2022

[1]J. Eduardo Méndez-Delgado

[1]Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität
Heidelberg, Mönchhofstraße 12-14, Heidelberg, D-69120, Baden-Württemberg,
Germany

2]Instituto de Astrofísica de Canarias, (IAC), Vía Láctea, 1, San Cristóbal de
La Laguna, E-38205, Santa Cruz de Tenerife, Spain

3]Departamento de Astrofísica, Universidad de La Laguna, Astrofísico Francisco
Sánchez, s/n., San Cristóbal de La Laguna, E-38206, Santa Cruz de Tenerife,
Spain

4]Instituto de Astronomía, Universidad Nacional Autónoma de México, Apartado
Postal 70-264, Coyoacán, 04510, Mexico City, México

# Temperature inhomogeneities cause the abundance discrepancy in H II regions

<EMAIL_ADDRESS>César Esteban  Jorge García-Rojas  Kathryn Kreckel
Manuel Peimbert  *  [  [  [

###### Abstract

H II regions, ionized nebulae where massive star formation has taken place,
exhibit a wealth of emission lines that are the fundamental basis for
estimating the chemical composition of the Universe. For more than 80 years, a
discrepancy of at least a factor of two between heavy-element abundances
derived with collisional excited lines (CELs) and the weaker recombination
lines (RLs) has thrown our absolute abundance determinations into doubt. Heavy
elements regulate the cooling of the interstellar gas, being essential to the
understanding of several phenomena such as nucleosynthesis, star formation and
chemical evolution. In this work, we use the best available deep optical
spectra of ionized nebulae to analyze the cause of this abundance discrepancy
problem. We find for the first time general observational evidence in favor of
the temperature inhomogeneities within the gas, quantified by $t^{2}$. The
temperature inhomogeneities inside H II regions are affecting only the gas of
high ionization degree and producing the abundance discrepancy problem. This
work implies that the metallicity determinations based on CELs must be
revised, as they can be severely underestimated, especially in the regions of
lower metallicity, such as the JWST high-z galaxies. We present methods to
estimate these corrections, which will be critical for robust interpretations
of the chemical composition of the Universe over cosmic time.

###### keywords:

H II regions, Interstellar abundances, Galaxy abundances, Galaxy chemical
evolution

Since the pioneering work by Wyse1942 , in essentially all studies where the
weak recombination lines (RLs) of heavy-element ions have been detected in
ionized nebulae, they imply systematically higher heavy element abundances
than those derived from the stronger collisionally excited lines (CELs). Given
that the line emission is produced by the same ion through different
mechanisms, the abundance discrepancy points to inconsistencies or missing
physics in the assumptions underlying the derivation of chemical abundances.
Several hypotheses have been proposed over the last 80 years in attempts to
resolve this issue. For instance, temperature inhomogeneities Peimbert1967 ,
chemical inhomogeneities Torres-Peimbert1990 , errors in the atomic
recombination coefficients rodriguez2010 , a non-Maxwellian electron velocity
distribution Nicholls2012 , recombination contributions to the auroral CELs
Rubin1986  and some others Peimbert2017 ; garciarojas20 . The lack of clear
observational confirmation of any of these ideas has prevented a general
solution to this problem until now.

In H II regions the highly ionized gas is usually concentrated in the volume
closest to the massive O or early B type stars, while the less ionized ions
are concentrated in outer shells. Therefore, it is common to estimate a
representative temperature for each volume of gas using CEL intensity ratios,
usually $T_{\rm e}$([O III] $\lambda 4363/\lambda 5007$) and $T_{\rm e}$([N
II] $\lambda 5755/\lambda 6584$) for the volume with high and low degree of
ionization, respectively. The reason why the existence of temperature
inhomogeneities within a given ionization zone can produce the abundance
discrepancy is that the emission of CELs increases exponentially with
temperature, whereas the emissivity of RLs depends on this parameter to a much
lesser extent (decreasing proportionally to a power of $T_{\rm e}$ close to
1). Therefore, in case of inhomogeneities, $T_{\rm e}$ derived from CEL
intensity ratios will be systematically biased towards higher values than the
average temperature Peimbert1967 . Then, by deriving the chemical composition
based on the intensity ratio of CELs and H I RLs, an exponential systematic
error towards lower abundances will be introduced. On the other hand, the
intensity ratio of RLs is less sensitive to temperature, making it more
suitable for deriving the true chemical composition of the gas. In the
paradigm proposed by Peimbert1967 ; Peimbert1969 , for a given ion $X^{i+}$,
the average temperature of the gas will be:

$T_{0}(X^{i+})=\frac{\int T_{\rm e}n_{\rm e}n(X^{i+})dV}{\int n_{\rm
e}n(X^{i+})dV},$ (1)

where $T_{\rm e}$, $n_{\rm e}$ are the electron temperature and density at a
given volume of the nebula, whereas $n(X^{i+})$ is the particle density of the
ion. If there are temperature inhomogeneities, these can be quantified by the
root mean square deviation from the averaged temperature:

$t^{2}(X^{i+})=\frac{\int[T_{\rm e}-T_{0}(X^{i+})]^{2}n_{\rm
e}n(X^{i+})dV}{T_{0}(X^{i+})^{2}\int n_{\rm e}n(X^{i+})dV}.$ (2)

We use a collection of 20 and 23 deep optical spectra of Galactic and
extragalactic H II regions, respectively as well as 8 spectra of Galactic ring
nebulae (RNe), which are nebulae created by mass-loss episodes from young very
massive stars. These data have the best quality available in the literature,
being carefully and homogeneously reduced and analyzed over more than 20 years
by our research group, containing the following characteristics: (i) have at
least one line detected from the recombination O II multiplet V1, free of line
blending with other lines that are not O II V1 RLs or observational issues.
(ii) uncertainties in the line ratios smaller than 40%. (iii) reliable
detections of both temperature-sensitive [N II] $\lambda 5755$ and [O III]
$\lambda 4363$ CELs. Following the so-called direct method, we calculate the
electron density of the nebulae, as well as $T_{\rm e}$([O III] $\lambda
4363/\lambda 5007$), $T_{\rm e}$([N II] $\lambda 5755/\lambda 6584$) and
$T_{\rm e}$([Ar III] $\lambda 5192/\lambda 7751$) when available. We derive
$T_{\rm e}$(O II V1/[O III]$\lambda 5007$) using the formalism proposed by
Peimbert2013  with the updated atomic data from Storey2017 .

Not surprisingly, in all cases, $\text{O}^{2+}/\text{H}^{+}$ derived from the
O II V1 RLs is found to be higher than the same ratio derived from the [O III]
$\lambda 5007$ CEL (see Table 8). The ratio of both ionic abundances is called
the abundance discrepancy factor (ADF). By comparing the $T_{\rm e}$([O III]
$\lambda 4363/\lambda 5007$) and $T_{\rm e}$(O II V1/[O III]$\lambda 5007$)
-determined using Eqs. 10 and 11 from Peimbert2013 -, we derive
$T_{0}(\text{O}^{2+})$ and $t^{2}(\text{O}^{2+})$. The last parameter is the
degree of spatial temperature variations within the high ionization zone that
is required in order to reconcile the $\text{O}^{2+}/\text{H}^{+}$ ratios
derived from RLs and CELs.

Since the observations of the extragalactic H II regions cover the complete
temperature structure, we will initially focus our analysis on these regions
in order to avoid the scatter that may be induced by aperture effects.
Contrary to what was argued in several studies garciarojas2007 ; Peimbert2017
; mendezdelgado22a  that were limited to a small number of H II regions, there
is no “typical” $t^{2}(\text{O}^{2+})$ value for these nebulae (See Table 7).
As pointed out by esteban02 ; Peimbert2012 ; Toribio17 , very high values of
$t^{2}(\text{O}^{2+})$ can be found in “low metallicity” H II regions.
However, the connection between $t^{2}(\text{O}^{2+})$ and the physical
conditions of the gas was not obvious in these previous studies. In Fig. 1 we
show the missing connection, $t^{2}(\text{O}^{2+})$ is linearly correlated
with $\Delta T_{\rm e}=T_{\rm e}$([O III] $\lambda 4363/\lambda 5007)-T_{\rm
e}$([N II] $\lambda 5755/\lambda 6584$), as follows:

$t^{2}\left(\text{O}^{2+}\right)=\left(2.90\pm 0.21\right)\times 10^{-5}\Delta
T_{\rm e}+\left(4.68\pm 0.18\right)\times 10^{-2}(\text{K}).$ (3)

Figure 1: Linear correlation between $t^{2}(\text{O}^{2+})$, the temperature
inhomogeneities parameter value required to solve the abundance discrepancy
problem and the difference of the derived temperatures of the ionized gas for
extragalactic H II regions. The color bar corresponds to the O/H abundance
derived from CELs assuming a homogeneous temperature structure ($t^{2}=0$).
The Pearson correlation coefficient of the fit (r) is 0.96.

The explanation and the implications of this correlation are the following:

  * •

The linear relationship between $t^{2}(\text{O}^{2+})$ and $\Delta T_{\rm e}$
is a consequence of the fact that $T_{\rm e}$([N II] $\lambda 5755/\lambda
6584$) behaves as the average temperature in the N+ volume (See Eq. (2)). This
implies that temperature inhomogeneities are negligible in the low ionization
zone (i.e. $t^{2}(\text{O}^{+})\approx 0$). This is demonstrated in Fig. 2,
where a tight linear correlation between $T_{\rm e}$([N II] $\lambda
5755/\lambda 6584$) and $T_{0}(\text{O}^{2+})$ is presented.

  * •

The fact that $T_{\rm e}$(O II V1/[O III]$\lambda 5007$) (practically
identical to $T_{0}(\text{O}^{2+})$ in H II regions) is correlated with
$T_{\rm e}$([N II] $\lambda 5755/\lambda 6584$) also demonstrates that the
first value is physically representing a gas temperature.

  * •

As $T_{\rm e}$(O II V1/[O III]$\lambda 5007$) $<$ $T_{\rm e}$([O III] $\lambda
4363/\lambda 5007)$, with the first being a real value of temperature, we show
that a physical process is acting preferentially in the inner high ionization
volume, increasing the intensity of the temperature sensitive [O III] $\lambda
4363$ CEL. This demonstrate the existence of real temperature inhomogenities.

  * •

Therefore $t^{2}(\text{O}^{2+})$ is not an ad-hoc parameter to solve the
abundance discrepancy of the O2+ ion, it is indeed describing inhomogenities
in the temperature of the highly ionized gas.

On the first point mentioned above, it should be noted that $T_{\rm e}$([N II]
$\lambda 5755/\lambda 6584$) is not involved in the estimation of
$T_{0}(\text{O}^{2+})$ or $T_{\rm e}$(O II V1/[O III]$\lambda 5007$) in any
sense. We interpret the relationship shown in Fig. 2 as a consequence of the
natural stratification of temperatures expected in the photoionized gas due to
the combination of the hardening of the stellar radiation and the stronger
cooling from [O III] lines, which are more efficient at cooling than those of
[O II] (stasinska:1980, ; Garnett:1992, ). The linear fit between both
quantities is presented in Eq. (4).

Figure 2: Relation between $T_{\rm e}$([N II] $\lambda 5755/\lambda 6584$) and
$T_{0}(\text{O}^{2+})$ for extragalactic H II regions.

$T_{0}(\text{O}^{2+})=\left(1.17\pm 0.05\right)\times T_{\rm
e}(\text{[N\,II]})-\left(3340\pm 470\right)(\text{K}).$ (4)

Figure 3: $t^{2}(\text{O}^{2+})$ versus $\Delta T_{\rm e}$ relation for
Galactic and extragalactic H II regions and ring nebulae.

When we extend the analysis to the Galactic H II regions and RNe, as shown in
Fig. 3, we observe that in general they follow the same trend as the
extragalactic H II regions. Five spectra from different areas of NGC 6888
esteban16 , a bubble of ionized gas created by the Wolf-Rayet WN6 star WR136
and three from NGC 7635 esteban16 , created by the O6.5(n)fp star BD+60 2522
sota11  and the surrounding interstellar gas show also a good agreement with
the general trend of the H II regions. This is remarkable in the case of some
peripheral zones of NGC 6888, that show particularly large values of
$t^{2}(\text{O}^{2+})$. This implies that stellar feedback processes can
contribute to the inhomogeneous heating of the gas and are related to the
origin of temperature inhomogeneities. This is consistent with the fact that
the gas with a high degree of ionization, which is located physically closer
to the ionizing stars in typical H II regions, is the most affected one by the
temperature inhomogeneities. Variations in the hardness of the stellar
ionizing spectra may also contribute to $t^{2}(\text{O}^{2+})$ Perez1997 ;
Ercolano07 .

To test the impact of our results on the metallicity of our sample of
extragalactic H II regions, we compare the effect of considering $t^{2}>0$
only in the high ionization volume. The results are shown in Fig. 4, and
highlight that the metallicity underestimation tends to be larger at lower
metallicities, reaching values as high as 0.5 dex. Considering these results,
we can infer a $T_{\rm e}$([N II] $\lambda 5755/\lambda 6584$)-metallicity
relation, provided in Eq. (5) and shown in Fig. 5, which allows a quick
estimation of the metallicity considering $t^{2}(\text{O}^{2+})>0$.

Figure 4: Effects on metallicity of considering temperature inhomogeneities
affecting only the high ionization volume in our sample of extragalactic H II
regions. Figure 5: $T_{\rm e}$([N II] $\lambda 5755/\lambda 6584$)-metallicity
relation considering $t^{2}(\text{O}^{2+})>0$ for our sample of extragalactic
H II regions.

$12+\text{log(O/H)}=\left(-1.19\pm 0.14\right)\times 10^{-4}T_{\rm
e}\text{([N\,II])}+\left(9.68\pm 0.15\right)\text{(K).}$ (5)

Based on deep optical spectra of Galactic and extragalactic H II regions and
ring nebulae, we conclude that temperature inhomogenities are present within
these nebulae. These inhomogeneities cause the long-standing discrepancy
between the heavy-element abundances determined with CELs and RLs. The
observational evidence show that the temperature inhomogenities affect only
the volume of high degree of ionization, the closest to the ionizing stars.
This is a change of paradigm even for the community who consider $t^{2}>0$ in
their studies. Stellar feedback processes and radiation hardness fluctuations
of the stellar spectra are potential candidates to produce the observed
inhomogeneities. The chemical abundances estimated with CELs, the most
accessible observationally, must be revised because they are underestimated.
Both the abundances determined by the direct method and those estimated by
strong lines ones calibrated by observations require revision, since both
depend on $T_{\rm e}$([O III] $\lambda 4363/\lambda 5007$). We provide Eq.
(3), Eq. (4) and Eq. (5), which allow us to consider the effect of temperature
inhomogenities in the calculation of chemical abundances even if only CELs are
observed. This is especially important in low metallicity H II regions where
the values of $t^{2}(\text{O}^{2+})$ are higher, and metallicities are
systematically underestimated (Fig. 4). This work has far-reaching
implications for chemical evolution studies of galaxies, where the build-up of
elements is treated as a cosmic clock. This is particular critical in our
examination of the mass-metallicity relationships of galaxies Maiolino19 , as
well as recent efforts to directly track chemical evolution over cosmic time
by using JWST to observe [O III] auroral lines in high-z galaxies arellano2022
; Curti2023 ; Katz:2023 . Based on our findings, $t^{2}$ should be considered
as a fundamental physical parameter both in observational and theoretical
works.

##  1 Methods

For the sample of nebulae presented in Tables 2, 3, 5 and 6, we derive the
physical conditions and ionic abundances by the so-called direct method in a
consistent way. All values obtained are based on the intensities reported in
the reference spectra. We discard the use of lines with observational issues
as telluric absorptions or sky line contaminations. We use PyNeb 1.1.13
(Luridiana:2015, ) and the atomic data set provided in Table 1 to estimate the
electron density ($n_{\rm e}$) and temperature ($T_{\rm e}$). As a first step,
we derive the $n_{\rm e}$-$T_{\rm e}$ cross-match convergence by solving the
statistical equilibrium equations with the [S II] $\lambda 6731/\lambda 6716$,
[O II] $\lambda 3726/\lambda 3729$, [Cl III] $\lambda 5538/\lambda 5518$, [Fe
III] $\lambda 4658/\lambda 4702$ and [Ar IV] $\lambda 4740/\lambda 4711$
density diagnostics and the [O III] $\lambda 4363/\lambda 5007$, [N II]
$\lambda 5755/\lambda 6584$, [Ar III] $\lambda 5192/\lambda 7135$ temperature
diagnostics, using the task getCrossTemDen of PyNeb. For each density
diagnostic, we average the convergence value of each cross-matching.
Considering that [S II] $\lambda 6731/\lambda 6716$ and [O II] $\lambda
3726/\lambda 3729$ have their maximum sensitivity with density in the range of
values $10^{2}\text{ cm}^{-3}<n_{\rm e}<10^{4}\text{ cm}^{-3}$ IFF05 ;
Tayal:2010 ; FroeseFischer:2004 ; Kisielius:2009 , whereas [Cl III] $\lambda
5538/\lambda 5518$, [Fe III] $\lambda 4658/\lambda 4702$ and [Ar IV] $\lambda
4740/\lambda 4711$ are good diagnostics in the range of $10^{3}\text{
cm}^{-3}<n_{\rm e}<10^{6}\text{ cm}^{-3}$ Fritzsche:1999 ; Butler:1989 ;
Mendoza:1982b ; Ramsbottom:1997 ; Quinet:1996 ; Zhang:1996 , we derive an
average representative $n_{\rm e}$ adopting the following criteria:

  * •

If $n_{\rm e}$([S II]) $<$ 100 cm-3, we adopt $n_{\rm e}<$ 100 cm-3.

  * •

If 100 cm-3 $<$ $n_{\rm e}$([S II]) $<$ 1000 cm-3, we adopt the average value
of $n_{\rm e}$([S II]) and $n_{\rm e}$([O II]).

  * •

If $n_{\rm e}$([S II]) $>$ 1000 cm-3, we take the average values of $n_{\rm
e}$([S II]), $n_{\rm e}$([O II]), $n_{\rm e}$([Cl III]), $n_{\rm e}$([Fe III])
and $n_{\rm e}$([Ar IV]) when available.

In all cases, the averaged values are weighted by the inverse of the square of
the error. All the extragalactic H II regions but one follow the first two
criteria and therefore in Tables 2, 4 we only present $n_{\rm e}$([O II]),
$n_{\rm e}$([S II]) as well as the adopted value. The exception is N 88A
dominguezguzman22 , where we follow the third criteria given its higher
density. Therefore, in addition to the values of $n_{\rm e}$([S II]) and
$n_{\rm e}$([O II]) shown in Table 2, we take into account $n_{\rm e}$([Cl
III])=$3890^{+280}_{-320}$ cm-3, $n_{\rm e}$([Ar IV])=$5860^{+910}_{-920}$
cm-3 and $n_{\rm e}$([Fe III])=$7570^{+3870}_{-2940}$ cm-3 for N 88A. Once
$n_{\rm e}$ is well established, we derive $T_{\rm e}$([O III] $\lambda
4363/\lambda 5007$), $T_{\rm e}$([N II] $\lambda 5755/\lambda 6584$) and
$T_{\rm e}$([Ar III] $\lambda 5192/\lambda 7751$) when available, using the
getTemDen task of PyNeb.

In the case of O II RLs, we consider only those from the multiplet V1,
individually measured or blended with other lines of the same multiplet. In
each region we sum the intensity of all the O II V1 observed lines and we
estimate the intensity of the complete multiplet with the effective
recombination coefficients from Storey2017 , which consider the population of
the O II levels. These values of the total intensity of multiplet V1 are
presented in the fifth column of the Table 7. The number of observed O II V1
lines is presented in the sixth column. Note that the relative intensity of
the O II V1 RLs is independent of the temperature, while it depends on the
density for values between $10^{2.5}\text{ cm}^{-3}<n_{\rm e}<10^{4}\text{
cm}^{-3}$ Storey2017 . Since the total intensity of the multiplet V1 is
independent of the density, this could introduce some errors in high-density
regions with an incorrect estimation of $n_{\rm e}$ (by an order of magnitude)
and when only one O II V1 RL is detected. However, this case does not occur in
our sample and our conclusions do not depend on this.

$T_{\rm e}$(O II V1/[O III]$\lambda 5007$) was derived using the
aforementioned O II V1 intensities with respect to [O III]$\lambda 5007$ and
is presented in the second column of Table 7 for each object of our sample.
The O II V1/[O III]$\lambda 5007$ line intensity ratio depends on the electron
temperature in a different proportion than [O III] $\lambda 4363$/$\lambda
5007$, given the different dependence of the emissivities of O II V1 and [O
III] $\lambda 4363$ lines with $T_{\rm e}$. If we assume that both RLs and
CELs arise from the same ionized gas, the difference between $T_{\rm e}$(O II
V1/[O III]$\lambda 5007$) and $T_{\rm e}$([O III] $\lambda 4363/\lambda 5007$)
give us an estimate of the temperature inhomogeneities. It should be noted
that the derived $T_{\rm e}$(O II V1/[O III]$\lambda 5007$) is the temperature
value that eliminates the discrepancy between the
$n(\text{O}^{2+})$/$n(\text{H}^{+})$ ratio derived with CELs and RLs. Using
the formalism of Peimbert2013  -Eqs. (10) and (11)-, we calculate $T_{0}$(O2+)
and $t^{2}$(O2+). It is important to highlight that the ADF is not synonymous
with $t^{2}$. ADF(O2+) is the consequence of an inhomogeneous temperature
structure affecting $T_{\rm e}$([O III] $\lambda 4363/\lambda 5007$) and
therefore both quantities are intrinsically related and described by both
$T_{0}$(O2+) and $t^{2}$(O2+) Peimbert1967 .

In the first part of this article, we show a tight relationship between
$t^{2}(\text{O}^{2+})$ and $\Delta T_{\rm e}=T_{\rm e}$([O III] $\lambda
4363/\lambda 5007)-T_{\rm e}$([N II] $\lambda 5755/\lambda 6584$). As
mentioned, this is a consequence of the fact that $T_{\rm e}$([N II] $\lambda
5755/\lambda 6584$) is linearly correlated with $T_{0}$(O2+) (or $T_{\rm e}$(O
II V1/[O III]$\lambda 5007$) as they are practically equivalent in the
analyzed H II regions). Therefore, Fig. 1 and Fig. 2 are complementary.
Mathematically, the formalism of Peimbert2013  predicts the linear fit shown
in Eq. (3) with the presence of any phenomenon that produces $T_{\rm e}$([O
III] $\lambda 4363/\lambda 5007$) $>$ $T_{\rm e}$(O II V1/[O III]$\lambda
5007$) (and consequently ADF(O2+)$>$0) and preserves the linearity between
$T_{0}$(O2+) and $T_{\rm e}$([N II] $\lambda 5755/\lambda 6584$). Temperature
inhomogeneities in the volume of high degree of ionization is the only
paradigm that fulfill these requirements as other explanations to the ADF(O2+)
would imply the invalidity of $T_{\rm e}$(O II V1/[O III]$\lambda 5007$) as a
real temperature diagnostic. We discard other explanations to the ADF(O2+) in
H II regions from the literature as follows:

  * •

If there were chemical inhomogeneities, they would create temperature
variations. Nevertheless, in that case, $T_{\rm e}$(O II V1/[O III]$\lambda
5007$) would not correlate with $T_{\rm e}$([N II] $\lambda 5755/\lambda
6584$) as the volumes emitting RLs and CELs would be different Zhang:2007 .

  * •

If the ADF(O2+) were created by fluorescent excitation of the O II V1 RLs,
then these lines would be enhanced in proportion to parameters different than
the electron temperature of the gas (such as the effective temperature of the
ionizing star or the optical depth). Therefore $T_{\rm e}$(O II V1/[O
III]$\lambda 5007$) and $T_{\rm e}$([N II] $\lambda 5755/\lambda 6584$) would
not correlate.

  * •

If the free electrons follow a kappa distribution instead of a Maxwellian one,
supra-thermal electrons would create temperature variations that can be
directly described by $t^{2}$. However, both observational and theoretical
evidence indicate the prevalence of a Maxwellian distribution of velocities
Ferland2016 .

  * •

In the case of errors in the recombination coefficients of the O II V1 RLs,
the observed ADF(O2+) would be approximately constantrodriguez2010 , which is
not the case.

  * •

In order to have an important recombination contribution to the auroral [O
III] $\lambda 4363$ line intensity, a large fraction of O3+/O is required.
This is not the case in the analyzed H II regions. Moreover, Fig. 6 shows that
$t^{2}(\text{O}^{2+})$ and $T_{\rm e}$([Ar III] $\lambda 5192/\lambda
7751)-T_{\rm e}$([N II] $\lambda 5755/\lambda 6584$) also have a correlation
despite of the larger scatter.

Figure 6: $t^{2}(\text{O}^{2+})$ compared with $T_{\rm e}$([Ar III] $\lambda
5192/\lambda 7751)-T_{\rm e}$([N II] $\lambda 5755/\lambda 6584$) for the
studied sample of extragalactic H II regions.

To ensure that our conclusions are free of selection bias, we searched for
spectra of extragalactic H II regions in the literature that follow the same
selection criteria of our study. Due to the difficulty of simultaneously
observing [N II] $\lambda 5755$, [O III] $\lambda 4363$ and the O II V1 RLs,
there are not many candidates. We study the 9 spectra presented in Table 4 by
analyzing them with the same methodology as for the rest of the nebulae. In
Fig. 7 we show that our conclusions do not depend on the adopted sample as the
H II regions from the literature follow the same trend.

Figure 7: $t^{2}(\text{O}^{2+})$ versus $\Delta T_{\rm e}$ for the
extragalactic H II regions of our sample (blue dots) and those from the
literature presented in Table 4 (green squares).

In Table 8 we present the O+/H+ (CELs), O2+/H+(CELs) and O2+/H+(RLs) ratios.
The ionic abundances are derived with the getIonAbundance task of PyNeb. In
the case of O+/H+, we use the [O II] $\lambda 3726+29$ intensity and $T_{\rm
e}$([N II] $\lambda 5755/\lambda 6584$). To derive O2+/H+(CELs), we use [O
III] $\lambda 5007$ and $T_{\rm e}$([O III] $\lambda 4363/\lambda 5007$),
whereas to derive O2+/H+(RLs) we use the O II V1 intensity and $T_{\rm e}$([O
III] $\lambda 4363/\lambda 5007$) (the temperature dependence is negligible).
As H I RLs are emitted both in the high and low ionization volumes, we can
apply the following relation Peimbert2000 :

$T_{\rm 0}(\text{H}^{+})\approx\frac{T_{\rm 0}(\text{O}^{+})\times
n(\text{O}^{+})+T_{\rm 0}(\text{O}^{2+})\times
n(\text{O}^{2+})}{n(\text{O}^{+})+n(\text{O}^{2+})},$ (6)

where $T_{\rm 0}(\text{O}^{+})$ and $n(\text{O}^{+})$ are the average
temperature and particle density of O+, respectively. As our results show that
$T_{\rm e}$([N II] $\lambda 5755/\lambda 6584$)$\approx T_{\rm
0}(\text{O}^{+})$, we can infer a $T_{\rm 0}(\text{H}^{+})$-metallicity
relation, as is presented in Fig. 8 and Eq. (7). This last relation is very
important as it permits to estimate the metallicity from radio observations,
where it is possible to measure $T_{\rm e}$(H I).

Figure 8: $T_{\rm 0}(\text{H}^{+})$-metallicity relation considering
$t^{2}(\text{O}^{2+})>0$ for our sample of extragalactic H II regions.

$12+\text{log(O/H)}=\left(-1.07\pm 0.09\right)\times 10^{-4}T_{\rm
0}(\text{H}^{+})+\left(9.44\pm 0.08\right)\text{(K).}$ (7)

When $T_{\rm e}$([N II] $\lambda 5755/\lambda 6584$)$\approx T_{\rm
0}(\text{O}^{+})$ is considered, Eq. (6) shows that it is possible to get
$T_{\rm 0}(\text{H}^{+})$ values which are close to $T_{\rm e}$([O III]
$\lambda 4363/\lambda 5007$) even if $t^{2}$(O2+)$>0$. This is due to the fact
that in the regions of low degree of ionization, the emission of H I RLs will
come essentially from the volume of O+, where temperature inhomogeneities are
negligible. On the other hand, $T_{\rm e}$([N II] $\lambda 5755/\lambda
6584$)$\approx T_{\rm 0}(\text{O}^{+})$ have larger values than $T_{\rm
0}(\text{O}^{2+})$ (see Fig. (2)). Therefore, finding some nebulae where
$T_{\rm e}$(H I) $\approx T_{\rm e}$([O III]) is not an argument against the
existence of temperature inhomogeneities. In Fig. 9 we show that in some
regions of our sample we could expect that $T_{\rm e}$(H I)$\approx$$T_{\rm
e}$([O III] $\lambda 4363/\lambda 5007$) even if $t^{2}$(O2+)$>0$.

Figure 9: Comparison between $T_{\rm e}$([O III] $\lambda 4363/\lambda 5007$)
and $T_{\rm 0}(\text{H}^{+})$, which was derived using Eq. (6) for our sample
of extragalactic H II regions.

An important point to mention is the possible existence of ADF(O+). To date,
there are no reported ADF(O+) (or from any ion of low degree of ionization) in
extragalactic H II regions. The available cases are limited to Galactic
planetary nebulae (PNe) and 3 Galactic H II regions: M8, M20 and the Orion
Nebula garciarojas2007 . Besides the possible contribution of sky
contamination in the O I 7773+ multiplet, it is necessary to study the
aperture effects on these nebulae, since echelle observations esteban04 ;
garciarojas06 ; garciarojas07  are limited to very small areas of the nebula.
For instance, in the dense gas of the Orion Nebula, a high density clump (such
as a proplyd or an Herbig-Haro object) can create a fake local peak of $T_{\rm
e}$([N II] $\lambda 5755/\lambda 6584$) mesadelgado08 ; mendezdelgado21b ,
giving the $n_{\rm e}$-sensitivity of [N II] $\lambda 5755/\lambda 6584$ at
values higher than 1000 cm-3. In any case, the ADF(O+) could have a negligible
effect on the integrated spectrum where the entire temperature structure is
encompassed. If a large ADF(O+) exists in extragalactic H II regions, this
work shows that the main cause would not be temperature inhomogeneities. But
before discussing a problem, we need evidence that it really exists.

Finally, we explore the effect of temperature inhomogeneities on the PNe shown
in Table 6 following the same methodology described for H II regions. Fig. 10
shows that, in general, PNe do not follow the same trend between
$t^{2}(\text{O}^{2+})$ and $\Delta T_{\rm e}$ as H II regions. It should be
noted that the ionizing sources of these objects are hotter, having a
considerable fraction of $\text{O}^{3+}/\text{O}$. Therefore the heating may
be affecting mainly the $\text{O}^{3+}$ volume, which is not accessible in the
optical range. Furthermore, there are strong indications that some PNe with
binary central stars can have inclusions of (at least) two distinct gas
components with different metallicities Liu:2001 ; Wesson2003 ; Liu2006 ;
Storey2014 ; garciarojas2022 . These chemical inhomogeneities also produce
temperature variations, but they imply the invalidity of
$t^{2}(\text{O}^{2+})$ derived from $T_{\rm e}$(O II V1/[O III]$\lambda 5007$)
as the emission of RLs and CELs would come from non related volumes Zhang:2007
. This is particularly important in the extreme ADF PNe Ou5 and Abell 46
corradi15 . The abundance discrepancy problem in PNe remains open and requires
further investigations, although Richer2022  found that the effect of
temperature inhomogeneities on these objects is not negligible .

Figure 10: $t^{2}(\text{O}^{2+})$ versus $\Delta T_{\rm e}$ relation for Galactic planetary nebulae. Table 1: Adopted atomic data set. Ion | Transition Probabilities | Collision Strengths | Effective recombination coefficients
---|---|---|---
H+ | - | - | Storey95
O+ | FroeseFischer:2004  | Kisielius:2009  | -
O2+ |  Wiese:1996 , Storey:2000  | Storey:2014  | Storey2017
N+ | FroeseFischer:2004  | Tayal:2011  | -
S+ | IFF05  | Tayal:2010  | -
Cl2+ | Fritzsche:1999  | Butler:1989  | -
Ar2+ |  Mendoza:1983b , Kaufman:1986  | Galavis:1995  | -
Ar3+ | Mendoza:1982b  | Ramsbottom:1997  | -
Fe2+ | Quinet:1996  | Zhang:1996  | -
|  |  |

Acknowledgments

JEM-D appreciates the fruitful conversations with Antonio Peimbert and Silvia
Torres-Peimbert on the formalism of temperature variations and chemical
inhomogeneities in the ionized gas. JEM-D acknowledges interesting discussions
with William J. Henney.

Authors’ contributions

JEM-D conducted the study with the original idea, compiled the appropriate
data, re-calculated the physical conditions and chemical abundances, wrote the
text, created the figures and interpreted the results. CE, JG-R, KK and MP
reviewed the consistency of the analysis, the formalism of temperature
fluctuations, contributed to data interpretation and discussion, and modified
the text. The participation of all the authors was essential for the
realization of this work.

Conflict of interest/Competing interests

The authors declare that they have no competing financial interests.

Data availability

All the data is public and available in cited the references. Our calculations
are entirely present in Tables 2-8.

Funding

JEM-D and KK gratefully acknowledge funding from the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation) in the form of an
Emmy Noether Research Group (grant number KR4598/2-1, PI Kreckel). CE and JG-R
acknowledge support from the Agencia Estatal de Investigación del Ministerio
de Ciencia e Innovación (AEI-MCINN) under grant Espectroscopía de campo
integral de regiones H II locales. Modelos para el estudio de regiones H II
extragalácticas with reference 10.13039/501100011033 and support under grant
P/308614 financed by funds transferred from the Spanish Ministry of Science,
Innovation and Universities, charged to the General State Budgets and with
funds transferred from the General Budgets of the Autonomous Community of the
Canary Islands by the MCIU. JG-R acknowledges support from an Advanced
Fellowship under the Severo Ochoa excellence program CEX2019-000920-S and
financial support from the Canarian Agency for Research, Innovation and
Information Society (ACIISI), of the Canary Islands Government, and the
European Regional Development Fund (ERDF), under grant with reference
ProID2021010074.

Additional Information

Correspondence should be addressed to JEM-D<EMAIL_ADDRESS>
##  Appendix A Physical conditions, ionic abundances and references

Table 2: Physical conditions for our sample of extragalactic H II regions. Region |  $n_{\rm e}$([O II]) |  $n_{\rm e}$([S II]) | Adop. $n_{\rm e}$ |  $T_{\rm e}$([O III]) |  $T_{\rm e}$([Ar III]) |  $T_{\rm e}$([N II]) | Ref.
---|---|---|---|---|---|---|---
| cm-3 | cm-3 | cm-3 | K | K | K |
NGC 5461 | $310^{+90}_{-80}$ | $220^{+110}_{-120}$ | $270\pm 100$ | $8460^{+200}_{-220}$ | - | $9100^{+300}_{-350}$ | esteban09
NGC 588 | $90^{+110}_{-70}$ | $150^{+120}_{-110}$ | $120^{+110}_{-90}$ | $10810^{+500}_{-380}$ | - | $10900^{+750}_{-1200}$ | Toribio16
NGC 595 | $60\pm 20$ | $40\pm 30$ | $<100$ | $7390^{+390}_{-400}$ | - | $8150^{+210}_{-140}$ | esteban09
K 932 | $250\pm 30$ | $110\pm 50$ | $180\pm 40$ | $8300^{+140}_{-130}$ | - | $9260^{+170}_{-190}$ | esteban09
IC 132 | $160^{+200}_{-110}$ | $200^{+170}_{-120}$ | $180^{+180}_{-120}$ | $10280^{+450}_{-540}$ | $12020^{+1000}_{-1150}$ | $11300^{+1050}_{-980}$ | Toribio16
N 11B | $290\pm 100$ | $260^{+60}_{-50}$ | $270\pm 80$ | $9140^{+130}_{-90}$ | $9680^{+260}_{-190}$ | $9780^{+160}_{-150}$ | dominguezguzman22
NGC 5471 | $210^{+60}_{-50}$ | $170^{+70}_{-60}$ | $190^{+60}_{-50}$ | $13820^{+190}_{-150}$ | $14520^{+1220}_{-1130}$ | $12180^{+540}_{-370}$ | esteban20
N 66A | $180^{+100}_{-90}$ | $180\pm 70$ | $180\pm 80$ | $12550\pm 180$ | $12220^{+690}_{-640}$ | $12010^{+330}_{-290}$ | dominguezguzman22
NGC 604 | $60\pm 20$ | $50^{+40}_{-30}$ | $<100$ | $8050^{+140}_{-200}$ | - | $8640^{+260}_{-240}$ | esteban09
NGC 6822 | $150^{+100}_{-90}$ | $110^{+90}_{-70}$ | $130^{+100}_{-80}$ | $11510^{+190}_{-260}$ | $11800^{+1330}_{-1420}$ | $11340^{+1290}_{-1720}$ | esteban14
UV-1 | $190\pm 70$ | $280\pm 80$ | $240\pm 80$ | $10840^{+190}_{-130}$ | $10610^{+1000}_{-1310}$ | $10130^{+520}_{-710}$ | lopezsanchez07
NGC 5408 | $220\pm 90$ | $200^{+110}_{-90}$ | $210^{+100}_{-90}$ | $15910^{+330}_{-460}$ | - | $11490^{+790}_{-800}$ | esteban14
NGC 1714 | $450^{+140}_{-130}$ | $340^{+140}_{-130}$ | $390^{+140}_{-130}$ | $9520^{+170}_{-220}$ | $9430^{+700}_{-770}$ | $10190^{+560}_{-420}$ | dominguezguzman22
N 81 | $440\pm 130$ | $340^{+80}_{-90}$ | $390^{+100}_{-110}$ | $12830^{+220}_{-250}$ | $11870^{+190}_{-270}$ | $11850^{+220}_{-280}$ | dominguezguzman22
IC 2111 | $290\pm 120$ | $240^{+120}_{-100}$ | $270^{+120}_{-110}$ | $9130^{+180}_{-200}$ | $9120^{+480}_{-740}$ | $9760^{+360}_{-310}$ | dominguezguzman22
NGC 2363 | $270^{+90}_{-100}$ | $170^{+120}_{-90}$ | $220^{+110}_{-100}$ | $16480^{+450}_{-390}$ | $15600^{+1200}_{-1100}$ | $12970^{+1220}_{-1080}$ | esteban09
30Dor | $440\pm 20$ | $350\pm 20$ | $390\pm 20$ | $9870^{+90}_{-40}$ | $9120^{+400}_{-300}$ | $10360^{+280}_{-240}$ | peimbert03
N 44C | $190^{+110}_{-80}$ | $100\pm 50$ | $140^{+80}_{-70}$ | $11280^{+150}_{-140}$ | $10630\pm 530$ | $10560^{+320}_{-330}$ | dominguezguzman22
HII-2 | $420^{+110}_{-90}$ | $380^{+100}_{-90}$ | $400^{+110}_{-90}$ | $11900^{+240}_{-190}$ | $12230^{+1210}_{-1300}$ | $10520^{+500}_{-530}$ | lopezsanchez07
NGC 5455 | $240^{+60}_{-50}$ | $160\pm 50$ | $200\pm 50$ | $9610^{+120}_{-150}$ | $10350^{+1120}_{-900}$ | $10120^{+200}_{-170}$ | esteban20
VS44 | $150\pm 20$ | $100^{+30}_{-40}$ | $<100$ | $8210^{+240}_{-170}$ | - | $8870^{+330}_{-250}$ | esteban09
N 88A | $2700^{+570}_{-400}$ | $1840^{+400}_{-310}$ | $3130\pm 1120$ | $13820^{+250}_{-190}$ | $20190^{+680}_{-670}$ | $13020^{+280}_{-310}$ | dominguezguzman22
HII-1 | $360\pm 90$ | $420^{+110}_{-90}$ | $390^{+100}_{-90}$ | $11950^{+240}_{-160}$ | $12210^{+1010}_{-1220}$ | $10810^{+460}_{-520}$ | lopezsanchez07
|  |  |  |  |  |  |

Table 3: Physical conditions of the adopted sample of Galactic ring nebulae. Region |  $n_{\rm e}$([S II]) |  $T_{\rm e}$([O III]) |  $T_{\rm e}$([Ar III]) |  $T_{\rm e}$([N II]) | Ref.
---|---|---|---|---|---
| cm-3 | K | K | K |
NGC 7635A2 | $120\pm 40$ | $8130^{+400}_{-550}$ | - | $8000^{+560}_{-600}$ | esteban16
NGC 7635A3 | $90^{+50}_{-40}$ | $7530^{+610}_{-520}$ | - | $8190^{+420}_{-300}$ | esteban16
NGC 7635A4 | $1450^{+130}_{-140}$ | $8650^{+350}_{-480}$ | $8410^{+720}_{-810}$ | $9010^{+110}_{-90}$ | esteban16
NGC 6888A2 | $290\pm 80$ | $12710^{+400}_{-410}$ | - | $7380\pm 110$ | esteban16
NGC 6888A3 | $210^{+100}_{-80}$ | $10040^{+500}_{-870}$ | - | $7570^{+160}_{-180}$ | esteban16
NGC 6888A4 | $120^{+80}_{-60}$ | $10050^{+820}_{-930}$ | - | $8800^{+200}_{-110}$ | esteban16
NGC 6888A5 | $170\pm 70$ | $9850^{+420}_{-580}$ | $7310^{+740}_{-610}$ | $8660^{+220}_{-240}$ | esteban16
NGC 6888A6 | $180^{+100}_{-90}$ | $9620^{+620}_{-870}$ | - | $8660^{+210}_{-160}$ | esteban16
|  |  |  |  |

Table 4: Physical conditions of the extragalactic H II regions from other research groups. Region |  $n_{\rm e}$([O II]) |  $n_{\rm e}$([S II]) | Adop. $n_{\rm e}$ |  $T_{\rm e}$([O III]) |  $T_{\rm e}$([Ar III]) |  $T_{\rm e}$([N II]) | Ref.
---|---|---|---|---|---|---|---
| cm-3 | cm-3 | cm-3 | K | K | K |
NGC 456a-1 | - | $290^{+40}_{-50}$ | $290^{+40}_{-50}$ | $12210^{+70}_{-130}$ | - | $11890^{+470}_{-380}$ | guseva11
NGC 456a-2 | - | $80^{+40}_{-30}$ | $<100$ | $11940^{+70}_{-100}$ | - | $10700^{+980}_{-760}$ | guseva11
NGC 6822V | $70^{+50}_{-30}$ | $90^{+70}_{-50}$ | $<100$ | $11700^{+280}_{-210}$ | - | $14520^{+1970}_{-2280}$ | peimbert05
NGC 5253C1 | - | $530^{+70}_{-50}$ | $530^{+70}_{-50}$ | $12140^{+80}_{-70}$ | - | $11420^{+100}_{-150}$ | guseva11
Mrk1259 | - | $780^{+80}_{-70}$ | $780^{+80}_{-70}$ | $9970^{+460}_{-260}$ | - | $7860^{+250}_{-280}$ | guseva11
NGC 5253C2 | - | $200\pm 40$ | $200\pm 40$ | $10150^{+80}_{-50}$ | - | $11010^{+440}_{-350}$ | guseva11
NGC 5253P2 | - | $810\pm 80$ | $810\pm 80$ | $12280^{+120}_{-110}$ | - | $11320^{+220}_{-200}$ | guseva11
NGC 346 | $40^{+30}_{-20}$ | $40^{+30}_{-20}$ | $<100$ | $12820^{+120}_{-110}$ | - | $10830^{+860}_{-880}$ | valerdi19
NGC 456-2 | $210\pm 20$ | $210\pm 50$ | $210\pm 40$ | $12070^{+170}_{-220}$ | $11320^{+1250}_{-1150}$ | $11110^{+1070}_{-760}$ | penaguerrero12
|  |  |  |  |  |  |

Table 5: Electron density values of the adopted sample of Galactic H II regions. Region |  $n_{\rm e}$([O II]) |  $n_{\rm e}$([S II]) |  $n_{\rm e}$([Fe III]) |  $n_{\rm e}$([Cl III]) |  $n_{\rm e}$([Ar IV]) | Adop. $n_{\rm e}$ | Ref.
---|---|---|---|---|---|---|---
| cm-3 | cm-3 | cm-3 | cm-3 | cm-3 | cm-3 |
NGC 3603 | $2600^{+800}_{-510}$ | $2890^{+1140}_{-650}$ | $8400^{+28360}_{-5500}$ | $4850^{+1350}_{-1570}$ | $1950^{+1620}_{-1210}$ | $2850\pm 750$ | garciarojas06
M 42-P1 | $4700^{+950}_{-870}$ | $2870^{+670}_{-600}$ | $6590^{+3200}_{-2010}$ | $5930^{+1380}_{-1020}$ | $5920^{+3800}_{-3310}$ | $3990\pm 1280$ | delgadoinglada16
M 42-2 | $5850^{+820}_{-770}$ | $3760^{+1390}_{-750}$ | $10340^{+2180}_{-2130}$ | $7510^{+820}_{-640}$ | $6690^{+580}_{-480}$ | $6500\pm 1240$ | mendezdelgado22b
Sh 2-100 | - | $390^{+230}_{-170}$ | $13340^{+21970}_{-9720}$ | $750^{+410}_{-330}$ | - | $390^{+230}_{-170}$ | esteban17
M 42-3 | $5320^{+710}_{-550}$ | $4100^{+1160}_{-950}$ | $11300^{+3410}_{-2330}$ | $7310^{+900}_{-830}$ | $5950^{+1410}_{-1170}$ | $5810\pm 1350$ | mendezdelgado21a
M 42-1 | $5340^{+720}_{-560}$ | $4180^{+1020}_{-800}$ | $10310^{+2850}_{-2670}$ | $6900^{+720}_{-610}$ | $4190^{+1380}_{-1270}$ | $5670\pm 1260$ | mendezdelgado21a
Sh 2-311 | $270^{+80}_{-60}$ | $300\pm 100$ | $6420^{+17160}_{-4890}$ | - | - | $290^{+90}_{-80}$ | garciarojas05
M 16 | $1160^{+210}_{-190}$ | $1080^{+220}_{-190}$ | $10160^{+20300}_{-8180}$ | $1190^{+530}_{-510}$ | - | $1130\pm 100$ | garciarojas06
M 42-bar | $4200^{+490}_{-410}$ | $3240^{+750}_{-570}$ | $4240^{+2010}_{-1790}$ | $4330^{+550}_{-640}$ | $30870^{+48400}_{-23610}$ | $4030\pm 480$ | delgadoinglada16
M 42-1 | $1110^{+80}_{-90}$ | $1320^{+190}_{-170}$ | $4120^{+1790}_{-1260}$ | $1540^{+230}_{-240}$ | - | $1190\pm 190$ | mendezdelgado21b
NGC 3576 | $1710^{+260}_{-280}$ | $1050^{+300}_{-270}$ | $1560^{+1350}_{-1380}$ | $2890^{+630}_{-620}$ | $3050^{+1620}_{-1380}$ | $1560\pm 550$ | garciarojas04
M 42 | $6790^{+2510}_{-1620}$ | $4550^{+3150}_{-1500}$ | $9550^{+3570}_{-2820}$ | $7020^{+610}_{-540}$ | $4810^{+1190}_{-900}$ | $6510\pm 1060$ | esteban04
M 17 | $500^{+110}_{-100}$ | $380\pm 110$ | $9560^{+32890}_{-7330}$ | $370^{+270}_{-200}$ | - | $440^{+110}_{-100}$ | garciarojas07
M 8 | $1630^{+670}_{-500}$ | $1230^{+210}_{-170}$ | $2440^{+1810}_{-1130}$ | $1870^{+250}_{-270}$ | $4140^{+5230}_{-2800}$ | $1480\pm 330$ | garciarojas07
M 42-4 | $4860^{+620}_{-510}$ | $3980^{+790}_{-660}$ | $9660^{+3090}_{-2230}$ | $6970^{+670}_{-630}$ | $5220^{+820}_{-710}$ | $5360\pm 1200$ | mendezdelgado21a
M 42-3 | $5350^{+720}_{-630}$ | $3950^{+860}_{-570}$ | $7580^{+2590}_{-1950}$ | $7650^{+810}_{-790}$ | $4670^{+500}_{-410}$ | $5170\pm 1180$ | mendezdelgado22b
Sh 2-288 | - | $430^{+250}_{-230}$ | $2960^{+6080}_{-2240}$ | $440^{+360}_{-270}$ | - | $430^{+250}_{-230}$ | esteban17
M 42 | $2710^{+690}_{-540}$ | $1800^{+570}_{-520}$ | $4370^{+6120}_{-3020}$ | $2120^{+970}_{-800}$ | $89060^{+317740}_{-63110}$ | $2200\pm 480$ | mesadelgado09
M 42-2 | $1460^{+140}_{-110}$ | $1160^{+190}_{-140}$ | $3530^{+2340}_{-1490}$ | $2000^{+500}_{-470}$ | - | $1380\pm 220$ | mendezdelgado21b
M 42-2 | $5110^{+660}_{-560}$ | $4090^{+890}_{-770}$ | $10160^{+2490}_{-1990}$ | $6510^{+650}_{-610}$ | $5870\pm 720$ | $5620\pm 1080$ | mendezdelgado21a
|  |  |  |  |  |  |

Table 6: Electron density values of the adopted sample of Galactic planetary nebulae. Region |  $n_{\rm e}$([O II]) |  $n_{\rm e}$([S II]) |  $n_{\rm e}$([Fe III]) |  $n_{\rm e}$([Cl III]) |  $n_{\rm e}$([Ar IV]) | Adop. $n_{\rm e}$ | Ref.
---|---|---|---|---|---|---|---
| cm-3 | cm-3 | cm-3 | cm-3 | cm-3 | cm-3 |
NGC 2440 | $4080^{+620}_{-590}$ | $2620^{+420}_{-380}$ | - | $5520^{+550}_{-510}$ | $5000^{+610}_{-600}$ | $3990\pm 1220$ | sharpee07
Hb 4 | $7200^{+13470}_{-3200}$ | $5200^{+5010}_{-2780}$ | - | $6930^{+1680}_{-1750}$ | $7320^{+1190}_{-1380}$ | $7060\pm 520$ | garciarojas12
NGC 5315 | $12510^{+22180}_{-6340}$ | $7920^{+11590}_{-4380}$ | $10730^{+19690}_{-7230}$ | $34670^{+11420}_{-9530}$ | $37220^{+10270}_{-8950}$ | $20930\pm 13320$ | madonna17
M 1-31 | $15130^{+29210}_{-7920}$ | $9990^{+7630}_{-4110}$ | - | $19820^{+14290}_{-9620}$ | - | $12140\pm 3840$ | garciarojas18
Cn 1-5 | $5070^{+2560}_{-1490}$ | $3930^{+1980}_{-1290}$ | $14260^{+21830}_{-9390}$ | $3910^{+860}_{-1010}$ | $10950^{+6910}_{-6020}$ | $4190\pm 1010$ | garciarojas12
H 1-40 | $7790^{+18670}_{-4100}$ | $8300^{+8690}_{-3460}$ | $16750^{+36490}_{-12980}$ | $7630^{+7420}_{-5100}$ | - | $8180\pm 1450$ | garciarojas18
H 1-50 | $10670^{+8880}_{-3730}$ | $7160^{+4300}_{-2650}$ | - | $12850^{+4170}_{-3710}$ | - | $9790\pm 2630$ | garciarojas18
Hen 2-158 | $3780^{+1180}_{-760}$ | $2750^{+770}_{-670}$ | $12130^{+30230}_{-9990}$ | $6470^{+4100}_{-3620}$ | $18870^{+22320}_{-12970}$ | $3220\pm 890$ | garciarojas18
IC 418 | $15380^{+8370}_{-4520}$ | $14210^{+9850}_{-5610}$ | - | $12200^{+1150}_{-1210}$ | $5130^{+4020}_{-2990}$ | $11640\pm 2220$ | sharpee03
PC 14 | $4520^{+1630}_{-1300}$ | $3070^{+1640}_{-960}$ | - | $3410^{+860}_{-830}$ | $4710^{+1120}_{-1140}$ | $3820\pm 660$ | garciarojas12
M 1-32 | $9570^{+14360}_{-5220}$ | $5940^{+12420}_{-3190}$ | $20710^{+20290}_{-10300}$ | $13460^{+3620}_{-3110}$ | - | $12350\pm 3120$ | garciarojas12
M 1-61 | $19180^{+25650}_{-9700}$ | $9820^{+14210}_{-5100}$ | $20290^{+34130}_{-16340}$ | $19550^{+5420}_{-3510}$ | $33540^{+9600}_{-6570}$ | $20900\pm 6910$ | garciarojas12
Ou5 | $1380^{+510}_{-390}$ | $220^{+220}_{-150}$ | - | - | $1200^{+1500}_{-820}$ | $800^{+360}_{-270}$ | corradi15
NGC 6369 | $3940^{+1540}_{-1060}$ | $3170^{+1530}_{-1000}$ | - | $4160^{+970}_{-1010}$ | $4960^{+1410}_{-1160}$ | $4070\pm 600$ | garciarojas12
Pe 1-1 | $21170^{+33240}_{-11750}$ | $9850^{+9830}_{-4670}$ | - | $31030^{+12290}_{-8480}$ | - | $17080\pm 9670$ | garciarojas12
IC 2501 | $16950^{+8770}_{-5170}$ | $8340^{+3510}_{-1910}$ | - | $9970^{+990}_{-960}$ | $8490^{+770}_{-660}$ | $9030\pm 970$ | sharpee07
M 1-30 | $4480^{+3020}_{-1550}$ | $5160^{+6130}_{-2420}$ | $9530^{+17230}_{-7780}$ | $7380^{+1240}_{-1450}$ | - | $6560\pm 1300$ | garciarojas12
IC 4191 | $14150^{+5370}_{-3740}$ | $7620^{+2830}_{-1930}$ | - | $14290^{+1550}_{-1090}$ | $11310^{+1090}_{-980}$ | $11990\pm 2020$ | sharpee07
Hen 2-96 | $13340^{+23340}_{-6310}$ | $8980^{+6130}_{-3290}$ | - | $23960^{+27980}_{-13770}$ | $38610^{+28930}_{-18170}$ | $10980\pm 6050$ | garciarojas18
M 3-15 | $9780^{+27490}_{-4980}$ | $5260^{+6820}_{-2970}$ | - | $9260^{+2760}_{-2190}$ | $8270^{+4480}_{-4220}$ | $8430\pm 1440$ | garciarojas12
Hen 2-86 | $11550^{+20490}_{-5240}$ | $9010^{+12200}_{-4470}$ | $41590^{+33180}_{-19220}$ | $21620^{+6190}_{-3980}$ | $36560^{+5390}_{-5470}$ | $24730\pm 10360$ | garciarojas12
M 2-31 | $7560^{+6610}_{-2410}$ | $4740^{+2150}_{-1330}$ | - | $9990^{+3790}_{-3290}$ | $8080^{+1670}_{-1510}$ | $6940\pm 1830$ | garciarojas18
NGC 5189 | $1270^{+380}_{-350}$ | $1000^{+450}_{-380}$ | - | $1370^{+550}_{-560}$ | $1240^{+650}_{-610}$ | $1130^{+410}_{-370}$ | garciarojas12
M 1-60 | $10590^{+15100}_{-4300}$ | $6170^{+3220}_{-1900}$ | - | $14110^{+8650}_{-5700}$ | $18230^{+2660}_{-3580}$ | $11210\pm 5650$ | garciarojas18
Hen 2-73 | $9100^{+5880}_{-3010}$ | $6510^{+4510}_{-2260}$ | - | $12660^{+4620}_{-3540}$ | - | $9040\pm 2610$ | garciarojas18
IC 4776 | $14320^{+23970}_{-7380}$ | $11380^{+9520}_{-4400}$ | $19480^{+27120}_{-10010}$ | $23470^{+6770}_{-6590}$ | $36820^{+3160}_{-3480}$ | $29950\pm 9850$ | sowicka17
M 1-25 | $12300^{+17390}_{-5210}$ | $6970^{+11720}_{-3690}$ | $11010^{+20430}_{-8120}$ | $13690^{+2900}_{-2250}$ | - | $12930\pm 1980$ | garciarojas12
M 1-33 | $5550^{+3300}_{-1390}$ | $4370^{+1750}_{-1250}$ | $14960^{+55300}_{-13430}$ | $7230^{+2650}_{-2370}$ | - | $5230\pm 1160$ | garciarojas18
M 2-36 | $3900^{+490}_{-450}$ | $2660^{+300}_{-270}$ | - | $5190^{+1130}_{-1200}$ | $3960^{+930}_{-870}$ | $3140\pm 710$ | espiritu21
Abell 46 | $3210^{+1060}_{-710}$ | $440^{+400}_{-310}$ | - | - | $1370^{+1630}_{-890}$ | $1820^{+730}_{-510}$ | corradi15
|  |  |  |  |  |  |

Table 7: Electron temperature values of the adopted sample of Galactic H II regions and planetary nebulae. Region |  $T_{\rm e}$([O III]) |  $T_{\rm e}$([Ar III]) |  $T_{\rm e}$([N II]) | Ref.
---|---|---|---|---
| K | K | K |
Galactic H II regions
NGC 3603 | $9020^{+130}_{-120}$ | - | $11040^{+650}_{-530}$ | garciarojas06
M 42-P1 | $8320^{+80}_{-60}$ | $7970\pm 440$ | $9500^{+250}_{-260}$ | delgadoinglada16
M 42-2 | $8500^{+60}_{-70}$ | $8100^{+130}_{-150}$ | $9810^{+230}_{-200}$ | mendezdelgado22b
Sh 2-100 | $8280^{+100}_{-120}$ | $7650^{+380}_{-520}$ | $8430^{+270}_{-300}$ | esteban17
M 42-3 | $8510\pm 60$ | $8260^{+160}_{-200}$ | $10090^{+230}_{-300}$ | mendezdelgado21a
M 42-1 | $8420^{+80}_{-60}$ | $8270^{+210}_{-220}$ | $9920^{+210}_{-200}$ | mendezdelgado21a
Sh 2-311 | $8960^{+90}_{-100}$ | $8830^{+890}_{-950}$ | $9230^{+170}_{-240}$ | garciarojas05
M 16 | $7600^{+140}_{-130}$ | - | $8280^{+230}_{-130}$ | garciarojas06
M 42-bar | $8470^{+90}_{-70}$ | $8330^{+320}_{-290}$ | $9000^{+130}_{-150}$ | delgadoinglada16
M 42-1 | $8020^{+60}_{-50}$ | - | $8510^{+140}_{-110}$ | mendezdelgado21b
NGC 3576 | $8450^{+40}_{-50}$ | $8590^{+340}_{-270}$ | $8710^{+160}_{-270}$ | garciarojas04
M 42 | $8380\pm 60$ | $8190^{+250}_{-360}$ | $9920^{+290}_{-220}$ | esteban04
M 17 | $7950^{+100}_{-90}$ | $8350^{+480}_{-510}$ | $8740^{+220}_{-180}$ | garciarojas07
M 8 | $8050^{+110}_{-100}$ | $7570\pm 310$ | $8330\pm 100$ | garciarojas07
M 42-4 | $8320^{+90}_{-60}$ | $8250^{+320}_{-360}$ | $9890^{+220}_{-210}$ | mendezdelgado21a
M 42-3 | $8410^{+50}_{-60}$ | $8310\pm 200$ | $9890^{+190}_{-260}$ | mendezdelgado22b
Sh 2-288 | $9260^{+520}_{-620}$ | - | $9390^{+340}_{-350}$ | esteban17
M 42 | $8180^{+140}_{-260}$ | $7880^{+460}_{-520}$ | $9430^{+380}_{-320}$ | mesadelgado09
M 42-2 | $8120^{+50}_{-70}$ | - | $8450^{+140}_{-150}$ | mendezdelgado21b
M 42-2 | $8390^{+70}_{-50}$ | $8330^{+180}_{-130}$ | $9860^{+230}_{-170}$ | mendezdelgado21a
Galactic planetary nebulae
NGC 2440 | $14850^{+290}_{-300}$ | $12120\pm 260$ | $13880^{+470}_{-450}$ | sharpee07
Hb 4 | $10010^{+260}_{-290}$ | $8290^{+550}_{-400}$ | $9810^{+440}_{-690}$ | garciarojas12
NGC 5315 | $8760^{+220}_{-250}$ | $8330^{+280}_{-320}$ | $10060^{+1130}_{-780}$ | madonna17
M 1-31 | $8310^{+180}_{-240}$ | - | $10210^{+410}_{-530}$ | garciarojas18
Cn 1-5 | $8740\pm 180$ | $7840^{+320}_{-330}$ | $8710^{+340}_{-210}$ | garciarojas12
H 1-40 | $10100^{+390}_{-370}$ | - | $13850^{+670}_{-1140}$ | garciarojas18
H 1-50 | $11090\pm 230$ | $10480\pm 820$ | $11840^{+510}_{-520}$ | garciarojas18
Hen 2-158 | $9280^{+180}_{-220}$ | - | $10100\pm 350$ | garciarojas18
IC 418 | $8770^{+90}_{-100}$ | $8600^{+380}_{-300}$ | $9340^{+280}_{-210}$ | sharpee03
PC 14 | $9270^{+210}_{-170}$ | $8830^{+440}_{-550}$ | $10220\pm 430$ | garciarojas12
M 1-32 | $9370^{+240}_{-210}$ | $8040^{+620}_{-800}$ | $8920^{+430}_{-490}$ | garciarojas12
M 1-61 | $9190^{+200}_{-240}$ | $8730^{+380}_{-370}$ | $12680^{+1310}_{-870}$ | garciarojas12
Ou5 | $12470^{+440}_{-380}$ | - | $25870^{+9940}_{-6420}$ | corradi15
NGC 6369 | $10650^{+330}_{-240}$ | $9280^{+800}_{-920}$ | $13320^{+570}_{-670}$ | garciarojas12
Pe 1-1 | $10100^{+340}_{-290}$ | $9220^{+550}_{-490}$ | $12250^{+1010}_{-1080}$ | garciarojas12
IC 2501 | $9410^{+80}_{-110}$ | $8840^{+320}_{-250}$ | $10930^{+230}_{-210}$ | sharpee07
M 1-30 | $6640^{+80}_{-170}$ | $6430^{+180}_{-250}$ | $6990^{+260}_{-230}$ | garciarojas12
IC 4191 | $9740^{+140}_{-150}$ | $12000^{+230}_{-130}$ | $12120^{+370}_{-410}$ | sharpee07
Hen 2-96 | $8990^{+170}_{-230}$ | - | $11540^{+800}_{-830}$ | garciarojas18
M 3-15 | $8360^{+250}_{-220}$ | - | $11210^{+660}_{-730}$ | garciarojas12
Hen 2-86 | $8320\pm 210$ | $9450\pm 370$ | $10260^{+1120}_{-780}$ | garciarojas12
|  |  |  |
Table 6: Continued. Region |  $T_{\rm e}$([O III]) |  $T_{\rm e}$([Ar III]) |  $T_{\rm e}$([N II]) | Ref.
---|---|---|---|---
| K | K | K |
M 2-31 | $9900^{+270}_{-190}$ | - | $11090^{+460}_{-430}$ | garciarojas18
NGC 5189 | $11450^{+300}_{-280}$ | $10310^{+460}_{-430}$ | $9480^{+450}_{-320}$ | garciarojas12
M 1-60 | $8800^{+210}_{-200}$ | - | $9810^{+540}_{-560}$ | garciarojas18
Hen 2-73 | $11770^{+380}_{-220}$ | $9650^{+1060}_{-1040}$ | $11480^{+460}_{-500}$ | garciarojas18
IC 4776 | $9960^{+150}_{-210}$ | $9230\pm 190$ | $10110^{+860}_{-920}$ | sowicka17
M 1-25 | $7800\pm 170$ | - | $8290^{+370}_{-280}$ | garciarojas12
M 1-33 | $8930^{+170}_{-200}$ | - | $9530^{+260}_{-270}$ | garciarojas18
M 2-36 | $8390^{+120}_{-100}$ | $7020^{+270}_{-590}$ | $14350^{+270}_{-480}$ | espiritu21
Abell 46 | $12930^{+260}_{-280}$ | - | $29300^{+18610}_{-9210}$ | corradi15
|  |  |  |
Table 7: O II V1 fluxes and their associated physical parameters of the H II regions and other nebulae. Region |  $T_{\rm e}$(O II/[O III]) |  $T_{0}$(O2+) |  $t^{2}$(O2+) | O II V1/H$\beta$ | No. | Ref.
---|---|---|---|---|---|---
| K | K |  | H$\beta$=100 | lines |
Extragalactic H II regions
NGC 5461 | $7640\pm 880$ | $7480\pm 1080$ | $0.027\pm 0.030$ | $0.387\pm 0.123$ | 2 | esteban09
NGC 588 | $9320\pm 600$ | $9330\pm 740$ | $0.044\pm 0.025$ | $0.281\pm 0.057$ | 5 | Toribio16
NGC 595 | $6380\pm 270$ | $6240\pm 430$ | $0.031\pm 0.015$ | $0.290\pm 0.057$ | 2 | esteban09
K 932 | $7460\pm 310$ | $7350\pm 370$ | $0.026\pm 0.011$ | $0.415\pm 0.070$ | 5 | esteban09
IC 132 | $9340\pm 730$ | $9390\pm 830$ | $0.026\pm 0.029$ | $0.323\pm 0.078$ | 3 | Toribio16
N 11B | $8140\pm 150$ | $8060\pm 170$ | $0.031\pm 0.006$ | $0.307\pm 0.023$ | 5 | dominguezguzman22
NGC 5471 | $12700\pm 2100$ | $12890\pm 2210$ | $0.032\pm 0.078$ | $0.146\pm 0.050$ | 2 | esteban20
N 66A | $11230\pm 440$ | $11330\pm 450$ | $0.041\pm 0.015$ | $0.128\pm 0.015$ | 1 | dominguezguzman22
NGC 604 | $7270\pm 250$ | $7170\pm 320$ | $0.025\pm 0.010$ | $0.354\pm 0.055$ | 5 | esteban09
NGC 6822 | $9740\pm 510$ | $9720\pm 590$ | $0.055\pm 0.018$ | $0.277\pm 0.046$ | 6 | esteban14
UV-1 | $8420\pm 1080$ | $8390\pm 1410$ | $0.071\pm 0.037$ | $0.398\pm 0.126$ | 2 | lopezsanchez07
NGC 5408 | $10610\pm 900$ | $10890\pm 1170$ | $0.162\pm 0.032$ | $0.207\pm 0.044$ | 6 | esteban14
NGC 1714 | $8470\pm 410$ | $8410\pm 490$ | $0.033\pm 0.015$ | $0.368\pm 0.064$ | 6 | dominguezguzman22
N 81 | $10100\pm 180$ | $10140\pm 190$ | $0.084\pm 0.009$ | $0.216\pm 0.013$ | 5 | dominguezguzman22
IC 2111 | $8300\pm 530$ | $8230\pm 620$ | $0.025\pm 0.018$ | $0.285\pm 0.060$ | 7 | dominguezguzman22
NGC 2363 | $12160\pm 1330$ | $12730\pm 1550$ | $0.129\pm 0.048$ | $0.142\pm 0.035$ | 5 | esteban09
30Dor | $8970\pm 270$ | $8940\pm 300$ | $0.027\pm 0.009$ | $0.339\pm 0.037$ | 8 | peimbert03
N 44C | $9010\pm 190$ | $8930\pm 230$ | $0.070\pm 0.007$ | $0.483\pm 0.039$ | 6 | dominguezguzman22
HII-2 | $8470\pm 1050$ | $8130\pm 1450$ | $0.108\pm 0.036$ | $0.477\pm 0.162$ | 1 | lopezsanchez07
NGC 5455 | $9000\pm 1360$ | $9000\pm 1520$ | $0.018\pm 0.045$ | $0.251\pm 0.083$ | 3 | esteban20
VS44 | $7220\pm 940$ | $7050\pm 1200$ | $0.031\pm 0.033$ | $0.332\pm 0.120$ | 5 | esteban09
N 88A | $11860\pm 180$ | $12060\pm 190$ | $0.060\pm 0.010$ | $0.183\pm 0.008$ | 5 | dominguezguzman22
HII-1 | $8540\pm 1020$ | $8360\pm 1460$ | $0.105\pm 0.037$ | $0.477\pm 0.161$ | 1 | lopezsanchez07
Galactic ring nebulae
NGC 7635A2 | $6140\pm 650$ | $5810\pm 970$ | $0.060\pm 0.028$ | $0.888\pm 0.262$ | 3 | esteban16
NGC 7635A3 | $6280\pm 430$ | $6040\pm 670$ | $0.041\pm 0.023$ | $0.695\pm 0.189$ | 3 | esteban16
NGC 7635A4 | $7170\pm 570$ | $7020\pm 780$ | $0.045\pm 0.022$ | $0.104\pm 0.027$ | 2 | esteban16
NGC 6888A2 | $5060\pm 170$ | $2380\pm 650$ | $0.244\pm 0.014$ | $2.224\pm 0.434$ | 1 | esteban16
NGC 6888A3 | $5470\pm 260$ | $4280\pm 680$ | $0.145\pm 0.022$ | $0.983\pm 0.229$ | 3 | esteban16
NGC 6888A4 | $6770\pm 770$ | $6180\pm 1330$ | $0.104\pm 0.039$ | $0.577\pm 0.169$ | 4 | esteban16
NGC 6888A5 | $6470\pm 410$ | $5840\pm 730$ | $0.106\pm 0.021$ | $0.721\pm 0.195$ | 5 | esteban16
NGC 6888A6 | $6940\pm 320$ | $6520\pm 580$ | $0.084\pm 0.024$ | $0.488\pm 0.097$ | 3 | esteban16
|  |  |  |  |  |
Table 7: Continued. Region |  $T_{\rm e}$(O II/[O III]) |  $T_{0}$(O2+) |  $t^{2}$(O2+) | O II V1/H$\beta$ | No. | Ref.
---|---|---|---|---|---|---
| K | K |  | H$\beta$=100 | lines |
Galactic H II regions
NGC 3603 | $7550\pm 560$ | $7410\pm 720$ | $0.046\pm 0.019$ | $0.644\pm 0.167$ | 4 | garciarojas06
M 42-P1 | $7580\pm 230$ | $7510\pm 280$ | $0.022\pm 0.008$ | $0.417\pm 0.052$ | 6 | delgadoinglada16
M 42-2 | $7390\pm 60$ | $7250\pm 80$ | $0.035\pm 0.003$ | $0.472\pm 0.015$ | 6 | mendezdelgado22b
Sh 2-100 | $7380\pm 320$ | $7280\pm 400$ | $0.028\pm 0.011$ | $0.501\pm 0.091$ | 6 | esteban17
M 42-3 | $7660\pm 120$ | $7560\pm 140$ | $0.027\pm 0.004$ | $0.403\pm 0.025$ | 5 | mendezdelgado21a
M 42-1 | $7730\pm 130$ | $7660\pm 160$ | $0.022\pm 0.005$ | $0.355\pm 0.025$ | 5 | mendezdelgado21a
Sh 2-311 | $7770\pm 900$ | $7750\pm 1120$ | $0.035\pm 0.031$ | $0.152\pm 0.048$ | 5 | garciarojas05
M 16 | $6240\pm 320$ | $6010\pm 420$ | $0.042\pm 0.011$ | $0.252\pm 0.058$ | 5 | garciarojas06
M 42-bar | $7620\pm 260$ | $7550\pm 290$ | $0.026\pm 0.008$ | $0.198\pm 0.028$ | 6 | delgadoinglada16
M 42-1 | $7170\pm 110$ | $7070\pm 140$ | $0.026\pm 0.004$ | $0.181\pm 0.012$ | 5 | mendezdelgado21b
NGC 3576 | $7140\pm 130$ | $6960\pm 160$ | $0.041\pm 0.004$ | $0.559\pm 0.043$ | 6 | garciarojas04
M 42 | $7370\pm 130$ | $7250\pm 160$ | $0.031\pm 0.005$ | $0.499\pm 0.038$ | 6 | esteban04
M 17 | $6980\pm 280$ | $6870\pm 340$ | $0.029\pm 0.009$ | $0.638\pm 0.108$ | 6 | garciarojas07
M 8 | $6670\pm 210$ | $6470\pm 280$ | $0.043\pm 0.008$ | $0.210\pm 0.030$ | 6 | garciarojas07
M 42-4 | $7550\pm 100$ | $7470\pm 120$ | $0.024\pm 0.004$ | $0.403\pm 0.021$ | 5 | mendezdelgado21a
M 42-3 | $7320\pm 80$ | $7200\pm 100$ | $0.033\pm 0.003$ | $0.498\pm 0.022$ | 6 | mendezdelgado22b
Sh 2-288 | $7440\pm 1080$ | $7420\pm 1520$ | $0.053\pm 0.042$ | $0.170\pm 0.062$ | 2 | esteban17
M 42 | $7460\pm 290$ | $7380\pm 360$ | $0.022\pm 0.011$ | $0.394\pm 0.061$ | 6 | mesadelgado09
M 42-2 | $6710\pm 150$ | $6480\pm 180$ | $0.044\pm 0.005$ | $0.305\pm 0.030$ | 4 | mendezdelgado21b
M 42-2 | $7670\pm 70$ | $7600\pm 90$ | $0.022\pm 0.003$ | $0.382\pm 0.012$ | 6 | mendezdelgado21a
Extragalactic H II regions from the literature
NGC 456a-1 | $9360\pm 780$ | $9270\pm 970$ | $0.089\pm 0.026$ | $0.212\pm 0.050$ | 2 | guseva11
NGC 456a-2 | $8920\pm 1020$ | $8830\pm 1330$ | $0.092\pm 0.035$ | $0.294\pm 0.095$ | 2 | guseva11
NGC 6822V | $10030\pm 1090$ | $10040\pm 1240$ | $0.051\pm 0.037$ | $0.249\pm 0.071$ | 4 | peimbert05
NGC 5253C1 | $11820\pm 720$ | $11910\pm 690$ | $0.009\pm 0.023$ | $0.166\pm 0.027$ | 2 | guseva11
Mrk1259 | $5400\pm 400$ | $4220\pm 760$ | $0.143\pm 0.018$ | $1.160\pm 0.333$ | 2 | guseva11
NGC 5253C2 | $9290\pm 590$ | $9270\pm 650$ | $0.027\pm 0.019$ | $0.270\pm 0.056$ | 2 | guseva11
NGC 5253P2 | $10030\pm 910$ | $10000\pm 1070$ | $0.071\pm 0.030$ | $0.281\pm 0.065$ | 2 | guseva11
NGC 346 | $9840\pm 530$ | $9830\pm 630$ | $0.092\pm 0.018$ | $0.261\pm 0.045$ | 4 | valerdi19
NGC 456-2 | $9940\pm 1230$ | $9970\pm 1510$ | $0.065\pm 0.043$ | $0.189\pm 0.054$ | 4 | penaguerrero12
|  |  |  |  |  |
Table 7: Continued. Region |  $T_{\rm e}$(O II/[O III]) |  $T_{0}$(O2+) |  $t^{2}$(O2+) | O II V1/H$\beta$ | No. | Ref.
---|---|---|---|---|---|---
| K | K |  | H$\beta$=100 | lines |
Galactic planetary nebulae
NGC 2440 | $11470\pm 330$ | $11750\pm 370$ | $0.104\pm 0.014$ | $0.394\pm 0.031$ | 4 | sharpee07
Hb 4 | $7030\pm 270$ | $6600\pm 400$ | $0.093\pm 0.012$ | $1.808\pm 0.282$ | 4 | garciarojas12
NGC 5315 | $7530\pm 230$ | $7390\pm 300$ | $0.038\pm 0.011$ | $1.011\pm 0.106$ | 6 | madonna17
M 1-31 | $6970\pm 550$ | $6820\pm 730$ | $0.041\pm 0.020$ | $1.300\pm 0.309$ | 3 | garciarojas18
Cn 1-5 | $7370\pm 450$ | $7180\pm 580$ | $0.043\pm 0.016$ | $1.138\pm 0.251$ | 3 | garciarojas12
H 1-40 | $7600\pm 1040$ | $7360\pm 1440$ | $0.077\pm 0.038$ | $1.084\pm 0.421$ | 1 | garciarojas18
H 1-50 | $8290\pm 390$ | $8070\pm 500$ | $0.086\pm 0.015$ | $1.259\pm 0.204$ | 3 | garciarojas18
Hen 2158 | $8190\pm 1010$ | $8200\pm 1220$ | $0.032\pm 0.034$ | $0.441\pm 0.159$ | 2 | garciarojas18
IC 418 | $7910\pm 230$ | $7830\pm 260$ | $0.027\pm 0.008$ | $0.207\pm 0.023$ | 8 | sharpee03
PC 14 | $7630\pm 400$ | $7460\pm 510$ | $0.050\pm 0.014$ | $1.362\pm 0.264$ | 3 | garciarojas12
M 1-32 | $7050\pm 260$ | $6710\pm 390$ | $0.072\pm 0.011$ | $0.691\pm 0.105$ | 2 | garciarojas12
M 1-61 | $7760\pm 350$ | $7620\pm 440$ | $0.045\pm 0.013$ | $0.946\pm 0.162$ | 5 | garciarojas12
Ou5 | $4380\pm 130$ | $1060\pm 630$ | $0.258\pm 0.014$ | $14.436\pm 2.766$ | 4 | corradi15
NGC 6369 | $9220\pm 630$ | $9180\pm 690$ | $0.044\pm 0.022$ | $0.624\pm 0.133$ | 3 | garciarojas12
Pe 1-1 | $8270\pm 550$ | $8130\pm 700$ | $0.057\pm 0.020$ | $0.815\pm 0.187$ | 4 | garciarojas12
IC 2501 | $9270\pm 180$ | $9260\pm 190$ | $0.005\pm 0.006$ | $0.463\pm 0.030$ | 8 | sharpee07
M 1-30 | $5440\pm 120$ | $5180\pm 190$ | $0.038\pm 0.006$ | $1.032\pm 0.116$ | 5 | garciarojas12
IC 4191 | $8040\pm 100$ | $7900\pm 130$ | $0.052\pm 0.005$ | $1.460\pm 0.062$ | 8 | sharpee07
Hen 2-96 | $8000\pm 590$ | $7890\pm 710$ | $0.032\pm 0.020$ | $0.780\pm 0.184$ | 5 | garciarojas18
M 3-15 | $6720\pm 660$ | $6530\pm 910$ | $0.049\pm 0.024$ | $1.792\pm 0.504$ | 2 | garciarojas12
Hen 2-86 | $7060\pm 160$ | $6890\pm 220$ | $0.039\pm 0.008$ | $1.321\pm 0.116$ | 7 | garciarojas12
M 2-31 | $7900\pm 530$ | $7680\pm 660$ | $0.063\pm 0.018$ | $1.091\pm 0.260$ | 4 | garciarojas18
NGC 5189 | $9370\pm 780$ | $9300\pm 960$ | $0.065\pm 0.028$ | $0.632\pm 0.152$ | 5 | garciarojas12
M 1-60 | $7010\pm 250$ | $6770\pm 360$ | $0.056\pm 0.010$ | $1.704\pm 0.247$ | 4 | garciarojas18
Hen 2-73 | $8770\pm 610$ | $8570\pm 800$ | $0.094\pm 0.022$ | $0.998\pm 0.228$ | 4 | garciarojas18
IC 4776 | $8390\pm 120$ | $8280\pm 150$ | $0.048\pm 0.007$ | $0.733\pm 0.034$ | 7 | sowicka17
M 1-25 | $6640\pm 340$ | $6450\pm 460$ | $0.037\pm 0.013$ | $0.994\pm 0.213$ | 4 | garciarojas12
M 1-33 | $6780\pm 210$ | $6460\pm 300$ | $0.067\pm 0.009$ | $1.931\pm 0.249$ | 4 | garciarojas18
M 2-36 | $5450\pm 70$ | $4770\pm 140$ | $0.092\pm 0.004$ | $4.826\pm 0.374$ | 8 | espiritu21
Abell 46 | $4240\pm 60$ | $320\pm 370$ | $0.279\pm 0.008$ | $11.149\pm 1.056$ | 6 | corradi15
|  |  |  |  |  |
Table 8: Ionic abundances of the H II regions and other nebulae. Region | 12+log(O+/H+) | 12+log(O2+/H+) | 12+log(O2+/H+) | Ref. |
---|---|---|---|---|---
| CELs | CELs $t^{2}$(O2+)=0 | RLs |  |
Extragalactic H II regions |
NGC 5461 | $7.78^{+0.08}_{-0.06}$ | $8.29\pm 0.05$ | $8.46^{+0.14}_{-0.13}$ | esteban09  |
NGC 588 | $7.40^{+0.27}_{-0.11}$ | $8.11^{+0.09}_{-0.06}$ | $8.33\pm 0.08$ | Toribio16  |
NGC 595 | $8.29^{+0.05}_{-0.04}$ | $8.02^{+0.14}_{-0.05}$ | $8.34^{+0.08}_{-0.09}$ | esteban09  |
K 932 | $7.87^{+0.05}_{-0.03}$ | $8.30\pm 0.03$ | $8.50\pm 0.07$ | esteban09  |
IC 132 | $7.17^{+0.21}_{-0.14}$ | $8.24^{+0.09}_{-0.06}$ | $8.38\pm 0.10$ | Toribio16  |
N 11B | $7.99^{+0.03}_{-0.04}$ | $8.17^{+0.03}_{-0.01}$ | $8.37\pm 0.03$ | dominguezguzman22  |
NGC 5471 | $7.17^{+0.07}_{-0.06}$ | $7.93^{+0.02}_{-0.01}$ | $8.05\pm 0.15$ | esteban20  |
N 66A | $7.49^{+0.06}_{-0.04}$ | $7.84\pm 0.02$ | $7.99\pm 0.05$ | dominguezguzman22  |
NGC 604 | $7.92\pm 0.06$ | $8.23\pm 0.04$ | $8.43\pm 0.07$ | esteban09  |
NGC 6822 | $7.37^{+0.36}_{-0.16}$ | $8.08^{+0.03}_{-0.02}$ | $8.31^{+0.08}_{-0.07}$ | esteban14  |
UV-1 | $7.80^{+0.14}_{-0.09}$ | $8.09\pm 0.02$ | $8.50^{+0.13}_{-0.14}$ | lopezsanchez07  |
NGC 5408 | $7.29^{+0.14}_{-0.12}$ | $7.70\pm 0.03$ | $8.18\pm 0.10$ | esteban14  |
NGC 1714 | $7.65^{+0.13}_{-0.08}$ | $8.27^{+0.03}_{-0.05}$ | $8.45\pm 0.07$ | dominguezguzman22  |
N 81 | $7.30^{+0.04}_{-0.03}$ | $7.90^{+0.03}_{-0.02}$ | $8.22\pm 0.03$ | dominguezguzman22  |
IC 2111 | $8.05^{+0.08}_{-0.06}$ | $8.18\pm 0.04$ | $8.34^{+0.09}_{-0.10}$ | dominguezguzman22  |
NGC 2363 | $6.57^{+0.12}_{-0.13}$ | $7.69^{+0.02}_{-0.03}$ | $8.02^{+0.11}_{-0.10}$ | esteban09  |
30Dor | $7.62\pm 0.05$ | $8.27\pm 0.01$ | $8.42\pm 0.05$ | peimbert03  |
N 44C | $7.30\pm 0.05$ | $8.23\pm 0.02$ | $8.56^{+0.04}_{-0.03}$ | dominguezguzman22  |
HII-2 | $7.66^{+0.11}_{-0.10}$ | $8.06\pm 0.02$ | $8.57^{+0.15}_{-0.14}$ | lopezsanchez07  |
NGC 5455 | $7.74\pm 0.03$ | $8.18\pm 0.03$ | $8.28^{+0.15}_{-0.14}$ | esteban20  |
VS44 | $7.91^{+0.08}_{-0.06}$ | $8.15^{+0.04}_{-0.06}$ | $8.41\pm 0.15$ | esteban09  |
N 88A | $6.88\pm 0.07$ | $8.00^{+0.02}_{-0.01}$ | $8.18\pm 0.02$ | dominguezguzman22  |
HII-1 | $7.59^{+0.09}_{-0.06}$ | $8.07\pm 0.02$ | $8.57\pm 0.16$ | lopezsanchez07  |
Galactic ring nebulae |
NGC 7635A2 | $7.93^{+0.31}_{-0.11}$ | $8.24^{+0.11}_{-0.08}$ | $8.82\pm 0.13$ | esteban16  |
NGC 7635A3 | $8.06^{+0.16}_{-0.07}$ | $8.31^{+0.18}_{-0.10}$ | $8.73\pm 0.11$ | esteban16  |
NGC 7635A4 | $8.16^{+0.03}_{-0.05}$ | $7.60^{+0.10}_{-0.08}$ | $7.95\pm 0.11$ | esteban16  |
NGC 6888A2 | $8.33\pm 0.04$ | $7.52\pm 0.03$ | $9.23\pm 0.09$ | esteban16  |
NGC 6888A3 | $8.13\pm 0.06$ | $7.69^{+0.15}_{-0.09}$ | $8.86\pm 0.10$ | esteban16  |
NGC 6888A4 | $7.47^{+0.06}_{-0.05}$ | $7.95\pm 0.13$ | $8.64^{+0.12}_{-0.13}$ | esteban16  |
NGC 6888A5 | $7.49\pm 0.06$ | $7.97^{+0.09}_{-0.07}$ | $8.74^{+0.12}_{-0.11}$ | esteban16  |
NGC 6888A6 | $7.57^{+0.05}_{-0.06}$ | $7.98^{+0.17}_{-0.11}$ | $8.56\pm 0.09$ | esteban16  |
|  |  |  |  |
Table 8: Continued. Region | 12+log(O+/H+) | 12+log(O2+/H+) | 12+log(O2+/H+) | Ref. |
---|---|---|---|---|---
| CELs | CELs $t^{2}$(O2+)=0 | RLs |  |
Galactic H II regions |
NGC 3603 | $7.36^{+0.13}_{-0.09}$ | $8.43^{+0.02}_{-0.03}$ | $8.74\pm 0.11$ | garciarojas06  |
M 42-P1 | $7.81^{+0.10}_{-0.07}$ | $8.39\pm 0.02$ | $8.55\pm 0.05$ | delgadoinglada16  |
M 42-2 | $7.74^{+0.07}_{-0.05}$ | $8.36\pm 0.02$ | $8.61^{+0.02}_{-0.01}$ | mendezdelgado22b  |
Sh 2-100 | $7.76^{+0.11}_{-0.06}$ | $8.38\pm 0.02$ | $8.59\pm 0.08$ | esteban17  |
M 42-3 | $7.75^{+0.07}_{-0.06}$ | $8.36^{+0.01}_{-0.02}$ | $8.55\pm 0.03$ | mendezdelgado21a  |
M 42-1 | $7.87\pm 0.06$ | $8.33^{+0.02}_{-0.01}$ | $8.49\pm 0.03$ | mendezdelgado21a  |
Sh 2-311 | $8.30\pm 0.04$ | $7.82\pm 0.02$ | $8.05^{+0.14}_{-0.15}$ | garciarojas05  |
M 16 | $8.47^{+0.06}_{-0.05}$ | $7.92^{+0.04}_{-0.03}$ | $8.31^{+0.10}_{-0.11}$ | garciarojas06  |
M 42-bar | $8.39\pm 0.04$ | $8.04\pm 0.02$ | $8.23\pm 0.06$ | delgadoinglada16  |
M 42-1 | $8.14^{+0.03}_{-0.04}$ | $7.96\pm 0.01$ | $8.17\pm 0.03$ | mendezdelgado21b  |
NGC 3576 | $8.06^{+0.08}_{-0.05}$ | $8.36\pm 0.01$ | $8.66\pm 0.03$ | garciarojas04  |
M 42 | $7.81^{+0.07}_{-0.06}$ | $8.40\pm 0.01$ | $8.64\pm 0.03$ | esteban04  |
M 17 | $7.82^{+0.06}_{-0.04}$ | $8.45\pm 0.02$ | $8.69^{+0.08}_{-0.07}$ | garciarojas07  |
M 8 | $8.34^{+0.04}_{-0.03}$ | $7.88^{+0.02}_{-0.03}$ | $8.24\pm 0.06$ | garciarojas07  |
M 42-4 | $7.81^{+0.06}_{-0.05}$ | $8.36\pm 0.02$ | $8.54\pm 0.02$ | mendezdelgado21a  |
M 42-3 | $7.68\pm 0.05$ | $8.38^{+0.01}_{-0.02}$ | $8.63\pm 0.02$ | mendezdelgado22b  |
Sh 2-288 | $8.22^{+0.08}_{-0.07}$ | $7.72^{+0.11}_{-0.08}$ | $8.11^{+0.17}_{-0.15}$ | esteban17  |
M 42 | $7.94\pm 0.07$ | $8.35^{+0.05}_{-0.04}$ | $8.51\pm 0.07$ | mesadelgado09  |
M 42-2 | $8.17^{+0.03}_{-0.04}$ | $8.03^{+0.02}_{-0.01}$ | $8.40\pm 0.04$ | mendezdelgado21b  |
M 42-2 | $7.82\pm 0.05$ | $8.36\pm 0.02$ | $8.52\pm 0.01$ | mendezdelgado21a  |
Extragalactic H II regions from the literature |
NGC 456a-1 | $7.65\pm 0.06$ | $7.84\pm 0.01$ | $8.22\pm 0.10$ | guseva11  |
NGC 456a-2 | $7.53^{+0.25}_{-0.10}$ | $7.93\pm 0.01$ | $8.34^{+0.15}_{-0.14}$ | guseva11  |
NGC 6822V | $6.91^{+0.25}_{-0.14}$ | $8.06^{+0.03}_{-0.02}$ | $8.27^{+0.13}_{-0.14}$ | peimbert05  |
NGC 5253C1 | $7.34\pm 0.02$ | $8.08\pm 0.01$ | $8.11\pm 0.07$ | guseva11  |
Mrk1259 | $8.36^{+0.08}_{-0.07}$ | $7.75^{+0.06}_{-0.05}$ | $8.97\pm 0.13$ | guseva11  |
NGC 5253C2 | $7.56^{+0.07}_{-0.05}$ | $8.17\pm 0.01$ | $8.31\pm 0.09$ | guseva11  |
NGC 5253P2 | $7.42^{+0.04}_{-0.03}$ | $8.07\pm 0.01$ | $8.35\pm 0.10$ | guseva11  |
NGC 346 | $7.32^{+0.14}_{-0.11}$ | $7.93\pm 0.01$ | $8.28^{+0.08}_{-0.07}$ | valerdi19  |
NGC 456-2 | $7.54^{+0.15}_{-0.11}$ | $7.88^{+0.02}_{-0.01}$ | $8.16^{+0.12}_{-0.13}$ | penaguerrero12  |
|  |  |  |  |
Table 8: Continued. Region | 12+log(O+/H+) | 12+log(O2+/H+) | 12+log(O2+/H+) | Ref. |
---|---|---|---|---|---
| CELs | CELs $t^{2}$(O2+)=0 | RLs |  |
Galactic planetary nebulae |
NGC 2440 | $7.41^{+0.09}_{-0.06}$ | $8.22^{+0.02}_{-0.03}$ | $8.50^{+0.03}_{-0.04}$ | sharpee07  |
Hb 4 | $7.33^{+0.19}_{-0.10}$ | $8.59\pm 0.05$ | $9.20\pm 0.07$ | garciarojas12  |
NGC 5315 | $7.83^{+0.32}_{-0.23}$ | $8.69^{+0.07}_{-0.05}$ | $8.95\pm 0.05$ | madonna17  |
M 1-31 | $7.68^{+0.13}_{-0.11}$ | $8.74^{+0.05}_{-0.04}$ | $9.06\pm 0.10$ | garciarojas18  |
Cn 1-5 | $8.10^{+0.13}_{-0.07}$ | $8.69\pm 0.04$ | $9.00^{+0.09}_{-0.10}$ | garciarojas12  |
H 1-40 | $7.02^{+0.13}_{-0.10}$ | $8.49^{+0.05}_{-0.04}$ | $8.96\pm 0.17$ | garciarojas18  |
H 1-50 | $7.38^{+0.10}_{-0.07}$ | $8.60^{+0.03}_{-0.04}$ | $9.04\pm 0.07$ | garciarojas18  |
Hen 2158 | $7.88\pm 0.07$ | $8.35\pm 0.03$ | $8.57^{+0.15}_{-0.16}$ | garciarojas18  |
IC 418 | $8.37^{+0.08}_{-0.06}$ | $8.08\pm 0.02$ | $8.26^{+0.05}_{-0.04}$ | sharpee03  |
PC 14 | $7.35^{+0.11}_{-0.08}$ | $8.73^{+0.04}_{-0.03}$ | $9.07^{+0.08}_{-0.09}$ | garciarojas12  |
M 1-32 | $8.25^{+0.17}_{-0.11}$ | $8.28^{+0.05}_{-0.04}$ | $8.78^{+0.07}_{-0.06}$ | garciarojas12  |
M 1-61 | $7.15^{+0.24}_{-0.14}$ | $8.63^{+0.06}_{-0.05}$ | $8.93\pm 0.07$ | garciarojas12  |
Ou5 | $6.27^{+0.48}_{-0.17}$ | $7.98^{+0.03}_{-0.04}$ | $10.06^{+0.09}_{-0.08}$ | corradi15  |
NGC 6369 | $6.91^{+0.10}_{-0.07}$ | $8.50^{+0.05}_{-0.03}$ | $8.73\pm 0.09$ | garciarojas12  |
Pe 1-1 | $7.48^{+0.25}_{-0.18}$ | $8.53^{+0.05}_{-0.04}$ | $8.85\pm 0.10$ | garciarojas12  |
IC 2501 | $7.50^{+0.04}_{-0.05}$ | $8.58\pm 0.02$ | $8.60\pm 0.03$ | sharpee07  |
M 1-30 | $8.42^{+0.14}_{-0.08}$ | $8.50^{+0.06}_{-0.04}$ | $8.96^{+0.04}_{-0.05}$ | garciarojas12  |
IC 4191 | $7.30\pm 0.08$ | $8.79^{+0.03}_{-0.02}$ | $9.10\pm 0.02$ | sharpee07  |
Hen 2-96 | $7.43^{+0.16}_{-0.14}$ | $8.63^{+0.05}_{-0.04}$ | $8.83\pm 0.10$ | garciarojas18  |
M 3-15 | $6.88^{+0.16}_{-0.08}$ | $8.78\pm 0.05$ | $9.19^{+0.12}_{-0.11}$ | garciarojas12  |
Hen 2-86 | $7.42^{+0.30}_{-0.21}$ | $8.76^{+0.05}_{-0.04}$ | $9.07\pm 0.04$ | garciarojas12  |
M 2-31 | $7.43\pm 0.08$ | $8.60\pm 0.05$ | $8.97\pm 0.10$ | garciarojas18  |
NGC 5189 | $8.13^{+0.11}_{-0.07}$ | $8.43\pm 0.04$ | $8.70^{+0.11}_{-0.10}$ | garciarojas12  |
M 1-60 | $7.74^{+0.21}_{-0.13}$ | $8.76^{+0.05}_{-0.04}$ | $9.17^{+0.06}_{-0.07}$ | garciarojas18  |
Hen 2-73 | $7.54^{+0.11}_{-0.10}$ | $8.51\pm 0.05$ | $8.93\pm 0.10$ | garciarojas18  |
IC 4776 | $7.76^{+0.45}_{-0.14}$ | $8.53\pm 0.03$ | $8.81\pm 0.02$ | sowicka17  |
M 1-25 | $8.29^{+0.10}_{-0.09}$ | $8.62\pm 0.05$ | $8.94\pm 0.09$ | garciarojas12  |
M 1-33 | $7.68^{+0.08}_{-0.05}$ | $8.72\pm 0.04$ | $9.22\pm 0.06$ | garciarojas18  |
M 2-36 | $6.95^{+0.05}_{-0.04}$ | $8.72^{+0.03}_{-0.02}$ | $9.61\pm 0.03$ | espiritu21  |
Abell 46 | $6.25^{+1.05}_{-0.19}$ | $7.75^{+0.03}_{-0.02}$ | $9.95\pm 0.04$ | corradi15  |
|  |  |  |  |

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