# Chemical abundances in Seyfert galaxies– IX. Helium abundance estimates

O. L. Dors1, M. Valerdi2, P. Freitas-Lemes1, A. C. Krabbe1, R. A. Riffel3, E.
B. Amôres4, R. Riffel5, M. Armah5, A. F. Monteiro6, C. B. Oliveira1
1UNIVAP - Universidade do Vale do Paraíba. Av. Shishima Hifumi, 2911, CEP:
12244-000, São José dos Campos, SP, Brazil
2Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Luis E. Erro
No. 1, Sta. Ma. Tonantzintla, Puebla, C.P. 72840, México.
3Departamento de Física, Centro de Ciências Naturais e Exatas, Universidade
Federal de Santa Maria, 97105-900, Santa Maria, RS, Brazil
4Departamento de Física, Universidade Estadual de Feira de Santana, Av.
Transnordenstina, S/N, CEP 44036-900 Feira de Santana, BA, Brazil
5 Departamento de Astronomia, Universidade Federal do Rio Grande do Sul, Av.
Bento Gonçalves 9500, Porto Alegre, RS, Brazil
6 Instituto 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 helium abundance relative to hydrogen (He/H), which
relied on direct measurements of the electron temperature, has been derived in
the narrow line regions (NLRs) from a local sample of Seyfert 2 nuclei. In
view of this, optical emission line intensities
[$3000\><\lambda($Å$)\><\>7000$] of 65 local Seyfert 2 nuclei ($z\><\>0.2$),
taken from Sloan Digital Sky Survey Data Release 15 and additional compilation
from the literature, were considered. We used photoionization model grid to
derive an Ionization Correction Factor (ICF) for the neutral helium. The
application of this ICF indicates that the NLRs of Seyfert 2 present a neutral
helium fraction of $\sim 50$ per cent in relation to the total helium
abundance. We find that Seyfert 2 nuclei present helium abundance ranging from
0.60 to 2.50 times the solar value, while $\sim 85$ per cent of the sample
present over-solar abundance values. The derived (He/H)-(O/H) abundance
relation from the Seyfert 2 is stepper than that of star-forming regions (SFs)
and this difference could be due to excess of helium injected into the
Interstellar Medium by the winds of Wolf Rayet stars. From a regression to
zero metallicity, by using Seyfert 2 estimates combined with SFs estimates, we
obtained a primordial helium mass fraction $Y_{\rm p}=0.2441\pm 0.0037$, a
value in good agreement with the one inferred from the temperature
fluctuations of the cosmic microwave background by the Planck Collaboration,
i.e. $Y_{\rm p}^{Planck}=0.2471\pm 0.0003$.

###### keywords:

galaxies: abundances; galaxies: active; galaxies: evolution; galaxies:
formation; galaxies: ISM; galaxies: nuclei

††pubyear: 2022††pagerange: Chemical abundances in Seyfert galaxies– IX.
Helium abundance estimates–8

Released 2021 Apr 20

##  1 Introduction

The helium abundance determination in the gas phase of Active Galactic Nuclei
(AGNs) and gaseous nebulae (H ii regions, H ii galaxies, Planetary Nebulae) is
essential to the characterization of the primordial stellar nucleosynthesis
after the Big Bang as well as in the study of the Interstellar Medium (ISM)
enrichment of galaxies along the Hubble time.

The first helium and heavy element determinations which relied on the direct
measurements of the electron temperature ($T_{\rm e}$-method111For a review of
the $T_{\rm e}$-method see Peimbert et al. (2017) and Pérez-Montero (2017).)
in AGNs seems to have been carried out by Osterbrock & Miller (1975) for the
radio galaxy 3C 405 (Cygnus A). These authors calculated the He abundance
using the $\rm He^{+}$ and $\rm He^{2+}$ ionic abundances and derived a value
of $y\sim 0.10$, where

$y=N(\mathrm{He})/N(\mathrm{H})$ (1)

the ratio of the total number densities of helium to hydrogen. Numerical
simulations by Shields (1974), which were carried out to reproduce
observational data for the Seyfert galaxy 3C 120, inferred a value of $y=0.09$
(see also Koski 1978; Cruz-Gonzalez et al. 1991) for this object. Based on the
results above it seems that no abnormal helium abundance has been found in the
local Seyferts in comparison to the solar value, $y_{\odot}=0.10$ (Grevesse et
al., 2010), which is generally used as standard reference and scale factor
(see Nicholls et al. 2017). However, helium abundance determination in a
sample of AGNs is necessary to confirm this result.

On the other hand, quasars seem to exhibit a different and wider range of $y$
values. For instance, Bahcall & Oke (1971), by using helium and hydrogen
emission-lines observed in the optical and ultraviolet and assuming
$y=y^{+}+y^{2+}$, estimated $y$ in the range 0.003-0.2 for 14 quasars. Baldwin
(1975), assuming a similar approach by Bahcall & Oke (1971), derived the $y$
for a sample of 14 low-redshift quasars ($z\approx 0.2$) and found values from
$\sim 0.1$ to $\sim 0.3$ (see also, Williams 1971; Jura 1973). The helium
estimates by these authors were based on the $T_{\rm e}$-method, i.e. a
conventional and reliable method (Pilyugin, 2003; Toribio San Cipriano et al.,
2017).

Regarding gaseous nebulae, the first He abundance in this class of object was
obtained by Aller & Menzel (1945) for 7 Galactic Planetary Nebulae by using
optical emission lines measured by Wyse (1942) and, derived the mean abundance
value of the helium relative to hydrogen as $\sim 0.10$. Thereafter this
pioneering work, Mathis (1957) obtained the first helium abundance estimation
from H ii regions, in this case in the Orion Nebula, deriving values in the
range $\sim$0.09–$\sim$0.16, depending on the electron temperature assumed in
the calculations. Subsequent studies have been extended to extragalactic
objects and the first helium abundance determination was obtained by Johnson
(1959) for 30 Doradus (for other pioneering works see: Aller & Faulkner 1962;
Mathis 1962, 1965; Faulkner & Aller 1965; Aller et al. 1968; Peimbert &
Spinrad 1970). Thanks to the (relatively) recent spectroscopic surveys, as the
Sloan Digital Sky Survey (SDSS, York et al. 2000), it has become possible to
derive the helium abundance for thousands of star-forming regions (SFs; H ii
regions and star-forming galaxies) with a wide range of metallicity ($Z$, e.g.
Izotov et al. 2007, 2013; Kurichin et al. 2021), i.e. $7.7\>\la
12+\log[(N(\mathrm{O})/N(\mathrm{H})]\la\>8.7$ or $0.10\>\la(Z/{\rm
Z_{\odot}})\la\>1.0$, assuming the solar oxygen value
$\log[(N(\mathrm{O})/N(\mathrm{H})]_{\odot}=-3.31$ (Allende Prieto et al.,
2001), thus allowing the estimation of the primordial helium abundance.

The usual formalism (Peimbert & Torres-Peimbert, 1974, 1976) establishes that
the helium mass fraction, defined by

$Y=\frac{m_{\rm He}}{m_{\rm gas}},$ (2)

has a relation with the metallicity ($Z$), given by

$Y=\frac{4y(1-Z)}{1+4y}.$ (3)

The $Z$ can be traced by the $N(\mathrm{O})/N(\mathrm{H})$222For simplicity,
along the paper, this ratio is defined by O/H.  abundance in SFs (e.g. Yates
et al. 2012; Kewley et al. 2019) and in AGNs (e.g. Storchi-Bergmann et al.
1998; Dors 2021) because the oxygen is the most abundant metal in the Universe
and emission lines (e.g. [O ii]$\lambda$3726, $\lambda 3729$, [O
iii]$\lambda$5007) of its most abundant ions are ubiquitous measured in the
rest-frame optical regime (e.g. Berg et al. 2016). Along this work $Z$ and O/H
are assumed interchangeably. Regarding the $Z-\rm(O/H)$ relation, Peimbert et
al. (2007) pointed out that the oxygen by mass is in order of $(55\pm 10)$ per
cent of the $Z$ value. It is beyond the scope of the present work to discuss
the $Z-\rm(O/H)$ relation. In any case, Peimbert et al. (2007) reported that
the error in the $\mathrm{O}/Z$ ratio translates into an error slightly
smaller than 0.0001 in the determination of the primordial $Y$ value. We
assumed the fixed relation $Z=20\rm(O/H)$ proposed by Pagel et al. (1992) and
used recently by Kumari et al. (2021). Thus, Equation 3 is given by

$Y=\frac{4y[1-20({\rm O/H})]}{1+4y}.$ (4)

The primordial helium abundance $Y_{p}$ is derived by extrapolating the
$Y-(\rm O/H)$ relation to oxygen abundance (or $Z$) equal to zero (for a
review on uncertainties in $Y$ determinations see Peimbert et al. 2003, 2007;
Olive & Skillman 2004). Recently, Kurichin et al. (2021), by using
spectroscopic data of 100 SFs taken from the SDSS (York et al., 2000), derived
the primordial helium mass $Y_{p}=0.2462\pm 0.0022$, which this result is in
consonance with the value inferred from the temperature fluctuations of the
cosmic microwave background by the Planck Collaboration (2020), i.e.
$Y_{p}^{Planck}=0.2471\pm 0.0003$ (see also Izotov et al. 2014; Aver et al.
2015; Peimbert et al. 2016; Cooke & Fumagalli 2018; Fernández et al. 2019;
Valerdi et al. 2019, 2021a; Hsyu et al. 2020).

The extrapolation of the $Y-(\rm O/H)$ relation to derive $Y_{p}$ is very
dependent on the extreme oxygen abundance values, i.e. on the lowest and
highest values derived for line emitter objects. Along decades, efforts have
been made to derive He and O abundances in Extremely metal-poor galaxies
(XMPs), in order to obtain $Y$ values close to $Y_{p}$ (e.g. Kunth & Sargent
1983; Skillman 1991; Skillman et al. 1994; Garnett & Kennicutt 1994; Olive et
al. 1997; Izotov & Thuan 1998; Peimbert et al. 2000; Izotov et al. 1999, 2007,
2009; Izotov et al. 2014; Annibali et al. 2019; Valerdi et al. 2021b; Aver et
al. 2021). However, despite efforts have been done to achieve direct oxygen
estimation in SFs in the high abundance regime [$\rm 12+\log(O/H)\>\ga\>8.7$
or ($Z/\rm Z_{\odot})\>\ga\>1.0]$ (e.g., see Kinkel & Rosa 1994; Bresolin et
al. 2004; Garnett et al. 2004; Castellanos et al. 2002; Liang et al. 2007;
Andrews & Martini 2013; Brown et al. 2016; Berg et al. 2020), helium abundance
determinations in these objects are barely found in the literature.

The inclusion of objects with high metallicity, for which direct electron
temperatures as well as $\rm He^{+}$ and $\rm He^{2+}$ abundances estimates
are possible, will result in a significant improvement in the determination of
the $Y-\rm O/H$ relation and, consequently, in the estimation of $Y_{p}$. In
this context, AGNs are ideal objects because they have higher gas ionization
degree (e.g. Richardson et al. 2014; Pérez-Díaz et al. 2021) and higher $Z$
(e.g. Storchi-Bergmann et al. 1998; Groves et al. 2006; Revalski et al. 2018a;
Revalski et al. 2021; Dors et al. 2020a) in comparison with H ii regions.
These physical features make it possible to precisely measure the total helium
abundance, since He ii lines are stronger in AGN spectra than those in SFs
and, they allow to constraint the $Y$ value in the high metallicity regime.

Large spectroscopic surveys, such as Sloan Digital Sky Survey (SDSS, York et
al. 2000), CALIFA (Sánchez et al., 2012), MaNGA (Bundy et al., 2015) and CHAOS
(Berg et al., 2015) have made thousands of emission lines from SFs and AGNs
available and these data have revolutionized our understanding of chemical
evolution of galaxies (see, for instance, Gómez et al. 2003; Glazebrook et al.
2003; Brinchmann et al. 2004; Izotov et al. 2006; Asari et al. 2007; Kewley &
Ellison 2008; Pilyugin et al. 2012; Sánchez et al. 2017; Ellison et al. 2018;
Yates et al. 2020; Berg et al. 2020, among others). However, majority of the
data from these surveys have been used to derive abundances mainly in SFs,
with AGNs still being understudied. In fact, most of the AGN studies have
relied on large surveys just to address the oxygen abundance and/or physical
properties (e.g., ionization degree, electron temperature, electron density)
of these objects (e.g. Groves et al. 2006; Zhang et al. 2008; Vaona et al.
2012; Ludwig et al. 2012; Zhang et al. 2013; Richardson et al. 2014; Coil et
al. 2015; Feltre et al. 2016; Kawasaki et al. 2017; Carvalho et al. 2020; Dors
et al. 2020a; Dors 2021; Agostino et al. 2021). The abundances of other
elements beyond the oxygen are poorly known in AGNs, in particular, the local
Seyfert 2, for which large amount of spectroscopic data are available in the
literature.

Dors et al. (2017), who built detailed photoionization models to reproduce
optical narrow emission line ratio intensities of a sample of 44 Seyfert 2
nuclei, presented the first quantitative estimations of the nitrogen abundance
for this class of object (see also Pérez-Montero et al. 2019; Ji et al. 2020;
Flury & Moran 2020; Dors et al. 2021). Recently, Dors et al. (2020b) proposed
a new methodology of the $T_{\rm e}$-method for AGNs which produce reliable
O/H abundances, slightly lower ($\approx 0.2$ dex) than those derived from
detailed photoionization models. Armah et al. (2021) and Monteiro & Dors
(2021), motivated by this new methodology and by the availability of
spectroscopic data in the literature, developed Ionization Correction Factors
(ICFs) as well as electron temperature relations based on photoionization
model results and, for the first time, derived the neon and argon abundances
in a sample of Seyfert 2 nuclei, respectively.

As a further study, in the present work, we apply the $T_{\rm e}$-method to a
combined spectroscopy data taken from the SDSS and additional data from
distinct authors with the goal to derive the $y$ values in a sample of local
Seyfert 2 galaxies. These estimates allow access to the helium abundance in a
higher metallicity regime than that in SFs and produce important constraints
to primordial helium abundance as well as to the studies of stellar
nucleosyntesis. The present study is organized as follows. In Sections 2 and 3
the observational data and the methodology used to estimate the helium and
oxygen abundances are presented, respectively. The results and discussion are
presented in Sect. 4. Finally, the conclusion of the outcome is given in Sect.
5.

##  2 Observational data

###  2.1 Seyfert 2 nuclei

In the present work we studied a subsample of the sample presented by Dors et
al. (2020a). These authors used the measurements of the SDSS-DR7 made
available by MPA/JHU333https://wwwmpa.mpa-garching.mpg.de/SDSS/DR7/ group to
obtain a sample of Seyfert 2 nuclei. Initially, by using the MPA/JHU data,
Dors et al. (2020a) carried out a cross-correlation between the galaxy
identification provided by the SDSS-DR7 and by the
NED/IPAC444ned.ipac.caltech.edu and obtained the classification of each object
in Seyfert 1 and 2 nuclei. After applying the criteria to separate SF and AGN
objects proposed by Kewley et al. (2001, 2006) and Pérez-Montero et al.
(2013), which consider a set of emission line intensity ratios in diagnostic
diagrams (Baldwin et al., 1981), 463 Seyfert 2 AGNs ($z\>\la 0.4$) with
reliable optical emission lines in the optical range
$3000\>\la\>\lambda(\textup{\AA})\>\la\>7500$ were selected.

The data from the MPA/JHU group do not contain measurements for the He
ii$\lambda$4686Å. Therefore, we downloaded from SDSS-DR15
database555https://dr15.sdss.org/optical/spectrum/search the spectra of the
463 objects selected by Dors et al. (2020a) in order to obtain a sub-sample of
Seyfert 2 nuclei in which it is possible to determine the parameters necessary
to calculate the He and O abundances through the $T_{\rm e}$-method. Firstly,
in each spectrum, we performed the extinction correction using the Cardelli et
al. (1989) law assuming the parameterized extinction coefficient $R_{V}$ =
3.1, a standard value for the diffuse interstellar medium. The Galactic
interstellar extinction values provided by Schlegel et al. (1998) and
calibrated by Schlafly & Finkbeiner (2011) obtained by using the VOTool for
interstellar extinction called GALExtin666http://www.galextin.org (Amôres et
al., 2021) were also assumed. We shifted the spectra for the rest frame
wavelength using the redsfhits available for each object and binned them with
bin size equal to 1Å.

Figure 1: Optical spectrum of one of the Seyfert 2 nucleus in our sample (see
Sect. 2.1) taken from SDSS DR15 and represented in black colour. The fitting
to the emission-line profiles using the IFSCUBE code (Ruschel-Dutra & de
Oliveira, 2020) is represented in red colour. The measured emission lines and
corresponding wavelength are indicated. Boxes show a zoom in regions of some
weak lines, as indicated.

The stellar population continuum was subtracted from the spectra to obtain the
pure nebular spectra using the stellar population synthesis  STARLIGHT code
(Cid Fernandes et al., 2005; Mateus et al., 2006; Asari et al., 2007). This
code fits the observed spectrum of a galaxy using a combination of Simple
Stellar Populations (SSPs), in different proportions and excluding the
emission lines. We used a basis of 45 synthetic SSP spectra with three
metallicities $Z$ = 0.004, 0.02 ($\mathrm{Z_{\odot}}$), and 0.05, assuming 15
ages ranging from 1 Myr to 13 Gyr, taken from the evolutionary synthesis
models of Bruzual & Charlot (2003). Prior to the fitting the synthetic spectra
to the observational ones, we convoluted the SSP stellar spectra adopting a
Gaussian function to achieve the same spectral resolution of the observational
data. A detailed description of the SSP spectra fitting to spectroscopic
observational data is given by Krabbe et al. (2011, 2017).

After the pure nebular spectra for the sample were obtained by subtracting the
contribution of the stellar component from the observed spectra, the emission-
lines were fitted using the publicly available ifscube package (Ruschel-Dutra
& de Oliveira, 2020; Ruschel-Dutra et al., 2021). Each emission line was
fitted by a single Gaussian function and the kinematics (line width and
centroid velocity) of lines from the same parent ion was kept tied. We also
included in the fit a third order polynomial to account for any residual
continuum emission. The uncertainties on the fluxes were obtained by
performing 100 iterations of Monte Carlo simulations of the emission-line fits
as the standard deviation of the fluxes obtained from these simulations. The
fluxes were corrected for extinction following the procedure described by
Riffel et al. (2021b), using the $\rm(H\alpha/H\beta)$ line ratio to estimate
the visual extinction, assuming the theoretical value for the
$\rm(H\alpha/H\beta)=2.86$ proposed by Hummer & Storey (1987) at a temperature
of 10 000 K and an electron density of 100 cm-3. A detailed analysis
justifying the assumption for considering $\rm(H\alpha/H\beta)=2.86$ for
reddening correction in AGNs was presented by Armah et al. (2021). We found
values of the extinction coefficient $A_{v}$ ranging from 0.02 to 0.4 mag.

It is clear hitherto that the most widely used method for estimating the dust
content is based on the relative strengths of the lower Balmer H I lines i.e.
H$\alpha$/H$\beta$. When using the gas emission lines as a dust tracer, the
canonical assumption is that the gas emission comes from the same position as
the emission from the ionization source, which is usually not the case,
because the gas in a spiral galaxy for instance is contained in a plane.
Generally, little is known about the nature and real distribution of dust in
AGNs (e.g. Heard & Gaskell, 2016; Baron et al., 2016; Gaskell, 2017, and
references therein). However, neglecting these uncertainties at first order
and considering the fact that H$\alpha$ and H$\beta$ are the strongest
recombination lines of hydrogen in the optical spectrum, the reddening effect
can be written on the reliance of the ratio H$\alpha$/H$\beta$. Assigning a
single extinction value is just a rough first approximation, therefore,
irrespective of the dereddening method used, it is good practice to verify
that the H$\alpha$/H$\beta$, H$\gamma$/H$\beta$ and H$\delta$/H$\beta$
emission line ratios have the expected values in comparison with the
theoretical Case B ratios of 2.86 or 3.1, 0.468 and 0.259 (Halpern, 1982;
Halpern & Steiner, 1983; Hummer & Storey, 1987; Osterbrock & Ferland, 2006),
respectively. On the other hand, H7 and H8 can not be considered in reddening
correction because they are usually blended with other emission lines.
Additionally, the signal-to-noise ratio for lines such as H9 and H10 is often
too low to allow for their detection with high precision in order to constrain
the reddening and underlying stellar absorption. Hence, as part of the
emission-line flux processing, the underlying continuum and absorption-line
spectra were fitted and eliminated, removing the effects of stellar Balmer
absorption on the H$\alpha$ and H$\beta$ (e.g. Moustakas & Kennicutt, 2006).
Finally, the amount of interstellar extinction obtained using
H$\alpha$/H$\beta$ is relatively in agreement with the amount of extinction
determined considering other line ratios, i.e. [S ii] $\lambda 4071$/[S ii]
$\lambda 10320$ (Wampler, 1971; Shields & Oke, 1975; Koski, 1978) or He ii
$\lambda 3203$/He ii $\lambda 4686$ (Shuder & Osterbrock, 1981).

From the resulting sample, we selected only the objects that present the
emission-lines [O ii]$\lambda 3726,\lambda 3729$ (hereafter [O ii]$\lambda
3727$), [O iii]$\lambda 4363$, He ii$\lambda 4686$, H$\beta$, [O iii]$\lambda
5007$, He i$\lambda 5876$, H$\alpha$, and [S ii]$\lambda 6716,\lambda 6731$
with a signal/noise ratio (S/N) higher than 2.0. The final sample resulted in
9 objects with redshift $z\>\la\>0.2$. In Figure 1, an example of a pure
Seyfert 2 nebular spectrum (in black) and the fitting (in red) produced by the
ifscube software (Ruschel-Dutra & de Oliveira, 2020) are shown.

In addition to the SDSS data, we compiled from the literature fluxes of
emission-lines from Seyfert 2 nuclei obtained by different authors. We applied
the same selection criteria used for the SDSS data to these additional
selected objects. This sample consists of 94 Seyfert 2 nuclei whose emission-
line intensities were reddening corrected by the authors from which the data
were taken. However, in the cases where the reddening correction was not
performed in the original works, the same procedure applied to the SDSS data
was considered. Since several measurements for the emission lines compiled
from the literature do not have their uncertainties listed in the original
papers where the data were compiled, we adopted a typical error of $10$ per
cent for strong emission-lines (e.g. [O iii]$\lambda$5007) and $20$ per cent
for weak emission lines (i.e. [O iii]$\lambda$4363, He ii$\lambda 4686$ and He
i$\lambda 5876$), as derived, for instance, by Kraemer et al. (1994).

Finally, we applied the criterion proposed by Kewley et al. (2001),

$\rm log([O\>III]\lambda 5007/H\beta)\>>\>\frac{0.61}{log([N\>II]\lambda
6584/H\alpha)-0.47}+1.19$ (5)

to separate SF and AGN objects. Additionally, the criterion proposed by Cid
Fernandes et al. (2010) to separate AGN-like and Low-ionization nuclear
emission-line region (LINER) objects, given by

$\rm log([O\>III]\lambda 5007/H\beta)\>>\>0.47+log([N\>II]\lambda
6584/H\alpha)\times 1.10,$ (6)

was also considered.

The final sample consists of 65 Seyfert 2 with redshift $z\>\la 0.2$ whose
reddening-correction line intensities (in relation to H$\beta=1.0$) are listed
in Table 2 in the Appendix. In Fig. 2, a diagnostic diagram log([O
iii]$\lambda 5007$/H$\beta$) versus log([N ii]$\lambda 6584$/H$\beta$), the
observational data for the objects as well as the curve representing the
criteria above are shown. It can be seen that the objects of our sample cover
a large range of ionization degree and metallicity, hence a wide range of [O
iii]/H$\beta$ and [N ii]/H$\alpha$ line ratio intensities are noted (e.g.
Groves et al. 2006; Feltre et al. 2016; Carvalho et al. 2020).

Figure 2: Diagnostic diagram log([O iii]$\lambda 5007$/H$\beta$]) versus
log([N ii]$\lambda 6584$/H$\alpha$]

). Blue points represent Seyfert 2 nuclei of our sample (see Sect. 2.1) while
black points are for SFs (see Sect. 2.2). Solid and dashed curves represent
the criteria proposed by Kewley et al. (2001) and Kauffmann et al. (2003),
given by Equations 5 and 7, respectively, to separate SF and AGN objects. The
red line represents the criterion proposed by Cid Fernandes et al. (2010) to
separate AGN-like and Low-ionization nuclear emission-line region (LINER)
objects, given by Eq. 6.

Figure 3: Bottom panel: Comparison between the [O ii]$\lambda$3727/H$\beta$
intensity line ratio, for part of the observational sample (AGNs and SFs),
whose reddening correction were carried out following the methodology
described in Sect. 2 and performed by the authors from which the data were
compiled. A one-to-one correlation is plotted as a solid line. Top panel:
Difference (D=y-x) between the intensities. Solid line represent the null
difference while dashed lines are the uncertainty of 0.1 dex in the line ratio
measurements. The mean difference ($\rm<D>$) in the measurements is indicated.

Dors et al. (2015) and Castro et al. (2017) presented a complete discussion on
the use of heterogeneous sample and its possible implications on abundance
estimates. Effects of aperture, electron density variation along the AGN
radius, X-Ray dominated regions, shock, and electron temperature fluctuations
in abundance determinations have also been presented by Dors et al. (2020a,
2021) and these are not repeated here. Basically, the effects of these
parameters on abundance estimates produce uncertainties of $\sim 0.1$ dex,
i.e. in order of those derived by applying the $T_{\rm e}$-method (e.g. Izotov
& Thuan 2008) and strong-line methods (e.g. Storchi-Bergmann et al. 1998).
Since it is not possible to estimate, for each AGN of our sample, the
aforementioned uncertainty is not considered in the resulting abundance
values.

We present a comparison between the logarithm of the [O
ii]$\lambda$3727/H$\beta$ intensity line ratio by adopting our extinction
correction procedure with that assumed by the authors from which the data were
compiled. This comparison was possible only for 46 objects (19 AGNs and 27
SFs) due to the fact that most of the original works present only the
reddening corrected intensity lines. In Fig. 3, bottom panel, this comparison
is shown where there exist a good agreement between them. In top panel of Fig.
3 the difference (D=y-x) is presented, where one can see the uncertainty due
the distinct approaches to extinction correction is in order of that produced
by the error measurements ($\sim 0.1$ dex, e.g. Kennicutt et al. 2003), with
the mean difference ($<\rm D>=0.04$ dex) being about null. Thus, distinct
methodologies employed for the extinction correction of intensity line ratios
introduce a minimal uncertainty in our abundance estimates.

###  2.2 Star forming regions

We compiled emission-line intensities of SFs from the literature with the goal
of comparing their estimates with our AGN results. We applied the same
criteria above in the selection of SFs, i.e. we selected only objects whose
emission-lines [O ii]$\lambda 3727$, [O iii]$\lambda 4363$, He ii$\lambda
4686$, H$\beta$, [O iii]$\lambda 5007$, He i$\lambda 5876$, H$\alpha$, and [S
ii]$\lambda 6716,\lambda 6731$ were measured. The measurements of these lines
make it possible to calculate the He and O abundances by using the $T_{\rm
e}$-method following a similar methodology applied to the Seyfert 2 sample.
Furthermore, we considered only the objects which satisfy the empirical
criterion proposed by Kauffmann et al. (2003)

$\rm log([O\>III]\lambda 5007/H\beta)\><\>\frac{0.61}{log([N\>II]\lambda
6584/H\alpha)-0.05}+1.3.$ (7)

In Table 4, the emission line intensities (in relation to H$\beta$=1) and the
original works from which data were taken are listed. The data consist of
reddening corrected emission lines of 85 H ii regions and star-forming
galaxies with redshift $z\><\>0.2$. In Fig. 2, the SF sample is represented by
black points, where we can see the very known sequence (e.g. Baldwin et al.
1981; Kauffmann et al. 2003) formed by this object class.

In Fig. 4, we plotted the logarithm of [O iii]$\lambda$5007/[O
ii]$\lambda$3727 versus He ii$\lambda$4686/He i$\lambda$5876 line ratios for
the AGN sample (blue points) and for the SF sample (black points). Despite the
scattering produced mainly for the SF data, it can be seen the expected result
that; a clear correlation is derived (see also, for instance, Deharveng et al.
2000) hence both line ratios are dependent on the ionization degree of the
gas. Moreover, a distinction between Seyfert and SFs can be observed in Fig. 4
due to the high excitation of Seyfert in comparison with SFs. In Fig. 4, we
observe a clear separation criterion, where objects with

$\log\left(\frac{\text{He\,{ii}}\lambda 4686}{\text{He\,{i}}\lambda
5876}\right)\>\ga\>-0.4$ (8)

are classified as Seyfert in this diagram, otherwise, as SF (see also Nakajima
& Maiolino 2022).

Figure 4: Logarithm of [O iii]$\lambda$5007/[O ii]$\lambda$3727 versus He
ii$\lambda$4686/He i$\lambda$5876\. Blue and black points represent Seyfert 2
nuclei (see Sect. 2.1) and SFs (see Sect. 2.2) of our samples, respectively,
as indicated. Red line indicates the separation criterion between Seyfert
nuclei and SFs given by Eq. 8.

##  3 Abundance determination

We calculated helium and oxygen abundances by using the observational data
sample of Seyfert 2 nuclei and SFs described in Sect. 2. Therefore, the [O
iii]$(1.33\times\lambda 5007)/\lambda 4363$ and [S ii]$\lambda 6716/\lambda
6731$ line ratios were used to derive electron temperature and density,
respectively, thus obtaining the ionic abundances of these elements.
Thereafter, we used photoionization models built with the Cloudy code (Ferland
et al., 2013) to produce a correction for the presence of $\rm He^{0}$ in the
calculation of the total He. In what follows, a description of the methodology
employed is presented for both object classes.

Table 1: Atomic dataset used for recombination and collisionally excited lines of selected element ions. | Transition probabilities |  |
---|---|---|---
Ion | and energy levels | Collisional strengths | Recombination coefficients
He+ | Porter et al. (2012) | — | Porter et al. (2012)
He2+ | Storey & Hummer (1995) | — | Storey & Hummer (1995)
O+ | Wiese et al. (1996) | Kisielius et al. (2009) | —
O2+ |  Froese Fischer & Tachiev (2004), Storey & Zeippen (2000) | Storey et al. (2014) | —

###  3.1 Seyfert

####  3.1.1 Temperature and density

To determine the abundance of an element it is necessary to estimate a
representative value for the electron temperature and density of the gas phase
occupied by the ions of this element.

Since the elements of interest are the He and O, which are in most part once
and twice ionized, following Valerdi et al. (2021a), we adopted the two zone
models, where the temperature for the high ionization zone, defined as $T_{\rm
high}$ is derived from the relation between this parameter and the [O
iii]($1.33\times\lambda 5007$)/$\lambda 4363$ line ratio, where we assumed, as
usual, [O iii]$(\lambda 4959)/(\lambda 5007)$ to be 0.33777For a detailed
discussion on the value of this ratio see Storey & Zeippen (2000). (Rosa,
1985). To calculate $T_{\rm high}$, and the electron density ($N_{\rm e}$)
from the $[\text{S\,{ii}}]\lambda 6716/\lambda 6731$ line ratio, we used the
version 1.1.13 of PyNeb code (Luridiana et al., 2015), which permits an
interactive procedure in the derivation of these parameters. We assumed the
atomic data of recombination and collisionally excited lines listed in Table 1
for the temperature, density and ionic abundance calculations.

For almost all the data in our sample it was not possible to obtain the direct
determination of $T_{\rm low}$ due to the lack of the [N ii]$\lambda$5755 and
[O ii]$\lambda$7319, $\lambda$7330 auroral line measurements. Thus, for
consistence, we used the theoretical relation between $T_{\rm low}$-$T_{\rm
high}$ proposed by Dors et al. (2020b), obtained through a grid of
photoionzation models simulating Narrow Line Regions (NLRs) of AGNs built with
the Cloudy code (Ferland et al., 2013) by Carvalho et al. (2020), given by

$t_{\mathrm{low}}=({\rm a}\times t_{\mathrm{high}}^{3})+({\rm b}\times
t_{\mathrm{high}}^{2})+({\rm c}\times t_{\mathrm{high}})+{\rm d},$ (9)

where $\rm a=0.17$, $\rm b=-1.07$, $\rm c=2.07$ and $\rm d=-0.33$, while
$t_{\mathrm{low}}$ and $t_{\mathrm{high}}$ represent $T_{\rm low}$ and $T_{\rm
high}$, respectively, in units of $10^{4}$ K. These temperatures predicted by
the models correspond to the mean temperature for $\rm O^{\rm+}$ ($T_{\rm
low}$) and $\rm O^{2+}$ ($T_{\rm high}$) over the nebular AGN radius times the
electron density.

In Riffel et al. (2021a), the relation represented by the Eq. 9 was compared
with electron temperature values derived from observational auroral emission
lines for a sample of 12 local AGNs, and a good agreement was found between
them. However, as pointed out by these authors, some cautions must be taken
into account in the use of Eq. 9 for AGNs with strong outflowing gas.

####  3.1.2 Helium abundance

The total helium abundance in relation to hydrogen
$y=N(\mathrm{He})/N(\mathrm{H})$ was considered to be

$y=y^{0}+y^{+}+y^{2+},$ (10)

where $y^{0}=N(\mathrm{He^{0}})/N(\mathrm{H^{+}+H^{0}})$,
$y^{+}=N(\mathrm{He^{+}})/N(\mathrm{H^{+}})$ and
$y^{2+}=N(\mathrm{He^{2+}})/N(\mathrm{H^{+}})$. The ionic abundance ratio
$y^{+}$ and $y^{2+}$ were derived from the He i$\lambda$5876/H$\beta$ and He
ii$\lambda$4696/H$\beta$ intensity line ratios, respectively. We used the two-
zone ionization model (e.g. Valerdi et al. 2019), which $T_{\rm low}$ (from
Eq. 9) and $T_{\rm high}$ (from direct estimation) were assumed in the $y^{+}$
and $y^{2+}$ calculation, respectively. Recently, Berg et al. (2021) proposed
a more detailed ionization model for H ii regions, i.e. the 4-zones model,
where the He+ is located in the low, intermediate, and high zones, i.e. in the
zones occupied for the $\rm O^{+}$ and $\rm O^{2+}$ ions. Thus, in principle,
$T_{\rm low}$ can be assumed as a representative temperature value for the
region occupied by the He+. It is worth noting that this is not a conventional
approach, therefore some previous studies assume $T_{\rm high}$ in the He+
abundance calculations. Concerning He2+, Berg et al. (2021) showed the it is
located mainly in the very-high-ionization zone. To derive the temperature of
the very-high-ionization zone the measurement of the [Ne iii]$(\lambda
3342/\lambda 3868)$ ratio is required, which is not available in our data
sample. Therefore, we assumed $T_{\rm high}$ in the abundance calculation of
this ion. Both ionic abundances were computed using the PyNeb code (Luridiana
et al., 2015). We consider the presence of $\rm He^{0}$ in the neutral and
ionized gas since this is expected in low ionization objects (Peña, 1986;
Dinerstein & Shields, 1986).

The fraction of $y^{0}$ in H ii regions and Planetary Nebulae has been
estimated to be in order of $\sim 3$ per cent of the total helium (e.g. Peña
1986; Peimbert et al. 1992) or even larger values could be predicted (e.g.
Deharveng et al. 2000). In fact, Méndez-Delgado et al. (2022) found that only
9/42 Galactic H ii regions have negligible contributions of $y^{0}$ (see also
Delgado-Inglada et al. 2014). Since AGNs present a large amount of molecular
gas (e.g., Rodríguez-Ardila et al. 2004; Davies et al. 2005; Rodríguez-Ardila
et al. 2005; Mazzalay et al. 2013; Riffel et al. 2013, 2018, 2021c;
Ramakrishnan et al. 2019; Riffel et al. 2019; Jarvis et al. 2020; Alonso-
Herrero et al. 2020) and have similar ionization parameter ($U$) other than
SFs (Pérez-Montero et al., 2019), a higher abundance of neutral and molecular
gas are expected in AGNs as compared to H ii regions, which favors the
presence of larger contribution of $y^{0}$ in the total helium abundance. In
fact, radio observations have shown the existence of a gas neutral reservoir
in the central parts of galaxies containing AGNs (e.g. Dressel et al. 1982;
Hutchings et al. 1987; Bertram et al. 2007; Ho et al. 2008; Bradford et al.
2018; Ellison et al. 2019; Combes et al. 2019) which can coexist with the
ionized gas. García-Burillo et al. (2014), who used the Atacama Large
Millimeter Array (ALMA) to map the emission of dense molecular gas in the
Seyfert 2 NGC 1068, showed an overlay of the CO(3–2) (a tracer of $\rm H_{2}$)
intensity contours on the Pa$\alpha$ emission obtained with the Hubble Space
Telescope. In addition, recently, do Nascimento et al. (2022) derived the O/H
abundance in NLR of 108 Seyfert nuclei and found that these values are lower
(by 0.16 to 0.30 dex) than those inferred by the radial gradients along their
galaxy discs and those from a matched control sample of no active galaxies.
This discrepancy could be due to the accretion of a metal-poor gas to the AGN
that feeds the nuclear supermassive black hole (SMBH), coming from the neutral
reservoir.

To estimate the abundance of $\rm y^{0}$, we used a grid of photoionization
models similar to that of Carvalho et al. (2020), built with the Cloudy code
version 17.00 (Ferland et al., 2013). These models were also used to derive
neon and argon ICFs by Armah et al. (2021) and Monteiro & Dors (2021),
respectively, considering a wide range of nebular parameters:

  * •

Metallicity: ($Z/\rm Z_{\odot})=3.0,2.0,1.0,0.75,0.5$, and $0.2$.

  * •

Electron density: $N_{\rm e}\>\rm(cm^{-3})=3000,1500,500,100$.

  * •

Ionization parameter ($U$): $\log U$ ranging from $-1.5$ to $-3.5$, with step
of 0.5 dex.

  * •

Spectra Electron Distribution (SED): The SED is parametrized by the continuum
between 2 keV and 2500Å (Tananbaum et al., 1979) and it is described by a
power law with a spectral index $\alpha_{ox}$=$-$0.8, $-$1.1 and $-1.4$.

The outermost nebular radius was considered by Carvalho et al. (2020) to be
the one where the electron temperature reaches 4000 K (the default value of
the Cloudy code), which produces a region with hydrogen almost completely
ionized. Since we are also interested in the neutral region, we rerun the grid
of models by Carvalho et al. (2020) but using the version 17.02 of the Cloudy
code (Ferland et al., 2013) and assuming the outermost radius where the
electron temperature reaches 1000 K; as was done by Dors et al. (2012), who
analysed the dominant excitation mechanism of [Fe ii] and $\rm H_{2}$ emission
lines in AGNs. These new models allow us to consider a larger part of the
neutral gas instead of stopping the calculations at outermost radius of the
modelled nebula where the temperature falls below 4000 K. We added cosmic-ray
background emission as a second ionizing source with a value of $\rm H_{2}$
ionization rate of $10^{-15}\>\rm s^{-1}$, which is about the same rate found
by McCall et al. (2003) for a Galactic line of sight. The cosmic-ray
background emission has little influence on the formation of emission lines
located in the ionized gas and/or in the ionization of elements with
ionization potential higher than the hydrogen one. In the models the abundance
of each ion was considered as the average over the nebular radius times the
electron density. For a detailed description of the photoionization models see
Carvalho et al. (2020).

Based on the model results, we assumed the ICF for the $y^{0}$ to be

${\mathrm{ICF}(y^{0})}=\frac{y}{y^{+}+y^{2+}}.$ (11)

In Fig. 5, the photoionization model predictions for $\mathrm{ICF}(y^{0})$
versus $\mathrm{x}=y^{+}/y^{2+}$ are shown, where the results are
discriminated according to distinct nebular parameters, as indicated. Any
dependence between the $\mathrm{ICF}(y^{0})$-x relation and $N_{\rm e}$ and
$Z$ can be seen. However, a clear dependence of this relation with the
ionization parameter $U$ and $\alpha_{ox}$ is noted, in the sense that a
stepper $\mathrm{ICF}(y^{0})$-x relation is derived for higher $U$ and
$\alpha_{ox}$ values. The dependence of this relation on these parameters is
due to the increase in the gas ionization degree, i.e. driven by $U$ and the
hardness of the SED ($\alpha_{ox}$), produces lower values of x.

Estimations of $\alpha_{ox}$ require observations of integrated nuclear flux
at optical and UV wavelengths (e.g. Worrall et al. 1987; Ho 1999; Miller et
al. 2011; Zhu et al. 2019; Zhu et al. 2021), and values of this parameter are
often times unavailable for AGNs. Moreover, detailed photoionization models by
Dors et al. (2017) and Bayesian-like approach by Pérez-Montero et al. (2019)
have predicted $\alpha_{ox}$ to be higher than $-1.2$ for Seyfert 2 nuclei.
Conversely, observational estimations of $\alpha_{ox}$ by Miller et al. (2011)
indicate that most AGNs have $\alpha_{ox}$ in the order of $-$1.4 and even
lower values ($\sim-2.0$) are derived for these objects. This discrepancy is
probably due to an extra physical process is missing in the models, probably
shocks (e.g. Contini 2019). Therefore, as a result of few AGNs estimations of
$\alpha_{ox}$ in comparison to those with emission-line measurements, and also
due to the existence of the discrepancy between model predictions and
observational estimations of $\alpha_{ox}$, this parameter was not directly
taken into account in the expression for the helium ICF derived here. In any
case, the gas ionization degree, traced by $U$, probably has a direct relation
with $\alpha_{ox}$.

We derive a bi-parametric calibration $\mathrm{ICF}(y^{0})=\mathrm{f(x,}\log
U)$ shown in Fig. 6 and given by

$\begin{split}\mathrm{z=[(0.14\pm 0.01)\times{\rm ln(x)}\times w]+[(0.09\pm
0.01)\times w{{}^{2}}]}\\\ +\mathrm{[(0.03\pm 0.01)\times\rm x]+[(0.18\pm
0.07)\times\rm w]+[(1.71\pm 0.08)]},\end{split}$ (12)

where $\mathrm{z=ICF}(y^{0})$, $\mathrm{x}=y^{+}/y^{2+}$ and $\mathrm{w}=\log
U$. The ionization parameter can be obtained using the semi-empirical
calibration proposed by Carvalho et al. (2020)

$\log U=(0.57\pm 0.01\>r^{2})+(1.38\pm 0.01\>r)-(3.14\pm 0.01),$ (13)

where $r$=log([O iii]$\lambda$5007/[O ii]$\lambda$3727). This calibration was
obtained through a comparison of observational optical narrow emission line
ratios of a sample of local Seyfert 2 nuclei with those predicted by
photoionization models. An expression for deriving the helium ICF taking into
account the ionization parameter but for H ii regions was also derived by
Sauer & Jedamzik (2002), by using a grid of photoionization models.

Figure 5: Photoionization model predictions (see Sect 3.1.2) for
$\mathrm{ICF}(y^{0})$ versus $y^{+}/y^{2+}$. In each plot, model results
assuming distinct nebular parameters are shown by different colours, as
indicated. $\mathrm{ICF}(y^{0})$ is defined as in Eq. 11. Figure 6: Bi-
parametric calibration among the $\mathrm{ICF}(y^{0})$,
$\mathrm{x}=y^{+}/y^{2+}$ and logarithm of the ionization parameter ($\log
U$). Points represent the photoionization model results (see Sect 3.1.2),
$\mathrm{ICF}(y^{0})$ is defined by Eq. 11. The surface is given by Eq. 12.

####  3.1.3 Oxygen abundance

The total oxygen abundance in relation to hydrogen was derived assuming

$\frac{N(\mathrm{O})}{N(\mathrm{H})}=\mathrm{ICF(O)}\>\times\>\left[\frac{N(\mathrm{O^{2+}})}{N(\mathrm{H^{+}})}+\frac{N(\mathrm{O^{+}})}{N(\mathrm{H^{+}})}\right],$
(14)

where ICF(O) is the Ionization Correction Factor for the oxygen which takes
into account the contribution of unobserved oxygen ions (e.g. $\rm O^{3+})$.
In fact, several studies have found a strong intensity of the [O
iv]$\lambda$25.89$\mu$m emission line in AGN spectra (e.g. Diamond-Stanic &
Rieke 2012; Fernández-Ontiveros et al. 2016), indicating a non-negligible
fraction of the $\rm O^{3+}$ abundance.

To calculate the ICF(O) the empirical expression proposed by Torres-Peimbert &
Peimbert (1977):

${\rm ICF(O)}=\frac{y^{+}+y^{2+}}{y^{+}},$ (15)

used in SF (e.g. Izotov et al. 2006; Valerdi et al. 2021a) and AGN (e.g. Flury
& Moran 2020; Dors et al. 2020b) abundances studies, was considered. To
calculate the ICF(O) for each object of the sample, we consider our helium
abundance results derived using the PyNeb code (Luridiana et al., 2015).

In Table 6 presented in the Appendix, we show the oxygen (ionic and total) and
helium abundances. To estimate the abundance uncertainties, due to few objects
present observational error in the line measurements, for all objects of the
AGN sample, we use a Monte Carlo simulations. For each diagnostic line, we
generate 1000 random values assuming a Gaussian distribution with a standard
deviation equal to the associated uncertainty of the line intensity involved
in the diagnostic.

###  3.2 Star-forming regions

To determine the He and O abundances for the SFs, we adopted a similar
procedure considered for the Seyfert sample. The ionic helium abundances were
also computed using the PyNeb code (Luridiana et al., 2015) which, $y^{2+}$
and $\mathrm{O^{2+}}$ were derived assuming the $T_{\rm high}$ and $N_{\rm
e}$, calculated for each object through the [O iii]($1.33\times\lambda
5007$)/$\lambda 4363$ and $[\text{S\,{ii}}]\lambda 6716/\lambda 6731$ line
ratios, respectively.

The $y^{+}$ and $\mathrm{O^{+}}$ were calculated assuming the $T_{\rm low}$
derived from the theoretical relation

$t_{\mathrm{low}}^{-1}\,=\,0.693\,t_{\mathrm{high}}^{-1}+0.281$ (16)

proposed by Pérez-Montero & Díaz (2003). We assume $T_{\rm low}\equiv T_{\rm
e}(\text{N\,{ii}})\approx T_{\rm e}(\text{O\,{ii}})$.

The total oxygen abundance is obtained as described previously:

$\mathrm{\frac{O}{H}=ICF(O)\times\frac{O^{+}}{H^{+}}+\frac{O^{2+}}{H^{+}}},$
(17)

where ICF(O) is same as Eq. 15.

In the same way, we assume the expression

$y=\mathrm{ICF}(y^{0})\times(y^{+}+y^{2+}),$ (18)

in the total helium abundance calculation. The $\mathrm{ICF}(y^{0})$
expression (Eq. 11) proposed for Seyferts can not be applied to SFs due to the
distinct ionization structure of these objects. Thus, we build a grid of
photoionization models simulating SFs by using the Cloudy code. The nebular
parameters are similar to those adopted by Dors et al. (2018) and they are
summarised in what follows.

  * •

Metallicity: $(Z/\mathrm{Z_{\odot}})=0.03,$ 0.2, 0.5 and 1.0. This metallicity
range includes values derived from the disk H ii regions (e.g. Berg et al.
2020) and in XPMs (e.g. Izotov et al. 1999).

  * •

Electron density: $N_{\rm e}\>\rm(cm^{-3})=100,$ 500 and 1 000, the same range
derived by Zhang et al. (2013) for SFs and calculated from
$[\text{S\,{ii}}]\lambda 6716/\lambda 6731$ line ratio.

  * •

Ionization parameter ($U$): $\log U$ ranging from $-1.5$ to $-3.5$, with step
of 0.5 dex. Similar range of $\log U$ was derived by Dors et al. (2011) for
local H ii regions (see also Ji & Yan 2022; Zinchenko et al. 2019; Pérez-
Montero 2014).

  * •

SED: synthetic spectra of stellar clusters formed by an instantaneous burst
and with ages equal to 0.01, 1.0, 2.5, 4.0 and 5.0 Myr, built with the
Starburst99 (Leitherer et al., 1999) were considered as ionizing source. The
value 0.01 Myr corresponds to the lowest age considered in the Starburst99. In
the interval 2.5 – 4.0 Myr OB stars become Wolf-Rayet stars producing an
increase in the number of ionizing photons (e.g. Leitherer & Heckman 1995;
Dopita et al. 2006; Vale Asari et al. 2016). Nebulae older than about 5 Myr
are difficult to observe because their original massive stars have cooled
emitting little ionizing photons (e.g., Garcia-Vargas et al. 1995; Mayya &
Prabhu 1996). We assumed the WM-basic stellar atmosphere models by Pauldrach
et al. (2001), and the GENEVA tracks with stellar rotation (Levesque et al.,
2012).

For these models the calculations stopped at outermost nebular radius where
the temperature falls below 4 000 K. We note that the photoionization model
results predict a very low $\rm He^{2+}$ abundance in comparison to those
derived from our observational data sample. This indicates that real SEDs of
the ionizing source of SFs are harder than the theoretical ones assumed here.
The Binary Population and Spectral Synthesis code (bpass, Stanway & Eldridge
2018) produces somewhat harder SEDs than the Starburt99 (e.g. D’Agostino et
al. 2019), however, the former might be more appropriate for moderate/low
metallicity SFs and less appropriate for high metallicity systems (Nakajima &
Maiolino, 2022). Due to the problem pointed out above, we derive a relation
between the ICF($\rm He^{0}$) and the $\rm O^{+}/O$ abundance ratio instead of
$y^{+}/y^{2+}$ as previously. In Fig. 7, the model results for the relation
ICF($\rm He^{0}$)-($\rm O^{+}/O$) are shown, where models assuming stellar
clusters with distinct ages are indicated. It can be seen that, for $(\rm
O^{+}/O)\>\la\>0.6$, higher ICFs are obtained for older models (4 and 5 Myr).
We did not find any dependence of the ICF($\rm He^{0}$)-($\rm O^{+}/O$)
relation with other nebular parameters. Dottori (1981) and Copetti et al.
(1986) proposed that the equivalent width of H$\beta$, the relative volume of
$\rm He^{+}$ and $\rm H^{+}$ zones and the [O iii]($\lambda 4959,\lambda
5007$)/H$\beta$ line ratio are good age H ii region indicators. However, the
change of the value of these indicators along the spiral disk galaxies can be
due to effects of variation of the hottest effective temperature of ionizing
stars (Shields & Tinsley, 1976) rather that evolution effects. Since our SF
sample is mostly composed of disk H ii regions, the age estimation, in
principle, is not correct and it was not carried out. Thus, a fit taken into
account all the points in Fig. 7 results in

$\mathrm{ICF}(y^{0})=\mathrm{a\times(O^{+}/O)^{b}+c},$ (19)

where $\mathrm{a=0.385\pm 0.017}$, $\mathrm{b=4.742\pm 0.275}$ and
$\mathrm{c=1.020\pm 0.002}$.

Figure 7: Calibration between the $\mathrm{ICF}(y^{0})$ and $(\rm O^{+}/O)$.
Points represent SF photoionization model results (see Sect 3.2) assuming
different ages for the ionizing source, as indicated. $\mathrm{ICF}(y^{0})$
and the curve are defined by Eq. 19.

The abundance uncertainties for this sample were derived taken into account
the error in the observational emission-line intensities published by the
authors which the data were compiled.

##  4 Results and Discussion

###  4.1 Density and temperature

The electron density values derived from the $[\text{S\,{ii}}]\lambda
6716/\lambda 6731$ line ratio for the Seyfert 2 sample are in the range of
$20\>\la\>N_{\rm e}(\rm cm^{-3})\>\la\>1200$, with a median value of $\sim
500$ $\rm cm^{-3}$, which is in agreement with the estimation obtained by Dors
et al. (2014). However, the derived mean value from our AGN sample is a factor
of about two lower than the one derived by Vaona et al. (2012), who used
optical spectra of $\sim 2\,300$ AGNs obtained with the SDSS-DR7 (York et al.,
2000). Thus, the discrepancy between our mean electron density result and the
one derived by Vaona et al. (2012) is probably due to the distinct sample of
objects. In any case, the $N_{\rm e}$ values are lower than the critical
density for the emission lines involved in this work (see, for instance, Vaona
et al. 2012), therefore, de-excitation effect has no influence on our
abundance calculations (e.g. Osterbrock & Ferland 2006).

The values derived for the SF sample are in the range of $20\>\la\>N_{\rm
e}(\rm cm^{-3})\>\la\>600$, with a mean value of $\sim 100$ $\rm cm^{-3}$.
This reflects the known discrepancy where NLRs of AGNs present higher electron
density than SFs (e.g. Zhang et al. 2013). In Fig. 8, panel (a), the
distribution of values for the $N_{\rm e}$ from both Seyfert and SF samples
are shown. From this figure it is clear that AGNs have $N_{\rm
e}\>\lesssim\>\rm 1200cm^{-3}$ while most SF ($\sim$ 90 percent) have $N_{\rm
e}\><\>\rm 200\,cm^{-3}$.

Figure 8: Panel (a): Electron density distributions, calculated from [S
ii]$\lambda 6716/\lambda 6731$ line ratio (see Sect. 3.1.1) by using the PyNeb
(Luridiana et al., 2015), for distinct samples of objects (see Sect. 2), as
indicated. Panel (b): As left panel but for $T_{\rm high}$ calculated through
the observational values of the [O iii]($1.33\times\lambda 5007$)/$\lambda
4363$ line ratio.

Regarding the electron temperature results, we derive values for $T_{\rm
high}$ from the Seyferts ranging from $\sim 9\,000$ K to $\sim 25\,000$ K
while values for SFs are in the range of $\sim 7300$ K–$20\,000$ K. In panel
(b) of Fig. 8, the distributions of these values for our Seyfert and SF
samples are shown. The Seyfert mean value is $\sim 15\>000$ K, similar to the
ones derived by Revalski et al. (2018a); Revalski et al. (2018b) for the
quasar type 2 Mrk 34 and for the Seyfert 2 Mrk 573, i.e. about 13 000 K,
respectively. Heckman & Balick (1979) suggested that AGNs with electron
temperature values higher than 20 000K, probably, present a secondary source
of energy in addition to photoionization, possibly the presence of shocks (see
also Dors et al. 2021 and references therein). It can be seen that majority
($\sim 92$ per cent) of the AGNs present $T_{\rm high}$ values lower than 20
000 K. Therefore, the objects of our sample, possibly, are mainly
(photo)ionized by the radiation from the AGN accretion disk (e.g. shocks can
be neglected). For SFs, a somewhat lower mean value of $\sim 11\>500$ K was
obtained.

Peimbert (1967) proposed the presence of temperature fluctuations to explain
the considerable differences found between the temperature estimations relied
on distinct methods in H ii regions. Recently, Riffel et al. (2021d), for the
first time, by using Gemini GMOS-IFU observations of three luminous nearby
Seyfert galaxies (Mrk 79, Mrk 348 and Mrk 607), quantified temperature
variations in this class of object. These authors derived a lower limit for
the temperature fluctuation parameter ($t^{2}$) to be from $\sim 0.04$ to
$\sim 0.1$, in order of those derived for H ii regions and Planetary Nebulae.
Although temperature fluctuations have little effect on helium abundance
estimates (e.g. Peimbert et al. 2012), the supposition of $t^{2}\>>\>0$ leads
to the derivation of higher O/H abundances and, consequently, lower ($\sim 3$
per cent) values of $Y_{\rm p}$ (Peimbert et al., 2002). Since estimations of
temperature fluctuation in AGNs are barely found in the literature, we assume
the temperature values based on [O iii] line ratio as fiducial values for the
high ionization zone of Seyfert nuclei. However, we emphasise that temperature
fluctuation can be present.

In Fig. 9, we assumed the range of observational He i$\lambda 5876$/H$\beta$
and He ii$\lambda 4686$/H$\beta$ line ratio values for our sample of objects
(listed in Table 2) and calculated the $y^{+}$ and $y^{2+}$ abundances
considering temperatures from 5 000 K to 25 000 K and a fixed value of $N_{\rm
e}=100\>\rm cm^{-3}$. It can be seen that the effect of varying the
temperature is in order of the uncertainty produced by the observational error
for the line measurements. Therefore, we emphasize that, if temperature
fluctuations exist in the objects of our sample, shocks or electron
temperature fluctuations affect only the oxygen abundance estimations, while
the helium estimations are reliable values.

Figure 9: Lower panel: Abundances of $y^{+}$ versus the He i$\lambda
5876$/H$\beta$ line ratio for distinct electron temperature values (in units
of $10^{4}$ K), as indicated, assuming a fixed value of $N_{\rm e}=100\>\rm
cm^{-3}$. Top panel: Same as lower panel but for $y^{2+}$ versus He ii$\lambda
4686$/H$\beta$. In both plots, the range of emission-line ratio values
(x-axes) represents the range of observational values of our sample of objects
listed in Table 2. The error bars represent the mean error in the emission-
line measurements of the sample of objects.

###  4.2 Ionization Correction Factor

Delgado-Inglada et al. (2014) computed a large grid of photoionization models
that covers a wide range of physical parameters of planetary nebulae (PNe).
They reported that the derivation of an ICF for neutral helium based on other
ions is not recommended because the relative populations of helium ions depend
essentially on the effective temperature ($T_{\rm eff}$) of the central star
($T_{\rm eff}$ drives the flux of the ionizing photons), whereas those from
metal ions also depend on the ionization parameter. These authors also pointed
out that the correction for neutral helium is important only in models with
ionizing sources at $T_{\rm eff}\>\la\>50\,000$ K. In the bi-parametric
expression for the Seyfert ICF($\rm He^{0})$ proposed here (Eq. 12), both
hardness of the ionizing radiation and the gas ionization degree are taken
into account by the $y^{+}/y^{2+}$ ratio and by the ionization parameter $U$.
For SFs, we notice a dependence between ICF($\rm He^{0})$ and the age of the
ionization source, while $T_{\rm eff}$ is similar to the age, since the
temperature of the hottest stars of the ionizing stellar cluster of an H ii
region drives the flux of the ionizing photons (Zastrow et al., 2013) and it
decreases with the time. However, the stellar evolution could have a minimal
effect on our helium neutral fraction estimation in SFs because we considered
the presence of He ii$\lambda 4876$ line as a selection criterion of the
sample, which led to the selection of H ii regions with young cluster ages. In
fact, Bresolin et al. (1999) showed that only photoionization models with
clusters younger than 3 Myr are able to reproduce optical emission line
intensities of H ii regions.

The application of the ICF($\rm He^{0}$), i.e. Eq. 12, to our AGN data yields
ICFs values ranging from 1.3 to 1.7, with a mean value of $\sim 1.5$. This
result indicates that in NLRs of Seyfert 2 the helium is $\sim 50$ per cent in
a neutral stage. As reported previously, radio and near-infrared (e.g.
Rodríguez-Ardila et al. 2004; Storchi-Bergmann et al. 2009; Riffel et al.
2010; Riffel et al. 2021c; Mezcua et al. 2015; Schönell et al. 2017; Bianchin
et al. 2022, among others) observations have shown that AGNs harbor a neutral
and warm (1000-3000 K) molecular gas reservoir. Therefore, a substantial
proportion of neutral helium is expected in Seyfert nuclei.

Figure 10: As Fig. 8 but for 12+log($y$) [panel (a)] and 12+log(O/H) [panel
(b)]. The blue lines in panels (a) and (b) represent the solar values derived
by Allende Prieto et al. (2001) and Grevesse et al. (2010), respectively.
These values correspond to 12+log($y$)${}_{\odot}=11.0$ and
12+log(O/H)${}_{\odot}=8.69$.

On the other hand, the application of Eq. 19 indicates that SFs have ICF($\rm
He^{0}$) ranging from 1.0 to 1.2, implying 70 per cent of the objects have
ICF($\rm He^{0}$)=1.0. The mean ICF($\rm He^{0}$) value for SFs is 1.03, i.e.
the helium is only $\sim 3$per cent in a neutral stage. Pagel et al. (1992),
following the methodology from Mathis (1982), proposed the use of the
abundance ratio

$\eta=\rm(O^{+}/S^{+})/(S^{2+}/O^{2+}),$ (20)

known by radiation softness parameter (Vilchez & Pagel, 1988), as a means of
estimating the significance of neutral helium in SFs. Pagel et al. (1992)
pointed out that, for H ii regions with $\log\eta\><\>0.9$, the fraction of
neutral helium into Strömgren sphere is negligible. Recently, by using
observational data from the MaNGA survey (Bundy et al., 2015), Kumari et al.
(2021) determined through the $T_{\rm e}$-method values of the $\eta$
parameter for 67 star-forming galaxies. These authors found values in the
range of $-0.4\>\la\>\log\eta\>\la\>0.6$. Bresolin et al. (2009) obtained
spectrophotometric data for 28 H ii regions in the spiral galaxy NGC 300 and,
also by using the $T_{\rm e}$-method, found that the majority of the objects
present $\log\eta$ around 0.7. Otherwise, most part of Galactic H ii region
observed by Méndez-Delgado et al. (2022) present $\log\eta\>>\>0.9$, i.e. a
non-negligible neutral helium abundance. Our results are in consonance with
those derived by Méndez-Delgado et al. (2022), who posited that, like Seyfert
nuclei, SFs can have a significant neutral helium fraction.

One of the major sources of the uncertainty in abundance estimates is the use
of ICFs, producing discrepancies by a factor of up to $\sim 4$ according to
the suppositions considered to derived them (e.g. Dors et al. 2013; Méndez-
Delgado et al. 2020). Unfortunately, AGN ICFs for the helium are not found in
the literature, therefore, it is not possible to estimate the ICF error in our
estimates. In any case, detailed models built with the goal of reproducing
line intensities of a large sample of AGNs (e.g. Dors et al. 2017) and SFs are
needed to validate the neutral ICFs proposed here.

###  4.3 Helium and oxygen abundances

Initially, we compare the $y$ and O/H range of values derived from our AGN
sample with those derived from SFs. This is significant since the helium
abundance at any ionization stage has hitherto been unknown for a large sample
of AGNs.

In Fig. 10, panel (a), the distribution of 12+log($y$) for the Seyfert 2 and
SF samples are shown. Also in this plot, a line indicating the solar value of
the helium abundance, i.e. 12+log($y$)${}_{\odot}=11.0$ derived by Grevesse et
al. (2010) is indicated. We can see that most Seyfert 2 present higher helium
abundance in comparison with those of SFs, with the Seyfert range being
$10.80\>\la\>[12+\log(y)]\>\la\>11.40$ or $0.60\>\la(y/y_{\odot})\>\la\>2.50$,
and a mean value of $<12+\log(y)>=11.11\pm 0.11$ or $<(y/y_{\odot})>\sim
1.30$. We can also note that the majority ($\sim 84$ per cent) of AGNs present
oversolar helium abundance. Concerning the SFs, we derived the range
$10.70\>\la\>[12+\log(y)]\>\la 11.10$ or $0.50\>\la(y/y_{\odot})\>\la 1.20$,
with a mean value $<12+\log(y)>=10.92\pm 0.05$ or $<(y/y_{\odot})>\sim 0.80$.

In Fig. 10, panel (b), the distribution of 12+log(O/H) for the Seyfert 2 and
SFs samples are shown. For the Seyfert sample, we derived the range
$8.20\>\la\>[12+\log(\rm O/H)]\>\la 9.10$, or $0.30\>\la(Z/\rm Z_{\odot})\>\la
2.6$, with most part ($\sim 63$ per cent) having oversolar abundance. The mean
value is $\rm<12+log(O/H)>=8.74\pm 0.16$ or $<(Z/\rm Z_{\odot})>\sim 1.10$.
This is a known result, i.e. subsolar metallicities are derived in few AGNs in
the local universe (e.g., Groves et al. 2006), independently of the method
used to estimate this parameter (Dors et al., 2020a). For SFs, the range of
$7.20\>\la\>[12+\log(\rm O/H)]\>\la 8.80$ or $0.03\>\la(Z/\rm Z_{\odot})\>\la
1.30$ is derived, being $\sim 8$ per cent of the objects presenting oversolar
oxygen abundance.

The lower helium and oxygen abundances in SFs in comparison with those in AGNs
is due to the fact that the latter are located in the central parts of
galaxies and, according to the inside-out scenario of galaxy formation (see
Mollá & Díaz 2005 and references therein) have experimented a longer time-
scale of chemical enrichment of the ISM in comparison with disk H ii regions
(most part of our SF sample). It is worth to mention that, our direct helium
estimates, based on the $y^{+}$ and $y^{2}$ ionic abundances of AGNs, seem to
be the unique for the very high metallicity regime, i.e. $(Z/\rm
Z_{\odot})\>>\>1.0$. This fact is very important in the derivation of the
$y$-O/H relation and of $Y_{\rm p}$ because our estimates, combined those for
XMPs, produce a wide range of metallicities likely not previously considered.

In Fig. 11, the total helium abundance [in units of 12+log($y$)] versus the
oxygen abundance [in units of 12+log(O/H)] from our Seyfert (blue points) and
SF (black points) samples are shown. Other than in AGNs, we note that the SFs
with the highest metallicities present near $y$ values. Similar results were
derived for nitrogen and argon by Carvalho et al. (2020) and Monteiro & Dors
(2021), respectively. Moreover, we notice two clear behaviours, a smooth
$y$-(O/H) relation for the low metallicity regime [$\rm
12+\log(O/H)\>\la\>8.5$ or ($Z/\rm Z_{\odot})\>\la\>0.6)$] and a stepper
relation for high metallicity regime. This difference could be due to an
excess of helium injected into the ISM by winds of Wolf Rayet stars, which are
more common in the high mettalicity environment (e.g. Maeder & Meynet 1994;
Leitherer et al. 1999; Pindao et al. 2002; Crowther et al. 2004; Bresolin et
al. 2005), containing hydrogen burning products (Pagel et al., 1992; Crowther
& Dessart, 1998). The scattering of the points observed in both kind of
objects in Fig. 11 is, probably, due to effects of different star formation
rate in them (e.g. Berg et al. 2020; Hayden-Pawson et al. 2022) and/or due to
radial migration of stars (Vincenzo et al., 2021; Johnson et al., 2022) rather
than evolutionary processes, by virtue of the fact that majority of the AGNs
and SFs of our sample are located in the local universe.

In order to derive an expression for the $y$-O/H relation, we performed 1000
bootstrap realisations (Davison & Hinkley, 1997) with Huber Regressor model
(Owen, 2007). The resulting fitting to the points obtained is given by

$\begin{split}{\rm w}=&(0.1215\pm 0.0422)\times{\rm x^{2}}-(1.8183\pm
0.6977)\times{\rm x}\\\ &+\mathrm{(17.6732\pm 2.8798)}\end{split}$ (21)

where w=12+log($y$) and x=12+log(O/H). Dopita et al. (2006), by using
abundance estimates of SFs obtained by Pagel et al. (1992) and Russell &
Dopita (1992), derived the relation

$y=0.0737+0.024\times(Z/\mathrm{Z_{\odot}}).$ (22)

We converted the $y$ and $Z/\mathrm{Z_{\odot}}$ values of this expression into
the same units assumed previously as well as extrapolated it for the high
metallicity regime. In Fig. 11, we compare the Dopita et al. (2006) relation
with our relation (Eq. 21), which it can be seen a good agreement between
both.

Figure 11: Abundances of 12+log($y$) versus 12+log(O/H). Blue and black points
represent the values for our sample of Seyfert 2 and SFs, respectively, listed
in Table 6. The red curve represents the fit to the points given by Eq. 21.
The green curve represents Eq. 22 derived by Dopita et al. (2006), but with
$y$ and $Z/\mathrm{Z_{\odot}}$ values converted into 12+log($y$) and
12+log(O/H), respectively.

###  4.4 Primordial helium abundance

Figure 12: Left panel: $Y$ versus the abundance ratio
$N(\mathrm{O})/N(\mathrm{H})$ derived by using the $T_{\rm e}$-method. $Y$
values are calculated as in Eq. 4. Blue and black points represent estimates
for our Seyfert 2 and SF samples, respectively. Red line represents the linear
regression to the points given by Eq. 23. The primordial helium abundance
derived from this linear regression, $Y_{\mathrm{p}}=0.2441\pm 0.0037$, is
indicated. Right panel: Estimates of the primordial helium abundance ($Y_{\rm
p}$) derived by different authors. The red line represents the estimation by
Planck Collaboration (2020), i.e. $Y_{\mathrm{p}}=0.2471\pm 0.0003$. Other
estimates correspond to: (1) This work ($Y_{\mathrm{p}}=0.2441\pm 0.0037$),
(2) Izotov et al. (2014), (3) Aver et al. (2015), (4) Peimbert et al. (2016),
(5) Cooke & Fumagalli (2018), (6) Fernández et al. (2019), (7) Valerdi et al.
(2019), (8) Hsyu et al. (2020), (9) Kurichin et al. (2021), (10) and (11)
estimates by Méndez-Delgado et al. (2022) for $t^{2}=0$ and $t^{2}\>>\>0$,
respectively. The $Y_{\rm p}$ value obtained by each author is listed by
Kurichin et al. (2021), with exception of the one derived by Méndez-Delgado et
al. (2022).

Searle & Sargent (1972) presented abundance analysis of the two compact dwarf
galaxies I Zw18 and II Zw40, and for the first time, suggested that metal-poor
objects, such as these, would be used to estimate the primordial helium
abundance. After this pioneering work, several studies have been undertaken in
an effort to address the observation of XMPs and objects in a wide range of
metallicities in order to derive $Y_{\rm p}$ (for a review see Peimbert 2008;
Ferland et al. 2010; Skillman et al. 2012; Peimbert et al. 2017).

Peimbert et al. (2007) listed the main error sources in the $Y_{\rm p}$
determination, which produce uncertainties from $\pm 0.0005$ to $\pm 0.0015$
in the final value of $Y_{\rm p}$, where the collisional excitation of the H i
lines and temperature structure were considered as the most important physical
conditions in the gaseous nebulae. Also, Méndez-Delgado et al. (2020) pointed
out that an important source of error in the $Y_{\rm p}$ estimates is related
to the ionization structure of the nebulae, i.e. the use of ICFs in the
estimation of the total helium abundance, since spectra of typical SF only
show recombination lines of $\rm He^{+}$.

In our case, probably, the main source of uncertainty in the $y$ estimation
and, consequently of $Y_{\rm p}$, is the fact that observational data of our
AGN sample, in opposite to the SF sample, do not have errors in the line
measurements for most of the objects and typical values for these were
considered (see Sect. 2). This procedure, combined with the uncertainty
produced by the use of ICF($\rm He^{0})$, certainly produced larger errors
than those discussed by Peimbert et al. (2007) and Méndez-Delgado et al.
(2020). Despite this drawback, our AGN estimates combined with estimations
from SFs are useful in the derivation of $Y_{\rm p}$ taking objects with very
high metallicity into account.

We calculated $Y$ values using our Seyfert 2 and SFs results, listed in Table
6 together with Eq. 4 for the purpose of estimating $Y_{\rm p}$ which rely on
a wide range of metallicities. These values are shown in panel (a) of Fig. 12.
It can be seen that Seyfert 2s show higher $Y$ and O/H values in comparison
with those in SFs. As previously, we performed 1000 bootstrap realisations to
obtain a linear fit that yielded the following relation

$Y=(94.0946\pm 9.9534)\times N(\mathrm{O})/N(\mathrm{H})+(0.2441\pm 0.0037)$
(23)

with a Pearson correlation coefficient of $R=0.57$. Thus, we derived the value
of $Y_{\mathrm{p}}=0.2441\pm 0.0037$.

In Fig. 12, panel (b), estimates of $Y_{\mathrm{p}}$ obtained by different
authors and methods are compared to our estimate. Also in this figure the line
representing the value derived by the Planck Collaboration (2020) is shown. It
is worthwhile to note that our $Y_{\mathrm{p}}$ value is in a good agreement
than the others, with exception of the estimation by Cooke & Fumagalli (2018)
which presents the highest error bars. We performed a linear fit to the points
considering only our SF estimates and found the expression:

$Y=(36.5264\pm 7.1944)\times N(\mathrm{O})/N(\mathrm{H})+(0.2459\pm 0.0024),$
(24)

with $Y_{\mathrm{p}}=0.2459\pm 0.0024$, i.e. a value somewhat higher than the
one obtained by assuming AGN and SF estimates. However, this value is in
consonance with the one inferred by the Planck Collaboration (2020) and by
other authors.

##  5 Conclusion

We used optical emission line intensities [$3000\><\lambda($Å$)\><\>7000$]
taken from SDSS DR15 and additional compilations from the literature to
derive, through $T_{\rm e}$-method, the helium and oxygen abundances relative
to hydrogen in the narrow line regions (NLRs) of a local ($z\><\>0.2$) sample
of 65 Seyfert 2 nuclei and 85 star-forming regions (SFs; i.e. H ii region,
star-forming galaxies). Photoionization model grids, built with the Cloudy
code and simulating NLRs and SFs, were used to obtain expressions for the
Ionization Correction Factor (ICF) of the neutral helium. The application of
these ICFs indicates that the NLRs of Seyfert 2 present a neutral helium
fraction in relation to the total helium abundance ranging from $\sim 20$ to
$\sim 70$ per cent (mean value $50$ per cent) and SFs from $\sim 0$ to $\sim
20$ per cent (mean value 3 per cent). The high neutral helium abundance in
AGNs it is due to these objects harbour a neutral and warm (1000-3000 K)
molecular gas reservoir. We found that Seyfert 2 nuclei present helium
abundance ranging from 0.60 to 2.50 times the solar value, which implies that
for $\sim 85$ per cent of the sample an oversolar helium abundance was
derived. Our results indicate that NLR of Seyfert 2 nuclei have a stepper
(He/H)-(O/H) relation than SFs. This difference could be due to excess of
helium injected into the ISM by winds of Wolf Rayet stars, which are more
common in the high mettalicity environment, i.e. $\rm 12+\log(O/H)\>\ga\>8.7$
[$(Z/Z_{\odot})\>\ga\>1.0$]. From a regression to zero metallicity, by using
Seyfert 2 and SFs estimates, we derived a primordial helium mass fraction
$Y_{\rm p}=0.2441\pm 0.0037$, a value in good agreement with the one inferred
from the temperature fluctuations of the cosmic microwave background by the
Planck Collaboration, i.e. $Y_{\rm p}^{Planck}=0.2471\pm 0.0003$.

## Data availability

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

## Acknowledgements

We are grateful to the referee for his/her dedicated work in reviewing our
paper. OLD and ACK are grateful to the Fundação de Amparo à Pesquisa do Estado
de São Paulo (FAPESP) and to Conselho Nacional de Desenvolvimento Científico e
Tecnológico (CNPq) for the financial support. CBO is grateful to the FAPESP
for the support under grant 2019/11934-0 and to the Coordenação de
Aperfeiçoamento de Pessoal de Nível Superior (CAPES). Funding for the Sloan
Digital Sky Survey has been provided by the Alfred P. Sloan Foundation, the
U.S. Department of Energy Office of Science, and the Participating
Institutions. SDSS acknowledges support and resources from the Center for
High-Performance Computing at the University of Utah. The SDSS web site is
www.sdss.org.

## References

  * Agostino et al. (2021) Agostino C. J., et al., 2021, arXiv e-prints, p. arXiv:2108.07812
  * Allende Prieto et al. (2001) Allende Prieto C., Lambert D. L., Asplund M., 2001, ApJ, 556, L63
  * Aller & Faulkner (1962) Aller L. H., Faulkner D. J., 1962, PASP, 74, 219
  * Aller & Menzel (1945) Aller L. H., Menzel D. H., 1945, ApJ, 102, 239
  * Aller et al. (1968) Aller L. H., Czyzak S. J., Walker M. F., 1968, ApJ, 151, 491
  * Alloin et al. (1992) Alloin D., Bica E., Bonatto C., Prugniel P., 1992, A&A, 266, 117
  * Alonso-Herrero et al. (2020) Alonso-Herrero A., et al., 2020, A&A, 639, A43
  * Amôres et al. (2021) Amôres E. B., et al., 2021, MNRAS, 508, 1788
  * Andrews & Martini (2013) Andrews B. H., Martini P., 2013, ApJ, 765, 140
  * Annibali et al. (2019) Annibali F., et al., 2019, MNRAS, 482, 3892
  * Armah et al. (2021) Armah M., et al., 2021, MNRAS,
  * Asari et al. (2007) Asari N. V., Cid Fernandes R., Stasińska G., Torres-Papaqui J. P., Mateus A., Sodré L., Schoenell W., Gomes J. M., 2007, MNRAS, 381, 263
  * Aver et al. (2015) Aver E., Olive K. A., Skillman E. D., 2015, J. Cosmology Astropart. Phys., 2015, 011
  * Aver et al. (2021) Aver E., Berg D. A., Hirschauer A. S., Olive K. A., Pogge R. W., Rogers N. S. J., Salzer J. J., Skillman E. D., 2021, arXiv e-prints, p. arXiv:2109.00178
  * Bahcall & Oke (1971) Bahcall J. N., Oke J. B., 1971, ApJ, 163, 235
  * Baldwin (1975) Baldwin J. A., 1975, ApJ, 201, 26
  * Baldwin et al. (1981) Baldwin J. A., Phillips M. M., Terlevich R., 1981, PASP, 93, 5
  * Baron et al. (2016) Baron D., Stern J., Poznanski D., Netzer H., 2016, ApJ, 832, 8
  * Berg et al. (2015) Berg D. A., Skillman E. D., Croxall K. V., Pogge R. W., Moustakas J., Johnson-Groh M., 2015, ApJ, 806, 16
  * Berg et al. (2016) Berg D. A., Skillman E. D., Henry R. B. C., Erb D. K., Carigi L., 2016, ApJ, 827, 126
  * Berg et al. (2020) Berg D. A., Pogge R. W., Skillman E. D., Croxall K. V., Moustakas J., Rogers N. S. J., Sun J., 2020, ApJ, 893, 96
  * Berg et al. (2021) Berg D. A., Chisholm J., Erb D. K., Skillman E. D., Pogge R. W., Olivier G. M., 2021, ApJ, 922, 170
  * Bergvall et al. (1986) Bergvall N., Johansson L., Olofsson K., 1986, A&A, 166, 92
  * Bertram et al. (2007) Bertram T., Eckart A., Fischer S., Zuther J., Straubmeier C., Wisotzki L., Krips M., 2007, A&A, 470, 571
  * Bianchin et al. (2022) Bianchin M., et al., 2022, MNRAS, 510, 639
  * Bradford et al. (2018) Bradford J. D., Geha M. C., Greene J. E., Reines A. E., Dickey C. M., 2018, ApJ, 861, 50
  * Bresolin et al. (1999) Bresolin F., Kennicutt Jr. R. C., Garnett D. R., 1999, ApJ, 510, 104
  * Bresolin et al. (2004) Bresolin F., Garnett D. R., Kennicutt Robert C. J., 2004, ApJ, 615, 228
  * Bresolin et al. (2005) Bresolin F., Schaerer D., González Delgado R. M., Stasińska G., 2005, A&A, 441, 981
  * Bresolin et al. (2009) Bresolin F., Gieren W., Kudritzki R.-P., Pietrzyński G., Urbaneja M. A., Carraro G., 2009, ApJ, 700, 309
  * Brinchmann et al. (2004) Brinchmann J., Charlot S., White S. D. M., Tremonti C., Kauffmann G., Heckman T., Brinkmann J., 2004, MNRAS, 351, 1151
  * Brown et al. (2016) Brown J. S., Martini P., Andrews B. H., 2016, MNRAS, 458, 1529
  * Bruzual & Charlot (2003) Bruzual G., Charlot S., 2003, MNRAS, 344, 1000
  * Bundy et al. (2015) Bundy et al. K., 2015, ApJ, 798, 7
  * Cardelli et al. (1989) Cardelli J. A., Clayton G. C., Mathis J. S., 1989, ApJ, 345, 245
  * Carvalho et al. (2020) Carvalho S. P., et al., 2020, MNRAS, 492, 5675
  * Castellanos et al. (2002) Castellanos M., Díaz A. I., Terlevich E., 2002, MNRAS, 329, 315
  * Castro et al. (2017) Castro C. S., Dors O. L., Cardaci M. V., Hägele G. F., 2017, MNRAS, 467, 1507
  * Cid Fernandes et al. (2005) Cid Fernandes R., Mateus A., Sodré L., Stasińska G., Gomes J. M., 2005, MNRAS, 358, 363
  * Cid Fernandes et al. (2010) Cid Fernandes R., Stasińska G., Schlickmann M. S., Mateus A., Vale Asari N., Schoenell W., Sodré L., 2010, MNRAS, 403, 1036
  * Coil et al. (2015) Coil A. L., et al., 2015, ApJ, 801, 35
  * Combes et al. (2019) Combes F., et al., 2019, A&A, 623, A79
  * Contini (2019) Contini M., 2019, MNRAS, 488, 4487
  * Cooke & Fumagalli (2018) Cooke R. J., Fumagalli M., 2018, Nature Astronomy, 2, 957
  * Copetti et al. (1986) Copetti M. V. F., Pastoriza M. G., Dottori H. A., 1986, A&A, 156, 111
  * Crowther & Dessart (1998) Crowther P. A., Dessart L., 1998, MNRAS, 296, 622
  * Crowther et al. (2004) Crowther P. A., Hadfield L. J., Schild H., Schmutz W., 2004, A&A, 419, L17
  * Croxall et al. (2015) Croxall K. V., Pogge R. W., Berg D. A., Skillman E. D., Moustakas J., 2015, ApJ, 808, 42
  * Croxall et al. (2016) Croxall K. V., Pogge R. W., Berg D. A., Skillman E. D., Moustakas J., 2016, ApJ, 830, 4
  * Cruz-Gonzalez et al. (1991) Cruz-Gonzalez I., Guichard J., Serrano A., Carrasco L., 1991, PASP, 103, 888
  * D’Agostino et al. (2019) D’Agostino J. J., Kewley L. J., Groves B., Byler N., Sutherland R. S., Nicholls D., Leitherer C., Stanway E. R., 2019, ApJ, 878, 2
  * Davies et al. (2005) Davies R. I., Sternberg A., Lehnert M. D., Tacconi-Garman L. E., 2005, ApJ, 633, 105
  * Davison & Hinkley (1997) Davison A. C., Hinkley D. V., 1997, Bootstrap methods and their application. No. 1, Cambridge university press
  * Deharveng et al. (2000) Deharveng L., Peña M., Caplan J., Costero R., 2000, MNRAS, 311, 329
  * Delgado-Inglada et al. (2014) Delgado-Inglada G., Morisset C., Stasińska G., 2014, MNRAS, 440, 536
  * Diamond-Stanic & Rieke (2012) Diamond-Stanic A. M., Rieke G. H., 2012, ApJ, 746, 168
  * Dinerstein & Shields (1986) Dinerstein H. L., Shields G. A., 1986, ApJ, 311, 45
  * Dopita et al. (2006) Dopita M. A., et al., 2006, ApJS, 167, 177
  * Dopita et al. (2015) Dopita M. A., et al., 2015, ApJS, 217, 12
  * Dors (2021) Dors O. L., 2021, MNRAS, 507, 466
  * Dors et al. (2011) Dors Jr. O. L., Krabbe A., Hägele G. F., Pérez-Montero E., 2011, MNRAS, 415, 3616
  * Dors et al. (2012) Dors Oli L. J., Riffel R. A., Cardaci M. V., Hägele G. F., Krabbe Á. C., Pérez-Montero E., Rodrigues I., 2012, MNRAS, 422, 252
  * Dors et al. (2013) Dors O. L., et al., 2013, MNRAS, 432, 2512
  * Dors et al. (2014) Dors O. L., Cardaci M. V., Hägele G. F., Krabbe Â. C., 2014, MNRAS, 443, 1291
  * Dors et al. (2015) Dors O. L., Cardaci M. V., Hägele G. F., Rodrigues I., Grebel E. K., Pilyugin L. S., Freitas-Lemes P., Krabbe A. C., 2015, MNRAS, 453, 4102
  * Dors et al. (2017) Dors O. L. J., Arellano-Córdova K. Z., Cardaci M. V., Hägele G. F., 2017, MNRAS, 468, L113
  * Dors et al. (2018) Dors O. L., Agarwal B., Hägele G. F., Cardaci M. V., Rydberg C.-E., Riffel R. A., Oliveira A. S., Krabbe A. C., 2018, MNRAS, 479, 2294
  * Dors et al. (2020a) Dors O. L., et al., 2020a, MNRAS, 492, 468
  * Dors et al. (2020b) Dors O. L., Maiolino R., Cardaci M. V., Hägele G. F., Krabbe A. C., Pérez-Montero E., Armah M., 2020b, MNRAS, 496, 3209
  * Dors et al. (2021) Dors O. L., Contini M., Riffel R. A., Pérez-Montero E., Krabbe A. C., Cardaci M. V., Hägele G. F., 2021, MNRAS, 501, 1370
  * Dottori (1981) Dottori H. A., 1981, Ap&SS, 80, 267
  * Dressel et al. (1982) Dressel L. L., Bania T. M., Oconnell R. W., 1982, ApJ, 259, 55
  * Durret (1994) Durret F., 1994, A&AS, 105, 57
  * Ellison et al. (2018) Ellison S. L., Sánchez S. F., Ibarra-Medel H., Antonio B., Mendel J. T., Barrera-Ballesteros J., 2018, MNRAS, 474, 2039
  * Ellison et al. (2019) Ellison S. L., Brown T., Catinella B., Cortese L., 2019, MNRAS, 482, 5694
  * Faulkner & Aller (1965) Faulkner D. J., Aller L. H., 1965, MNRAS, 130, 393
  * Feltre et al. (2016) Feltre A., Charlot S., Gutkin J., 2016, MNRAS, 456, 3354
  * Ferland et al. (2010) Ferland G. J., Izotov Y., Peimbert A., Peimbert M., Porter R. L., Skillman E., Steigman G., 2010, in Charbonnel C., Tosi M., Primas F., Chiappini C., eds, Proceedings of the International Astronomical Union Vol. 268, Light Elements in the Universe. pp 163–167, doi:10.1017/S1743921310004011
  * Ferland et al. (2013) Ferland G. J., et al., 2013, RMXAA, 49, 137
  * Fernández-Ontiveros et al. (2016) Fernández-Ontiveros J. A., Spinoglio L., Pereira-Santaella M., Malkan M. A., Andreani P., Dasyra K. M., 2016, ApJS, 226, 19
  * Fernández et al. (2019) Fernández V., Terlevich E., Díaz A. I., Terlevich R., 2019, MNRAS, 487, 3221
  * Flury & Moran (2020) Flury S. R., Moran E. C., 2020, MNRAS, 496, 2191
  * Froese Fischer & Tachiev (2004) Froese Fischer C., Tachiev G., 2004, Atomic Data and Nuclear Data Tables, 87, 1
  * García-Burillo et al. (2014) García-Burillo S., et al., 2014, A&A, 567, A125
  * Garcia-Vargas et al. (1995) Garcia-Vargas M. L., Bressan A., Diaz A. I., 1995, A&AS, 112, 35
  * Garnett & Kennicutt (1994) Garnett D. R., Kennicutt Robert C. J., 1994, ApJ, 426, 123
  * Garnett et al. (2004) Garnett D. R., Kennicutt Robert C. J., Bresolin F., 2004, ApJ, 607, L21
  * Gaskell (2017) Gaskell C. M., 2017, MNRAS, 467, 226
  * Glazebrook et al. (2003) Glazebrook K., et al., 2003, ApJ, 587, 55
  * Gómez et al. (2003) Gómez P. L., et al., 2003, ApJ, 584, 210
  * Grevesse et al. (2010) Grevesse N., Asplund M., Sauval A. J., Scott P., 2010, Ap&SS, 328, 179
  * Groves et al. (2006) Groves B. A., Heckman T. M., Kauffmann G., 2006, MNRAS, 371, 1559
  * Hägele et al. (2008) Hägele G. F., Díaz Á. I., Terlevich E., Terlevich R., Pérez-Montero E., Cardaci M. V., 2008, MNRAS, 383, 209
  * Halpern (1982) Halpern J. P., 1982, PhD thesis, Harvard University, Cambridge, MA.
  * Halpern & Steiner (1983) Halpern J. P., Steiner J. E., 1983, ApJ, 269, L37
  * Hayden-Pawson et al. (2022) Hayden-Pawson C., et al., 2022, MNRAS, 512, 2867
  * Heard & Gaskell (2016) Heard C. Z. P., Gaskell C. M., 2016, MNRAS, 461, 4227
  * Heckman & Balick (1979) Heckman T. M., Balick B., 1979, A&A, 79, 350
  * Ho (1999) Ho L. C., 1999, ApJ, 516, 672
  * Ho et al. (2008) Ho L. C., Darling J., Greene J. E., 2008, ApJS, 177, 103
  * Hsyu et al. (2020) Hsyu T., Cooke R. J., Prochaska J. X., Bolte M., 2020, ApJ, 896, 77
  * Hummer & Storey (1987) Hummer D. G., Storey P. J., 1987, MNRAS, 224, 801
  * Hutchings et al. (1987) Hutchings J. B., Gower A. C., Price R., 1987, AJ, 93, 6
  * Izotov & Thuan (1998) Izotov Y. I., Thuan T. X., 1998, ApJ, 500, 188
  * Izotov & Thuan (2008) Izotov Y. I., Thuan T. X., 2008, ApJ, 687, 133
  * Izotov et al. (1997) Izotov Y. I., Thuan T. X., Lipovetsky V. A., 1997, ApJS, 108, 1
  * Izotov et al. (1999) Izotov Y. I., Chaffee F. H., Foltz C. B., Green R. F., Guseva N. G., Thuan T. X., 1999, ApJ, 527, 757
  * Izotov et al. (2006) Izotov Y. I., Stasińska G., Meynet G., Guseva N. G., Thuan T. X., 2006, A&A, 448, 955
  * Izotov et al. (2007) Izotov Y. I., Thuan T. X., Stasińska G., 2007, ApJ, 662, 15
  * Izotov et al. (2009) Izotov Y. I., Guseva N. G., Fricke K. J., Papaderos P., 2009, A&A, 503, 61
  * Izotov et al. (2013) Izotov Y. I., Stasińska G., Guseva N. G., 2013, A&A, 558, A57
  * Izotov et al. (2014) Izotov Y. I., Thuan T. X., Guseva N. G., 2014, MNRAS, 445, 778
  * Jarvis et al. (2020) Jarvis M. E., et al., 2020, MNRAS, 498, 1560
  * Ji & Yan (2022) Ji X., Yan R., 2022, A&A, 659, A112
  * Ji et al. (2020) Ji X., Yan R., Riffel R., Drory N., Zhang K., 2020, MNRAS, 496, 1262
  * Johnson (1959) Johnson H. M., 1959, PASP, 71, 301
  * Johnson et al. (2022) Johnson J. W., Weinberg D. H., Vincenzo F., Bird J. C., Griffith E. J., 2022, arXiv e-prints, p. arXiv:2202.04666
  * Jura (1973) Jura M., 1973, ApJ, 181, 627
  * Kauffmann et al. (2003) Kauffmann G., et al., 2003, MNRAS, 346, 1055
  * Kawasaki et al. (2017) Kawasaki K., Nagao T., Toba Y., Terao K., Matsuoka K., 2017, ApJ, 842, 44
  * Kennicutt et al. (2003) Kennicutt Robert C. J., Bresolin F., Garnett D. R., 2003, ApJ, 591, 801
  * Kewley & Ellison (2008) Kewley L. J., Ellison S. L., 2008, ApJ, 681, 1183
  * Kewley et al. (2001) Kewley L. J., Dopita M. A., Sutherland R. S., Heisler C. A., Trevena J., 2001, ApJ, 556, 121
  * Kewley et al. (2006) Kewley L. J., Groves B., Kauffmann G., Heckman T., 2006, MNRAS, 372, 961
  * Kewley et al. (2019) Kewley L. J., Nicholls D. C., Sutherland R. S., 2019, ARA&A, 57, 511
  * Kinkel & Rosa (1994) Kinkel U., Rosa M. R., 1994, A&A, 282, L37
  * Kisielius et al. (2009) Kisielius R., Storey P. J., Ferland G. J., Keenan F. P., 2009, MNRAS, 397, 903
  * Koski (1978) Koski A. T., 1978, ApJ, 223, 56
  * Krabbe et al. (2011) Krabbe A. C., Pastoriza M. G., Winge C., Rodrigues I., Dors O. L., Ferreiro D. L., 2011, MNRAS, 416, 38
  * Krabbe et al. (2017) Krabbe A. C., Rosa D. A., Pastoriza M. G., Hägele G. F., Cardaci M. V., Dors O. L. J., Winge C., 2017, MNRAS, 467, 27
  * Kraemer et al. (1994) Kraemer S. B., Wu C.-C., Crenshaw D. M., Harrington J. P., 1994, ApJ, 435, 171
  * Kumari et al. (2021) Kumari N., Amorín R., Pérez-Montero E., Vílchez J., Maiolino R., 2021, MNRAS, 508, 1084
  * Kunth & Sargent (1983) Kunth D., Sargent W. L. W., 1983, ApJ, 273, 81
  * Kurichin et al. (2021) Kurichin O. A., Kislitsyn P. A., Klimenko V. V., Balashev S. A., Ivanchik A. V., 2021, MNRAS, 502, 3045
  * Leitherer & Heckman (1995) Leitherer C., Heckman T. M., 1995, ApJS, 96, 9
  * Leitherer et al. (1999) Leitherer C., et al., 1999, ApJS, 123, 3
  * Levesque et al. (2012) Levesque E. M., Leitherer C., Ekstrom S., Meynet G., Schaerer D., 2012, ApJ, 751, 67
  * Liang et al. (2007) Liang Y. C., Hammer F., Yin S. Y., Flores H., Rodrigues M., Yang Y. B., 2007, A&A, 473, 411
  * Ludwig et al. (2012) Ludwig R. R., Greene J. E., Barth A. J., Ho L. C., 2012, ApJ, 756, 51
  * Luridiana et al. (2015) Luridiana V., Morisset C., Shaw R. A., 2015, A&A, 573
  * Maeder & Meynet (1994) Maeder A., Meynet G., 1994, A&A, 287, 803
  * Mateus et al. (2006) Mateus A., Sodré L., Cid Fernandes R., Stasińska G., Schoenell W., Gomes J. M., 2006, MNRAS, 370, 721
  * Mathis (1957) Mathis J. S., 1957, ApJ, 125, 328
  * Mathis (1962) Mathis J. S., 1962, ApJ, 136, 374
  * Mathis (1965) Mathis J. S., 1965, PASP, 77, 90
  * Mathis (1982) Mathis J. S., 1982, ApJ, 261, 195
  * Mayya & Prabhu (1996) Mayya Y. D., Prabhu T. P., 1996, AJ, 111, 1252
  * Mazzalay et al. (2013) Mazzalay X., et al., 2013, MNRAS, 428, 2389
  * McCall et al. (2003) McCall B. J., et al., 2003, Nature, 422, 500
  * Méndez-Delgado et al. (2020) Méndez-Delgado J. E., Esteban C., García-Rojas J., Arellano-Córdova K. Z., Valerdi M., 2020, MNRAS, 496, 2726
  * Méndez-Delgado et al. (2022) Méndez-Delgado J. E., Amayo A., Arellano-Córdova K. Z., Esteban C., García-Rojas J., Carigi L., Delgado-Inglada G., 2022, MNRAS, 510, 4436
  * Mezcua et al. (2015) Mezcua M., Prieto M. A., Fernández-Ontiveros J. A., Tristram K., Neumayer N., Kotilainen J. K., 2015, MNRAS, 452, 4128
  * Miller et al. (2011) Miller B. P., Brandt W. N., Schneider D. P., Gibson R. R., Steffen A. T., Wu J., 2011, ApJ, 726, 20
  * Mollá & Díaz (2005) Mollá M., Díaz A. I., 2005, MNRAS, 358, 521
  * Monteiro & Dors (2021) Monteiro A. F., Dors O. L., 2021, MNRAS, 508, 3023
  * Moustakas & Kennicutt (2006) Moustakas J., Kennicutt Robert C. J., 2006, ApJS, 164, 81
  * Nakajima & Maiolino (2022) Nakajima K., Maiolino R., 2022, MNRAS, 513, 5134
  * Nicholls et al. (2017) Nicholls D. C., Sutherland R. S., Dopita M. A., Kewley L. J., Groves B. A., 2017, MNRAS, 466, 4403
  * Olive & Skillman (2004) Olive K. A., Skillman E. D., 2004, ApJ, 617, 29
  * Olive et al. (1997) Olive K. A., Steigman G., Skillman E. D., 1997, ApJ, 483, 788
  * Osterbrock & Ferland (2006) Osterbrock D. E., Ferland G. J., 2006, Astrophysics of gaseous nebulae and active galactic nuclei. UNIVERSITY SCIENCE BOOKS
  * Osterbrock & Miller (1975) Osterbrock D. E., Miller J. S., 1975, ApJ, 197, 535
  * Owen (2007) Owen A. B., 2007, Contemporary Mathematics, 443, 59
  * Pagel et al. (1992) Pagel B. E. J., Simonson E. A., Terlevich R. J., Edmunds M. G., 1992, MNRAS, 255, 325
  * Pauldrach et al. (2001) Pauldrach A. W. A., Hoffmann T. L., Lennon M., 2001, A&A, 375, 161
  * Peña (1986) Peña M., 1986, PASP, 98, 1061
  * Peimbert (1967) Peimbert M., 1967, ApJ, 150, 825
  * Peimbert (2008) Peimbert M., 2008, arXiv e-prints, p. arXiv:0811.2980
  * Peimbert & Spinrad (1970) Peimbert M., Spinrad H., 1970, ApJ, 159, 809
  * Peimbert & Torres-Peimbert (1974) Peimbert M., Torres-Peimbert S., 1974, ApJ, 193, 327
  * Peimbert & Torres-Peimbert (1976) Peimbert M., Torres-Peimbert S., 1976, ApJ, 203, 581
  * Peimbert et al. (1992) Peimbert M., Torres-Peimbert S., Ruiz M. T., 1992, RMXAA, 24, 155
  * Peimbert et al. (2000) Peimbert M., Peimbert A., Ruiz M. T., 2000, ApJ, 541, 688
  * Peimbert et al. (2002) Peimbert A., Peimbert M., Luridiana V., 2002, ApJ, 565, 668
  * Peimbert et al. (2003) Peimbert M., Peimbert A., Luridiana V., Ruiz M. T., 2003, in Perez E., Gonzalez Delgado R. M., Tenorio-Tagle G., eds, Astronomical Society of the Pacific Conference Series Vol. 297, Star Formation Through Time. p. 81 (arXiv:astro-ph/0211497)
  * Peimbert et al. (2007) Peimbert M., Luridiana V., Peimbert A., 2007, ApJ, 666, 636
  * Peimbert et al. (2012) Peimbert A., Peña-Guerrero M. A., Peimbert M., 2012, ApJ, 753, 39
  * Peimbert et al. (2016) Peimbert A., Peimbert M., Luridiana V., 2016, RMXAA, 52, 419
  * Peimbert et al. (2017) Peimbert M., Peimbert A., Delgado-Inglada G., 2017, PASP, 129, 082001
  * Pérez-Díaz et al. (2021) Pérez-Díaz B., Masegosa J., Márquez I., Pérez-Montero E., 2021, MNRAS, 505, 4289
  * Pérez-Montero (2014) Pérez-Montero E., 2014, MNRAS, 441, 2663
  * Pérez-Montero (2017) Pérez-Montero E., 2017, PASP, 129, 043001
  * Pérez-Montero & Díaz (2003) Pérez-Montero E., Díaz A. I., 2003, MNRAS, 346, 105
  * Pérez-Montero et al. (2013) Pérez-Montero et al. E., 2013, A&A, 549, A25
  * Pérez-Montero et al. (2019) Pérez-Montero E., Dors O. L., Vílchez J. M., García-Benito R., Cardaci M. V., Hägele G. F., 2019, MNRAS, 489, 2652
  * Phillips et al. (1983) Phillips M. M., Charles P. A., Baldwin J. A., 1983, ApJ, 266, 485
  * Pilyugin (2003) Pilyugin L. S., 2003, A&A, 399, 1003
  * Pilyugin et al. (2012) Pilyugin L. S., Vílchez J. M., Mattsson L., Thuan T. X., 2012, MNRAS, 421, 1624
  * Pindao et al. (2002) Pindao M., Schaerer D., González Delgado R. M., Stasińska G., 2002, A&A, 394, 443
  * Planck Collaboration (2020) Planck Collaboration 2020, A&A, 641, A6
  * Porter et al. (2012) Porter R. L., Ferland G. J., Storey P. J., Detisch M. J., 2012, MNRAS, 425, L28
  * Ramakrishnan et al. (2019) Ramakrishnan V., et al., 2019, MNRAS, 487, 444
  * Revalski et al. (2018a) Revalski M., Crenshaw D. M., Kraemer 2018a, ApJ, 856, 46
  * Revalski et al. (2018b) Revalski M., et al., 2018b, ApJ, 867, 88
  * Revalski et al. (2021) Revalski M., et al., 2021, ApJ, 910, 139
  * Richardson et al. (2014) Richardson C. T., Allen J. T., Baldwin J. A., Hewett P. C., Ferland G. J., 2014, MNRAS, 437, 2376
  * Riffel et al. (2010) Riffel R. A., Storchi-Bergmann T., Nagar N. M., 2010, MNRAS, 404, 166
  * Riffel et al. (2013) Riffel R., Rodríguez-Ardila A., Aleman I., Brotherton M. S., Pastoriza M. G., Bonatto C., Dors O. L., 2013, MNRAS, 430, 2002
  * Riffel et al. (2018) Riffel R. A., et al., 2018, MNRAS, 474, 1373
  * Riffel et al. (2019) Riffel R., et al., 2019, MNRAS, 486, 3228
  * Riffel et al. (2021a) Riffel R. A., et al., 2021a, MNRAS, 501, L54
  * Riffel et al. (2021b) Riffel R., et al., 2021b, MNRAS, 501, 4064
  * Riffel et al. (2021c) Riffel R. A., et al., 2021c, MNRAS, 504, 3265
  * Riffel et al. (2021d) Riffel R. A., Dors O. L., Krabbe A. C., Esteban C., 2021d, MNRAS, 506, L11
  * Rodríguez-Ardila et al. (2004) Rodríguez-Ardila A., Pastoriza M. G., Viegas S., Sigut T. A. A., Pradhan A. K., 2004, A&A, 425, 457
  * Rodríguez-Ardila et al. (2005) Rodríguez-Ardila A., Riffel R., Pastoriza M. G., 2005, MNRAS, 364, 1041
  * Rogers et al. (2021) Rogers N. S. J., Skillman E. D., Pogge R. W., Berg D. A., Moustakas J., Croxall K. V., Sun J., 2021, ApJ, 915, 21
  * Rosa (1985) Rosa M., 1985, The Messenger, 39, 15
  * Ruschel-Dutra & de Oliveira (2020) Ruschel-Dutra D., de Oliveira B. D., 2020, danielrd6/ifscube v1.0, doi:10.5281/zenodo.3945237, https://doi.org/10.5281/zenodo.3945237
  * Ruschel-Dutra et al. (2021) Ruschel-Dutra D., et al., 2021, MNRAS, 507, 74
  * Russell & Dopita (1992) Russell S. C., Dopita M. A., 1992, ApJ, 384, 508
  * Sánchez et al. (2012) Sánchez et al. S. F., 2012, A&A, 538, A8
  * Sánchez et al. (2017) Sánchez S. F., et al., 2017, MNRAS, 469, 2121
  * Sauer & Jedamzik (2002) Sauer D., Jedamzik K., 2002, A&A, 381, 361
  * Schlafly & Finkbeiner (2011) Schlafly E. F., Finkbeiner D. P., 2011, ApJ, 737, 103
  * Schlegel et al. (1998) Schlegel D. J., Finkbeiner D. P., Davis M., 1998, ApJ, 500, 525
  * Schönell et al. (2017) Schönell Astor J. J., Storchi-Bergmann T., Riffel R. A., Riffel R., 2017, MNRAS, 464, 1771
  * Searle & Sargent (1972) Searle L., Sargent W. L. W., 1972, ApJ, 173, 25
  * Shields (1974) Shields G. A., 1974, ApJ, 191, 309
  * Shields & Oke (1975) Shields G. A., Oke J. B., 1975, ApJ, 197, 5
  * Shields & Tinsley (1976) Shields G. A., Tinsley B. M., 1976, ApJ, 203, 66
  * Shuder (1980) Shuder J. M., 1980, ApJ, 240, 32
  * Shuder & Osterbrock (1981) Shuder J. M., Osterbrock D. E., 1981, ApJ, 250, 55
  * Skillman (1991) Skillman E. D., 1991, PASP, 103, 919
  * Skillman et al. (1994) Skillman E. D., Televich R. J., Kennicutt Robert C. J., Garnett D. R., Terlevich E., 1994, ApJ, 431, 172
  * Skillman et al. (2012) Skillman E., Aver E., Olive K., 2012, Memorie della Societa Astronomica Italiana Supplementi, 22, 164
  * Stanway & Eldridge (2018) Stanway E. R., Eldridge J. J., 2018, MNRAS, 479, 75
  * Storchi-Bergmann et al. (1998) Storchi-Bergmann T., Schmitt H. R., Calzetti D., Kinney A. L., 1998, AJ, 115, 909
  * Storchi-Bergmann et al. (2009) Storchi-Bergmann T., McGregor P. J., Riffel R. A., Simões Lopes R., Beck T., Dopita M., 2009, MNRAS, 394, 1148
  * Storey & Hummer (1995) Storey P. J., Hummer D. G., 1995, MNRAS, 272, 41
  * Storey & Zeippen (2000) Storey P. J., Zeippen C. J., 2000, MNRAS, 312, 813
  * Storey et al. (2014) Storey P. J., Sochi T., Badnell N. R., 2014, MNRAS, 441, 3028
  * Tananbaum et al. (1979) Tananbaum H., et al., 1979, ApJ, 234, L9
  * Thomas et al. (2017) Thomas A. D., et al., 2017, ApJS, 232, 11
  * Toribio San Cipriano et al. (2017) Toribio San Cipriano L., Domínguez-Guzmán G., Esteban C., García-Rojas J., Mesa-Delgado A., Bresolin F., Rodríguez M., Simón-Díaz S., 2017, MNRAS, 467, 3759
  * Torres-Peimbert & Peimbert (1977) Torres-Peimbert S., Peimbert M., 1977, RMXAA, 2, 181
  * Vale Asari et al. (2016) Vale Asari N., Stasińska G., Morisset C., Cid Fernandes R., 2016, MNRAS, 460, 1739
  * Valerdi et al. (2019) Valerdi M., Peimbert A., Peimbert M., Sixtos A., 2019, ApJ, 876, 98
  * Valerdi et al. (2021a) Valerdi M., Peimbert A., Peimbert M., 2021a, MNRAS, 505, 3624
  * Valerdi et al. (2021b) Valerdi M., Barrera-Ballesteros J. K., Sánchez S. F., Espinosa-Ponce C., Carigi L., Mejía-Narváez A., 2021b, MNRAS, 505, 5460
  * Vaona et al. (2012) Vaona L., Ciroi S., Di Mille F., Cracco V., La Mura G., Rafanelli P., 2012, MNRAS, 427, 1266
  * Vilchez & Pagel (1988) Vilchez J. M., Pagel B. E. J., 1988, MNRAS, 231, 257
  * Vincenzo et al. (2021) Vincenzo F., et al., 2021, arXiv e-prints, p. arXiv:2106.03912
  * Wampler (1971) Wampler E. J., 1971, ApJ, 164, 1
  * Wiese et al. (1996) Wiese W. L., Fuhr J. R., Deters T. M., 1996, Atomic transition probabilities of carbon, nitrogen, and oxygen : a critical data compilation
  * Williams (1971) Williams R. E., 1971, ApJ, 167, L27
  * Worrall et al. (1987) Worrall D. M., Giommi P., Tananbaum H., Zamorani G., 1987, ApJ, 313, 596
  * Wyse (1942) Wyse A. B., 1942, ApJ, 95, 356
  * Yates et al. (2012) Yates R. M., Kauffmann G., Guo Q., 2012, MNRAS, 422, 215
  * Yates et al. (2020) Yates R. M., Schady P., Chen T. W., Schweyer T., Wiseman P., 2020, A&A, 634, A107
  * York et al. (2000) York D. G., Adelman J., Anderson John E. J., Anderson S. F., Annis J., Bahcall 2000, AJ, 120, 1579
  * Zastrow et al. (2013) Zastrow J., Oey M. S., Veilleux S., McDonald M., 2013, ApJ, 779, 76
  * Zhang et al. (2008) Zhang K., Wang T., Dong X., Lu H., 2008, ApJ, 685, L109
  * Zhang et al. (2013) Zhang Z. T., Liang Y. C., Hammer F., 2013, MNRAS, 430, 2605
  * Zhu et al. (2019) Zhu S. F., Brandt W. N., Wu J., Garmire G. P., Miller B. P., 2019, MNRAS, 482, 2016
  * Zhu et al. (2021) Zhu S. F., Timlin J. D., Brandt W. N., 2021, MNRAS, 505, 1954
  * Zinchenko et al. (2019) Zinchenko I. A., Dors O. L., Hägele G. F., Cardaci M. V., Krabbe A. C., 2019, MNRAS, 483, 1901
  * do Nascimento et al. (2022) do Nascimento J. C., et al., 2022, MNRAS, 513, 807

Table 2: Reddening corrected emission line intensities (in relation to $\rm H\beta=1.0$) of the Seyfert 2 sample described in Sect. 2.1.  ObjID | [O ii] | [O iii] | He ii | [O iii] | He i | $\rm H\alpha$ | [N ii] | [S ii] | [S ii] | Ref.
---|---|---|---|---|---|---|---|---|---|---
|  $\lambda$3727 |  $\lambda$4363 |  $\lambda$4686 |  $\lambda$5007 |  $\lambda$5876 |  $\lambda$6563 |  $\lambda$6583 |  $\lambda$6716 |  $\lambda$6731 |
J013957.81-004504.2 | 2.31$\pm$0.22 | 0.06$\pm$0.01 | 0.16$\pm$0.01 |  7.45$\pm$0.11 | 0.06$\pm$0.02 | 2.86$\pm$0.04 | 2.51$\pm$0.04 | 0.79$\pm$0.02 | 0.67$\pm$0.02 | 1
J033923.14-054841.5 | 2.63$\pm$0.20 | 0.09$\pm$0.01 | 0.26$\pm$0.01 |  7.90$\pm$0.02 | 0.09$\pm$0.01 | 2.86$\pm$0.01 | 1.52$\pm$0.01 | 0.53$\pm$0.01 | 0.45$\pm$0.01 | 1
J074257.23+333217.9 | 1.93$\pm$0.09 | 0.04$\pm$0.01 | 0.08$\pm$0.01 | 3.03$\pm$0.01 | 0.10$\pm$0.01 | 2.86$\pm$0.01 | 1.63$\pm$0.01 | 0.49$\pm$0.01 | 0.43$\pm$0.01 | 1
J093509.12+002557.4 | 2.58$\pm$0.10 | 0.07$\pm$0.01 | 0.11$\pm$0.01 | 3.86$\pm$0.02 | 0.07$\pm$0.01 | 2.86$\pm$0.01 | 2.12$\pm$0.01 | 0.59$\pm$0.01 | 0.54$\pm$0.01 | 1
J095759.45+022810.5 | 3.17$\pm$0.23 | 0.08$\pm$0.01 | 0.26$\pm$0.01 |  7.59$\pm$0.07 | 0.08$\pm$0.01 | 2.86$\pm$0.03 | 2.12$\pm$0.02 | 0.84$\pm$0.01 | 0.69$\pm$0.01 | 1
J100602.50+071131.8 | 6.21$\pm$0.04 | 0.15$\pm$0.01 | 0.27$\pm$0.01 |  7.61$\pm$0.01 | 0.09$\pm$0.01 | 2.86$\pm$0.01 | 1.85$\pm$0.01 | 0.62$\pm$0.01 | 0.51$\pm$0.01 | 1
J100921.26+013334.5 | 3.31$\pm$0.28 | 0.14$\pm$0.01 | 0.31$\pm$0.01 | 12.29$\pm$0.07 | 0.11$\pm$0.01 | 2.86$\pm$0.02 | 2.89$\pm$0.02 | 0.72$\pm$0.01 | 0.74$\pm$0.01 | 1
J101754.72-002811.9 | 2.34$\pm$0.14 | 0.12$\pm$0.01 | 0.27$\pm$0.01 | 6.05$\pm$0.03 | 0.11$\pm$0.01 | 2.86$\pm$0.01 | 1.75$\pm$0.01 | 0.53$\pm$0.01 | 0.43$\pm$0.01 | 1
J102039.81+642435.8 | 4.38$\pm$1.00 | 0.17$\pm$0.01 | 0.25$\pm$0.01 | 8.82$\pm$0.06 | 0.07$\pm$0.01 | 2.86$\pm$0.02 | 2.72$\pm$0.02 | 0.76$\pm$0.01 | 0.58$\pm$0.01 | 1
J112850.39+021016.2 | 2.97$\pm$0.20 | 0.28$\pm$0.02 | 0.28$\pm$0.02 | 6.75$\pm$0.15 | 0.16$\pm$0.03 | 2.86$\pm$0.07 | 1.79$\pm$0.05 | 0.64$\pm$0.03 | 0.51$\pm$0.03 | 1
Mrk 176 | 3.54 | 0.32 | 0.43 | 14.36 | 0.10 | 2.81 | 2.99 | 0.56 | 0.54 | 2
3C 33 | 4.93 | 0.32 | 0.26 | 12.68 | 0.096 | 2.63 | 1.76 | 0.87 | 0.73 | 2
Mrk 3 | 3.52 | 0.24 | 0.18 | 12.67 | 0.084 | 3.10 | 3.18 | 0.73 | 0.82 | 2
Mrk 573 | 2.92 | 0.18 | 0.36 | 12.12 | 0.10 | 2.95 | 2.57 | 0.75 | 0.80 | 2
Mrk 78 | 4.96 | 0.14 | 0.35 | 11.94 | 0.10 | 2.46 | 2.32 | 0.68 | 0.61 | 2
Mrk 348 | 4.45 | 0.26 | 0.22 | 11.74 | 0.12 | 2.76 | 2.28 | 1.09 | 1.25 | 2
Mrk 34 | 3.43 | 0.15 | 0.28 | 11.46 | 0.12 | 2.99 | 2.18 | 0.82 | 0.80 | 2
Mrk 1 | 2.79 | 0.21 | 0.30 | 10.95 | 0.10 | 2.66 | 2.21 | 0.49 | 0.52 | 2
Mrk 270 | 5.64 | 0.28 | 0.22 | 8.71 | 0.19 | 3.14 | 2.93 | 1.21 | 1.39 | 2
III Zw 55 | 3.19 | 0.25 | 0.20 | 6.92 | 0.090 | 2.86 | 3.87 | 0.66 | 0.74 | 2
3C 452 | 4.81 | 0.18 | 0.059 | 6.85 | 0.17 | 2.98 | 3.58 | 1.10 | 0.77 | 2
Mrk 198 | 2.51 | 0.12 | 0.075 | 5.56 | 0.11 | 3.02 | 2.26 | 0.89 | 0.68 | 2
Mrk 268 | 3.75 | 0.25 | 0.078 | 4.82 | 0.095 | 3.38 | 4.94 | 1.28 | 1.08 | 2
NGC 2110 | 4.38 | 0.17 | 0.06 | 4.76 | 0.14 | 2.66 | 3.76 | 1.52 | 1.42 | 3
ESO 138 G1 | $2.35\pm 0.08$ | $0.34\pm 0.02$ | $0.30\pm 0.02$ | $8.71\pm 0.36$ | $0.11\pm 0.02$ | $3.00\pm 0.13$ | $0.68\pm 0.03$ | $0.47\pm 0.03$ | $0.48\pm 0.03$ | 4
NGC 3081 | 2.19 | 0.24 | 0.44 | 12.62 | 0.10 | 2.84 | 2.47 | 0.60 | 0.66 | 5
NGC 4388 | 2.73 | 0.16 | 0.21 | 10.55 | 0.11 | 2.84 | 1.50 | 0.72 | 0.62 | 5
NGC 5135 | 2.06 | 0.11 | 0.20 | 4.42 | 0.10 | 2.83 | 2.50 | 0.40 | 0.38 | 5
NGC 5728 | 3.50 | 0.47 | 0.32 | 10.85 | 0.15 | 2.83 | 3.93 | 0.44 | 0.435 | 5
Akn 347a | 2.72 | 0.42 | 0.33 | 15.15 | 0.12 | 3.18 | 3.93 | 0.93 | 0.89 | 6
UM 16a | 3.05 | 0.25 | 0.37 | 13.8 | 0.18 | 2.77 | 1.66 | 0.47 | 0.48 | 6
Mrk 612a | 1.90 | 0.20 | 0.16 | 9.09 | 0.20 | 2.81 | 3.81 | 0.78 | 0.57 | 6
Mrk 573 | $2.13\pm 0.05$ | $0.14\pm 0.011$ | $0.29\pm 0.02$ | $10.26\pm 0.05$ | $0.09\pm 0.01$ | $2.86\pm 0.05$ | $2.34\pm 0.04$ | $0.79\pm 0.01$ | $0.73\pm 0.02$ | 7
NGC 2992 | $3.38\pm 0.11$ | $0.21\pm 0.027$ | $0.07\pm 0.02$ | $5.25\pm 0.09$ | $0.08\pm 0.01$ | $2.86\pm 0.02$ | $2.70\pm 0.03$ | $0.52\pm 0.01$ | $0.47\pm 0.01$ | 7
IC 2560 | $1.65\pm 0.02$ | $0.16\pm 0.017$ | $0.26\pm 0.06$ | $10.69\pm 0.10$ | $0.10\pm 0.01$ | $2.86\pm 0.08$ | $2.88\pm 0.07$ | $0.74\pm 0.02$ | $0.79\pm 0.01$ | 7
NGC 5664 | $1.83\pm 0.05$ | $0.02\pm 0.006$ | $0.12\pm 0.01$ | $2.95\pm 0.07$ | $0.09\pm 0.01$ | $2.86\pm 0.12$ | $1.70\pm 0.11$ | $0.58\pm 0.03$ | $0.43\pm 0.07$ | 7
NGC 5728 | $2.32\pm 0.03$ | $0.11\pm 0.016$ | $0.17\pm 0.01$ | $9.10\pm 0.11$ | $0.08\pm 0.01$ | $2.86\pm 0.13$ | $3.53\pm 0.12$ | $0.97\pm 0.06$ | $0.66\pm 0.03$ | 7
ESO 339-G11 | $2.39\pm 0.12$ | $0.14\pm 0.074$ | $0.13\pm 0.01$ | $7.86\pm 0.05$ | $0.09\pm 0.01$ | $2.86\pm 0.12$ | $3.97\pm 0.09$ | $0.69\pm 0.02$ | $0.64\pm 0.02$ | 7
NGC 6890 | $1.66\pm 0.04$ | $0.23\pm 0.037$ | $0.19\pm 0.01$ | $10.90\pm 0.03$ | $0.06\pm 0.02$ | $2.86\pm 0.10$ | $2.85\pm 0.09$ | $0.43\pm 0.01$ | $0.39\pm 0.01$ | 7
IC 5063 | $2.88\pm 0.06$ | $0.12\pm 0.008$ | $0.09\pm 0.01$ | $7.83\pm 0.07$ | $0.08\pm 0.01$ | $2.86\pm 0.06$ | $1.81\pm 0.06$ | $0.77\pm 0.06$ | $0.77\pm 0.02$ | 7
NGC 7130 | $1.75\pm 0.03$ | $0.09\pm 0.005$ | $0.15\pm 0.01$ | $4.62\pm 0.05$ | $0.05\pm 0.01$ | $2.86\pm 0.01$ | $3.64\pm 0.00$ | $0.50\pm 0.05$ | $0.50\pm 0.01$ | 7
NGC 7582 | $1.24\pm 0.02$ | $0.03\pm 0.002$ | $0.11\pm 0.05$ | $2.14\pm 0.10$ | $0.10\pm 0.01$ | $2.86\pm 0.02$ | $1.86\pm 0.02$ | $0.40\pm 0.01$ | $0.38\pm 0.01$ | 7
NGC 7590 | $3.32\pm 0.19$ | $0.05\pm 0.027$ | $0.07\pm 0.03$ | $3.47\pm 0.16$ | $0.06\pm 0.02$ | $2.86\pm 0.11$ | $2.39\pm 0.18$ | $0.98\pm 0.08$ | $0.78\pm 0.04$ | 7
Cygnus A | 5.01 | 0.20 | 0.27 | 12.30 | 0.07 | 3.09 | 6.16 | 1.65 | 1.51 | 8
Mrk 1157a | 7.32 | 0.25 | 0.24 | 9.81 | 0.12 | 2.82 | 3.07 | 0.65 | 0.69 | 9
ESO 428-G14 | 2.22 | 0.24 | 0.19 | 11.2 | 0.16 | 2.90 | 3.13 | 0.83 | 0.88 | 10
ESO 137-G34 | 3.07 | 0.11 | 0.21 | 9.35 | 0.11 | 3.10 | 3.35 | 0.98 | 1.20 | 11
IC 3639 | 1.24 | 0.09 | 0.12 | 5.68 | 0.10 | 3.10 | 2.52 | 0.68 | 0.73 | 11
IC 4777 | 2.32 | 0.07 | 0.17 | 6.34 | 0.10 | 3.10 | 3.82 | 0.92 | 0.87 | 11
IC 4995 | 1.32 | 0.20 | 0.27 | 11.87 | 0.08 | 3.10 | 2.49 | 0.68 | 0.76 | 11
IRAS 11215-2806 | 2.48 | 0.14 | 0.25 |  7.25 | 0.11 | 3.10 | 1.74 | 0.84 | 0.79 | 11
Table 3: continued

ObjID | [O ii] | [O iii] | He ii | [O iii] | He i | $\rm H\alpha$ | [N ii | [S ii] | [S ii] | Ref.
---|---|---|---|---|---|---|---|---|---|---
|  $\lambda$3727 |  $\lambda$4363 |  $\lambda$4686 |  $\lambda$5007 |  $\lambda$5876 |  $\lambda$6563 |  $\lambda$6583 |  $\lambda$6716 |  $\lambda$6731 |
MCG-01-24-012 | 3.31 | 0.16 | 0.20 | 8.51 | 0.09 | 3.10 | 1.77 | 0.97 | 0.86 | 11
MCG-02-51-008 | 2.35 | 0.05 | 0.09 | 4.23 | 0.10 | 3.10 | 2.10 | 0.84 | 0.63 | 11
NGC 1125 | 3.13 | 0.08 | 0.14 | 5.86 | 0.10 | 3.10 | 2.30 | 0.79 | 0.78 | 11
NGC 1194 | 1.64 | 0.08 | 0.06 | 6.21 | 0.11 | 3.10 | 1.61 | 1.01 | 0.77 | 11
NGC 1320 | 0.98 | 0.13 | 0.37 | 9.34 | 0.11 | 3.10 | 2.21 | 0.65 | 0.62 | 11
NGC 3281 | 2.06 | 0.09 | 0.29 |  7.71 | 0.11 | 3.10 | 2.85 | 0.88 | 0.76 | 11
NGC 3393 | 2.23 | 0.10 | 0.26 | 9.428 | 0.12 | 3.10 | 3.13 | 0.92 | 0.93 | 11
NGC 4939 | 2.05 | 0.12 | 0.30 | 10.03 | 0.12 | 3.10 | 4.16 | 0.91 | 0.99 | 11
NGC 4968 | 1.64 | 0.22 | 0.27 | 9.45 | 0.12 | 3.10 | 3.28 | 0.62 | 0.65 | 11
NGC 5427 | 2.15 | 0.13 | 0.18 |  7.96 | 0.14 | 3.10 | 3.95 | 0.80 | 0.88 | 11
NGC 5643 | 2.74 | 0.12 | 0.24 | 8.60 | 0.04 | 3.10 | 2.98 | 0.97 | 0.91 | 11
NGC 5990 | 1.88 | 0.01 | 0.07 | 2.16 | 0.09 | 3.10 | 2.06 | 0.48 | 0.42 | 11
NGC 7682 | 2.85 | 0.16 | 0.19 | 9.34 | 0.09 | 3.10 | 3.03 | 1.09 | 1.17 | 11
PKS 1306-241 | 3.47 | 0.04 | 0.05 | 3.82 | 0.10 | 3.10 | 1.25 | 0.69 | 0.61 | 11

References: (1) SDSS-DR7 (York et al., 2000), (2) Koski (1978), (3) Shuder
(1980), (4) Alloin et al. (1992), (5) Phillips et al. (1983), (6) Shuder &
Osterbrock (1981), (7) Dopita et al. (2015), (8) Osterbrock & Miller (1975),
(9) Durret (1994), (10) Bergvall et al. (1986). (11) Thomas et al. (2017).

Table 4: Reddening corrected emission line intensities (in relation to $\rm H\beta=1.0$) of the SF sample described in Sect. 2.2.  ObjID | [O ii] | [O iii] | He ii | [O iii] | He i | $\rm H\alpha$ | [N ii] | [S ii] | [S ii] | Ref.
---|---|---|---|---|---|---|---|---|---|---
|  $\lambda$3727 |  $\lambda$4363 |  $\lambda$4686 |  $\lambda$5007 |  $\lambda$5876 |  $\lambda$6563 |  $\lambda$6583 |  $\lambda$6716 |  $\lambda$6731 |
NGC3184-72.8+91.3 | $1.82\pm 0.01$ | $0.002\pm 0.0010$ | $0.011\pm 0.0010$ | $0.384\pm 0.002$ | $0.083\pm 0.001$ | $2.801\pm 0.027$ | $0.923\pm 0.008$ | $0.352\pm 0.003$ | $0.253\pm 0.002$ | 1
NGC3184+14.9-139.6 | $2.47\pm 0.04$ | $0.008\pm 0.0010$ | $0.024\pm 0.0030$ | $1.445\pm 0.016$ | $0.081\pm 0.006$ | $2.883\pm 0.046$ | $0.789\pm 0.012$ | $0.424\pm 0.006$ | $0.303\pm 0.005$ | 1
NGC3184+80.0-148.2 | $2.88\pm 0.03$ | $0.004\pm 0.0010$ | $0.007\pm 0.0010$ | $0.860\pm 0.018$ | $0.110\pm 0.010$ | $2.937\pm 0.056$ | $0.828\pm 0.016$ | $0.439\pm 0.009$ | $0.321\pm 0.007$ | 1
NGC3184-93.3-142.3 | $2.20\pm 0.03$ | $0.008\pm 0.0020$ | $0.001\pm 0.0010$ | $1.902\pm 0.031$ | $0.129\pm 0.010$ | $2.840\pm 0.067$ | $0.543\pm 0.013$ | $0.385\pm 0.009$ | $0.263\pm 0.006$ | 1
NGC3184-172.5-30.2 | $2.32\pm 0.01$ | $0.014\pm 0.0010$ | $0.003\pm 0.0010$ | $2.434\pm 0.017$ | $0.124\pm 0.004$ | $2.801\pm 0.023$ | $0.485\pm 0.005$ | $0.251\pm 0.002$ | $0.183\pm 0.001$ | 1
+164.6+9.9 | $1.94\pm 0.04$ | $0.002\pm 0.0002$ | $0.009\pm 0.0010$ | $0.980\pm 0.020$ | $0.116\pm 0.002$ | $3.015\pm 0.060$ | $0.650\pm 0.027$ | $0.161\pm 0.006$ | $0.116\pm 0.005$ | 2
+17.3-235.4 | $2.43\pm 0.03$ | $0.004\pm 0.0005$ | $0.001\pm 0.0004$ | $1.170\pm 0.023$ | $0.110\pm 0.002$ | $2.865\pm 0.057$ | $0.650\pm 0.020$ | $0.240\pm 0.007$ | $0.170\pm 0.005$ | 2
+189.2-136.3 | $1.60\pm 0.03$ | $0.006\pm 0.0002$ | $0.010\pm 0.0017$ | $2.603\pm 0.052$ | $0.140\pm 0.002$ | $2.815\pm 0.056$ | $0.400\pm 0.014$ | $0.113\pm 0.004$ | $0.090\pm 0.003$ | 2
-183.9-179.0 | $1.82\pm 0.03$ | $0.003\pm 0.0007$ | $0.001\pm 0.0004$ | $1.534\pm 0.031$ | $0.110\pm 0.002$ | $2.955\pm 0.059$ | $0.510\pm 0.020$ | $0.223\pm 0.009$ | $0.155\pm 0.007$ | 2
+225.6-124.1 | $2.49\pm 0.04$ | $0.006\pm 0.0004$ | $0.002\pm 0.0004$ | $1.747\pm 0.035$ | $0.118\pm 0.002$ | $2.874\pm 0.057$ | $0.530\pm 0.011$ | $0.252\pm 0.005$ | $0.179\pm 0.003$ | 2
+117.9-235.0 | $2.57\pm 0.06$ | $0.006\pm 0.0008$ | $0.018\pm 0.0017$ | $1.381\pm 0.028$ | $0.115\pm 0.003$ | $2.850\pm 0.057$ | $0.420\pm 0.015$ | $0.202\pm 0.007$ | $0.146\pm 0.005$ | 2
-200.3-193.6 | $2.00\pm 0.04$ | $0.006\pm 0.0006$ | $0.010\pm 0.0017$ | $1.966\pm 0.039$ | $0.114\pm 0.003$ | $2.697\pm 0.054$ | $0.380\pm 0.015$ | $0.230\pm 0.009$ | $0.161\pm 0.007$ | 2
+96.7+266.9 | $2.50\pm 0.05$ | $0.003\pm 0.0006$ | $0.003\pm 0.0004$ | $0.820\pm 0.016$ | $0.091\pm 0.002$ | $2.976\pm 0.060$ | $0.710\pm 0.026$ | $0.430\pm 0.016$ | $0.300\pm 0.012$ | 2
+252.2-109.8 | $2.44\pm 0.05$ | $0.007\pm 0.0005$ | $0.004\pm 0.0003$ | $1.623\pm 0.032$ | $0.099\pm 0.002$ | $2.794\pm 0.056$ | $0.600\pm 0.023$ | $0.370\pm 0.014$ | $0.260\pm 0.010$ | 2
+254.6-107.2 | $1.60\pm 0.05$ | $0.013\pm 0.0003$ | $0.008\pm 0.0010$ | $3.455\pm 0.069$ | $0.144\pm 0.004$ | $2.421\pm 0.048$ | $0.370\pm 0.020$ | $0.144\pm 0.008$ | $0.120\pm 0.006$ | 2
+281.4-71.8 | $2.84\pm 0.04$ | $0.007\pm 0.0005$ | $0.011\pm 0.0013$ | $1.621\pm 0.032$ | $0.120\pm 0.002$ | $2.885\pm 0.058$ | $0.430\pm 0.015$ | $0.191\pm 0.007$ | $0.130\pm 0.005$ | 2
-243.0+159.6 | $2.81\pm 0.05$ | $0.002\pm 0.0004$ | $0.003\pm 0.0005$ | $0.860\pm 0.017$ | $0.089\pm 0.003$ | $2.798\pm 0.056$ | $0.670\pm 0.027$ | $0.400\pm 0.016$ | $0.280\pm 0.012$ | 2
-297.7+87.1 | $3.01\pm 0.08$ | $0.005\pm 0.0005$ | $0.010\pm 0.0013$ | $1.197\pm 0.024$ | $0.109\pm 0.004$ | $2.811\pm 0.056$ | $0.630\pm 0.029$ | $0.370\pm 0.018$ | $0.270\pm 0.015$ | 2
-309.4+56.9 | $2.45\pm 0.06$ | $0.004\pm 0.0005$ | $0.008\pm 0.0013$ | $1.094\pm 0.022$ | $0.073\pm 0.003$ | $2.785\pm 0.056$ | $0.640\pm 0.028$ | $0.400\pm 0.017$ | $0.280\pm 0.013$ | 2
+354.1+71.2 | $2.43\pm 0.06$ | $0.019\pm 0.0005$ | $0.001\pm 0.0002$ | $3.520\pm 0.070$ | $0.113\pm 0.002$ | $2.887\pm 0.058$ | $0.330\pm 0.014$ | $0.218\pm 0.009$ | $0.159\pm 0.007$ | 2
-164.9-333.9 | $2.28\pm 0.05$ | $0.008\pm 0.0002$ | $0.007\pm 0.0011$ | $2.441\pm 0.049$ | $0.125\pm 0.002$ | $2.796\pm 0.056$ | $0.290\pm 0.013$ | $0.152\pm 0.006$ | $0.108\pm 0.004$ | 2
+360.9+75.3 | $1.75\pm 0.04$ | $0.017\pm 0.0005$ | $0.002\pm 0.0002$ | $3.537\pm 0.071$ | $0.114\pm 0.003$ | $2.884\pm 0.058$ | $0.250\pm 0.012$ | $0.168\pm 0.008$ | $0.120\pm 0.005$ | 2
-377.9-64.9 | $2.87\pm 0.07$ | $0.007\pm 0.0003$ | $0.004\pm 0.0003$ | $1.324\pm 0.026$ | $0.095\pm 0.002$ | $2.797\pm 0.056$ | $0.570\pm 0.026$ | $0.430\pm 0.020$ | $0.300\pm 0.017$ | 2
-99.6-388.0 | $1.87\pm 0.04$ | $0.020\pm 0.0004$ | $0.005\pm 0.0008$ | $3.882\pm 0.078$ | $0.125\pm 0.003$ | $2.663\pm 0.053$ | $0.260\pm 0.012$ | $0.150\pm 0.007$ | $0.122\pm 0.005$ | 2
-397.4-71.7 | $2.41\pm 0.05$ | $0.010\pm 0.0016$ | $0.014\pm 0.0031$ | $1.847\pm 0.037$ | $0.065\pm 0.003$ | $2.691\pm 0.054$ | $0.440\pm 0.016$ | $0.310\pm 0.012$ | $0.212\pm 0.008$ | 2
-226.9-366.4 | $3.94\pm 0.09$ | $0.008\pm 0.0006$ | $0.006\pm 0.0007$ | $1.514\pm 0.030$ | $0.109\pm 0.002$ | $2.752\pm 0.055$ | $0.400\pm 0.016$ | $0.290\pm 0.012$ | $0.204\pm 0.008$ | 2
-405.5-157.7 | $3.14\pm 0.06$ | $0.010\pm 0.0009$ | $0.011\pm 0.0020$ | $1.299\pm 0.026$ | $0.114\pm 0.005$ | $2.801\pm 0.056$ | $0.510\pm 0.021$ | $0.360\pm 0.015$ | $0.250\pm 0.011$ | 2
-345.5+273.8 | $3.52\pm 0.07$ | $0.039\pm 0.0014$ | $0.008\pm 0.0016$ | $4.450\pm 0.100$ | $0.100\pm 0.017$ | $2.810\pm 0.056$ | $0.380\pm 0.021$ | $0.550\pm 0.030$ | $0.400\pm 0.022$ | 2
-410.3-206.3 | $3.18\pm 0.08$ | $0.006\pm 0.0007$ | $0.004\pm 0.0010$ | $1.462\pm 0.029$ | $0.111\pm 0.003$ | $2.736\pm 0.055$ | $0.460\pm 0.021$ | $0.250\pm 0.012$ | $0.173\pm 0.008$ | 2
-371.1-280.0 | $2.52\pm 0.04$ | $0.016\pm 0.0003$ | $0.004\pm 0.0005$ | $2.665\pm 0.053$ | $0.111\pm 0.002$ | $2.865\pm 0.057$ | $0.360\pm 0.014$ | $0.270\pm 0.010$ | $0.195\pm 0.008$ | 2
-368.3-285.6 | $2.36\pm 0.04$ | $0.016\pm 0.0003$ | $0.003\pm 0.0004$ | $3.231\pm 0.065$ | $0.118\pm 0.002$ | $2.932\pm 0.059$ | $0.350\pm 0.013$ | $0.222\pm 0.008$ | $0.166\pm 0.006$ | 2
-392.0-270.1 | $1.55\pm 0.03$ | $0.021\pm 0.0004$ | $0.008\pm 0.0012$ | $3.721\pm 0.074$ | $0.117\pm 0.002$ | $2.879\pm 0.058$ | $0.223\pm 0.009$ | $0.138\pm 0.005$ | $0.105\pm 0.004$ | 2
-481.4-0.5 | $3.17\pm 0.07$ | $0.039\pm 0.0007$ | $0.009\pm 0.0013$ | $2.843\pm 0.057$ | $0.091\pm 0.002$ | $2.443\pm 0.049$ | $0.190\pm 0.011$ | $0.250\pm 0.015$ | $0.180\pm 0.011$ | 2
-453.8-191.8 | $2.65\pm 0.06$ | $0.036\pm 0.0009$ | $0.003\pm 0.0004$ | $3.747\pm 0.075$ | $0.103\pm 0.002$ | $2.620\pm 0.052$ | $0.185\pm 0.007$ | $0.204\pm 0.008$ | $0.142\pm 0.005$ | 2
+331.9+401.0 | $2.05\pm 0.04$ | $0.029\pm 0.0015$ | $0.003\pm 0.0009$ | $3.610\pm 0.072$ | $0.098\pm 0.006$ | $2.812\pm 0.056$ | $0.157\pm 0.007$ | $0.128\pm 0.005$ | $0.089\pm 0.004$ | 2
+509.5+264.1 | $2.04\pm 0.04$ | $0.033\pm 0.0006$ | $0.004\pm 0.0001$ | $4.173\pm 0.083$ | $0.107\pm 0.002$ | $2.832\pm 0.057$ | $0.153\pm 0.006$ | $0.157\pm 0.005$ | $0.110\pm 0.004$ | 2
+266.0+534.1 | $2.85\pm 0.07$ | $0.053\pm 0.0024$ | $0.030\pm 0.0054$ | $4.707\pm 0.094$ | $0.099\pm 0.014$ | $2.759\pm 0.055$ | $0.190\pm 0.012$ | $0.230\pm 0.014$ | $0.160\pm 0.010$ | 2
+667.9+174.1 | $1.21\pm 0.03$ | $0.088\pm 0.0027$ | $0.006\pm 0.0002$ | $6.740\pm 0.100$ | $0.110\pm 0.002$ | $2.714\pm 0.054$ | $0.082\pm 0.004$ | $0.105\pm 0.004$ | $0.086\pm 0.003$ | 2
+1.0+885.8 | $2.56\pm 0.06$ | $0.027\pm 0.0007$ | $0.017\pm 0.0008$ | $1.839\pm 0.037$ | $0.097\pm 0.007$ | $2.654\pm 0.053$ | $0.118\pm 0.006$ | $0.167\pm 0.007$ | $0.115\pm 0.005$ | 2
+6.6+886.3 | $2.37\pm 0.05$ | $0.039\pm 0.0010$ | $0.009\pm 0.0008$ | $2.688\pm 0.054$ | $0.103\pm 0.004$ | $2.682\pm 0.054$ | $0.111\pm 0.005$ | $0.163\pm 0.006$ | $0.112\pm 0.004$ | 2
NGC5194+30.2+2.2 | $1.51\pm 0.03$ | $0.013\pm 0.0035$ | $0.020\pm 0.0023$ | $0.341\pm 0.006$ | $0.062\pm 0.001$ | $2.960\pm 0.059$ | $1.394\pm 0.028$ | $0.266\pm 0.005$ | $0.246\pm 0.004$ | 3
NGC 2403-38+51 | $2.03\pm 0.13$ | $0.006\pm 0.0010$ | $0.018\pm 0.0110$ | $1.446\pm 0.114$ | $0.110\pm 0.008$ | $2.949\pm 0.182$ | $0.478\pm 0.028$ | $0.173\pm 0.013$ | $0.135\pm 0.011$ | 4
NGC 2403+7+37 | $2.12\pm 0.14$ | $0.007\pm 0.0010$ | $0.006\pm 0.0040$ | $1.429\pm 0.121$ | $0.114\pm 0.008$ | $2.952\pm 0.187$ | $0.455\pm 0.034$ | $0.178\pm 0.013$ | $0.131\pm 0.010$ | 4
NGC 2403+119-28 | $2.47\pm 0.10$ | $0.006\pm 0.0020$ | $0.008\pm 0.0050$ | $2.098\pm 0.094$ | $0.123\pm 0.006$ | $3.017\pm 0.126$ | $0.437\pm 0.027$ | $0.221\pm 0.014$ | $0.167\pm 0.014$ | 4
NGC 2403-59+118 | $1.47\pm 0.10$ | $0.005\pm 0.0010$ | $0.020\pm 0.0130$ | $2.230\pm 0.184$ | $0.130\pm 0.009$ | $2.939\pm 0.182$ | $0.266\pm 0.182$ | $0.147\pm 0.012$ | $0.104\pm 0.009$ | 4
NGC 2403+96+30 | $2.38\pm 0.05$ | $0.008\pm 0.0010$ | $0.008\pm 0.0040$ | $2.159\pm 0.070$ | $0.120\pm 0.005$ | $2.909\pm 0.092$ | $0.361\pm 0.020$ | $0.190\pm 0.011$ | $0.151\pm 0.009$ | 4
NGC 2403+44+82 | $2.99\pm 0.21$ | $0.005\pm 0.0010$ | $0.014\pm 0.0090$ | $1.383\pm 0.117$ | $0.114\pm 0.007$ | $3.067\pm 0.189$ | $0.453\pm 0.033$ | $0.204\pm 0.014$ | $0.144\pm 0.014$ | 4
NGC 2403+166-140 | $1.99\pm 0.14$ | $0.010\pm 0.0010$ | $0.014\pm 0.0090$ | $2.132\pm 0.180$ | $0.129\pm 0.010$ | $2.923\pm 0.183$ | $0.260\pm 0.021$ | $0.182\pm 0.015$ | $0.133\pm 0.011$ | 4
NGC 2403-99-59 | $3.31\pm 0.18$ | $0.007\pm 0.0010$ | $0.003\pm 0.0020$ | $1.699\pm 0.108$ | $0.109\pm 0.005$ | $2.992\pm 0.145$ | $0.482\pm 0.034$ | $0.345\pm 0.017$ | $0.247\pm 0.013$ | 4
NGC 2403-196+58 | $1.90\pm 0.07$ | $0.007\pm 0.0010$ | $0.006\pm 0.0040$ | $2.160\pm 0.084$ | $0.117\pm 0.005$ | $2.902\pm 0.102$ | $0.315\pm 0.023$ | $0.150\pm 0.008$ | $0.110\pm 0.006$ | 4
NGC 2403-22-162 | $3.63\pm 0.15$ | $0.009\pm 0.0020$ | $0.020\pm 0.0160$ | $1.792\pm 0.083$ | $0.116\pm 0.007$ | $2.881\pm 0.108$ | $0.394\pm 0.024$ | $0.331\pm 0.019$ | $0.241\pm 0.016$ | 4
NGC 2403+160-251 | $2.83\pm 0.20$ | $0.026\pm 0.0030$ | $0.015\pm 0.0030$ | $3.160\pm 0.261$ | $0.109\pm 0.007$ | $2.976\pm 0.178$ | $0.204\pm 0.017$ | $0.201\pm 0.014$ | $0.143\pm 0.011$ | 4
SDSS J1455 | $1.11\pm 0.01$ | $0.102\pm 0.0030$ | $0.007\pm 0.0009$ | $6.135\pm 0.033$ | $0.114\pm 0.003$ | $2.775\pm 0.018$ | $0.079\pm 0.002$ | $0.100\pm 0.002$ | $0.008\pm 0.002$ | 5
SDSS J1657 | $0.84\pm 0.02$ | $0.085\pm 0.2690$ | $0.032\pm 0.0043$ | $6.151\pm 0.037$ | $0.106\pm 0.007$ | $2.789\pm 0.014$ | $0.043\pm 0.002$ | $0.077\pm 0.002$ | $0.005\pm 0.002$ | 5
Reg-1 | $0.27\pm 0.01$ | $0.057\pm 0.0020$ | $0.023\pm 0.0070$ | $1.810\pm 0.080$ | $0.093\pm 0.003$ | $2.810\pm 0.100$ | $0.010\pm 0.002$ | $0.021\pm 0.001$ | $0.015\pm 0.001$ | 6
Table 5: continued

ObjID | [O ii] | [O iii] | He ii | [O iii] | He i | $\rm H\alpha$ | [N ii] | [S ii] | [S ii] | Ref.
---|---|---|---|---|---|---|---|---|---|---
|  $\lambda$3727 |  $\lambda$4363 |  $\lambda$4686 |  $\lambda$5007 |  $\lambda$5876 |  $\lambda$6563 |  $\lambda$6583 |  $\lambda$6716 |  $\lambda$6731 |
J0118+3512 | $0.84\pm 0.01$ | $0.064\pm 0.0016$ | $0.032\pm 0.0020$ | $3.062\pm 0.005$ | $0.114\pm 0.004$ | $3.349\pm 0.005$ | $0.039\pm 0.002$ | $0.110\pm 0.003$ | $0.085\pm 0.002$ | 7
J1322+5425 | $0.43\pm 0.01$ | $0.075\pm 0.0013$ | $0.010\pm 0.0008$ | $2.938\pm 0.005$ | $0.084\pm 0.001$ | $2.670\pm 0.008$ | $0.015\pm 0.001$ | $0.044\pm 0.001$ | $0.031\pm 0.001$ | 7
0723+692A | $0.61\pm 0.01$ | $0.143\pm 0.0010$ | $0.009\pm 0.0010$ | $6.591\pm 0.007$ | $0.106\pm 0.001$ | $2.788\pm 0.004$ | $0.024\pm 0.001$ | $0.049\pm 0.001$ | $0.037\pm 0.001$ | 8
0723+692B | $1.57\pm 0.01$ | $0.082\pm 0.0040$ | $0.014\pm 0.0040$ | $4.303\pm 0.031$ | $0.102\pm 0.003$ | $2.794\pm 0.023$ | $0.055\pm 0.003$ | $0.114\pm 0.003$ | $0.082\pm 0.003$ | 8
0749+568 | $1.66\pm 0.04$ | $0.098\pm 0.0110$ | $0.018\pm 0.0080$ | $4.880\pm 0.099$ | $0.111\pm 0.009$ | $2.797\pm 0.064$ | $0.076\pm 0.007$ | $0.178\pm 0.011$ | $0.114\pm 0.008$ | 8
0907+543 | $0.94\pm 0.02$ | $0.121\pm 0.0080$ | $0.029\pm 0.0010$ | $6.838\pm 0.109$ | $0.106\pm 0.007$ | $2.803\pm 0.053$ | $0.033\pm 0.005$ | $0.065\pm 0.006$ | $0.050\pm 0.005$ | 8
0917+527 | $1.88\pm 0.01$ | $0.092\pm 0.0040$ | $0.023\pm 0.0030$ | $4.680\pm 0.003$ | $0.103\pm 0.003$ | $2.797\pm 0.019$ | $0.058\pm 0.002$ | $0.164\pm 0.003$ | $0.114\pm 0.003$ | 8
0926+606 | $1.78\pm 0.01$ | $0.083\pm 0.0030$ | $0.016\pm 0.0020$ | $4.772\pm 0.026$ | $0.104\pm 0.003$ | $2.804\pm 0.017$ | $0.083\pm 0.002$ | $0.182\pm 0.003$ | $0.146\pm 0.003$ | 8
0930+554 | $0.40\pm 0.00$ | $0.060\pm 0.0020$ | $0.027\pm 0.0020$ | $1.961\pm 0.008$ | $0.081\pm 0.001$ | $2.930\pm 0.012$ | $0.013\pm 0.001$ | $0.031\pm 0.001$ | $0.023\pm 0.001$ | 8
1030+583 | $0.96\pm 0.00$ | $0.104\pm 0.0020$ | $0.024\pm 0.0020$ | $5.028\pm 0.021$ | $0.099\pm 0.002$ | $2.786\pm 0.013$ | $0.031\pm 0.001$ | $0.096\pm 0.002$ | $0.067\pm 0.001$ | 8
1116+583B | $0.58\pm 0.02$ | $0.117\pm 0.0120$ | $0.025\pm 0.0100$ | $4.842\pm 0.111$ | $0.101\pm 0.009$ | $2.777\pm 0.072$ | $0.027\pm 0.007$ | $0.068\pm 0.007$ | $0.065\pm 0.008$ | 8
1205+557 | $2.13\pm 0.02$ | $0.083\pm 0.0070$ | $0.018\pm 0.0070$ | $3.714\pm 0.043$ | $0.099\pm 0.005$ | $2.714\pm 0.035$ | $0.083\pm 0.005$ | $0.183\pm 0.007$ | $0.130\pm 0.007$ | 8
1222+614 | $1.16\pm 0.00$ | $0.102\pm 0.0020$ | $0.017\pm 0.0020$ | $5.955\pm 0.022$ | $0.100\pm 0.002$ | $2.761\pm 0.012$ | $0.038\pm 0.001$ | $0.090\pm 0.001$ | $0.065\pm 0.001$ | 8
1223+487 | $0.71\pm 0.00$ | $0.127\pm 0.0010$ | $0.012\pm 0.0010$ | $5.543\pm 0.008$ | $0.102\pm 0.001$ | $2.777\pm 0.005$ | $0.029\pm 0.001$ | $0.061\pm 0.001$ | $0.045\pm 0.001$ | 8
1256+351 | $1.10\pm 0.00$ | $0.089\pm 0.0010$ | $0.011\pm 0.0010$ | $5.802\pm 0.009$ | $0.106\pm 0.001$ | $2.819\pm 0.005$ | $0.046\pm 0.001$ | $0.095\pm 0.001$ | $0.071\pm 0.001$ | 8
1319+579A | $1.02\pm 0.00$ | $0.093\pm 0.0020$ | $0.008\pm 0.0010$ | $6.700\pm 0.028$ | $0.113\pm 0.002$ | $2.827\pm 0.014$ | $0.050\pm 0.001$ | $0.101\pm 0.001$ | $0.079\pm 0.001$ | 8
1319+579B4 | $2.44\pm 0.06$ | $0.050\pm 0.0150$ | $0.038\pm 0.0230$ | $3.282\pm 0.073$ | $0.094\pm 0.011$ | $2.815\pm 0.069$ | $0.161\pm 0.013$ | $0.374\pm 0.017$ | $0.273\pm 0.015$ | 8
1319+579C | $2.38\pm 0.01$ | $0.033\pm 0.0030$ | $0.014\pm 0.0040$ | $3.520\pm 0.025$ | $0.106\pm 0.003$ | $2.852\pm 0.022$ | $0.150\pm 0.003$ | $0.269\pm 0.004$ | $0.192\pm 0.004$ | 8
1358+576 | $1.67\pm 0.01$ | $0.089\pm 0.0030$ | $0.012\pm 0.0020$ | $4.874\pm 0.026$ | $0.112\pm 0.002$ | $2.803\pm 0.017$ | $0.108\pm 0.003$ | $0.153\pm 0.003$ | $0.111\pm 0.002$ | 8
1441+294 | $1.50\pm 0.03$ | $0.069\pm 0.0100$ | $0.019\pm 0.0130$ | $4.927\pm 0.099$ | $0.116\pm 0.009$ | $2.824\pm 0.064$ | $0.083\pm 0.008$ | $0.204\pm 0.011$ | $0.138\pm 0.010$ | 8
1533+574B | $2.03\pm 0.01$ | $0.065\pm 0.0040$ | $0.011\pm 0.0030$ | $5.329\pm 0.035$ | $0.108\pm 0.003$ | $2.849\pm 0.021$ | $0.087\pm 0.002$ | $0.167\pm 0.003$ | $0.117\pm 0.002$ | 8
Pox 105 | $1.25\pm 0.00$ | $0.113\pm 0.0000$ | $0.015\pm 0.0000$ | $5.540\pm 0.000$ | $0.096\pm 0.000$ | $2.800\pm 0.000$ | $0.064\pm 0.000$ | $0.084\pm 0.000$ | $0.058\pm 0.000$ | 9
Pox 120 | $0.79\pm 0.00$ | $0.135\pm 0.0000$ | $0.016\pm 0.0000$ | $6.290\pm 0.000$ | $0.101\pm 0.000$ | $2.780\pm 0.000$ | $0.048\pm 0.000$ | $0.074\pm 0.000$ | $0.047\pm 0.000$ | 9
Pox 139 | $1.47\pm 0.00$ | $0.096\pm 0.0000$ | $0.023\pm 0.0000$ | $5.710\pm 0.000$ | $0.101\pm 0.000$ | $2.800\pm 0.000$ | $0.019\pm 0.000$ | $0.117\pm 0.000$ | $0.077\pm 0.000$ | 9
UM 160 A | $1.33\pm 0.03$ | $0.085\pm 0.0068$ | $0.004\pm 0.0012$ | $5.240\pm 0.524$ | $0.100\pm 0.006$ | $2.800\pm 0.028$ | $0.048\pm 0.003$ | $0.111\pm 0.006$ | $0.085\pm 0.005$ | 10
UM 160 B | $1.48\pm 0.03$ | $0.066\pm 0.0066$ | $0.023\pm 0.0035$ | $4.740\pm 0.474$ | $0.096\pm 0.007$ | $2.780\pm 0.055$ | $0.071\pm 0.005$ | $0.152\pm 0.009$ | $0.102\pm 0.006$ | 10
UM 420 B | $2.57\pm 0.05$ | $0.061\pm 0.0073$ | $0.023\pm 0.0058$ | $4.260\pm 4.260$ | $0.113\pm 0.006$ | $2.810\pm 0.056$ | $0.245\pm 0.009$ | $0.250\pm 0.010$ | $0.196\pm 0.009$ | 10
TOL 0513-393 | $0.53\pm 0.01$ | $0.155\pm 0.0061$ | $0.010\pm 0.0015$ | $7.760\pm 0.776$ | $0.128\pm 0.005$ | $2.820\pm 0.028$ | $0.045\pm 0.002$ | $0.062\pm 0.003$ | $0.053\pm 0.003$ | 10
TOL 2146-391-C | $0.61\pm 0.00$ | $0.127\pm 0.0026$ | $0.017\pm 0.0009$ | $5.941\pm 0.059$ | $0.109\pm 0.002$ | $2.820\pm 0.028$ | $0.027\pm 0.001$ | $0.066\pm 0.001$ | $0.052\pm 0.001$ | 11
TOL 2146-391-E | $0.64\pm 0.00$ | $0.127\pm 0.0038$ | $0.018\pm 0.0013$ | $5.897\pm 0.058$ | $0.106\pm 0.003$ | $2.770\pm 0.027$ | $0.028\pm 0.001$ | $0.067\pm 0.002$ | $0.052\pm 0.002$ | 11
TOL 0357-3915-C | $0.81\pm 0.01$ | $0.123\pm 0.0043$ | $0.019\pm 0.0016$ | $6.549\pm 0.065$ | $0.111\pm 0.003$ | $2.800\pm 0.028$ | $0.055\pm 0.002$ | $0.065\pm 0.002$ | $0.049\pm 0.002$ | 11
TOL 0357-3915-E | $0.85\pm 0.01$ | $0.116\pm 0.0058$ | $0.013\pm 0.0019$ | $6.300\pm 0.063$ | $0.107\pm 0.005$ | $2.810\pm 0.042$ | $0.058\pm 0.004$ | $0.070\pm 0.004$ | $0.054\pm 0.003$ | 11
NGC 346 | $0.80\pm 0.01$ | $0.070\pm 0.0014$ | $0.002\pm 0.0002$ | $5.220\pm 0.044$ | $0.108\pm 0.001$ | $2.820\pm 0.023$ | $0.038\pm 0.001$ | $0.074\pm 0.001$ | $0.053\pm 0.001$ | 12

References: (1) Berg et al. (2020), (2) Croxall et al. (2016), (3) Croxall et
al. (2015), (4) Rogers et al. (2021), (5) Hägele et al. (2008), (6) Annibali
et al. (2019), (7) Hsyu et al. (2020), (8) Izotov et al. (1997), (9) Kunth &
Sargent (1983), (10) Valerdi et al. (2021a), (11) Peimbert et al. (2012), (12)
Valerdi et al. (2019).

Table 6: Chemical abundances for the Seyfert 2 and Star-forming samples. ObjID |  a O+/H+ |  a O2+/H+ | ICF(O) |  b O/H |  a He+/H+ |  a He2+/H+ | ICF(He) |  b He/H
---|---|---|---|---|---|---|---|---
Seyfert 2
J013957.81-004504.2 |  8.564 $\pm$ 0.041 |  8.324 $\pm$ 0.006 | 1.3 |  8.901 $\pm$ 0.129 |  10.626 $\pm$ 0.144 |  10.120 $\pm$ 0.027 | 1.5 |  10.918 $\pm$ 0.075
J033923.14-054841.5 |  8.522 $\pm$ 0.033 |  8.185 $\pm$ 0.001 | 1.3 |  8.815 $\pm$ 0.026 |  10.805 $\pm$ 0.048 |  10.339 $\pm$ 0.017 | 1.5 |  11.114 $\pm$ 0.023
J074257.23+333217.9 |  8.366 $\pm$ 0.021 |  7.700 $\pm$ 0.001 | 1.1 |  8.491 $\pm$ 0.018 |  10.852 $\pm$ 0.044 |  9.833 $\pm$ 0.055 | 1.3 |  11.007 $\pm$ 0.031
J093509.12+002557.4 |  8.438 $\pm$ 0.017 |  7.647 $\pm$ 0.002 | 1.2 |  8.580 $\pm$ 0.019 |  10.700 $\pm$ 0.061 |  9.981 $\pm$ 0.039 | 1.4 |  10.931 $\pm$ 0.037
J095759.45+022810.5 |  8.631 $\pm$ 0.033 |  8.208 $\pm$ 0.004 | 1.4 |  8.912 $\pm$ 0.029 |  10.757 $\pm$ 0.056 |  10.338 $\pm$ 0.017 | 1.6 |  11.092 $\pm$ 0.026
J100602.50+071131.8 |  8.825 $\pm$ 0.003 |  7.904 $\pm$ 0.001 | 1.4 |  9.012 $\pm$ 0.014 |  10.807 $\pm$ 0.046 |  10.370 $\pm$ 0.015 | 1.6 |  11.158 $\pm$ 0.021
J100921.26+013334.5 |  8.599 $\pm$ 0.036 |  8.377 $\pm$ 0.002 | 1.3 |  8.931 $\pm$ 0.025 |  10.888 $\pm$ 0.038 |  10.416 $\pm$ 0.014 | 1.5 |  11.191 $\pm$ 0.020
J101754.72-002811.9 |  8.404 $\pm$ 0.026 |  7.801 $\pm$ 0.002 | 1.3 |  8.615 $\pm$ 0.022 |  10.895 $\pm$ 0.040 |  10.370 $\pm$ 0.016 | 1.5 |  11.183 $\pm$ 0.021
J102039.81+642435.8 |  8.681 $\pm$ 0.099 |  7.979 $\pm$ 0.003 | 1.4 |  8.914 $\pm$ 0.083 |  10.699 $\pm$ 0.061 |  10.334 $\pm$ 0.017 | 1.6 |  11.066 $\pm$ 0.027
J112850.39+021016.2 |  8.734 $\pm$ 0.029 |  7.456 $\pm$ 0.010 | 1.2 |  8.850 $\pm$ 0.033 |  11.049 $\pm$ 0.082 |  10.409 $\pm$ 0.031 | 1.4 |  11.298 $\pm$ 0.046
Mrk176 |  8.564 $\pm$ 0.008 |  8.115 $\pm$ 0.004 | 1.5 |  8.882 $\pm$ 0.012 |  10.849 $\pm$ 0.028 |  10.576 $\pm$ 0.007 | 1.6 |  11.238 $\pm$ 0.012
3C33 |  8.740 $\pm$ 0.006 |  7.998 $\pm$ 0.005 | 1.3 |  8.939 $\pm$ 0.010 |  10.835 $\pm$ 0.028 |  10.361 $\pm$ 0.011 | 1.5 |  11.144 $\pm$ 0.014
Mrk3 |  8.549 $\pm$ 0.008 |  8.144 $\pm$ 0.005 | 1.3 |  8.796 $\pm$ 0.010 |  10.771 $\pm$ 0.032 |  10.194 $\pm$ 0.015 | 1.5 |  11.035 $\pm$ 0.018
Mrk573 |  8.492 $\pm$ 0.010 |  8.244 $\pm$ 0.005 | 1.4 |  8.844 $\pm$ 0.011 |  10.848 $\pm$ 0.028 |  10.488 $\pm$ 0.008 | 1.6 |  11.196 $\pm$ 0.012
Mrk78 |  8.782 $\pm$ 0.006 |  8.351 $\pm$ 0.005 | 1.4 |  9.071 $\pm$ 0.010 |  10.851 $\pm$ 0.027 |  10.469 $\pm$ 0.008 | 1.6 |  11.204 $\pm$ 0.012
Mrk348 |  8.654 $\pm$ 0.007 |  8.032 $\pm$ 0.005 | 1.2 |  8.836 $\pm$ 0.007 |  10.927 $\pm$ 0.023 |  10.286 $\pm$ 0.013 | 1.4 |  11.173 $\pm$ 0.013
Mrk34 |  8.590 $\pm$ 0.008 |  8.280 $\pm$ 0.005 | 1.3 |  8.871 $\pm$ 0.008 |  10.929 $\pm$ 0.022 |  10.376 $\pm$ 0.010 | 1.5 |  11.202 $\pm$ 0.012
Mrk1 |  8.450 $\pm$ 0.010 |  8.073 $\pm$ 0.005 | 1.4 |  8.740 $\pm$ 0.011 |  10.849 $\pm$ 0.027 |  10.416 $\pm$ 0.009 | 1.5 |  11.167 $\pm$ 0.013
Mrk270 |  8.844 $\pm$ 0.005 |  7.707 $\pm$ 0.007 | 1.2 |  8.936 $\pm$ 0.006 |  11.123 $\pm$ 0.014 |  10.298 $\pm$ 0.013 | 1.4 |  11.320 $\pm$ 0.009
IIIZw55 |  8.655 $\pm$ 0.009 |  7.543 $\pm$ 0.009 | 1.3 |  8.799 $\pm$ 0.011 |  10.799 $\pm$ 0.031 |  10.260 $\pm$ 0.014 | 1.5 |  11.086 $\pm$ 0.016
3C452 |  8.771 $\pm$ 0.006 |  7.710 $\pm$ 0.009 | 1.0 |  8.825 $\pm$ 0.006 |  11.088 $\pm$ 0.017 |  9.719 $\pm$ 0.048 | 1.4 |  11.242 $\pm$ 0.012
Mrk198 |  8.446 $\pm$ 0.012 |  7.722 $\pm$ 0.011 | 1.1 |  8.556 $\pm$ 0.011 |  10.898 $\pm$ 0.025 |  9.815 $\pm$ 0.037 | 1.3 |  11.049 $\pm$ 0.018
Mrk268 |  8.930 $\pm$ 0.007 |  7.241 $\pm$ 0.012 | 1.1 |  8.983 $\pm$ 0.008 |  10.824 $\pm$ 0.027 |  9.861 $\pm$ 0.033 | 1.3 |  10.991 $\pm$ 0.019
NGC2110 |  8.796 $\pm$ 0.006 |  7.387 $\pm$ 0.012 | 1.1 |  8.836 $\pm$ 0.007 |  10.992 $\pm$ 0.018 |  9.736 $\pm$ 0.043 | 1.3 |  11.131 $\pm$ 0.013
ESO138G1 |  8.572 $\pm$ 0.015 |  7.596 $\pm$ 0.018 | 1.4 |  8.752 $\pm$ 0.027 |  10.885 $\pm$ 0.079 |  10.439 $\pm$ 0.029 | 1.5 |  11.198 $\pm$ 0.037