# Chemical abundances in Seyfert galaxies – VIII. Argon abundance estimates

A. F. Monteiro,1,2 O. L. Dors,1
1Universidade do Vale do Paraíba. Av. Shishima Hifumi, 2911, CEP: 12244-000,
São José dos Campos, SP, Brazil
2Instituto Federal do Maranhão. Av. Newton Bello s/n, CEP: 65906-335,
Imperatriz, MA, Brazil E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

For the first time, the argon abundance relative to hydrogen abundance (Ar/H)
in the narrow line region of a sample of Seyfert 2 nuclei has been derived. In
view of this, optical narrow emission line intensities of a sample of 64 local
Seyfert 2 nuclei ($z\><\>0.25$) taken from Sloan Digital Sky Survey DR7 and
measured by the MPA/JHU group were considered. We adopted the $T_{\rm
e}$-method for AGNs, which is based on direct determination of the electron
temperature, together with a grid of photoionization model results, built with
the Cloudy code, to obtain a method for the derivation of the Ar/H abundance.
We find that for a metallicity range of $\rm 0.2\>\la\>(Z/{\rm
Z_{\odot}})\>\la\>2.0$, Seyfert 2 nuclei present Ar/H abundance ranging from
$\sim 0.1$ to $\sim 3$ times the argon solar value, adopting $\rm
log(O/H)_{\odot}=-3.31$ and $\rm log(Ar/H)_{\odot}=-5.60$. These range of
values correspond to $\rm 8.0\>\la\>(12+log(O/H)\>\la\>9.0$ and $\rm
5.4\>\la\>(12+log(Ar/H)\>\la\>6.9$, respectively. The range of Ar/H and Ar/O
abundance values obtained from our sample are in consonance with estimations
from extrapolations of the radial abundance gradients to the central parts of
the disk for four spiral galaxies. We combined our abundance results with
estimates obtained from a sample of H ii galaxies, which were taken from the
literature, and found that the Ar/O abundance ratio decreases slightly as the
O/H abundance increases.

###### keywords:

galaxies: Seyfert – galaxies: active – galaxies: abundances –ISM: abundances
–galaxies: evolution –galaxies: nuclei

††pubyear: 2020††pagerange: Chemical abundances in Seyfert galaxies – VIII.
Argon abundance estimates–Chemical abundances in Seyfert galaxies – VIII.
Argon abundance estimates

##  1 Introduction

Active Galactic Nuclei (AGNs) present strong metal emission-lines in their
optical spectra, which when combined with hydrogen recombination lines, make
it possible to estimate the abundance of heavy elements and the metallicity in
the gas phase of these objects. AGNs play an essential role in chemical
abundance studies of nearby objects and of the early stages of galaxy
formation due to the aforementioned feature and to their high luminosity.

Among the heavy elements, oxygen presents strong emission lines (i.e. [O
ii]$\lambda$3726, $\lambda$3729; [O iii]$\lambda$5007) emitted by its most
abundant ions ($\rm O^{+}$, $\rm O^{2+}$) in the optical spectrum of gaseous
nebulae (H ii regions, Planetary Nebulae) and AGNs (e.g. Koski 1978; van Zee
et al. 1998; Kennicutt et al. 2003; Maciel et al. 2007; Dopita et al. 2015;
Flury & Moran 2020; Dors et al. 2020a). Therefore, the total metallicity ($Z$)
of the gas phase from emission lines emitter objects is commonly traced by the
oxygen abundance relative to hydrogen (O/H, e.g. McGaugh 1991; Yates et al.
2012; Kewley et al. 2019). Other elements such as the noble gases (e.g. Ne,
Ar) present emission-lines in the optical spectrum emitted by only few of
their ions (e.g. $\rm Ne^{2+},Ar^{2+}$), which make it necessary to apply
Ionization Correction Factors (ICFs) proposed by Peimbert & Costero (1969)
(see Stasińska 2002; Delgado-Inglada et al. 2014; Dors et al. 2013; Dors et
al. 2016) in order to account for the unobserved ions in the estimation of the
total abundance. The use of ICFs can introduce uncertainties in order of 20%
(e.g. Henry et al. 1996; Alexander & Balick 1997; Croxall et al. 2016) in the
resulting total abundance (for a detailed discussion on ICF uncertainties see
Delgado-Inglada et al. 2014). Despite this drawback, noble gases can be used
to derive the metallicity with some advantages over oxygen, as they are also
useful elements for determining constraints in stellar nucleosynthesis
studies. Noble gas atoms can not combine in molecules formation and they can
not be trapped in dust grains due to their quantum configuration, unlike the
oxygen which is depleted onto dust in order of 0.1 dex (e.g. Izotov et al.
2006; Pilyugin et al. 2007).

The $T_{\rm e}$-method, which is based on direct estimation of the electron
temperature, is widely used in the literature as the most reliable approach
for determining the chemical abundance of heavy metals in gaseous nebulae (for
a review see Peimbert et al. 2017; Pérez-Montero 2017). The $T_{\rm e}$-method
has been bolstered by the consonance between O/H abundance estimates in H ii
regions in the solar vicinity and those obtained from observations of the weak
interstellar O i$\lambda$1356 line towards stars (see Pilyugin 2003 and
references therein). Moreover, in the Milky Way and in nearby galaxies, good
agreement between O/H abundance estimates in H ii regions and in B-type stars
has recently been derived (e.g. Toribio San Cipriano et al. 2017). In this
regard, abundance determinations of heavy metals (O, N, S, Ar, etc.) based on
the $T_{\rm e}$-method have been carried out in thousands of star-forming
regions (SFs; i.e. H ii regions, H ii galaxies) at the local universe and for
certain objects at high redshifts over decades (see Dors et al. 2020a and
reference therein).

Unfortunately, the situation is opposite for AGNs, where, except from oxygen,
the majority of the abundances for other elements are not available in the
literature. In fact, the most complete metal abundance determinations based on
$T_{\rm e}$-method was carried out by Osterbrock & Miller (1975) for Cygnus A
($z=0.05607$), who derived the O, N, Ne, S, and Fe abundances in relation to
hydrogen. After this pioneering work some few studies have applied the $T_{\rm
e}$-method to abundance estimations in AGNs, however, in most cases, only
oxygen abundance determinations have been derived (e.g. Alloin et al. 1992;
Izotov & Thuan 2008; Revalski et al. 2018a; Revalski et al. 2018b, 2021; Dors
et al. 2015, 2020b, 2020a). Recently, Flury & Moran (2020), adopting a
methodology based on a reverse-engineering of the $T_{\rm e}$-method, derived
the first (N/O)-(O/H) relation for AGNs. Although studies relied on
photoionization models have been applied to derive metal abundance in AGNs
(e.g. Stasińska 1984; Ferland & Osterbrock 1986; Storchi-Bergmann et al.
1998a; Groves et al. 2006; Feltre et al. 2016; Castro et al. 2017; Pérez-
Montero et al. 2019; Thomas et al. 2019; Carvalho et al. 2020; Dors et al.
2021; Pérez-Díaz et al. 2021), most of them have produced only estimations for
O/H or metallicity. Since the electron temperatures throughout the emission
nebula are computed by thermal balancing (see the seminal paper by Williams
1967), the abundances of the most important elements are used as input
parameters in photoionization models. All the lines, even if not observed,
contribute to the gas cooling rate. In most of the papers which describe the
results obtained by using photoionization models, the element relative
abundances to H, which were not found to be particularly different from the
solar ones, are unfortunately not published in the literature.

The use of photoionization model to derive abundance of different elements
other than the oxygen (e.g. N, S, Ar) is (relatively) difficult, hence, it is
necessary to find a solution for the electron temperature (or for O/H, the
main cooler element) and for the ionization degree of the gas. Afterwards, the
lines of the element under study must be adjusted in order to obtain its
abundance (see, for instance, Pérez-Montero & Díaz 2007; Pérez-Montero et al.
2010; Contini 2017; Congiu et al. 2017; Dors et al. 2017; Polles et al. 2019;
Dors et al. 2021). This procedure can produce a degeneracy among nebular
parameters, resulting in somewhat uncertain elemental abundances (Morisset et
al., 2016; Morisset, 2018). In this sense, the use of the $T_{\rm e}$-method
produces more exact elemental abundance values in comparison with those
estimated through photoionization models.

In particular, the argon abundance determination in AGNs is very important in
the study of galaxy evolution and stellar nucleosynthesis, since the stellar
production and later ejection of this element to the Interstellar Medium (ISM)
in the high metallicity regime can be accessed. The stellar nucleosynthesis
theory predicts a primary origin for oxygen and argon (also for sulphur and
neon) which are predominantly produced on relatively short timescales by core-
collapse supernovae (SNe; massive stars) explosions (e.g. Woosley & Weaver
1995). Thus, assuming a universal Initial Mass Function (IMF)111For a
discussion on the universality of the IMF see, for example, Bastian et al.
(2010)., there is expectation for a relatively constant value of the Ar/O
abundance ratio with the O/H (or metallicity) variation, as derived by several
authors in chemical abundance studies of SFs (e.g. Thuan et al. 1995; Izotov &
Thuan 1999; van Zee & Haynes 2006; Guseva et al. 2011; van Zee & Haynes 2006).
However, some authors have found different behaviour of Ar/O with O/H. For
example, Izotov et al. (2006), who used a large sample of star-forming
galaxies whose observational data were taken from SDSS-DR3 (Abazajian et al.,
2005), found that Ar/O abundance ratio decreases by 0.15 dex with the increase
of O/H for the range $\rm 7.1\>\la\>12+\log(O/H)\>\la\>8.5$ (see also Pérez-
Montero et al. 2007). On the other hand, recent results from the CHAOS project
(Berg et al., 2015) derived by Berg et al. (2020), who applied the $T_{\rm
e}$-method to 190 individual H ii regions located in nearby galaxies, found
Ar/O about constant and similar to the solar value for the range $\rm
8.3\>\la\>12+\log(O/H)\>\la\>9.0$, and a high decrease of this abundance ratio
for the very low abundance regime. Finally, Kennicutt et al. (2003) hinted
that the Ar/O abundance decreases at high metallicity ($\rm
8.5\>\la\>12+\log(O/H)\>\la\>8.7$) in the M 101 spiral galaxy.

For the very high metallicity regime ($\rm 12+\log(O/H)\>\ga\>8.8$), the
behaviour of Ar/O with O/H is poorly known as well as its abundance in AGNs.
Recently, Dors et al. (2020a) adapted the $T_{\rm e}$-method to chemical
abundance studies of AGNs, which made it possible to obtain direct O/H
estimates up-to the very high metallicity regime, i.e. $\rm 12+log(O/H)\approx
9.3$, an abundance value which is about 0.3 dex higher than the maximum value
obtained for SFs (Pilyugin et al., 2007; Berg et al., 2020). Therefore,
abundance studies in AGNs through the $T_{\rm e}$-method allow for the
calculations of reliable Ar/H abundances in this class of object and further
investigating the Ar/O-O/H relation at very high metallicity regime, which is
inaccessible in SF abundance studies.

In this context, we used the $T_{\rm e}$-method and developed a new
methodology based on photoionization model to calculate the abundance of the
argon relative to hydrogen in the narrow-line regions (NLRs) of Seyfert 2
galaxies, whose data were taken from the SDSS-DR7 (York et al., 2000). The
present study is organized as follows. In Section 2, the observational data
and the methodology used to estimate the oxygen and argon abundances are
presented. The results and the discussion are presented in Sect. 3. Finally,
the conclusion of the outcome is given in Sect. 4.

##  2 Methodology

To determine the total abundance of the argon and oxygen in relation to
hydrogen abundance (Ar/H, O/H), firstly, we consider optical emission-line
intensities of AGNs type Seyfert 2 from Sloan Digital Sky Survey Data Release
7 (SDSS-DR7, York et al. 2000). These observational data were used to
calculate the Ar/H and O/H abundances using the $T_{\rm e}$-method. We used
photoionization models, built with the Cloudy code (Ferland et al., 2017), in
order to obtain an ICF for the $\rm Ar^{2+}$ and an estimation of the
temperature for the gas region occupied by this ion. In what follows, a
description of the observational data and the methodology adopted to obtain
the abundances are presented.

###  2.1 Observational data

We used optical ($3000\><\>\lambda($Å$)\><\>7200$) reddening-corrected
emission-line intensities of a sample of Seyfert 2 nuclei obtained from the
SDSS-DR7 (York et al., 2000) data made available by MPA/JHU
group222https://wwwmpa.mpa-garching.mpg.de/SDSS/DR7/. The sample consists of
463 Seyfert 2 nuclei with redshift $z\>\la\>0.4$ and stellar masses of the
hosting galaxies in the range of $9.4\>\la\>\log(M/{\rm
M_{\odot}})\>\la\>11.6$ selected by Dors et al. (2020b). From this sample, we
considered a sub-sample containing only objects which have the [O
ii]$\lambda$3726+3729, [O iii]$\lambda$4363, [O iii]$\lambda$5007, H$\alpha$,
[S ii]$\lambda$6716, [S ii]$\lambda$6731 and [Ar iii]$\lambda$7135 emission-
lines measured with an error lower than 50 %. This criterion reduced the
sample to 64 objects out of the 463 selected by Dors et al. (2020b), with
redshif in the range of $0.04\>\la\>z\>\la\>0.25$ and range of the stellar
masses of the hosting galaxies $9.9\>\la\>\log(M/{\rm M_{\odot}})\>\la\>11.2$.

Figure 1: Diagnostic diagram log([O iii]$\lambda$5007/H$\beta$) versus log([N
ii]$\lambda$6584/H$\alpha$). Red points represent our sample of Seyfert 2
nuclei (see Sect. 2.1) whose observational emission-line ratios were taken
from the SDSS-DR7 (York et al., 2000) and measured by the MPA/JHU group. The
solid black line represents the AGN/Star-forming region separation line
proposed by Kewley et al. (2001) and given by the Equation 1

.

In Figure 1, a standard Baldwin, Phillips & Terlevich diagram (Baldwin et al.,
1981) log([O iii]$\lambda$5007/H$\beta$) versus log([N
ii]$\lambda$6584/H$\alpha$), the observational line ratio intensities for the
64 objects are represented by red points. Also in this figure, the theoretical
classification criterion (represented by the black line) proposed by Kewley et
al. (2001), which depict that objects with

$\rm log([O\>III]\lambda 5007/H\beta)\>>\>\frac{0.61}{log([N\>II]\lambda
6584/H\alpha)-0.47}+1.19$ (1)

are classified as AGNs, otherwise, as SFs, is shown. It can be seen that the
sample cover a large range of ionization degree and metallicity hence a wide
range of [O iii]/H$\beta$ and [N ii]/H$\alpha$ are observed (e.g. Groves et
al. 2006; Feltre et al. 2016; Carvalho et al. 2020).

The electron density ($N_{\rm e}$) of each one of the 64 Seyfert 2 nuclei was
calculated from the $[\text{S\,{ii}}]\lambda 6716/\lambda 6731$ line ratio,
assuming an electron temperature of 10 000 K, and using the PyNeb routine
(Luridiana et al., 2015). In Fig. 2 a histogram with the $N_{\rm e}$
distribution of our sample is shown.

Figure 2: Histogram showing the distribution of electron density values from
our sample of 64 objects (see Sect. 2.1) calculated with PyNeb routine
(Luridiana et al., 2015) and considering an electron temperature of $10^{4}$
K. The y-axis represents the number of object with a given range of electron
density value.

It can be seen that the $N_{\rm e}$ values for our sample (the maximum value
is about 3000 cm-3) are lower than the critical density (i.e.
$10^{4-8}\rm\>cm^{-3}$, see Vaona et al. 2012) of the emission lines involved
in the present study, therefore, effects of collisional de-excitation are
negligible in our abundance estimates. In Dors et al. (2020b), a complete
description of the selection criteria adopted to obtain the sample as well as
a discussion about aperture effects on the abundance determination is
presented. Moreover, effects of electron density variation along the AGN
radius, X-Ray dominated regions, shock and electron temperature fluctuations
in abundance determinations have been discussed by Dors et al. (2020a) and
Dors et al. (2021) and these are not repeated here.

###  2.2 $T_{\rm e}$-method

It was possible to estimate the Ar/H and O/H abundances through the $T_{\rm
e}$-method for the sample of 64 objects. In view of the $T_{\rm e}$-method, we
followed a similar methodology proposed by Pérez-Montero (2017) and Dors et
al. (2020a).

####  2.2.1 Oxygen abundance

First, for each object, we calculated the temperature of the high ionisation
gas zone ($t_{3}$) and the electron density ($N_{\rm e}$) based on the
dependence of these nebular parameters on the [O iii]($\lambda 4949$+$\lambda
5007$)/$\lambda 4363$ and [S ii]$\lambda 6716$/$\lambda 6731$ line ratios,
respectively. We used the function getCrossTemDen from the PyNeb code
(Luridiana et al., 2015), where the value of each parameter was obtained by
interacting over the two sensitive line ratios above. The errors in $N_{\rm
e}$ and $t_{3}$ were calculated adding a Monte Carlo random-gauss values to
the sample with the function addMonteCarloObs in the PyNeb code. The symbol
$t_{3}$ represents the electron temperature in units of $10^{4}$ K. The mean
value derived for $t_{3}$ from our sample is $\sim 1.5$ and the uncertainty is
$\sim 0.3$. For the electron density, we found a mean value of $470\>\rm
cm^{-3}$ and an uncertainty of $\sim 250\>\rm cm^{-3}$.

Since it is not possible to estimate the temperature for the low ionization
gas zone ($t_{2}$) due to the absence of the auroral [N ii]$\lambda$5755 and
[O ii]$\lambda$7319, $\lambda$7330 line intensities, the following theoretical
relation (Eq. 2) between $t_{2}$-$t_{3}$, derived by Dors et al. (2020a) for
chemical abundance studies of AGNs and obtained by using a photoionzation
model grid built with the Cloudy code (Ferland et al., 2013) by Carvalho et
al. (2020), was adopted:

$t_{2}=({\rm a}\times t_{3}^{3})+({\rm b}\times t_{3}^{2})+({\rm c}\times
t_{3})+{\rm d},$ (2)

where $\rm a=0.17$, $\rm b=-1.07$, $\rm c=2.07$ and $\rm d=-0.33$, while
$t_{2}$ and $t_{3}$ are in units of $10^{4}$ K. In Riffel et al. (2021) this
theoretical $t_{2}$-$t_{3}$ relation was compared with direct electron
temperature estimations, calculated through observational auroral emission
lines for a sample of AGNs, and a good agreement was found between them.
However, these authors indicated that some cautions must be taken into account
in the use of Eq. 2 for AGNs with strong outflowing gas.

To calculate the ionic abundances of O2+ and O+ relative to H+ the expressions
provided by Pérez-Montero (2017):

$12+\log\left(\frac{\mathrm{O}^{2+}}{\mathrm{H}^{+}}\right)=\log\left(\frac{1.33\times
I([\text{O\,{iii}}]\lambda 5007)}{I(\mathrm{H\beta})}\right)+6.1868\\\
+\frac{1.2491}{t_{3}}-0.55816\log(t_{3})$ (3)

and

$12+\log\left(\frac{\mathrm{O}^{+}}{\mathrm{H}^{+}}\right)=\log\left(\frac{I([\text{O\,{ii}}]\lambda
3726+\lambda 3729)}{I({\rm H}\beta)}\right)+5.887\\\
+\frac{1.641}{t_{2}}-0.543\log(t_{2})+0.000114\,n_{\rm e},$ (4)

respectively, where $n_{\rm e}$ is the electron density $N_{\rm e}$ in units
of 104 cm-3, were used. The uncertainty of $t_{3}$ was considered in the
determination of $t_{2}$. Thus, in the derivation of $\rm O^{2+}/H^{+}$ ionic
abundance the uncertainties of the [O iii]/H$\beta$ line ratio and of $t_{3}$
were taken into account. The same procedure was considered for the derivation
of $\rm O^{+}/H^{+}$, where the $n_{\rm e}$ and $t_{2}$ uncertainties were
also taken into account.

Finally, the total abundance of the oxygen is approximated by

${\rm\frac{O}{H}=ICF(O)\>\times\>\left[\frac{O^{2+}}{H^{+}}+\frac{O^{+}}{H^{+}}\right]}.$
(5)

It is not possible to derive ICF(O), for instance through the expressions
proposed by Torres-Peimbert & Peimbert (1977) and Izotov et al. (2006), due to
the absence of the He ii$\lambda$4686 emission line in our observational data.
Therefore, we assumed ICF(O)=1.20, an average value obtained by Flury & Moran
(2020) and Dors et al. (2020a). Oxygen ICF values translates into an abundance
correction for AGNs of $\sim$0.1 dex, which is in agreement with the
uncertainty derived in H ii regions via $T_{\rm e}$-method estimates (e.g.
Kennicutt et al. 2003; Hägele et al. 2008; Berg et al. 2020).

####  2.2.2 Argon abundance

Generally, to estimate the temperature of the electrons excitating the $\rm
Ar^{2+}$, the approach proposed by Garnett (1992) which is based on
photoionization model results is assumed in chemical abundance studies of SFs
(e.g. Kennicutt et al. 2003; Hägele et al. 2008). A similar electron
temperature is assumed for the gas regions where the $\rm Ar^{2+}$ and $\rm
S^{2+}$ ions are located, i.e.

$T_{\rm e}(\text{Ar\,{iii}})=T_{\rm e}(\text{S\,{iii}}).$ (6)

The $T_{\rm e}(\text{S\,{iii}})$ can be calculated directly from [S
iii]($\lambda 9069$+$\lambda 9532$)/$\lambda 6312$ or through the following
theoretical relation proposed by Garnett (1992), i.e.

$T_{\rm e}(\text{S\,{iii}})=0.83\>T_{\rm e}(\text{O\,{iii}})+1700\rm\>K$ (7)

when [S iii]($\lambda 9069$+$\lambda 9532$)/$\lambda 6312$ line ratio can not
be measured. In Eq. 7, $T_{\rm e}(\text{O\,{iii}})=t_{3}\>\times\>10^{4}\>\rm
K$.

However, Dors et al. (2020a) showed that, in general, AGNs present a distinct
electron temperature structure than H ii regions (see also Dors et al. 2021;
Riffel et al. 2021; Armah et al. 2021). Thus, it is worthwhile to ascertain
the validity of Eqs. 6 and 7 for AGNs. In view of this, we used the results
from the photoionization model grid by Carvalho et al. (2020) and considered
predictions for $T_{\rm e}(\text{A\,{iii}})$ and $T_{\rm e}(\text{S\,{iii}})$.
This grid of photoionization models considered a wide range of AGN nebular
parameters whose optical predicted emission lines reproduce those of a large
sample of Seyfert 2 nuclei (for a detailed description of these models see
Carvalho et al. 2020). The temperature values predicted by the photoionization
models and considered here correspond to the mean temperature for $\rm
Ar^{2+}$ and $\rm S^{2+}$ over the nebular AGN radius times the electron
density. In Fig. 3, bottom panel, the photoionization model predictions for
$T_{\rm e}(\text{S\,{iii}})$ versus $T_{\rm e}(\text{Ar\,{iii}})$ (in units of
$10^{4}$ K) and the approach given by Eq. 6 are shown. It can be seen that, in
contrast to H ii regions, $T_{\rm e}(\text{A\,{iii}})$ is generally higher
than $T_{\rm e}(\text{S\,{iii}})$, indicating that Eq. 6 is not valid for AGN
abundance studies. The same can be seen in Fig. 3, top panel, where the AGN
model predictions show a large deviation from the temperature relation given
by Eq. 7.

Figure 3: Temperature values for the $\rm S^{2+}$, $\rm Ar^{2+}$ and $\rm
O^{2+}$ predicted by the photoionization models built by Carvalho et al.
(2020) by using the Cloudy code (Ferland et al., 2013). The values correspond
to the model predicted mean temperature (in units of $10^{4}$ K) for each ion
over the nebular AGN radius times the electron density. Bottom panel:
temperature values for the $\rm S^{2+}$ versus those for $\rm A^{2+}$. The
black line corresponds to equality between the temperatures (Eq. 6) proposed
by Garnett (1992) for H ii regions. Red points represent photoionization model
results. Top panel: same as the bottom panel but for $\rm S^{2+}$ versus
$t_{3}$, where $t_{3}$ represents the temperature for $\rm O^{2+}$. Black line
represents Eq. 7 proposed by Garnett (1992).

In order to estimate a more precise temperature to derive the $\rm
Ar^{2+}/H^{+}$ ionic abundance, the photoionization models by Carvalho et al.
(2020) were used to obtain a relation between $T_{\rm e}(\text{Ar\,{iii}})$
and $t_{3}$ as shown in Fig. 4 because $t_{3}$ can be derived directly from [O
iii]($\lambda 4959+\lambda 5007$)/$\lambda 4363$ observational line ratio of
our sample. In Fig. 4, $t_{\rm e}(\text{Ar\,{iii}})$ corresponds to the value
of $T_{\rm e}(\text{Ar\,{iii}})$ in units of $10^{4}$ K. It can be seen from
Fig. 4 that there is a good correlation between the temperatures and a fit to
the points results in

$t_{\rm e}(\text{Ar\,{iii}})=(-0.45\pm 0.03)\times t_{3}^{2}+(1.61\pm
0.09)\times t_{3}-(0.24\pm 0.06).$ (8)

Figure 4: Same as Fig. 3 but for $T_{\rm e}(\text{Ar\,{iii}})$ versus $t_{3}$.
Black curve represents a fit to the points represented by Eq. 8.

The $\rm Ar^{2+}/H^{+}$ ionic abundance is calculated by the expression also
provided by Pérez-Montero (2017)

$\displaystyle 12+\log(\frac{{\rm Ar^{2+}}}{{\rm H^{+}}})\\!\\!\\!$
$\displaystyle=$
$\displaystyle\\!\\!\\!\log\big{(}\frac{I[\text{Ar\,{iii}}]\lambda
7135}{I{\rm(H\beta)}}\big{)}+6.100$ (9)
$\displaystyle\\!\\!\\!+\frac{0.86}{t_{\rm
e}(\text{Ar\,{iii}})}-0.404\times\log t_{\rm e}(\text{Ar\,{iii}}).$

To calculate the total argon abundance in relation to the hydrogen (Ar/H)
using only the $\rm Ar^{2+}/H^{+}$ abundance it is necessary to consider an
ICF in order to take into account the presence of ions with other ionization
levels. In fact, ions such as $\rm Ar^{3+}$ and $\rm Ar^{4+}$ have emission
lines (e.g. [Ar iv]$\lambda$4740, [Ar v]$\lambda$7006) present in optical AGN
spectra (e.g. Koski 1978; Alloin et al. 1992). Hitherto, no ICF for the argon
abundance determinations in AGNs has been proposed in the literature and, in
principle, due to distinct ionization structure of AGNs, theoretical ICFs
proposed by H ii regions (e.g. Mathis 1985; Izotov et al. 2006; Pérez-Montero
et al. 2007; Berg et al. 2020; Amayo et al. 2021) can not be applied to this
class of objects. In this sense, we used the Carvalho et al. (2020)
photoionization models to derive an argon ICF, defined by

$\rm ICF(Ar^{2+})=(Ar/H)/(Ar^{2+}/H^{+})$ (10)

and in terms of the function $\rm x=[O^{2+}/(O^{+}+O^{2+})]$ ionic abundance
ratio. In Fig. 5 the results for ICF($\rm Ar^{2+}$) versus x are shown. A fit
to the points produces the relation

$\rm ICF(Ar^{+})=(a\>x^{2})+(b\>x)+c,$ (11)

where $\rm a=20.88\pm 3.80$, $\rm b=-9.74\pm 3.64$ and $\rm c=2.68\pm 0.69$. A
large scattering of the points can be seen in Fig. 5. We investigated the
source of this scattering to ascertain whether it is due to variation in the
nebular parameters $N_{\rm e}$, $\alpha_{ox}$ (slope of the Spectral Energy
Distribution, SED333See Krabbe et al. 2021 for a detailed description of this
SED.) and ionization parameter $U$ (not shown). We did not find any dependence
of these parameters with the ICF($\rm Ar^{2+}$)-x relation. However, a clear
dependence between ICF($\rm Ar^{2+}$) and x on the gas metallicity is noted in
Fig. 5, in the sense that for a fixed x value, we derive a higher ICF value
with the decrease of the metallicity. A dependence between the metallicity and
ICF-x relations for distinct elements was also derived by Izotov et al. (2006)
for SFs.

Figure 5: ICF for $\rm Ar^{2+}$ (as defined in Eq. 10) as a function of the
$\rm x=[O^{2+}/(O^{+}+O^{2+})]$ abundance ratio. Points represent results from
photoionization models built by Carvalho et al. (2020). Model results assuming
different metallicities (in relation to the solar value) are represented by
different colours, as indicated. The curve represents a fit to all the points
given by the Eq. 11.

Thus, in order to obtain a more exact ICF derivation, we produce a bi-
parametric function, i.e. $\rm ICF(Ar^{2+})=f[12+\log(O/H),x]$. We converted
the metallicity ($Z$) assumed in the photoionization models built by Carvalho
et al. (2020) in oxygen abundance through the expression

$12+\log({\rm O/H})=12+\log[(Z/{\rm Z_{\odot}})\>\times\>10^{\log(\rm
O/H)_{\odot}}],$ (12)

where $\log(\rm O/H)_{\odot}=-3.31$ (Allende Prieto et al., 2001). In Fig. 6
the bi-parametric calibration is shown where the points represent the
photoionization model results. We fit two functions, one for $\rm x\><\>0.6$
represented by a blue surface in Fig. 6 and given by

$\displaystyle{\rm ICF}(\mathrm{Ar^{2+}})$ $\displaystyle=(1.51\pm
0.3)x^{2}-(6.82\pm 1.55)y^{2}$ (13) $\displaystyle-(1.68\pm 0.52)xy-(27.18\pm
5.19)x$ $\displaystyle+(10.88\pm 4.72)y+124.6\pm 22.32$

where $\rm y=12+\log(\mathrm{O/H})$ and $\rm x=[O^{2+}/(O^{+}+O^{2+})]$ and
another one for $\rm x\>>\>0.6$ represented by the green surface and given by

$\displaystyle{\rm ICF}(\mathrm{Ar^{2+}})$ $\displaystyle=(1.82\pm
142.29)x^{2}+(107.86\pm 21.07)y^{2}$ (14) $\displaystyle-(35.61\pm
7.13)xy-(14.54\pm 33.81)x$ $\displaystyle+(188\pm 53.96)y+27.73\pm 142.29.$

Figure 6: Bi-parametric calibration among the $\rm ICF(Ar^{2+})$, $\rm
12+\log(O/H)$ and $\rm x=[O^{2+}/(O^{+}+O^{2+})]$. Points represent the
photoionization model results built by Carvalho et al. (2020) while the
surfaces represent the best fit to the points. The blue surface is given by
Eq. 13 and valid it is for $\rm x\><\>0.6$ while the green surface, given by
Eq. 14, is valid for $\rm x\>>\>0.6$.

The expressions above were applied to derive the total abundance of the argon
in relation to the hydrogen (Ar/H).

The mean errors for the 12+log(Ar/H) and 12+log(O/H) abundances derived for
the objects of our sample are $\sim$0.25 dex and $\sim$0.13 dex, respectively.
These errors are in order of those derived for O/H abundance determinations in
nearby AGNs by Revalski et al. (2018a); Revalski et al. (2018b, 2021), who
also applied the $T_{\rm e}$-method. However, they are somewhat ($\sim$ 0.1
dex) higher than those derived for disk H ii regions located in nearby
galaxies (e.g. Berg et al. 2020), because the [O iii]$\lambda$4363 auroral
line is weaker in AGNs than in H ii regions, resulting in a higher uncertainty
in its flux, which in turn implies a larger uncertainty in the AGN abundance
values.

In Table 1, the SDSS identification of the objects of the sample, electron
temperature and electron density values, argon ICF values, ionic and total
abundances, redshift, and stellar mass of the hosting galaxies are listed.

Table 1: Results obtained from our sample of objects. Columns: (1) SDSS name,
(2) $T_{\rm e}$(O iiii) (in K), (3) $T_{\rm e}$(A iiii) (in K), (4) Electron
density (in units of $\rm cm^{-3}$), (5) ICF($\rm Ar^{2+}$), (6) $\rm
12+\log(O^{+}/H^{+})$, (7) $\rm 12+\log(O^{2+}/H^{+})$, (8) $\rm
12+\log(A^{2+}/H^{+})$, (9) 12+log(O/H), (10) 12+log(Ar/H), (11) redshift and
(12) Mass (in units of $10^{7}\>\rm M_{\odot}$).

(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12)
---|---|---|---|---|---|---|---|---|---|---|---
J101754.72-002811.9 | 14510 | 11481 | 298 | 2.79 | 8.03 | 7.87 | 5.98 | 8.34 | 6.43 | 0.1817 | 11.13
J101536.21+005459.3 | 18252 | 11994 | 184 | 2.14 | 8.39 | 7.78 | 5.60 | 8.56 | 5.93 | 0.1202 | 10.71
J104426.16+001707.3 | 8872 | 8343 | 292 | 2.40 | 8.30 | 8.41 | 6.31 | 8.74 | 6.69 | 0.1502 | 10.71
J105408.69-000111.0 | 16992 | 11971 | 227 | 2.39 | 8.42 | 7.33 | 5.36 | 8.53 | 5.74 | 0.1081 | 10.21
J111652.97+010615.5 | 16865 | 11952 | 259 | 2.84 | 8.05 | 7.49 | 5.54 | 8.23 | 6.00 | 0.1309 | 10.70
J114017.31-001543.3 | 13459 | 10677 | 505 | 2.46 | 8.17 | 7.99 | 6.09 | 8.47 | 6.48 | 0.1245 | 10.62
J113049.84+005346.7 | 19873 | 11827 | 600 | 2.35 | 8.37 | 7.49 | 5.62 | 8.50 | 5.99 | 0.1043 | 10.70
J113326.76+001443.9 | 14509 | 11386 | 497 | 2.61 | 8.16 | 7.54 | 5.62 | 8.33 | 6.03 | 0.1143 | 10.48
J115616.76-002221.0 | 15385 | 11724 | 781 | 2.16 | 8.31 | 7.96 | 6.40 | 8.55 | 6.74 | 0.1092 | 10.74
J122012.58-010531.5 | 11277 | 10039 | 1443 | 2.18 | 8.39 | 8.43 | 6.24 | 8.79 | 6.58 | 0.1183 | 10.55
J123441.93-010034.7 | 14568 | 11518 | 381 | 2.52 | 8.15 | 7.75 | 5.55 | 8.37 | 5.95 | 0.0801 | 10.25
J124116.14+004423.0 | 14438 | 11537 | 659 | 2.24 | 8.26 | 8.02 | 5.90 | 8.54 | 6.26 | 0.0900 | 10.74
J130433.90+000402.9 | 16195 | 11896 | 158 | 2.56 | 8.19 | 7.53 | 5.92 | 8.35 | 6.33 | 0.2463 | 11.23
J132625.73-002148.6 | 17204 | 11988 | 273 | 2.89 | 8.10 | 7.25 | 5.53 | 8.24 | 5.99 | 0.1893 | 10.78
J134005.97-010646.4 | 20688 | 11681 | 189 | 2.35 | 8.48 | 7.29 | 5.43 | 8.59 | 5.81 | 0.1295 | 10.77
J133821.79+002329.2 | 12623 | 10797 | 233 | 2.60 | 8.17 | 8.25 | 6.14 | 8.59 | 6.55 | 0.1292 | 10.87
J140301.05+005343.5 | 14002 | 11329 | 155 | 3.03 | 7.94 | 7.65 | 5.51 | 8.20 | 5.99 | 0.1664 | 10.61
J145956.36-002821.5 | 12503 | 10682 | 202 | 2.57 | 8.13 | 8.01 | 6.14 | 8.45 | 6.55 | 0.1096 | 10.84
J130354.71-030631.8 | 11344 | 10073 | 757 | 1.84 | 8.53 | 8.40 | 6.28 | 8.85 | 6.55 | 0.0778 | 10.65
J171544.02+600835.4 | 17771 | 12000 | 819 | 2.14 | 8.38 | 7.79 | 5.59 | 8.56 | 5.92 | 0.1569 | 10.98
J172028.98+584749.6 | 14587 | 11494 | 494 | 2.92 | 8.03 | 7.42 | 5.29 | 8.21 | 5.75 | 0.1269 | 10.84
J172352.43+582318.5 | 17778 | 11997 | 939 | 2.91 | 8.07 | 7.31 | 5.20 | 8.22 | 5.66 | 0.0799 | 10.24
J153035.77+001517.7 | 11505 | 10165 | 207 | 2.28 | 8.24 | 7.93 | 5.87 | 8.50 | 6.23 | 0.0721 | 10.53
J002312.34+003956.3 | 19764 | 11869 | 447 | 2.06 | 8.54 | 7.73 | 5.67 | 8.68 | 5.98 | 0.0727 | 10.16
J012937.25-003838.6 | 14176 | 11401 | 141 | 2.57 | 8.16 | 7.60 | 5.51 | 8.34 | 5.92 | 0.1794 | 11.06
J012720.32+010214.6 | 9838 | 9066 | 498 | 2.27 | 8.41 | 8.55 | 6.36 | 8.87 | 6.72 | 0.1745 | 11.09
J013957.81-004504.2 | 11872 | 10381 | 441 | 2.74 | 8.11 | 8.18 | 6.40 | 8.52 | 6.83 | 0.1616 | 10.83
J014153.97+010505.4 | 19553 | 11866 | 581 | 2.23 | 8.40 | 7.62 | 5.33 | 8.55 | 5.68 | 0.1013 | 10.95
J011016.00+150515.9 | 12920 | 10890 | 534 | 2.28 | 8.27 | 8.19 | 6.10 | 8.61 | 6.46 | 0.0597 | 10.19
J013555.82+143529.6 | 12902 | 10883 | 267 | 2.52 | 8.14 | 7.86 | 5.68 | 8.40 | 6.08 | 0.0719 | 10.83
J074213.71+391705.3 | 10451 | 9509 | 201 | 2.40 | 8.22 | 8.19 | 6.19 | 8.59 | 6.57 | 0.0704 | 9.94
J082017.99+465125.3 | 12773 | 10823 | 130 | 2.13 | 8.46 | 7.70 | 5.64 | 8.61 | 5.97 | 0.0524 | 10.35
J082910.18+504005.7 | 11671 | 10220 | 205 | 2.00 | 8.44 | 7.92 | 5.91 | 8.64 | 6.21 | 0.0739 | 9.99
J085223.96+531550.6 | 17610 | 11995 | 524 | 2.52 | 8.27 | 7.40 | 5.54 | 8.41 | 5.94 | 0.1280 | 10.78
J095123.44+581621.2 | 18905 | 11952 | 140 | 2.45 | 8.48 | 6.96 | 5.12 | 8.58 | 5.51 | 0.1486 | 10.91
J033923.14-054841.5 | 12841 | 10856 | 331 | 2.54 | 8.16 | 8.13 | 5.86 | 8.52 | 6.27 | 0.0848 | 10.26
J091605.16+002030.3 | 12682 | 10791 | 482 | 1.83 | 8.53 | 8.14 | 5.77 | 8.76 | 6.03 | 0.1434 | 10.97
J093509.12+002557.4 | 15921 | 11833 | 551 | 2.70 | 8.11 | 7.52 | 5.24 | 8.29 | 5.68 | 0.1512 | 10.78
J100013.84+624703.4 | 10996 | 9868 | 488 | 2.55 | 8.15 | 8.09 | 5.96 | 8.50 | 6.37 | 0.1145 | 10.33
J102039.81+642435.8 | 15695 | 11779 | 172 | 2.29 | 8.25 | 7.86 | 5.47 | 8.47 | 5.83 | 0.1223 | 10.74
J095759.45+022810.5 | 12988 | 10905 | 325 | 2.35 | 8.23 | 8.11 | 6.12 | 8.55 | 6.49 | 0.1194 | 10.56
J100921.26+013334.5 | 13197 | 11029 | 735 | 2.20 | 8.32 | 8.27 | 6.04 | 8.68 | 6.39 | 0.1437 | 10.72
J112748.89+020302.6 | 16053 | 11845 | 451 | 2.25 | 8.30 | 7.76 | 5.53 | 8.49 | 5.88 | 0.1267 | 10.80
J114304.62+013946.2 | 10858 | 9810 | 197 | 2.03 | 8.38 | 8.04 | 5.94 | 8.62 | 6.25 | 0.0928 | 10.84
J114029.55+022744.6 | 20626 | 11680 | 375 | 2.48 | 8.28 | 7.44 | 5.23 | 8.42 | 5.62 | 0.1230 | 10.63
J115854.96+033254.9 | 15449 | 11741 | 373 | 2.27 | 8.36 | 7.63 | 5.41 | 8.51 | 5.77 | 0.0841 | 10.51
J125503.63+012233.7 | 13282 | 11026 | 731 | 2.09 | 8.37 | 8.25 | 5.94 | 8.69 | 6.26 | 0.1642 | 10.93
J125209.68+021558.0 | 15928 | 11815 | 200 | 2.53 | 8.28 | 7.38 | 5.26 | 8.41 | 5.66 | 0.2064 | 10.95
J130220.35+024048.8 | 13312 | 11045 | 710 | 2.33 | 8.23 | 7.85 | 5.98 | 8.46 | 6.35 | 0.1766 | 10.93
J134959.37+030058.0 | 14538 | 11545 | 346 | 2.25 | 8.26 | 7.97 | 6.17 | 8.52 | 6.52 | 0.1097 | 10.35
J140231.58+021546.3 | 11109 | 9934 | 263 | 2.03 | 8.44 | 8.42 | 6.07 | 8.81 | 6.38 | 0.1797 | 11.06
J143214.54+023228.5 | 15605 | 11787 | 439 | 2.31 | 8.26 | 7.77 | 5.58 | 8.46 | 5.95 | 0.1123 | 10.91
J074257.23+333217.9 | 14084 | 11333 | 366 | 2.77 | 8.05 | 7.66 | 5.53 | 8.27 | 5.97 | 0.1474 | 10.71
J090246.69+520932.8 | 13797 | 11254 | 290 | 2.34 | 8.22 | 8.02 | 5.70 | 8.51 | 6.07 | 0.1375 | 10.95
J141530.97+035916.6 | 16651 | 11928 | 463 | 2.41 | 8.40 | 7.31 | 5.56 | 8.52 | 5.95 | 0.0805 | 10.49
J141351.75+042208.9 | 16889 | 11957 | 293 | 2.47 | 8.23 | 7.57 | 5.41 | 8.40 | 5.80 | 0.1449 | 10.60
J144925.29+044157.2 | 9467 | 8810 | 126 | 1.91 | 8.46 | 8.15 | 6.14 | 8.71 | 6.42 | 0.0824 | 10.04
J151244.15+042848.3 | 14481 | 11439 | 575 | 2.37 | 8.23 | 7.73 | 5.66 | 8.43 | 6.04 | 0.0796 | 10.34
J155404.39+545708.2 | 12320 | 10609 | 147 | 2.48 | 8.20 | 8.20 | 6.00 | 8.58 | 6.39 | 0.0457 | 9.91
J164938.71+420658.4 | 14941 | 11624 | 345 | 2.34 | 8.30 | 7.63 | 5.61 | 8.46 | 5.98 | 0.1503 | 10.58
J165944.29+392846.1 | 16801 | 11947 | 285 | 2.32 | 8.32 | 7.62 | 5.78 | 8.48 | 6.15 | 0.0818 | 10.09
J100602.50+071131.8 | 14649 | 11535 | 1588 | 1.87 | 8.64 | 7.95 | 5.76 | 8.80 | 6.04 | 0.1205 | 11.19
J163344.99+372335.1 | 20228 | 11735 | 771 | 2.50 | 8.21 | 7.57 | 5.54 | 8.38 | 5.94 | 0.1748 | 10.80
J125558.75+291459.4 | 11324 | 10055 | 366 | 2.00 | 8.44 | 8.36 | 6.21 | 8.78 | 6.51 | 0.0681 | 9.91

##  3 Results and Discussion

The total argon abundance relative to hydrogen (Ar/H) in gaseous nebulae has
been derived mainly through measurements of the [Ar iii]$\lambda
7135$/H$\beta$ and the assumptions considered to convert this line ratio into
the $\rm Ar^{2+}/H^{+}$ ionic abundance as well as by using an expression for
the ICF($\rm Ar^{2+}$) (e.g. Kennicutt et al. 2003). In some few cases, it has
been also possible to measure the [Ar iv]$\lambda$4740 and [Ar v]$\lambda$7006
emission lines and deriving the $\rm Ar^{3+}/H^{+}$ and $\rm Ar^{4+}/H^{+}$
ionic abundances, respectively (e.g. Koski 1978; French 1981; Pagomenos et al.
2018), producing a more exact Ar/H determination, i.e.

$\rm\frac{Ar}{H}=ICF(Ar)\times\left[\frac{Ar^{2+}}{H^{+}}+\frac{Ar^{3+}}{H^{+}}+\frac{Ar^{4+}}{H^{+}}\right]$
(15)

(e.g. Wesson et al. 2005). However, the [Ar iv]$\lambda$4740 and [Ar
v]$\lambda$7006 emission lines are weak in most part of low ionization
objects, therefore, it is most convenient to use only the strong [Ar
iii]$\lambda 7135$ (e.g. Kennicutt et al. 2003; Zurita & Bresolin 2012). In
our case, the emission line measurements made available by the MPA/JHU group
only allowed us to derive $\rm Ar^{2+}/H^{+}$ ionic abundance and then apply
the ICF (Eq. 13) to obtain the total argon abundance (Ar/H). The application
of the $T_{\rm e}$-method to AGNs was recently proposed by Dors et al. (2020a)
and the ICF for the argon, proposed in this study, hitherto, is the first one
for this class of objects. Thus, it is worthwhile to analyse the derived ICF
values for our sample as well as to compare it with other proposed derivations
for gaseous nebulae. In Fig. 7, bottom panel, the distribution of the argon
ICF values derived from our sample through Eq. 13 is shown. We derived ICF
values ranging from $\sim 1.8$ to $\sim 3$, with an averaged value of $2.38\pm
0.27$. Also in Fig. 7, top panel, the argon ICF distribution for 53 SFs (49
disk H ii regions and 4 H ii galaxies) compiled from the literature is shown.
We notice that majority of SFs present lower ICFs in comparison with those
derived from our sample of Seyfert 2 nuclei, implying that $\sim 90\%$ of the
SFs have $\rm ICF(Ar^{2+})\>\la\>2$ and an average value of about 1.5. These
results point to the known fact that the gas phase in Seyfert 2 has a higher
excitation degree than SFs.

Figure 7: Bottom panel: distribution of the ICF values for the argon from our
sample of Seyfert 2 (see Sect. 2.1) derived by using Eqs. 13 and 14. The
averaged value is indicated. Top panel: Same as the bottom panel but for ICFs
of SFs (H ii regions and H ii galaxies) derived by Berg et al. (2020, 2015),
Croxall et al. (2016, 2015), Bresolin et al. (2009), Hägele et al. (2008), and
Lee & Skillman (2004).

Regarding abundance estimates, our results for Seyfert 2 nuclei can be used to
verify a possible secondary stellar production of the argon at the very high
metallicity regime $\rm[12+log(O/H)\>\ga\>8.8]$, because the maximum value
derived in most part of SFs through the $T_{\rm e}$-method is in the order of
12+log(O/H)$\sim 8.7$ (e.g. Kennicutt et al. 2003; Berg et al. 2020; Yates et
al. 2020). In Fig. 8, the total argon abundance [in units of 12+log(Ar/H)]
versus the oxygen abundance [in units of 12+log(O/H)] from our sample of
Seyfert 2 nuclei is shown. Also in this figure, abundance results based on
$T_{\rm e}$-method for galaxy nuclei with star formation derived by Izotov et
al. (2006) (whose observational data were also taken from SDSS; Abazajian et
al. 2005) as well as results for H ii galaxies obtained by Hägele et al.
(2008) are shown. In this case, we chose to compare our results only with
those from star-forming galaxies (excluding disk H ii regions) because SFs are
subject to similar physical processes like those in AGNs. The following are
few examples which underscore such similarities.

  1. 1.

SFs and AGNs can present gas outflows (e.g. Hopkins et al. 2012; Hirschmann et
al. 2013; Chisholm et al. 2017; Riffel et al. 2014; Riffel et al. 2021; Riffel
2021; Couto et al. 2021).

  2. 2.

In the case of spiral galaxies the presence of bars might produce a falling of
gas into the central regions in both objects (e.g. Athanassoula 1992).

These processes can regulate the star formation as well as modify the gas
enrichment (e.g. Oppenheimer et al. 2010; Krumholz et al. 2017; Su et al.
2017; James et al. 2020) and could not be present in isolated H ii regions.
From Fig. 8, we observe a clear linear relation between Ar/H and O/H
indicating a primary production of the argon in a wide metallicity regime. A
fit to the points (considering Seyfert 2 and SFs) produces the expression

$\rm 12+log(Ar/H)=[(0.89\pm 0.01)\times 12+log(O/H)]-(1.50\pm 0.15),$ (16)

represented in Fig. 8 by a solid blue line. The dashed lines in this figure
represent the uncertainty of $\pm 0.1$ dex in abundance estimations (e.g.
Kennicutt et al. 2003). It is noteworthy to point out from Fig. 8 that, for
very high O/H values, a slight deviation of the points representing AGNs
results from Eq. 16. This can be an indication of a secondary argon production
at very high metallicity regime. In view of this, we tested several polynomial
fittings considering different limits for oxygen abundance looking for a
transition from primary to secondary Ar production, but no satisfactory
solution was obtained. Therefore, we emphasize that our results obtained from
AGNs, when combined with those from star-forming galaxies, indicate that the
argon has a primary stellar production in a wide metallicity range.

Figure 8: Total argon abundance [in units of 12+log(Ar/H)] versus the oxygen
abundance [in units of 12+log(O/H)]. Red points represent abundance results
from our sample of Seyfert 2. Black points represent abundance results from H
ii galaxies obtained through $T_{\rm e}$-method by Izotov et al. (2006) and
Hägele et al. (2008). The solid line represents a fit to the points (Eq. 16)
while the dashed lines represent the uncertainty of $\pm 0.1$ dex in H ii
region abundance estimations (e.g. Kennicutt et al. 2003).

The heavy elements in AGNs are mainly produced by stellar evolution in the ISM
located at few kpc away from the nuclei (e.g. Boer & Schulz 1993; Elmegreen et
al. 2002; Díaz et al. 2007; Dors et al. 2008; Böker et al. 2008; Riffel et al.
2009; Hägele et al. 2013; Álvarez-Álvarez et al. 2015; Riffel et al. 2016;
Pilyugin et al. 2020; Ma et al. 2021) and then transported to the supermassive
black hole. Additional metal enrichment by stars can also be obtained by two
ways:

  1. 1.

$in$ $situ$ star formation embedded in the thin AGN accretion disk (e.g.
Collin & Zahn 1999; Goodman & Tan 2004; Collin & Zahn 2008; Wang et al. 2011;
Mapelli et al. 2012; Davies & Lin 2020; Cantiello et al. 2021) and by

  2. 2.

capture of stars orbiting the central regions of galaxies (e.g. Syer et al.
1991; Artymowicz et al. 1993).

Both processes can produce different chemical evolution of AGNs in comparison
with that of SFs. For instance, the maximum oxygen abundance in the centres of
most luminous star-forming galaxies has been found to be 12+log(O/H)$\sim 8.9$
(e.g. Pilyugin et al. 2007) while Seyfert 2 nuclei can reach up to $\sim 9.2$
dex (e.g. Dors et al. 2020a; Dors 2021), i.e. there is an additional
enrichment in Seyferts in comparison with metal rich H ii regions. Moreover,
recently, Armah et al. (2021) found that Ne/H abundance in a small sample of
Seyfert 2s is nearly 2 times higher than those in SFs. Thus, determining metal
abundance in AGNs, in this case argon abundance, can produce constraints in
studies on star nucleosynthesis in the very high metallicity regime and in
different boundary conditions than those in SFs.

As a result, it is important to verify the range of Ar/H abundance in AGNs,
since these objects present, in general, higher metallicity (or O/H abundance)
than star-forming regions (e.g. Groves et al. 2006; Dors et al. 2020a). In
Fig. 9, the distributions of argon abundance [in units of 12+log(Ar/H)] and
log(Ar/O) for our sample and the solar value for these abundances are shown.
In Table 2 the minimum, maximum and the mean abundance values, taken from Fig.
9, as well as the oxygen abundance values (not shown in Fig. 9) are listed. We
also listed in Table 2 the minimum, maximum and mean abundance values ($W_{\rm
v}$) in relation to the corresponding solar value, defined by

$W_{\rm v}^{\rm X}=\rm X(v)/X_{\odot},$ (17)

where X is a given abundance ratio. The solar argon and oxygen abundances are
those derived by Grevesse & Sauval (1998) and Allende Prieto et al. (2001),
respectively. It can be inferred from Table 2 that the maximum Ar/H and Ar/O
abundance ratios in our sample of AGNs are higher than the solar values, i.e.
$\sim 2.7$ and $\sim 4.0$ times the solar values, respectively. However, the
$W_{\rm max.}^{\rm Ar/H}$ and $W_{\rm max.}^{\rm Ar/O}$ can even be higher
than the ones found in this work due to the sample considered. Actually, the
$W_{\rm max.}^{\rm O/H}$ derived for our sample is about 1.5 times the solar
value. Dors et al. (2020a) found $W_{\rm max.}^{\rm O/H}\sim 3.2$ after
considering a larger sample of SDSS Seyfert 2 nuclei without adopting the [Ar
iii] emission line presence as a selection criterion. Thus, this disparity
indicates the probable existence of oversolar Ar/H and Ar/O values higher than
those listed in Table 2.

Figure 9: Left panel: distribution of argon abundance [in units of 12+log(Ar/H)] for our sample of Seyfert 2 nuclei. The red line represents the solar argon abundance [$\rm 12+log(Ar/H)_{\odot}=6.40$] derived by Grevesse & Sauval (1998). Right panel: same as the left panel but for log(Ar/O). The red line represent the solar argon abundance [$\rm\log(Ar/O)_{\odot}=-2.29$] derived by Grevesse & Sauval (1998) and Allende Prieto et al. (2001). Table 2: Minimum, maximum and the mean abundance ratio values for our sample (see Sect. 2.1) derived through $T_{\rm e}$-method adapted for AGNs (see Sect. 2.2). The abundance values are obtained from the distributions presented in Fig. 9. The $W_{\rm min.}^{\rm X}$, $W_{\rm max.}^{\rm X}$ and $W_{\rm mean}^{\rm X}$ are calculated from Eq. 17 and represent abundance values relative to the solar values. The solar argon and oxygen abundances considered were those derived by Grevesse & Sauval (1998) and Allende Prieto et al. (2001). Abundance ratio | Min. | Max. | Mean | $W_{\rm min.}^{\rm X}$ | $W_{\rm max.}^{\rm X}$ | $W_{\rm mean}^{\rm X}$
---|---|---|---|---|---|---
12+log(Ar/H) | 5.51 | 6.84 | $6.14\pm 0.32$ | 0.13 | 2.75 | $0.54^{+0.60}_{-0.27}$
log(Ar/O) | $-3.06$ | $-1.68$ | $-2.37\pm 0.28$ | 0.16 | 3.98 | $0.97^{+0.61}_{-0.53}$
12+log(O/H) | 8.20 | 8.87 | $8.52\pm 0.16$ | 0.30 | 1.51 | $0.67^{+0.30}_{-0.20}$

In order to compare the abundance range of Ar/H and Ar/O derived through the
new methodology from the $T_{\rm e}$-method for AGNs with those obtained from
other methods, we compiled from the literature Ar/H and Ar/O radial gradients
derived in spiral galaxies and calculated by the standard $T_{\rm e}$-method.
We extrapolated these radial gradients to the central part of the galaxies
(i.e. galactocentric distance $R=0$). This methodology makes it possible to
infer indirect and independent values of abundances in the nuclei of spiral
galaxies (e.g. Vila-Costas & Edmunds 1992; van Zee et al. 1998; Pilyugin et
al. 2004; Zinchenko et al. 2019). As usual, we assume that the Ar/H and Ar/O
radial abundance gradients are represented by

$Y^{\rm X}=Y{{}_{0}}^{\rm X}+[grad\,Y^{\rm X}\times R(\rm kpc)],$ (18)

where $Y^{\rm X}$ represents the value of the abundance ratio X [12+log(Ar/H)
or log(Ar/O)], $Y_{0}^{\rm X}$ is the extrapolated value of X to the galactic
center, i.e. at radial distance $R=0$, and $grad\,Y^{\rm X}$ is the slope of
the distribution expressed in units of $\rm dex\>kpc^{-1}$. As pointed out by
Pilyugin et al. (2004), the accuracy of radial abundance gradient
determinations is defined not only by the large number of objects considered
but also by the distribution of these objects along the galactic radius. Under
this supposition, we take into consideration published data from the
literature for X abundance values of H ii regions derived by using the $T_{\rm
e}$-method and located at galactocentric distances in spiral galaxies within
the range $0.2\>\>\la\>(R/R_{25})\>\la\>1$, where $R$ is the galactocentric
distance and $R_{25}$ is the $B$-band isophote at a surface brightness of 25
mag arcsec-2. It was possible to obtain the Ar/H and Ar/O radial gradients in
four spiral galaxies. In Table 3, the identification of each galaxy, the
number ($N$) of H ii regions considered in deriving the radial gradients, the
$Y{{}_{0}}^{\rm X}$ and $grad\,Y^{\rm X}$ values as well as references to the
original studies from which the data were obtained are listed. Also in Table
3, the $Y_{0}^{\rm X}$ in relation to the solar value, defined by

$W_{0}^{X}=Y_{0}^{\rm X}/(\rm X)_{\odot}$ (19)

is listed. In Fig. 10, the $W_{0}^{\rm X}$ values for the four spiral
galaxies, listed in Table 3, are represented by red points and compared with
those for the range of values (hatched areas) derived for our sample and
listed in Table 2. It can be seen that our range of abundance estimates are in
consonance with the values obtained by independent abundance estimates from
the radial gradients. Obviously, a more exact comparison would be obtained if
both Ar/H and O/H abundances in the AGNs and the radial abundances of these
elements in the host galaxies were determined, such as studies carried out for
the oxygen by Storchi-Bergmann et al. (1998b) and Dors et al. (2015).

Table 3: Parameters of the radial abundance gradients derived for the Ar/H and Ar/O abundance ratios in a sample of spiral galaxies. $N$ represents the number of H ii regions considered in the estimations of the gradients. $Y{{}_{0}}$, $grad\,Y$ and $W_{0}$ are defined in Eqs. 18 and 19. In the last column, the original works from which the radial gradients were compiled are listed. Object | $N$ |  | $Y{{}_{0}}^{\rm Ar/H}$ | $grad\,Y^{\rm Ar/H}$ | $W_{0}^{\rm Ar}$ |  | $Y{{}_{0}}^{\rm Ar/O}$ | $grad\,Y^{\rm Ar/O}$ | $W_{0}^{\rm Ar/O}$ | Reference
---|---|---|---|---|---|---|---|---|---|---
NGC 5194 | 28 |  | $6.55\pm 0.12$ | $-0.015\pm 0.026$ | $1.41^{+0.45}_{-0.33}$ |  | $-2.22\pm 0.11$ | $+0.013\pm 0.023$ | $1.16^{+0.35}_{-0.24}$ | Croxall et al. (2015)
NGC 628 | 45 |  | $6.77\pm 0.55$ | $-0.070\pm 0.009$ | $2.34^{+5.97}_{-1.66}$ |  | $-1.92\pm 0.04$ | $-0.037\pm 0.006$ | $2.33^{+0.24}_{-0.19}$ | Berg et al. (2015)
NGC 300 | 28 |  | $6.32\pm 0.03$ | $-0.106\pm 0.011$ | $0.84^{+0.05}_{-0.03}$ |  | $-2.24\pm 0.03$ | $-0.028\pm 0.009$ | $1.12^{+0.12}_{-0.07}$ | Bresolin et al. (2009)
NGC 5457 | 16 |  | $6.40\pm 0.07$ | $-0.020\pm 0.003$ | $1.00^{+0.17}_{-0.14}$ |  | $-2.36\pm 0.01$ | $-0.008\pm 0.002$ | $0.84^{+0.03}_{-0.01}$ | Kennicutt et al. (2003)

Figure 10: Comparison between argon abundance in relation to the solar value
for $W_{0}^{\rm Ar}=\rm(Ar)/(Ar)_{\odot}$ (bottom panel) and $W_{0}^{\rm
Ar/O}=\rm(Ar/O)/(Ar/O)_{\odot}$ (top panel). Points represent estimates from
radial abundance extrapolations to the central parts (galactocentric distance
$R=0$) from the four spiral galaxies listed in Table 3 and indicated in the
x-axis

. The hatched areas represent the range of abundance ratio values derived for
our sample of Seyfert 2 listed in Table 2.

Finally, in Fig. 11, our Seyfert 2 estimates (red points) for (Ar/O) versus
(O/H) abundances and those calculated through the $T_{\rm e}$-method for star-
forming nuclei by Izotov et al. (2006) and H ii galaxies by Hägele et al.
(2008) are shown. As for the neon and sulphur (see Dors et al. 2013; Dors et
al. 2016 and references therein) several studies on (Ar/O) versus (O/H) have
yielded conflicting results. For instance, Izotov et al. (2006), by correcting
the depletion of oxygen onto dust grains (which is in order of $\sim 0.1\>\rm
dex$) found a negative slope for Ar/O versus O/H for the range $\rm
7.1\>\la\>[12+log(O/H)]\>\la\>8.6$, which correspond to the metallicity range
$\rm 0.03\>\la\>(Z/\rm Z_{\odot})\>\la 0.7$. This negative slope is strongly
influenced by estimations in objects with very low metallicity $\rm[\rm
12+\log(O/H)]\>\la\>7.5]$, in which oversolar Ar/O abundance values are
derived. Although this result of a negative slope is in consonance with the
one found by Pérez-Montero et al. (2007), who considered H ii galaxies and H
ii regions estimates, these authors derived solar Ar/O abundance ratios for
objects at low metallicity regime and subsolar values for the ones at high
metallicity regime. Finally, Berg et al. (2020), who took into account the
$T_{\rm e}$-method abundance estimates for 190 disk H ii regions, derived sub-
solar Ar/O abundance ratio for some few H ii regions with low metallicity
$[\rm 12+\log(O/H)\>\la\>8.0$]. In principle, a possible explanation for the
discrepancies above is the use of different argon ICFs by the authors rather
than the consideration of distinct samples. In any case, it can be seen from
Fig. 11 that, a slight decrease of Ar/O with the increase of O/H, when our
estimates are combined with those for H ii galaxies. It is worth to mention
that, for $[\rm 12+\log(O/H)\>\ga\>8.0$] our Ar/O estimates are in consonance
with those derived for H ii galaxies. A linear regression to the points
produces

$\rm log(Ar/O)=(-0.11\pm 0.02)\>x-(1.51\pm 0.15),$ (20)

where x=log(O/H).

Figure 11: Relation between log(Ar/O) and 12+log(O/H). Red points represent
estimations for our sample of Seyfert 2 while black points represent compiled
estimations for H ii galaxies derived by Izotov et al. (2006) and Hägele et
al. (2008). The blue solid line represents the linear regression to the points
given by Eq. 20. The dashed green line represents the solar value,
log(Ar/O)${}_{\odot}=-2.29$, derived by Grevesse & Sauval (1998) and Allende
Prieto et al. (2001).

##  4 Conclusions

For the fist time, quantitative argon abundances, based on $T_{\rm e}$-method
adapted for AGNs, is derived for the narrow regions of Seyfert 2 nuclei. In
view of this, we compiled from Sloan Digital Sky Survey Data Release 7 (SDSS-
DR7) optical narrow emission line fluxes for 64 Seyfert 2 galaxies in the
local universe ($z\><\>0.25$) and calculated the abundance of the argon and
oxygen in relation to hydrogen (Ar/H, O/H). The total argon abundance relative
to hydrogen (Ar/H) was derived for each object of the sample through the $\rm
Ar^{2+}/H^{+}$ ionic abundance and by using a theoretical expression for the
Ionization Correction Factor (ICF) obtained from photoionization model results
built with the Cloudy code. These results from the models were also used to
derive an appropriate temperature for the $\rm Ar^{2+}$ [$T_{\rm
e}(\text{Ar\,{iii}})$] which can be derived by its dependence on the
temperature for $\rm O^{2+}$ [$T_{\rm e}(\text{O\,{iii}})$] calculated by
using the observational [O iii]($\lambda$4959+$\lambda$5007)/$\lambda$4363
line ratio. We obtained the following conclusions:

  1. 1.

The equality between the temperatures $T_{\rm e}(\text{S\,{iii}})$=$T_{\rm
e}(\text{Ar\,{iii}})$, usually assumed in abundance studies of star-forming
regions, is not valid for Seyfert 2 since the nebular gas region occupied by
$\rm Ar^{2+}$ tends to have a lower temperature than the nebular gas region
occupied by $\rm S^{2+}$.

  2. 2.

A bi-parametric expression for the ICF($\rm Ar^{2+}$) as function of the $\rm
x=[O^{2+}/(O^{+}+O^{2+})]$ abundance ratio and the oxygen abundance [in units
of 12+log(O/H)] is proposed to derive the total argon abundance.

  3. 3.

For the range of oxygen abundance $\rm 8.0\>\la\>[12+\log(O/H)]\>\la\>9.0$ or
metallicity $0.20\>\la\>(Z/\rm\rm Z_{\odot})\>\la\>2.0$, we found that our
sample of Seyfert 2 present A/H abundances ranging from $\sim 0.1$ to $\sim 3$
times the argon solar value, indicating that most of the objects ($\sim 75\%)$
have subsolar argon abundance.

  4. 4.

The range of Ar/H and Ar/O abundance values obtained for our sample are in
consonance with those estimated from extrapolations to the central parts of
radial abundance gradients derived in the disk of four spiral galaxies.

  5. 5.

We found a slight tendency of Ar/O abundance ratio decreases with O/H.

  6. 6.

Finally, the Ar/O abundance values for our sample of Seyfert 2 are in
consonance with estimations for H ii galaxies $[\rm 12+\log(O/H)\>\ga\>8.0$],
indicating that there is not an over enrichment of argon in AGNs, at least for
the metallicity range considered.

## Acknowledgements

AFM gratefully acknowledges support from Coordenação de Aperfeiçoamento de
Pessoal de Nível Superior (CAPES). OLD is grateful to Fundação de Amparo à
Pesquisa do Estado de São Paulo (FAPESP) and Conselho Nacional de
Desenvolvimento Científico e Tecnológico (CNPq).

##  5 DATA AVAILABILITY

The data underlying this article will be shared on reasonable request with the
corresponding author.

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