 0.17$ | $-2.37\pm 0.11$ | $-0.85\pm 0.15$
0.10 - 0.15 | $-2.51\pm 0.15$ | $-1.16\pm 0.16$ | $-2.18\pm 0.15$ | $-1.02\pm 0.26$
0.15 - 0.20 | $-2.51\pm 0.20$ | $-1.31\pm 0.25$ | $-2.02\pm 0.15$ | $-0.96\pm 0.30$
0.20 - 0.25 | $-2.36\pm 0.30$ | $-1.32\pm 0.36$ | $-1.71\pm 0.23$ | $-0.66\pm 0.55$
0.25 - 0.30 | $-2.57\pm 0.00$ | $-1.99\pm 0.01$ | $-1.50\pm 0.27$ | $-0.51\pm 0.60$
$\log_{10}\mathrm{SFR/SFR_{MS}}$ | $\log_{10}\ A$ | $k$ | $\log_{10}\ A$ | $k$
-3.00 - (-)1.80 | $-2.79\pm 0.15$ | $-1.10\pm 0.15$ |  |
-1.80 - (-)0.965 | $-2.42\pm 0.09$ | $-0.73\pm 0.11$ |  |
-0.965 - (-)0.3 |  |  | $-2.22\pm 0.09$ | $-0.64\pm 0.12$
-0.30 - 0.30 |  |  | $-2.24\pm 0.08$ | $-0.86\pm 0.13$
0.30 - 1.30 |  |  | $-1.95\pm 0.14$ | $-0.90\pm 0.27$
Table A1: Best-fit coefficients used to fit equation (7) to all probability
distribution configurations.

##  Appendix B Other Probability Distributions

Figures 9 and 10 show the probability distributions for star-forming and
quiescent AGN, split by redshift, and $\log_{10}\mathrm{(SFR/SFR_{MS})}$. The
remaining trends with sBHAR are presented for the sake of transparency, to
show the strength of our power law fits to the data. All the plots have the
same form as figure 5.

Figure 9: Additional probability distribution used to calculate fits and
associated error regions for the other host galaxy properties. This figure
shows the probability of a galaxy hosting an AGN as a function of
$\mathrm{\lambda_{sBHAR}}$ and split into bins of redshift. The star-forming
AGN population is shown as blue stars, and the quiescent AGN population as red
circles. As with figure 5, power laws (dashed lines) have been fit to the data
in each panel and displayed alongside their $1\sigma$ uncertainty (pale
region). These plots were constructed using the method outlined in section
6.1. Figure 10: Additional probability distribution used to calculate fits and
associated error regions for the other host galaxy properties. This figure
shows the probability of a galaxy hosting an AGN as a function of
$\mathrm{\lambda_{sBHAR}}$ and split into bins of
$\log_{10}\mathrm{(SFR/SFR_{MS})}$ (see (§3.2 for more information on how this
quantity was calculated). The star-forming AGN population is shown as blue
stars, and the quiescent AGN population as red circles. As with figure 5,
power laws (dashed lines) have been fit to the data in each panel and
displayed alongside their $1\sigma$ uncertainty (pale region). These plots
were constructed using the method outlined in section 6.1.