# HII regions in CALIFA survey: II. The relation between their physical
properties and galaxy evolution

C. Espinosa-Ponce1, S. F. Sánchez1, C. Morisset2, J. K. Barrera-Ballesteros1,
L. Galbany3,4, R. García-Benito5, E. A. D. Lacerda1, D. Mast6,7
1Universidad Nacional Autónoma de México, Instituto de Astronomía, AP 70-264,
CDMX 04510, México
2Universidad Nacional Autónoma de México, Instituto de Astronomía, AP 106,
Ensenada 22800, BC, México
3Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans,
s/n, E-08193 Barcelona, Spain.
4Institut d’Estudis Espacials de Catalunya (IEEC), E-08034 Barcelona, Spain.
5Instituto de Astrofísica de Andalucía, CSIC, Apartado de correos 3004,
E-18080 Granada, Spain
6Universidad Nacional Córdoba. Observatorio Astronómico de Córdoba. Córdoba,
Argentina.
7Consejo de Investigaciones Científicas y Técnicas de la República Argentina,
Avda. Rivadavia 1917, C1033AAJ, CABA, Argentina E-mail:
<EMAIL_ADDRESS><EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present in here the exploration of the physical properties of the sample of
H ii regions and aggregations of the last H ii regions catalog of the CALIFA
survey. This sample comprises the optical spectroscopic properties of more
than $\sim$26,000 ionized regions corresponding to 924 galaxies from the
Integral Field Spectroscopy data, including the flux intensity and equivalent
widths and the properties of their underlying stellar population. In the
current study we derive a set of physical quantities for all these regions
based on those properties, including (i) the fraction of young stars; (ii) the
ionization strength (using six different estimations); (iii) the oxygen
abundance (using 25 different calibrators); (iv) the nitrogen and nitrogen-to-
oxygen abundance; (v) the dust extinction and (vi) the electron density. Using
this dataset we explore how the loci in the classical diagnostic diagrams are
connected with those quantities, the radial distributions of these parameters,
and the inter-relations between themselves and with the properties of the
underlying stellar populations. We conclude that many properties of the H ii
regions are tightly related to the galactic stellar evolution at the location
where those regions are observed. Those properties are modulated only as a
second-order effect by the properties of the ionizing stars and the ionized
nebulae that do not depend on the astrophysical context in which they are
formed. Our results highlight the importance of H ii regions to explore the
chemical evolution in galaxies, clarifying which of their properties can be
used as proxies of that evolution.

###### keywords:

ISM: HII regions – ISM: general – galaxies: ISM – galaxies: star formation –
techniques: spectroscopic

††pubyear: 2020††pagerange: HII regions in CALIFA survey: II. The relation
between their physical properties and galaxy evolution–12

##  1 Introduction

H ii regions are gas nebulae ionized by young and massive, short-lived, OB
stars (e.g., Strömgren, 1939). Due to their nature, they are tracers of the
star-formation processes in galaxies, frequently found in late-type/disk
galaxies (e.g., Kennicutt & Hodge, 1980), although they have been recently
observed in some early-type ones (e.g., Gomes et al., 2016). Their nebular
emission lines make possible to directly measure the gas-phase abundance at
discrete spatial positions in galaxies (e.g., Searle, 1971; Peimbert et al.,
1978; Kennicutt & Garnett, 1996; Kennicutt et al., 2003). Hence, they are one
of the primary tools for constraining galactic chemical evolution theories
(e.g., Carigi et al., 2019), as the present abundances are the consequence of
the enrichment history (Maiolino & Mannucci, 2019; Kewley et al., 2019;
Sánchez, 2020). This connection induces relations between their observational
properties, the chemical composition, the properties of the underlying stellar
populations, and the global properties of their host galaxies (e.g. Sánchez et
al., 2015b; Espinosa-Ponce et al., 2020).

Previous studies have determined essential relationships, galaxy wide
patterns, and scaling laws between the chemical abundances in galaxies and
their physicals properties. Among them, the most relevant ones are the surface
brightness-metallicity, mass-metallicity, and luminosity-metallicity relations
(Lequeux et al., 1979; Skillman et al., 1989; Vila-Costas & Edmunds, 1992;
Zaritsky et al., 1994; Tremonti et al., 2004; Barrera-Ballesteros et al.,
2018), characteristics vs. integrated abundances (Moustakas & Kennicutt,
2006), or characteristic shapes of abundance gradients (e.g. Vila-Costas &
Edmunds, 1992). These relations were derived either for integrated properties
of galaxies or using limited samples of H ii regions (and for a small number
of galaxies), limiting our understanding of the chemical evolution derived
from them.

In the last years, the new generation of emission-line surveys based on
Integral Field Spectroscopy (IFS) instruments and multi-object spectrometers,
covering large Fields-of-view (FoVs), offer catalogs of H ii regions with
hundreds of objects covering the full optical extension of nearby galaxies
(e.g., Rosales-Ortega et al., 2010; Sánchez et al., 2012a, 2014). The H ii
region catalogs produced by these surveys are based on large samples of
galaxies covering a wide range of morphological types (Sánchez et al., 2012b,
2013). Significant results have been determined using these catalogs: (i) the
existence of a typical abundance gradient (Sánchez et al., 2014, 2015a;
Sánchez-Menguiano et al., 2018), (ii) the deviations from this radial
abundance gradient induced by spiral arms (Sánchez-Menguiano et al., 2020) and
their azimuthal variations (Vogt et al., 2017), (iii) the correlation between
the oxygen abundance of H ii regions and the stellar mass densities of
underlying stellar populations (Rosales-Ortega et al., 2012; Barrera-
Ballesteros et al., 2016), (iv) the existence of average patterns in the
radial gradient of different physical properties (Sánchez et al., 2012b), (v)
the existence of a large number of H ii regions contaminated by supernovae
remnants (Cid Fernandes et al., 2021), (vi) chemical evolution models at kpc
scales (Barrera-Ballesteros et al., 2018), and (vii) the comparison between
the pre-SNe feedback and environmental pressure across the optical extension
of spiral galaxies (Barnes et al., 2021), among the most important ones.

In Espinosa-Ponce et al. (2020), we presented a new catalog of H ii regions
based on the Calar Alto Legacy Integral Field Area Survey (CALIFA Sánchez et
al., 2012a) data. We used the extended sample (hereafter, eCALIFA) that
comprises the CALIFA (692 galaxies) and PISCO samples (232 galaxies) (Sánchez
et al., 2016b; Galbany et al., 2018). We use the tool
pyhiiexplorer111https://github.com/cespinosa/pyHIIexplorerV2 to detect,
segregate, and extract the main spectroscopic properties of these H ii
regions. Then, we built the most extensive and homogeneous catalog of
spectroscopic properties of H ii regions in the nearby Universe. This catalog
has allowed us to confirm the correlations between the ionization conditions
in H ii regions and the properties of the underlying stellar populations. In
particular, the relation between [O iii]$\lambda 5007/$H$\beta$ and [N
ii]$\lambda 6583/$H$\alpha$ ratios with the age and metallicity of the
underlying stellar populations (previously found in Sánchez et al., 2015b).
More recently we have used this catalog to explore the [$\alpha$/Fe] patterns
in galaxies (Sánchez, 2020).

In the current study we derive the main physical properties of the H ii
regions in this catalog, including different derivations for the oxygen and
nitrogen abundances using a wide set of state-of-the art calibrators, together
with estimations of the ionization strength, electron density, and dust
extinction. We explore the distribution of those properties in the classical
diagnostic diagrams, connecting them with stellar population properties.
Finally, we explore the gradients of all the derived physical properties and
characterize them by the mass and morphology of the galaxies.

The structure of the article is as follows: the data explored in this study
are described in Sec. 2, including a brief description of the sample of
galaxies, and the procedure to detect and extract the properties of the H ii
regions; the analysis and results are presented in Sec. 3, with the
derivations of the properties for the H ii regions described in 3.1. The main
trends across the diagnostic diagrams are presented in Sec. 3.2, while the
radial gradients are shown in Sec. 3.3. Finally, the relations of the oxygen
abundance with other physical properties of the H ii regions and the
properties of the underlying stellar populations are shown in Sec. 3.4 and
Sec. 3.5, respectively; the main conclusions of this study are presented in
Sec. 5.

##  2 Data

We use the catalog of spectroscopic properties of HII regions described in the
previous section. This catalog was extracted from the sample of $\sim 1000$
galaxies comprising the eCALIFA survey. This sample was primarily diameter-
selected to have a characteristic projected size of $\sim$60$\arcmin$ (Walcher
et al., 2014). It spans through a narrow redshift range centred at $z\sim
0.015$, covering a wide range of stellar masses and morphologies. In summary,
it is a somehow representative sample of the galaxies in the nearby universe.

The whole dataset was observed at the 3.5m telescope of the Calar Alto
Observatory, using the Potsdam Multi Aperture Spectrograph (PMAS; Roth et al.,
2005) in the Pmas fiber PAcK configuration (PPAK; Kelz et al., 2006). This
configuration provides a sufficient field-of-view ($74^{\prime\prime}\times
64^{\prime\prime}$) to map the full optical extent of these galaxies. It is
possible to map up to 2.5 effective radii due the diameter sample selection,
described before. The observing strategy guaranteed a final spatial resolution
of $FWHM\sim 2.4^{\prime\prime}$ ($\sim 0.8$ kpc) at the sample’s average
redshift (Sánchez et al., 2016b). The current sample was observed using the
V500 setup, which provides a spectral resolution of $\lambda/\Delta\lambda\sim
850$ and a wavelength range ($3745-7200$Å). This is sufficient to study the
most important ionized gas emission lines in the optical range (from [O
ii]$\lambda 3727$ to [S ii]$\lambda 6731$, at the average redshift of the
explored galaxies). The wavelength range and resolution are good enough to
deblend these emission lines from the underlying stellar population, and to
derive the main properties of both components (e.g. Cid Fernandes et al.,
2013, 2014; Kehrig et al., 2012; Sánchez et al., 2012a, 2016a).

The data was reduced with the CALIFA v2.2 pipeline (which is described in
detail in Sánchez et al., 2016b). The reduction comprises the standard
procedures for this kind of data outlined in (Sánchez, 2006). This procedure
provides for each observed galaxy a regular-gridded data-cube, with two axis
recording the spatial dimensions (with a sampling size of 1$\arcsec$/spaxel),
and the remaining one recording the spectral dimension. These data cubes were
analyzed using the pipe3d pipeline in order to derive the spatial resolved
properties of the ionized gas emission lines and the stellar population. This
tool was developed (and it has been used) to analyze different IFS data, e.g.
CALIFA (Sánchez-Menguiano et al., 2016; López-Cobá et al., 2019), MaNGA
(Barrera-Ballesteros et al., 2018; Ibarra-Medel et al., 2016; Sánchez et al.,
2018), MUSE (López-Cobá et al., 2020), and SAMI (Sánchez et al., 2019). The
underlying stellar population is fitted using the GSD156 single stellar
population library (Cid Fernandes et al., 2013), which comprises 156
templates: 39 stellar ages (from 1 Myr to 14.1 Gyr), and four metallicities
(Z/Z⊙=0.2, 0.4, 1, and 1.5). The derived stellar spectrum model then is
subtracted from the original one for each spaxel to obtain gas-pure data-cube,
that it is then analyzed to extract the properties of the emission lines. The
final dataproducts of this analysis is a set of maps that retain the world
coordinate system of the original cubes comprising the spatial distribution of
each particular quantity.

The segregation of H ii regions and extraction of the corresponding emission
lines information is performed by applying the pyhiiexplorer tool to the
dataproducts provided by pipe3d. This semiautomatic procedure detect and
segregate candidates to H ii regions based on three assumptions: (i) H ii
regions have a strong and peaky H$\alpha$ emission that is clearly
recognizable above both the continuum emission and the diffuse ionized gas
(DIG) emission across the galaxies; (ii) the typical size of an extragalactic
H ii regions at this cosmological distance is of the order of the size of the
PSF; (iii) the underlying stellar population at the location of the selected
regions has enough young stars to produce the observed ionization, as
described in detail in Espinosa-Ponce et al. (2020). The input parameters used
to identify the ionized regions are: (i) a flux intensity threshold for each
ionized region peak emission of $3\times
10^{-17}\,\mathrm{erg}\,\mathrm{s}^{-1}\,\mathrm{cm}^{-2}\,\mathrm{arcsec}^{-1}$,
(ii) a minimum relative flux to the peak emission for associated spaxels of
the same H ii region of 5%, (iii) a maximum distance to the peak spaxel of
$5.5$ arcsec, and (iv) an absolute flux intensity threshold of
$0.5\,\mathrm{erg}\,\mathrm{s}^{-1}\,\mathrm{cm}^{-2}\,\mathrm{arcsec}^{-1}$
in the adjacent pixels to associate them to the peak spaxel. The initial
sample of ionized regions identified by pyHIIexplorer includes the information
of $38\,807$ objects from $924$ galaxies. The $\sim 70\%$ of the total sample
corresponds to H ii regions, the $6.4\%$ corresponds to DIG powered by hot old
low mass evolved stars (HOLMES), and $\sim 3\%$ corresponds to AGN-like (for
further details see Espinosa-Ponce et al., 2020).

The result of this analysis for the full eCALIFA sample is a catalog that
comprises the information of 51 emission lines in the considered wavelength
range and the properties of the underlying stellar population for $\sim$26,000
H ii regions. However, not all those regions are suitable for exploring the
distributions along the diagnostic diagrams and to derive good quality
physical quantities, as we will show in the forthcoming sections. Therefore we
select a sub-sample of regions following the procedures that we will describe
in Sec 3.1. We use this catalog as the starting point of the current analysis.

##  3 Analysis and Results

We focus in this study on the exploration of the physical properties of H ii
regions, trying to determine connections between the ionization conditions,
the nebular emission and the properties of the underlying stellar populations.
Such connection may unveil which properties of H ii regions are related to the
evolution of different locations in galaxies (and which ones are not).

###  3.1 Empirical estimation of physical properties of HII regions

The physical properties of H ii regions have been frequently explored using
the classical diagnostic diagrams (Baldwin et al., 1981; Veilleux &
Osterbrock, 1987; Kewley et al., 2001). It is known that the location in these
diagrams depends on the properties of the ionizing source (a stellar
population in the case of an H ii region), and the internal physical
conditions, structure, and chemical composition of the ionized gas (e.g. Evans
& Dopita, 1985; Dopita & Evans, 1986; Kewley et al., 2001; Kauffmann et al.,
2003; Sánchez et al., 2015a). In summary, six main parameters define the
location in these diagrams: (i) the shape/hardness of the ionizing spectral
energy distribution (SED), that in an H ii region is defined by the sum of the
spectra of the ionizing stars (a cluster of them at the typical resolution of
our data); (ii) the mean ionization parameter across the nebula, defined as
the Lyman continuum photons with respect to the total amount of hydrogen
(defined as $U$, see below); (iii) the chemical abundance of different
elements in the ionized gas, relative to hydrogen (e.g., O/H, N/H…); (iv) the
electron density of the gas (e.g., Sánchez et al., 2015b; Morisset et al.,
2016; Kewley et al., 2019), denoted as $n_{e}$; (v) the dust extinction,
characterized by the extinction at the V-band (AV) and a certain extinction
curve and (vi) the optical depth at 13.6 eV (matter-bounded regions show
higher ionization, due to the reduction of the low ionization zone). Following
Sánchez et al. (2014), we investigate the main trends across the diagnostic
diagrams of different physical properties of the H ii regions: fraction of
young stars, ionization parameter, oxygen abundance, nitrogen abundance,
electron density, and dust extinction.

The fraction of young stars that contributes to the observed spectrum within
the aperture at which the H ii region (or cluster) is selected as a gauge of
how strong is the contribution of the ionizing OB stars. It is also a proxy of
how evolved is the area in the galaxy (or the host galaxy itself), since it
weights the relative amount of old-stars with respect to the ionizing ones.
Furthermore, it is a proxy of the shape/hardness of the ionizing spectrum,
since this will be the product of the mix of the young and old ionizing stars
(e.g., hot evolved stars, HOLMES, Flores-Fajardo et al., 2011). In (Espinosa-
Ponce et al., 2020) we defined this parameter as the fraction of light in the
V-band corresponding to stars younger that 350 Myr.

The ionization parameter is defined as $U(r)=Q(H^{0})/4\pi r^{2}n_{H}c$, where
$Q(H^{0})$ is the number of $H^{0}$-ionizing photons emitted by the source per
unit of time, $r$ is the distance between the source and a particular location
within the nebula, $n_{H}$ is the hydrogen density, and $c$ is the speed of
light. By measuring the ratio between the photons and the hydrogen atom
densities, $U$ gives an insight to the efficiency of the radiation that ionize
the gas. The higher $U$ is, the easier the radiation can ionize metals. The
value of U is straightforward to determine in theoretical models, but
difficult to determine from observations. Its mean value within an H ii region
is usually estimated using different line ratios, like [O ii]$/$[O iii], as
photoionization models unveil a connection with this parameter and O+/O++
(e.g. Díaz et al., 2000). However, the reported connection depends strongly on
many other properties of the nebulae, in particular on its shape (shell or
filled), on the shape of the ionizing SED as well as on the optical depth of
the nebula at 13.6 eV. Despite of this issue, different calibrators have been
proposed that links this proxy with $U$ (Díaz et al., 2000; Dors et al., 2011;
Morisset et al., 2016; Kewley et al., 2019, e.g.). We adopted as fiducial
calibrator the one presented by Morisset et al. (2016), which is an update of
the relation first proposed by Díaz et al. (2000) and Dors et al. (2011). The
[S ii]/[S iii] line ratio is frequently claimed to get a better estimation of
the ionization parameter (Kewley et al., 2019), but the [S iii]$\lambda
9069+\lambda 9532$ emission line are not available in the spectral range of
our data. Additional estimators of $U$ have been considered along this
article, and discussed in Appendix F.

The abundance of a particular element (e.g., oxygen), may be derived in theory
by adding up all its ionic abundances. On the one hand, this can be done by
measuring the flux of the recombination lines corresponding to the considered
element. Unfortunately, most of those lines are extremely weak in the optical
range. If those lines are not accessible, it is possible to derive O/H using
the direct method, this is by measuring the flux of collisionally excited
lines (read Peimbert et al., 2017; Pérez-Montero, 2017, for a review on this
topic). For doing so, it is required to derive the electronic temperature and
density of the nebulae. The estimation of the temperature requires to derive
the flux ratio between a set of auroral to nebular lines, e.g., [O
iii]$\lambda 4363/\lambda 5007$. Then the O/H is derived computing first
certain ionic abundances. This method assumes that the temperature
distribution is homogeneous for each considered ion through the ionized
extension of the H ii region. If this is not the case, it is still possible to
apply the so-called $t^{2}$ correction (Peimbert, 1967). The direct method
relies on auroral lines that are brighter than the recombination ones, but are
very weak too (e.g., [OIII]$\lambda 4363$). In many cases they are not
accessible with the usual depth and resolution of the IFS data of the most
recent galaxy surveys (see Marino et al., 2013, as an example).

When neither the recombination nor the auroral lines are detected or
accessible, the estimation of the gas-phase abundance relies on the use of
known relations between particular strong emission line ratios and the
required physical properties to derive the abundance (e.g., Te, Alloin et al.,
1979; Pilyugin & Mattsson, 2011), and/or the abundances themselves (Peimbert
et al., 2017). These estimations are called strong-lines calibrators, and they
can be derived using two approaches: (1) by comparing the ratios of strong
emission lines with direct estimation of the oxygen abundances from
observational datasets (based either on the direct method or by the use of
collisional lines). Then, a polynomial fitting is performed (Marino et al.,
2013; Pilyugin & Mattsson, 2011; Pilyugin & Grebel, 2016, e.g.) or another
more complex regression techniques (e.g. machine learning Ho, 2019); and, (2)
using grids of photoionization models to derive the relation between oxygen
abundances and emission line ratios (e.g. Kewley & Dopita, 2002; Thomas et
al., 2018). Unfortunately, the derived oxygen abundance using the two methods
shows a discrepancy up to $\sim 0.1$-$0.4$ dex (Kewley & Ellison, 2008; Blanc
et al., 2015). This discrepancy may be due to (i) the presence of electron
temperature fluctuations in HII regions (Peimbert, 1967), (ii) uncertain
ionization corrections factors, (iii) over-simplicity of the photoionization
models used to obtain calibrations (Kennicutt et al., 2003) or (iv) high
energetic electrons following a non-Maxwellian distribution (e.g. the $\kappa$
distribution Nicholls et al., 2012), among other reasons. The most used
strong-line indicators are based on the following emission lines:
[OII]$\lambda 3727$, H$\beta$, [OIII]$\lambda 5007$, H$\alpha$, [NII]$\lambda
6583$, [SII]$\lambda 6717+31$. They comprise N2 ($\equiv$[NII]/H$\alpha$), O3
($\equiv$[OIII]/H$\beta$), O2 ($\equiv$[OII]/H$\beta$), S2
($\equiv$[SII]/H$\alpha$), the combination among them, like R23
($\equiv$O2+O3), O3N2 ($\equiv$O3/N2), N2O2 ($\equiv$N2/O2) or N2S2
($\equiv$N2/S2), and more complex combinations, like the $P$ parameter (e.g.
Pilyugin et al., 2010). Each one of these line ratios present different
strengths and caveats for the oxygen abundance calculation (e.g. Curti et al.,
2020). An additional complication is that many of the adopted emission line
ratios present a bi-valuated relation with the oxygen abundance defining upper
and lower oxygen branches (e.g. R23 Peimbert et al., 2017).

In this work, we calculate the oxygen abundance with different strong-lines
calibrators proposed by Kewley & Dopita (2002), Kobulnicky & Kewley (2004),
Pettini & Pagel (2004), Tremonti et al. (2004), Pilyugin et al. (2010);
Pilyugin & Mattsson (2011); Pilyugin & Grebel (2016), Marino et al. (2013), Ho
(2019), and Curti et al. (2020). They comprise an heterogeneous compilation of
calibrators, both empirical and theoretical, and using different indicators
and mathematical procedures to anchor the abundance. We adopt the Ho (2019)
calibrator as the fiducial one along this article, although we provide the
measurements of the remaining ones in our published catalog (see Appendix A).

As we discussed for the oxygen abundance, the nitrogen abundance determination
has similar issues. Moreover, the recombination and auroral nitrogen emission
lines are even more difficult to detect than those of the oxygen.
Nevertheless, there are relations between several strong emission line ratios
and the nitrogen abundance that could be used for the abundance determination
(i.e. strong-line calibrations). In this work, we estimate the nitrogen
abundance (N/H) and nitrogen-to-oxygen relative abundance (N/O) with the
calibrations described by Pilyugin & Grebel (2016) and Ho (2019). We adopt
this later one as our fiducial one.

Figure 1: Average physical properties (left panel), together with their
standard deviation (right panel) for the H ii regions at a certain location
within the [O iii]$\lambda 5007/$H$\beta$ vs. [N ii]$\lambda 6583/$H$\alpha$
diagnostic diagram. In each panel the color code represents a physical
property described in the text: top left panel: fraction of young stars to the
total luminosity, $f_{y}$; top right panel: ionization parameter; middle left
panel: oxygen abundance; middle right panel: nitrogen-to-oxygen abundance;
bottom left panel: dust extinction ; and bottom right panel: electron density
($\log(n_{e})$). In each panel, the scale of the colormap was selected to
cover the dynamical range of the physical parameter: $\pm$3$\sigma$ range
around the mean value in the left panels, and between zero and 2$\sigma$ in
the right panels, for all parameters but $A_{\mathrm{V}}$. For this parameter
the dynamical range in the left panel is restricted to 0 and two times the
mean value ($\sim$2 mag). The inset within each panel shows the distribution
of the corresponding property. The contour represent the density distribution
enclosing 95$\%$ of the regions. For all the panels, the dot-dashed line,
dashed-line, dotted-line, and solid line represents the demarcation lines
proposed by Kewley et al. (2001); Kauffmann et al. (2003); Stasińska et al.
(2008); Espinosa-Ponce et al. (2020), respectively.

The electron density, $n_{e}$, is derived from the ratio of emission lines of
the same ion originated from levels with similar energy (e.g. Osterbrock,
1989). In those cases the emission line ratio does not depend strongly on the
temperature (Peimbert et al., 2017). In particular, we use the [S ii] doublet,
by solving the equation:

$\frac{[\text{S\,{ii}}]\lambda 6717}{[\text{S\,{ii}}]\lambda
6731}=1.49\frac{1+3.77x}{1+12.8x}$ (1)

where $x=10^{-4}n_{e}t^{-1/2}$ and $t$ is the electron temperature in units of
$10^{4}$ K (McCall et al., 1985). We assume a typical electron temperature of
$T=10^{4}$ , that corresponds to the usual conditions in H ii regions
(Osterbrock, 1989). We should note that, as we indicate before, the dependence
with the $t_{e}$ is very weak. Unfortunately, the [S ii] doublet ratio is
sensitive to electron density only for a limited range of values (from
$\sim$50 cm${}^{-}3$ to $\sim$7000 cm${}^{-}3$). Nevertheless, this calibrator
is reasonably robust to study the main trends explored in this study.

The dust extinction ($A_{v}$) was estimated using the Balmer line ratio
(H$\alpha$/H$\beta$). We assume the extinction law by Cardelli et al. (1989)
using a theoretical value for the unobscured line ratio for case B
recombination H$\alpha$/H$\beta=2.86$ (for $T_{e}=10\,000$ K and $n_{e}=100$
cm3) and a specific dust extinction of $R_{v}=3.1$. Despite the dependence
between the H$\alpha$/H$\beta$ and the electron density and the temperature,
we consider this variations negligible (Sánchez et al., 2007).

A catalog with all the physical properties derived for the H ii regions is
distributed as described in Appendix A. From this catalog we apply different
filters to ensure the quality of the derived properties: (i) the [O
iii]/H$\beta$, [N ii]/H$\alpha$, [S ii]/H$\alpha$, [O i]/H$\beta$and [O
ii]/H$\alpha$line ratios should be positive and finite. Each of these
consecutive cuts implies a reduction in the original number of $\sim 26,000$ H
ii regions by 712, 189, 288, 3326 and 8886 regions, respectively. Therefore,
the strongest reduction is due to the presence or absence of [O ii]
($\sim$30%) in the wavelength range sampled by the data (due to the redshift),
followed by the detectability of [O i] ($\sim$12%). The final number of
selected H ii regions after applying these filter is $\sim$15,000; (ii) we
select those regions for which we can derived all the quantities enlisted
along this sub-section (EW(H$\alpha$), $f_{y}$, $U$, O/H, N/O, $n_{e}$ and
AV), for the fiducial calibrators. This further filter removes just $\sim$500
additional regions; (iii) we exclude those regions above the Kewley et al.
(2001) demarcation line in the diagnostic diagrams (that we will show in the
forthcoming sections). This filter excludes $\sim$450 regions; finally, (iv)
we exclude those regions that are hosted by a galaxies with a inclination
greater than 70∘. This final filter excludes $\sim 3600$ regions corresponding
to 177 galaxies. The final catalog once applied all the filters comprises
$\sim$11,000 regions. The H ii regions sample have a threshold in S/N$>3$ for
H$\alpha$ emission line from the initial selection of H ii regions (Espinosa-
Ponce et al., 2020).

###  3.2 Trends across the line-ratios diagnostic diagrams

In this section, we describe the observed trends of these properties across
the emission-line diagnostic diagrams. These diagrams show the distribution of
pairs of strong emission line ratios among the ones described in the previous
section to classify their primary ionization source. The most frequently used
one, known as the BPT diagram, represents the O3 versus N2 line ratios
(Baldwin et al., 1981). Other diagnostic diagrams involving different line
ratios were proposed by Veilleux et al. (2001), and a combination of them with
the equivalent width of H$\alpha$, EW(H$\alpha$), was first proposed by Cid
Fernandes et al. (2010). In all those diagrams there have been defined a set
of demarcation lines that segregate certain regions associated with particular
ionization sources (e.g., AGNs/SF Kewley et al., 2001; Kauffmann et al., 2003;
Stasińska et al., 2008), although its ability to distinguish between them is
now under discussion (e.g. Sánchez et al., 2021a).

Beside the ionizing source, the location of an H ii region on this diagram
depends on their physical properties (see Kewley et al., 2019; Sánchez et al.,
2021a, and reference therein, for a discussion). In the particular case of H
ii regions, different theoretical works using photoionization models predict
the location on the BPT diagrams according to the metallicity and the
ionization parameter (e.g., Kewley & Dopita, 2002; Morisset et al., 2016).
They found a primary trend in which metal-poor H ii regions are located in the
upper-left zone of the diagram, while metal-rich ones are located in the
right-bottom zone. Unfortunately, the photoionization models present different
degeneracies in this diagnostic diagram between the oxygen abundance, the
ionization strength, and the relative nitrogen-to-oxygen abundance (among
others). As a result, one location in the diagram can be reproduced by a set
of different models corresponding to different physical conditions. From the
observational point of view other trends have been reported. For instance,
Sánchez et al. (2015a) described a clear trend in which H ii regions located
in regions with older stellar populations are more frequently found in the
bottom-right part of the diagram, while those with younger stellar populations
are found towards the upper-left zone. This trend, clearly connected with the
one described for the metallicity, cannot be explained by photoionization
models, being a consequence of the linked co-evolution of the stellar
populations and their metal content at a certain location in galaxies.
Furthermore, other physical properties show additional trends across the
diagnostic diagrams. For instance, there is a clear trend with the electron
density easily explained by photoionization models (e. g. Kewley et al.,
2013). Finally, it was described a trend with dust extinction, despite the
fact that the involved line ratios are almost insensitive to dust Sánchez et
al. (2015a), and even with the gas velocity dispersion (Law et al., 2021).

Figure 1 shows the distribution of the physical properties described in Sec. 3
across the BPT diagram for our sample of H ii regions. To generate this figure
each physical property is averaged (left panels) for those regions at the same
location within the diagram. Once derived the mean value we estimate the
standard deviation around it (right panels). We first explore the trends with
the fraction of young stars. The H ii regions located on the upper-left zone
of the diagram show the largest value of $f_{y}$; meanwhile, the HII regions
located on the bottom-right zone had the lowest one. This result agrees with
the trends already reported by Sánchez et al. (2015a), highlighting the
connection between the properties of the underlying stellar population and the
observed line ratios. Thus, H ii regions generated in (less) evolved regions
of a galaxy, those with (younger) older and (less) more metal rich stellar
populations, are preferentially found in the areas with (higher) lower
$f_{y}$. Similar trend is observed in the top-right panel of Fig. 1, that
shows the same distribution color-coded by the ionization parameter. The H ii
regions with a high value of the ionization parameters are located in the
upper zone of the diagram, and regions with low values of $U$ are located in
the bottom zone. A connection between $U$, $f_{y}$, and the metal content in H
ii regions maybe be the reason for these trends (e.g. Ji & Yan, 2021).

The middle panels of Fig. 1 show the same distribution color-coded by the
oxygen abundance (left) and the nitrogen-to-oxygen relative abundance (right).
As expected, the metal-poor H ii regions are located in the upper-left zone of
the diagram, and the metal-rich ones are located in the bottom-right zone. A
similar trend is found for the nitrogen-oxygen ratio, as a direct consequence
of relation between this quantity and the oxygen abundance (e.g. Matteucci,
1986; Vila-Costas & Edmunds, 1993; Pilyugin et al., 2012). Thus, the H ii
regions with the lowest value of N/O ratio are located on the upper-left zone
of the diagram, and those with the largest ratio value are located on the
bottom-right zone.

The distribution traced by the electron density ($n_{e}$) is shown in the
bottom-right panel of Fig. 1. The regions with the highest electron density
($\sim$103cm-3) are found on the right-hand area of the diagram, near to the
edge of the classical location of H ii regions. Then, it is appreciated a
sharp transition to values $\sim$102cm-3, distributed along that classical
loci of these regions. An increase of $n_{e}$ towards the upper-right is
predicted by photoionization models (e. g. Kewley et al., 2013). However, the
described distribution is not that easily replicated based only on these
models. We must remark that electron density derived with the [S ii] lines
ratio is reliable between $\sim 10^{2}$ cm-3 and $\sim 10^{4}$ cm-3. For our
current sample we are in any case in the low-density regime for all H ii
regions.

Finally, the bottom-left panel of Fig. 1 shows the distribution of H ii
regions across the BPT diagram with a color code representing the dust
extinction. There is a clear trend across the diagnostic diagram: dust
extinction is lower in the H ii regions located in the upper left-hand region,
and it is higher in those regions at the bottom right-hand end and in the
upper right-hand end of the diagram. The regions with the largest dust
extinction are located in the intermediate area delimited by Kauffmann et al.
(2003) and Kewley et al. (2001) curves. Like in the case of some of the
distributions discussed before, this result is not predicted by
photoionization models which most of the time do not consider this parameter.
We should note that the two line ratios involved in this diagram ([N ii] and O
iii) are expected to be insensitive to dust extinction.

The distribution of the same physical properties for a set of additional
diagnostic diagrams ([OIII]$\lambda 5007/$H$\beta$ vs. [SII]$\lambda
6716+30/$H$\alpha$ and [OIII]$\lambda 5007/$H$\beta$ vs. [OI]$\lambda
6300/$H$\alpha$) are shown in Appendix B. In all cases the distributions
cannot be reproduced based on predictions from simple photoionization models.
Their origin should be related to the properties of the ambient in which the H
ii regions are formed. In summary, young massive stars born in regions with a
large number of old stars (i.e., low $f_{y}$), would be formed from a gas that
has been recycled and enriched by previous stellar generations (i.e., high
oxygen abundance and N/O ratio). The gas from which it is formed should
present also a larger amount of dust, and therefore a stronger dust
extinction. More difficult is to interpret the trends described for the
ionization parameter and the electron density. A possible explanation for the
trend described by $U$ could be that H ii regions of a high metal content gas,
ionized by a cluster of stars with a narrow range of ages, may present a lower
ionization parameter due to metal blanketing. However, in this case O/H and
$U$ should present just opposite trends across the diagram, and this is
clearly not the case. On the other hand, for the electron density, the results
suggest that regions with higher dust extinction (i.e., corresponding to large
gas densities Brinchmann et al., 2004; Barrera-Ballesteros et al., 2020) do
have larger ne too. This would imply that their internal pressure should be
also higher, in agreement with the trends recently reported by Barnes et al.
(2021). In this case, since $U$ depends inversely on the electron density the
trend observed for this parameter could be a combination of the trends
reported for both O/H and $n_{e}$. Another possibility would be that for the
same ionizing stellar cluster the ionization $U$ decreases as $A_{\rm V}$
increases, as a pure consequence of the dust extinction decreases the
available UV ionizing photons (Ji & Yan, 2021). Finally, the observed trend
for $U$ could be a consequence of all those effects combined together.
Besides, this result suggests that the diagnostic diagrams do not provide a
proper description of the properties of H ii regions, therefore the models
need to consider a parameter space with higher dimensions.

Figure 2: Radial distribution of the $f_{y}$ (top panels) and EW(H$\alpha$)
(bottom panels) along the galactocentric distance for the H ii regions in our
catalog. Each symbol corresponds to the average value of the corresponding
parameter in bins of 0.5 effective radius for each stellar mass bin (color
coded) and morphology (different panels) of their host galaxy, with its size
being proportional to the number of H ii regions in each bin. The solid lines
link the different values corresponding to the same stellar mass bin. The
average standard error of each parameter in each panel is represented with an
error bar.

Figure 3: Similar figure as Fig. 2, for the $\log(U)$ (top panels),
12+log(O/H) (middle panels) and log(N/O) (bottom panels) parameters.

The outlined interpretation holds if the described distributions, traced by
the average values of the considered parameters, are indeed representative of
the bulk sample of H ii regions. In other words, if the dispersion around
these mean values are small compared to the typical value themselves. As
indicated before, the distributions of the standard deviations are shown in
the right panels of Fig. 1 for the same physical parameters shown in the left
panels. It is appreciated that in all cases the standard deviation is small
with respect to the dynamical range of the data. However, there are
differences parameter to parameter. For instance, $f_{y}$ and O/H present very
low standard deviations, of the order of $\sim$0.05-0.1 dex, at almost any
location within the diagram, what indicates that indeed the mean values
describe well the behavior of the H ii regions. Slightly larger dispersions
are observed for log(U) and N/O ($\sim$0.2-0.3 dex), both of them distributed
in the same way along the explored diagrams. Thus, despite of the larger
spread, for both parameters the mean value seem to describe well the
distributions. Much larger scatters are found for $n_{e}$ and $A_{\rm V}$,
with values around $\sim$0.6 dex, for the first parameter, and $\sim$0.3-0.8
mag, for the second one, respectively. Despite the fact that their dynamical
ranges are larger, it is clear that the trends reported based on the mean
values are just valid at a first order. Furthermore, in these two parameters a
trend is observed in the standard deviation, that appears to be smaller at the
upper-left area of the diagram than at the bottom-right one. Those regions
corresponds to areas with relatively larger electron densities and dust
extinction (left panel). Therefore, at this locations the reported trends for
$n_{e}$ and $A_{\rm V}$ should not be interpreted just as an increase of both
parameters, but as an enlargement of the range of values for both of them.
Accordingly, the outlined trends between both parameters and other physical
quantities (O/H and in particular $U$) discussed in the previous paragraph
should be revised, considering that they most probably would present larger
scatters as $n_{e}$ and $A_{\rm V}$ increases.

###  3.3 Radial distributions of the physical properties

Figure 4: Similar figure as Fig. 2, for the $n_{e}$ (top panels), and AV
(bottom panels) parameters.

The exploration of the distribution of the physical properties of the H ii
regions across the BPT diagram, shown in the previous section, indicates that
the location on this diagram and therefore the observed line ratios present
clear dependencies with the physical properties. Since many of these physical
quantities are tightly connected with the evolution of the stellar populations
(in particular fy, O/H and N/O, but also $A_{\rm V}$), they should present
patterns and variations with the same parameters that affects that evolution:
(i) galactocentric distances; (ii) stellar mass and (iii) morphology of the
host galaxies (e.g. García-Benito et al., 2017; Sánchez, 2020).

In this section we present the radial distribution of the properties described
in Sec. 3.1 for galaxies of different stellar mass and morphology. For each H
ii region we derive its galactocentric distance, taking into account the
effects of inclination. Then, we normalize the distance by effective radius of
the corresponding host galaxy ($R_{e}$, derived following Walcher et al.,
2014). Then, for each galaxy, we obtain the azimuthal average of each property
in radial bins of 0.5 $r/R_{e}$ (a size that guarantees a sufficient number of
H ii regions within each bin). Finally, we segregate the galaxies in four bins
of stellar mass (log(M∗/Msun=7-9.5, 9.5-10.5, 10.5-11.0 and 11.0-13.0), and
six morphological types (E/S0, Sa, Sb, Sbc, Sc and Sd/Sm/Irr). For each sub-
sample we obtain the average radial distribution of each physical property.
Finally, in order to quantify the variation in the scale and gradient of each
property, we perform a linear fitting to each average radial distribution.

Figure 2, 3 and 4 summarize the result of this analysis. For each physical
property we show the average radial profile segregated by the stellar mass of
the galaxies for all the sample (first column panels), and for each
morphological type (right panels). The values of the zero-point ($c_{0}$), and
slopes ($c_{1}$), derived from the linear regression to each of these radial
distributions are presented in Appendix D, listed in Tables 2, 3-8. The zero-
point corresponds to the value of the physical quantity in the central regions
of the galaxies while the slope is a gauge of the strength of the radial
gradients.

The upper panels of Fig. 2 shows the radial profiles for the $f_{y}$. In
general, the HII regions in the inner areas of the galaxies show a lower value
of $f_{y}$ than those regions in the outer ones. In addition, there is a clear
trend with the stellar mass. The $f_{y}$ is higher for low values of the
stellar mass. On the contrary, this fraction is lower for those H ii regions
located in more massive galaxies. We find a similar trend for EW(H$\alpha$),
which radial distributions are shown in the lower panels of Fig .2. The H ii
regions with the largest EW(H$\alpha$) are located in the outer regions of
low-mass galaxies, and those with the lowest values of this parameter are
located in the inner regions of high-mass galaxies. These trends has been
already explored in previous studies (e.g. González Delgado et al., 2016;
Belfiore et al., 2017b; Sánchez et al., 2018). They are the consequences of
the higher star-formation rates with respect to the already accumulated
stellar mass (i.e., higher specific star-formation rates, sSFRs) found in the
outer regions of low-mass galaxies, in combination with the larger amount of
stars formed in earlier star-formation episodes in the center of high-mass
galaxies and their lower actual sSFR. In summary, both relations are a
consequence of the so-called local-downsizing (Pérez et al., 2013) and the
inside-out quenching/ageing (Belfiore et al., 2017b). Those trends with the
stellar mass are modulated by the morphology. The few earlier type galaxies
with H ii regions show lower values of both $f_{y}$ and EW(H$\alpha$), and a
weak negative gradient (i.e., decrease with the galactocentric distance). On
the contrary, spiral galaxies present higher values and a clear positive
gradient. This suggests that the general trend described before is dominated
by late-type galaxies, with early-types presenting a slightly different
pattern.

The upper panels of Fig. 3 show the radial profiles of the ionization
parameter. There is no clear trend of this parameter with the galactocentric
distance for any of the explored mass bins. However, the ionization parameter
shows a higher value for the lowest stellar mass bin than for the other ones.
Although we should note that the mean error for this mass bin is higher than
other ones. When segregating by morphology we find a variety of behaviors
without a clear pattern. If any, the trend with the stellar mass is much more
clear for the very late spiral galaxies (Sd/Sm).

The central panels of Fig. 3 show the radial profiles of the oxygen abundance.
There is a clear and well-known trend of this parameter with the
galactocentric distance and stellar mass. The H ii regions with higher oxygen
abundances are located in the inner regions of the galaxy, and those with
lower oxygen abundances are towards the outer zones. Also, there is a clear
dependence between oxygen abundance and stellar mass (a consequence of the
well known Mass-Metallicity relation, e.g., Garnett, 2002; Tremonti et al.,
2004). Low-mass galaxies generally host the more metal-poor HII regions, and
high-mass galaxies host the metal-rich ones. The negative gradient was first
described for the Milky-Way and galaxies of a similar mass by Searle (1971)
and Peimbert et al. (1978), and it has been deeply explored by many previous
studies (e.g., Sánchez et al., 2013; Esteban & García-Rojas, 2018). The slope
of the gradient presents a dependence with the mass as well, with more massive
galaxies presenting flatter gradients (as already reported by Belfiore et al.,
2017b). Both trends are modulated by the morphology, with early-type galaxies
showing an even flatter gradient, with even positive gradients observed (as
noticed by Sánchez et al., 2021a). Finally, the range of values for the oxygen
abundances is larger in late-type galaxies than in early-types. These results
speak against a single characteristic oxygen abundance gradient for all
galaxies as proposed by Sánchez et al. (2013), where most of the explored
galaxies have similar stellar mass as the MW (for which the range of slopes is
rather narrow). Indeed, they are more in agreement with the recent results by
Belfiore et al. (2017b), Boardman et al. (2020) and Zinchenko et al. (2021),
where it was reported that the slope indeed depends on different properties of
the galaxies, including the stellar mass.

A similar trend is found for the radial gradient of the nitrogen-to-oxygen
ratio, which radial profiles are found in the bottom panel of Figure 3. In
average the H ii regions with a high N/O ratio are located in the inner areas
of galaxies, and those with lower N/O are located in the outer zones. This
result is in agreement with the most recent explorations of those
distributions (Pérez-Montero et al., 2016; Belfiore et al., 2017b; Zinchenko
et al., 2021). Also, there is a clear dependence of the N/O ratio with the
stellar mass. The lower N/O ratios are found on H ii regions hosted on low-
mass galaxies, and the higher values are on regions in high-mass galaxies.
This, again, is a consequence of a global relation between this parameter and
the stellar mass (e.g. Schaefer et al., 2020, for a recent study), that can be
a consequence of the N/O-O/H relation via the MZR. A less clear pattern is
observed in the slopes of the gradients. For early-type galaxies they seem to
be flatter in average. However, for the more massive ones it was reported the
highest negative gradient of all the sample (although the low number statistic
of this particular subsample does not allow us to make a strong statement in
this regards).

Figure 5: Relation between the oxygen abundances and the others physical
properties of HII regions. The oxygen abundance is compared with i) $f_{y}$
(top left); ii) EW(H$\alpha$) (top middle); iii) ionization parameter (top
right); iv) nitrogen-oxygen ratio (bottom left); v) dust extinction (bottom
middle); and, v) electron density (bottom right). The contours represents the
density distribution, the outermost contour enclose the 90$\%$ of the regions,
the middle contour enclose the 75$\%$ of the regions, and the innermost
contour encloses the 60$\%$ of the regions.

The top panels of Figure 4 show the same distributions for the dust
extinction. For this parameter both the stellar mass and the morphology play a
clear role. In general the two more massive bins correspond to the higher
values of the dust extinction. In both cases they present a negative radial
gradient (i.e., more dust towards the center). The highest values are found
for the highest mass bin. For the third mass bin the distribution shows a
slight decline with the radius too, but less evident than in the other two
cases. Finally, for the lowest mass bin there is a positive gradient, with
more dust in outer regions. These trends trace the presence of molecular gas
in these galaxies via the metallicity (Brinchmann et al., 2004; Barrera-
Ballesteros et al., 2020, 2021b), suggesting that in more massive galaxies it
is clearly concentrated in the central regions. When exploring the dust
content by morphology, it is clear that the most massive Sa galaxies, at any
galactocentric distances, and E/S0, in the outer regions, are those with the
highest dust content. On the other hand low-mass Sd/Sm/Irr are those with the
lowest dust content. Regarding the gradient, clear negative slopes are found
for Sa of any mass and for the more massive late-type galaxies, then the slope
seems to become shallower and finally positive for the lowest-mass latest-type
galaxies. The gradient does not present a clear pattern for E/S0 galaxies,
maybe due to the limited number of H ii regions in these galaxies. If any,
they present a flat distribution of AV.

Finally, the bottom panels of Figure 4 show the radial profiles of the
electron density. In general, the denser H ii regions are located towards the
center of the galaxies. This result is expected since at the central regions
of the galaxies, with larger values of the stellar and molecular gas surface
densities, the pressure is expected to be larger (e.g. Barrera-Ballesteros et
al., 2021a; Barnes et al., 2021). Then the density declines and rise again in
the outer regions. There is a slight trend between the electron density and
the stellar mass, with denser regions hosted by high-mass galaxies. Again,
this could be a consequence of the effect of the pressure. Indeed a similar
trend is described with the morphology, with earlier galaxies showing the
higher values of this quantity. The pattern with the radial trend is less
evident, with slopes covering a wide range of values for any morphology and
stellar mass.

###  3.4 Relation between oxygen abundance and others physical properties of
HII regions

So far we have explored how the physical properties of H ii regions distribute
along the diagnostic diagrams (Sec. 3.2 and App. B), and along the
galactocentric distance (Sec. 3.3). In this section we explore the dependence
of these parameters among themselves. For doing so we adopted the oxygen
abundance as the primary property, studying how the rest of the parameters
correlate (or not) with O/H. We quantify the correlations based on the Pearson
correlation coefficient between each pair of explored parameters. To
characterize the relation between them we explore three different linear
regressions: (i) fitting Y vs. X, (ii) fitting X vs. Y, and (iii) deriving the
bisector line between both previous relations. We adopt as the best relation
the one that minimize the dispersion of the residuals ($\sigma$). Regardless
of the procedure that provides the best fit of the three outlined before we
report the parameters of the relation between the Y and X axis, i.e.,
y$=c_{1}x+c_{0}$.

Figure 5 shows the derived distributions for all the parameters described in
Sec. 3.1, where clear trends are appreciated. Regarding fy and EW(H$\alpha$),
they both show a clear decline with the oxygen abundance, with more metal rich
regions corresponding to those having a low fraction of young stars and low
values of the equivalent width of H$\alpha$. This is expected based on the
distributions described for the BPT diagrams shown in Sec. 3.2 (and Espinosa-
Ponce et al., 2020) and the radial distributions shown in Sec. 3.3, as well.
Regions of high O/H correspond to those located in areas with higher stellar
mass density, based on the resolved MZR relation (e.g., Rosales-Ortega et al.,
2012; Barrera-Ballesteros et al., 2016), i.e., the regions with the brightest
continuum emission. Thus, this is the location where fy and EW(H$\alpha$) is
expected to be lower, for H ii regions ionized by the same kind of stellar
clusters with similar H$\alpha$ luminosities. In consequence there is a
relative significant correlation between both parameters ($\rho=$-0.58 and
-0.46, for fy and EW(H$\alpha$) respectively), parametrized by a clear
negative slope ($c_{1}$=$-$0.91 and $-$1.36, respectively), and with a small
scatter ($\sigma=$0.12 and 0.19 dex, respectively). Thus, for these two
parameters the reported relations are a pure consequence of the differential
stellar/chemical evolution of galaxies in different locations.

The relations of O/H with log(U) and the N/O ratio have a different nature. In
principle, those relations are not expected to be connected with the
properties and evolution of the underlying stellar population in the areas in
which the H ii regions are formed, like the former two. Early explorations on
the properties of H ii regions suggest that log(U) declines with O/H (e.g.
Dopita & Evans, 1986), a trend that has been ample adopted in the literature,
in particular when photoionization models are used to derive both parameters
(e.g. Thomas et al., 2018). Empirically, it has been clearly found with
empirical calibrators of log(U) are used (e.g., Sánchez et al., 2015b).
However, using photoionization models a loose relation is found between both
parameters, tighter at high oxygen abundances than at low ones (e.g., Morisset
et al., 2016). This trend can be characterized using a linear relation only at
first order. Consequently we found a weaker trend between both parameters as
the one described for the other two ones ($\rho=-0.23$), parametrized by a
linear relation with a slope of $c_{1}=-0.7$, and a large standard deviation
compared with the dynamical range of log(U), $\sigma=0.2$ dex. Indeed, it is
clearly observed that the negative trend is obtained, for the fiducial
calibrators adopted for both parameters, only in the low abundance regime. At
high abundance there is an apparent turn-up of log(U), that reach high values.
Contrary to other distributions explored in this study we find a strong
dependence on the actual adopted calibrators on the observed trends between
both parameters. Appendix F includes similar explorations for the different
ionization parameter calibrators included in our catalog of physical
properties of H ii regions. The expected decline of $U$ with the abundance is
not observed in most of the cases. Only for the $U$ calibrators reported by
Dors et al. (2011) and Morisset et al. (2016) there is a weak trend like the
one reported here, with the corresponding up-turn. In other cases, like the
values provided by the NB code (Thomas et al., 2018, respectively), the
distribution is discrete and does not show a clear trend. In other cases, like
HCm (Pérez-Montero, 2014) the distribution covers the same range of parameters
as the one shown by our fiducial calibrator, but with two clear discrete
clouds. Finally, for the case of the values reported by the IZI code (Blanc et
al., 2015; Mingozzi et al., 2020) the ionization parameter seems to be
constant.

The nature of this predicted relation is still broadly unclear (see Ji & Yan,
2021, , for an extensive discussion) . Early explanations involved (i) a
correlation between the initial mass function (IMF) and the metallicity, (ii)
an effect of the dust absorption, and (iii) an environmental effect in the
sense that H ii regions that are formed in the inner and outer regions of
galaxies present physical differences (e.g. Dopita & Evans, 1986). The first
of this hypothesis requires that a low metal ISM enhances the upper end of the
IMF because of the increased Jeans mass, producing an apparent larger log(U),
while metal rich gas, that cool faster, may result in a lower IMF cutoff and
therefore a lower apparent log(U). Recent results have suggested that this
IMF-Z relation is indeed present, at least for early-type galaxies (Martín-
Navarro et al., 2015). On the other hand, the dust absorption may produce a
soften of the radiation field, producing low-excitation H ii regions in dusty
environments. If this is the main driver between the log(U)-O/H relation a
decrease (increase) is expected of the ionization parameter (oxygen abundance)
with the dust extinction. We will get back to that later on in Sec. 4.
Finally, the environmental scenario suggests that H ii regions in the central
locations of galaxies are more numerous and they have a smaller average
surface brightness (Dopita & Evans, 1986). The reason for that could be the
enhancement of the cooling and fragmentation induced by the metallicity:
molecular clouds in regions of larger metal content would fragment in smaller
clouds and collapse to form smaller and lower surface-brightness H ii regions.
Since both the larger metal content and the highest molecular gas surface
density are found in the central regions of galaxies, the log(U)-O/H relation
would naturally emanate from the two observed trends. However, this was never
confirmed. More recently it has been suggested that blanketing due to metal
content may be responsible of this relation (e.g. Sánchez et al., 2015b; Ji &
Yan, 2021), although it is not clear if this effect may produce a soften or a
harder radiation field. All these explanations suggest that log(U) is
considered as a tracer of the hardness of the ionizing source. However, this
is not completely true. The issue is due to the fact that the empirical
indicators adopted to trace log(U) actually trace the excitation level of the
gas, that depends on both log(U) and the shape of the ionizing source (and
also changes if the cloud is matter- or radiation-bounded). In summary what
theory defines as this parameter and what we actually trace may well be two
different things. Most probably there is no simple explanation to this
relation, if it exists, and a combination of all the former scenarios is
required to describe it. We should note that this correlation is not observed
for all calibrators, and using a different combination of them could produce
very different results.

Figure 6: Relation between the oxygen abundances and physical properties of
underlying stellar populations of H ii regions. The oxygen is compared with i)
luminosity-weighted age, $\mathcal{A}_{\star,L}$ (left panel, ii) luminosity-
weighted metallicity, $\mathcal{Z}_{\star,L}$ (middle panel) of underlying
stellar population. The right panel shows the relative oxygen abundance of H
ii regions with respect to the Z-elements of underlying stellar populations
([O/Z]) vs the metallicity of stellar population, [Z/H]. The density contours
are the same that used in Figure 5.

The relative nitrogen-to-oxygen abundance presents, as expected, a strong
positive correlation with the oxygen abundance ($\rho=$0.83), as seen in Fig.
5. This distribution is well characterized by a tight ($\sigma=$0.09 dex)
linear relation of slope c1$=$0.96 (for the range of abundances covered by the
current dataset). This well known relation is a consequence of the
differential nature of the oxygen and nitrogen production. Oxygen is a primary
element, which production depends only on physical processes (Matteucci, 1986;
Maiolino & Mannucci, 2019). However, nitrogen has both a primary and secondary
nature. At low metallicity, i.e., 12+log(O/H)$\lesssim$8, is may be primary,
and therefore the N/O ratio would be independent of O/H. On the contrary, at
high metallicity, i.e., 12+log(O/H)$\geq$8.2, its production depends on the
initial abundance of other elements, in particular oxygen. Thus, in this
regime we observe the reported linear relation between both quantities,
corresponding to the regime of oxygen abundances covered by our catalog of H
ii regions. With the current data we just appreciate that the linear relation
is blended at low metallicity, hinting the reported plateau. This flattening
(i.e., constant N/O) is observed at low-O/H H ii regions (or galaxies) (e.g.,
Izotov et al., 2012; Vincenzo et al., 2016). Recent result have shown that
there are secondary trends in this relation, being modulated by the global
stellar mass and the local star-formation efficiency (SFE, Schaefer et al.,
2020), although they could be due to systematics in the adopted calibrators.
In our data it is observed a clear segregation of the relation between N/O and
O/H as a function of the EW(H$\alpha$). This segregation may be connected with
the one reported by Schaefer et al. (2020), once considered the relation
between EW(H$\alpha$) and SFE (e.g. Colombo et al., 2018; Sánchez et al.,
2021a). Despite of this difference both results suggest a possible lack of
universality of the N/O-O/H relation, or they highlight the effects of the
systematics in the adopted calibrators (that were different in both studies).

The distribution of the dust extinction of the ionized gas as a function of
the oxygen abundance presented in Fig 5 shows that both parameters do not
present a clear correlation ($c_{0}=$0.2). Both parameters present a fuzzy
trend that can be characterized by the linear relation with a positive slope
of $c_{1}=$1.86 mag/dex. Consistently with the weakness of the relation the
scatter is considerably larger than the one reported for other relations
described between the explored parameters ($\sigma$=0.36 mag), apart from the
log(U)-O/H one. This weak trend is better appreciated when considering the
radial gradients observed for both the oxygen abundance and the dust
extinction. Those azimuthal averaged values for galaxies of the same mass and
morphology (Fig. 3 and 4), present very similar radial trends that would
directly produce a relation between both quantities. Despite of this average
trends, the dispersion around this relation for individual H ii regions is
large. Taking into account the direct relation between the dust extinction and
the gas column density (Schmidt, 1959; Barrera-Ballesteros et al., 2020), this
relation may suggest that regions with higher metallicity are those with
higher molecular gas surface density, what would be against one of the lines
of reasoning by Dopita & Evans (1986) to explain the relation between log(U)
and O/H, discussed before. Again, this relation highlights the strong
connection between different properties of the H ii regions and the
local/resolved properties of the location in which they are formed in
galaxies. The fact that it is weaker/loose than other ones described in here,
like the N/O-O/H or the EW(H$\alpha$)- or $f_{y}$-O/H one, indicates that
there is a clear hierarchy between the explored relations. The N/O-O/H
relation seems to be more universal (i.e., independent of properties external
to the nebulae itself), despite the possible secondary trend reported. On the
other hand, the relations with EW(H$\alpha$), $f_{y}$ and $A_{V}$ seem to be
deeply related with the location in the galaxy in which the H ii region is
formed, and the imprints that the evolution and chemical enrichment have left
in the properties of the ISM. The fact that the relation with $A_{V}$ is the
weakest indicates that this relation is strongly modulated by the dependence
of both parameters with other physical properties. This is not a total
surprise. Based on Eq. 13 of Brinchmann et al. (2004), the relation between
$A_{V}$ and O/H should depends at least on the molecular gas surface density
and on the dust-to-metal ratio of the ionized gas, two parameters that are
clearly non constant across the extension of a galaxy.

Finally, Fig. 5 shows that the distribution of the electron density is
essentially insensitive to the oxygen abundance (bottom-middle panel). Both
parameters present the weakest correlation coefficient among the explored ones
($\rho=$0.16), with a large dispersion around the estimated linear regression
($\sigma$=0.2 dex). Contrary to all the remaining parameters, the electron
density is clearly unconnected with the oxygen abundance. Furthermore, it
seems to be totally insensitive to the described connection with the evolution
of the stellar population or the location at which the H ii regions are
formed, observed in all the properties explored so far.

###  3.5 Relation between the oxygen abundance and physical properties of
underlying stellar populations

Most of the relations between the different explored parameters described in
Sec. 3.4 suggest a direct connection between the oxygen abundance of H ii and
the properties of the surrounding underlying stellar population. Such
connection is behind the recently proposed relations between O/H and different
local/resolved properties in galaxies, such as the stellar surface mass
density (rMZR Rosales-Ortega et al., 2012; Barrera-Ballesteros et al., 2016),
the gas fraction and/or the escape velocity (Barrera-Ballesteros et al.,
2018). Based on these results, we explore in this section the relation between
the properties of the underlying stellar population and the oxygen abundance
for our sample of H ii regions.

Fig. 6, left-panel, shows the distribution of $\mathcal{A}_{\star,L}$ as a
function of O/H. There is a strong correlation between both parameters, with a
correlation coefficient of $\rho=$0.66. We estimate the best linear relation
between the two parameters by exploring the linear regressions assuming that
either the $\mathcal{A}_{\star,L}$ or the O/H is the independent parameter
(i.e., fitting Y vs. X, or X vs. Y), or neither of them (i.e., deriving the
bisector line between themselves. The best linear relation for the
$\mathcal{A}_{\star,L}$-O/H distribution results from the fitting of the later
(X-axis) versus the former (Y-axis), corresponding to a slope of $c_{1}=$1.51
(where y$=c_{1}x+c0$, see Fig. 6), and a standard deviation in the Y-axis of
$\sigma=$0.15 dex. Since the age of the ionizing stellar populations in an H
ii region is very similar in all of them, being limited to less than 10 Myr,
the reported $\mathcal{A}_{\star,L}$ is essentially tracing the distribution
of ages of the underlying stellar population. Therefore, this correlation
indicates that the more metal-rich H ii regions are formed in areas of the
galaxies which bulk stellar population was formed long ago in cosmological
times. On the contrary, metal poor H ii regions are formed in areas where the
stellar population has been formed along a wider range of times, and therefore
they present a broader range of ages. Since the oxygen abundance is tightly
connected with the amount of stars formed, as indicated before, the reason
behind that correlation is that older stellar populations were formed in star-
formation processes that were stronger and sharper, peaked in earlier
cosmological times. This is the basis of local downsizing (e.g. Pérez et al.,
2013), a proved scenario in which regions of larger stellar mass density
formed they stars earlier and following more abrupt SFHs than regions of
smaller stellar mass density (e.g. García-Benito et al., 2017; Sánchez, 2020).
As a consequence these locations have both older stellar populations and a
higher metal enrichment. Indeed the distribution of EW(H$\alpha$) along this
figure follows almost the same distribution of both O/H and
$\mathcal{A}_{\star,L}$, highlighting the fact that regions located in areas
with relative low sSFR nowadays (low EW(H$\alpha$)) are those that have
accumulated their stellar mass (and metals) long before, and therefore they
have the older stellar populations. On the contrary, areas with relative large
sSFR (high EW(H$\alpha$)) are those that are still actively forming stars,
having accumulated their stellar mass (and metals) more recently.

This scenario implies a connection between the oxygen abundance of the H ii
regions and the metallicity of the underlying stellar population as well,
since they are the result of the local metal enrichment. Fig. 6, central
panel, shows the distribution of these two parameters. As expected, the
stellar metallicity, $\mathcal{Z}_{\star,L}$, presents a very loose trend with
O/H ($\rho=0.27$). Once again, the best linear relation is derived by fitting
the oxygen abundance (X-axis) to the $\mathcal{Z}_{\star,L}$(Y-axis),
corresponding to a slope of $c_{1}=$0.81, and a standard deviation of
$\sigma=$0.15 dex. However, the correlation is much weaker than the one found
between O/H and $\mathcal{A}_{\star,L}$. It is worth noticing that
$\mathcal{Z}_{\star,L}$is the average of the metallicities of all the stellar
populations in which the observed spectra is decomposed. By construction it
essentially traces iron trapped on the surviving stars. On the other hand, O/H
traces the oxygen abundance, i.e., the abundance of an $\alpha$ element, at
the ISM of the H ii region. This abundance should be the same as the one of
the young ionizing stars, recently formed ($\sim$4Myr) from this gas.
Therefore both parameters trace a different type of element at different time
scales and for different families of stars. It is important to recall that
iron is mostly produced and expelled to the media by SNIa, being the product
of the collapse of binary systems of average massive stars, while oxygen is
essentially produced by core-collapsed supernovae (CCSN) produced at the death
of very massive stars. Thus, $\mathcal{Z}_{\star,L}$and O/H may present
significant differences in their corresponding chemical enrichment histories
(see Maiolino & Mannucci, 2019, for a review on the topic). The current LW
stellar metallicity depends on both the final stellar mass and the shape of
the star-formation histories (SFH, e.g., Camps-Fariña et al., 2021). On the
other hand, the oxygen abundance follows more tightly the strength rather than
the shape of the SFH, being more strongly tied to the final stellar mass (e.g.
Lacerda et al., 2020) and the stellar mass surface density (e.g. Gallazzi et
al., 2005; González Delgado et al., 2016; Sánchez, 2020). The relative
weakness of the observed correlation and the large standard deviation suggest
that both parameters are connected, but without one fully following the other.

Finally, right panel of Fig. 6 shows the distribution of the [O/Z] ratio along
$\mathcal{Z}_{\star,L}$. This ratio was constructed by subtracting
$\mathcal{Z}_{\star,L}$ to the O/H normalized to the solar value (assuming a
12+log(O/H)⊙=8.69 Asplund et al., 2009), as described in detail in Sánchez et
al. (2021b). In this recent letter we demonstrated that this parameters is a
good tracer of the $\alpha$-enhancement at the location of H ii regions in
galaxies. As reported in Sánchez et al. (2021b), [O/Z] declines with
$\mathcal{Z}_{\star,L}$, following a weak correlation ($\rho=$-0.35), that, it
is better described by the linear regression of the former parameter (Y-axis)
versus the later one (X-axis). This relation shows a slope of $c_{1}=$-1.61.
The dispersion around this trend is similar to the one reported for the
relation between O/H and $\mathcal{Z}_{\star,L}$ ($\sigma=$0.13 dex), despite
the fact that the current correlation is slightly stronger for this one.
Furthermore, as explicitly discussed in Sánchez et al. (2021b), the dispersion
is modulated by a secondary trend with the $\mathcal{A}_{\star,L}$ of the
underlying stellar population, that in the current figure is coded by the
EW(H$\alpha$) (based on the correspondence between both parameters discussed
before). It is appreciated that a sequence of relations between [O/Z] and
$\mathcal{Z}_{\star,L}$ with a different zero-point (and maybe different
slopes) for each value of EW(H$\alpha$) would produce a significant lower
scatter than a single relation for the bulk of H ii regions. This is in
agreement with the strength of the relation between O/H and
$\mathcal{A}_{\star,L}$ reported before, that, based on the results presented
in Sánchez et al. (2021b) and the distribution observed in here is most
probably equally modulated by [Z/H], highlighting the connection between both
parameters. It is worth noticing that these trends are fully compatible with
those found for individual stars in the MW (e.g. Hayden et al., 2015) and
galaxy wide integrated populations (e.g. Walcher et al., 2014). The
straightforward interpretation of this relation is a consequence of the
differential enrichment histories between the $\alpha$ and iron peak elements
(e.g. Hayden et al., 2015; Walcher et al., 2016; Yu et al., 2021). As
discussed before, this relation is heavily modulated by either the shape IMF,
the shape of the star-formation histories, or a combination of both, as
predicted by the chemical evolution models (e.g. Carigi et al., 2019; Weinberg
et al., 2017, and references therein).

##  4 Discussion

Along this study we have explored the physical properties of the catalog of
$\sim$26,000 H ii regions and aggregations extracted from the CALIFA IFS data
presented by Espinosa-Ponce et al. (2020). First, we studied how these
properties distribute across the diagnostic diagrams (Sec. 3.2, and App.B). As
already shown in Espinosa-Ponce et al. (2020), our selection of H ii regions,
purely based on basic properties of these regions222(1) to present a
clumpy/peaky shape in the emission line maps; (2) to present a minimum
$f_{y}$; and (3) to present and EW(H$\alpha$) compatible with that $f_{y}$,
recovers the well-known distributions along the diagnostic diagrams for these
objects. Just a small fraction of the finally selected regions ($<$4%) are
located above the classical demarcation lines proposed by Kewley et al.
(2001), based on theoretical considerations and photoinization models. Thus,
the proposed selection reproduce the expectations by these models, without
requiring a prior selection based on line ratios.

Any set of photoinization models aimed to reproduce the emission line ratios
produced by the ionization due to young massive OB stars (e.g. Kewley et al.,
2001; Morisset et al., 2016) cover the observed distribution (e.g. Sánchez et
al., 2015b). However, it is well known that (i) these models are heavily
degenerated, i.e., a set of line ratios (e.g., O3 vs N2) can be reproduced by
a different set of physical properties associated with different kind of
modeled H ii regions (for instance, two values of log(U) and O/H), and (ii)
physically possible photoionization models cover a much wider region of the
diagrams than the actually covered by the observed regions. As a consequence
photoinization models, per se, cannot predict univocally the physical
properties of these regions, like the oxygen abundance or the ionization
parameter, purely based on the line ratios involved in the diagnostic
diagrams. However, there are clear trends between the physical parameters and
the observed line ratios. In Sec. 3.2 we show that the actual values of
several physical parameters of H ii regions are well defined by the location
on these diagrams. Although we observed a certain degree of data scattering,
in general, it is much lower than the dynamical range of the explored
parameter: e.g., Fig. 1 (and also in Fig. 7, 9, 8). This result was already
reported in Sánchez et al. (2015b), using a smaller sample of H ii regions.
Furthermore, the connection between different physical properties and the
location in the diagnostic diagram is not putative of H ii regions. It is
observed in other sources of ionization, as a connection between line ratios
and the dynamical stage of the underlying stellar population (e.g., Law et
al., 2021), the velocity dispersion of the ionized gas (e.g. D’Agostino et
al., 2019), or the morphology, the stellar mass and the galactocentric
distance (e.g. Sánchez, 2020). Again, none of those trends can be predicted by
photoinization models. The reason behind this discrepancy is that
photoinization models are physical models of the ionized regions, but they do
not include the astrophysical context in which the ionization is produced.
Thus, given a certain ionizing source (e.g., an OB star), a certain geometry
and density distribution of the ionized nebulae, and a certain chemical
composition of this nebulae, photoionization models are able to predict a set
of line ratios. However, they are unable to determine which type of ionizing
source, which type of geometry or which chemical composition is found at a
certain location within a certain type of galaxy. Essentially, they ignore the
constrains in which star-formation and chemical enrichment took place in
galaxies (and within galaxies).

The reported trends along the diagnostic diagrams are not a consequence of the
predictions of how the ionization happens. They are the consequence of the
spatially resolved evolution of the stellar populations, the consequent
chemical enrichment at the location in which H ii regions are formed, and
maybe the kind of nebulae that can be formed at different locations. Because
of this, there are well defined gradients in all physical properties (e.g.,
O/H, N/O, AV, as seen in Fig. 3 and Fig. 4), well described in the literature
(e.g. Searle, 1971; Peimbert et al., 1978; Vila-Costas & Edmunds, 1992;
Sánchez et al., 2014; Belfiore et al., 2017b; Esteban & García-Rojas, 2018).
These gradients have been frequently used to explore the star-formation
histories and chemical enrichment histories in other galaxies (e.g., Tissera
et al., 2013; Belfiore et al., 2019) and in the Milky-Way (e.g. Carigi et al.,
2019). However, it is not so frequently acknowledged that they left imprints
in the physical properties of H ii regions that are fossil records of those
processes. This perspective was proposed by Sánchez et al. (2015b), once it
was observed the direct connection between the line ratios observed in H ii
regions and the physical properties of the underlying stellar populations
(like the B-V color Sánchez et al., 2012a). These results were confirmed by
Espinosa-Ponce et al. (2020), where it was explored the direct relation
between those line ratios and physical properties of the stellar populations,
like the $\mathcal{A}_{\star,L}$ and $\mathcal{Z}_{\star,L}$.

As indicated before, photoinization models require to be combined with
empirical relations between different physical quantities, like the N/O-O/H
and the log(U)-O/H relations explored in Sec 3.4 (Dopita et al., 2013; Vale
Asari et al., 2016), to make predictions on those properties based on the
observed line ratios. On the contrary, they may lead to significant errors and
miss-interpretations. For instance, the average physical properties of those
models that reproduce the observed line ratios are not observed previously in
the literature or are not in general representative of the real physical
properties, if they are heavily degenerated. Indeed, in many cases they are
substantially wrong. The most simple example of this situation is the well
known bi-valuate relation between the R23 line ratio and the oxygen abundance
(e.g. Pagel et al., 1979).

The nature of these relations between N/O, log(O/H) and log(U) is
astrophysical as well. As indicated before, the N/O-O/H relation is a
consequence of the primary production of oxygen and the primary and secondary
production of nitrogen (Edmunds & Pagel, 1978; Alloin et al., 1979; Mollá &
Díaz, 2005). In particular, the secondary production, that depends on the
previous production of oxygen (and carbon), is the mechanism behind the
relation above 12+log(O/H)$>$8.2 observed in Fig. 5. The flatenning at lower
oxygen abundances is due to the primary phases of the production of nitrogen,
that is observed when the location in which the H ii region is form has not
reached the required oxygen abundance needed to ignite the secondary
production in the newly formed stars. Thus, it depends on the location within
galaxies, the stellar mass of those galaxies (a gauge of the oxygen
abundance), and their morphological type (e.g. Belfiore et al., 2017a,
Schaefer et al. in prep). On the other hand, the nature of the log(U)-O/H
relation is less clear. Different mechanisms were already proposed in early
explorations by Evans & Dopita (1985) and Dopita & Evans (1986), as discussed
in Sec. 3.4. All of them require a connection between this relation and the
location in which the H ii is formed: (i) a change in the IMF and its
connection with the oxygen abundance; (ii) an effect of the dust or the metal
blanketing on the hardness of the ionization and (iii) an environmental bias
on which kind of nebulae is formed.

As indicated before, a non universal or variable IMF and its connection with
galaxy (or local) properties is a topic of discussion. Chabrier (2003)
reviewed the possible variability of the IMF depending on the environment
within a galaxy, although some recent results indicate that this many not be
the case (e.g. Wegg et al., 2017). A possible time evolution from early
cosmological times has been proposed too (e.g. Vazdekis et al., 1996), what
would explain the differential $\alpha$-enhancement in different regions
within our Galaxy (e.g. Carigi et al., 2019) or among different galaxies (e.g.
Walcher et al., 2014). Since in this period the star-formation was dominated
by present day early-type galaxies (e.g. Sánchez et al., 2019), or in the
bulge/center of early spirals (e.g. Li et al., 2015; García-Benito et al.,
2019), this time change would imply an environmental dependency of the IMF
too. Recent explorations have shown further relations between the shape of the
IMF and other galaxy (or regions within galaxies) properties, such as the
stellar metallicity (e.g. Martín-Navarro et al., 2015) or the velocity
dispersion (McDermid et al., 2015). Those relations may be well
interconnected, and connected with the time evolution discussed before. In any
case, if this is the cause of the log(U)-O/H relation, the connection would be
deeply related on how the star-formation happens due to how the metallicity
enhances the cooling, fragmentation and collapse of the molecular clouds
(Dopita & Evans, 1986). Thus, this relation would be a consequence of the
enrichment process, but only through this physical connection. The possible
effect of the dust and/or metal blanketing on the hardness of the radiation
has a similar origin, since those regions with stronger metal enrichment would
be those suffering this effect more clearly.

The final scenario proposed for the observed log(U)-O/H by Dopita & Evans
(1986) has a totally different origin. They proposed that H ii regions are
formed in locations within a galaxy with larger molecular gas densities (i.e.,
the center) may have a smaller surface brightness. The reason for that could
be, one more time, the enhancement of the cooling and fragmentation induced by
the metallicity: molecular clouds in regions of larger metal content would
fragment in smaller clouds and collapse to form smaller and lower surface-
brightness H ii regions. Since both the larger metal content and the highest
molecular gas surface density are found in the central regions of galaxies,
the log(U)-O/H relation would naturally emanate from the two observed trends.
The local pressure may also play a role in this regards, in addition to the
direct effect of the metal content. Radial declines in the pressure are
suggested based on the relations proposed by Barrera-Ballesteros et al.
(2021a) and the direct estimations reported by Barnes et al. (2021). A high
pressure may facilitate the fragmentation and collapse of smaller molecular
clouds and the formation of lower surface brightness H ii regions. We should
not exclude that the log(U)-O/H anti-correlation is the consequence of a
combined effect of all the reported scenarios that operate at a different
level but simultaneously. This could be the reason why the relation is weaker
and less well defined as other trends found along this study, due to its
multi-parametric nature.

Finally, we should acknowledge that not all the properties of the H ii regions
depends on the star-formation and chemical evolution of galaxies. It is
obvious that the age of the ionizing population is independent of those
processes by definition of these regions (i.e., ionized by young massive OB-
stars), although their metallicity depends on the evolution. The electron
density seems to be decoupled of the evolution processes in galaxies as well,
at least to the precision in which we can measure this parameter with our
current dataset. We should highlight that the average values reported for this
parameter ($n_{e}\sim$300), although they are similar to the ones reported
using IFS data with similar spatial and spectral resolutions (e.g. Sánchez et
al., 2012b), they are larger than the ones recently reported for similar data
with better spatial and spectral resolutions (Barnes et al., 2021). Thus, we
need to explore the reported trends with better quality data and other ionic
line rations to understand these discrepancies and confirm (or not) our
results.

##  5 Conclusions

Along this study we explored the connection between the physical properties of
a large catalog of H ii regions extracted from a representative sample of the
galaxies in the nearby universe, finding that:

  * •

The location of the H ii regions across the classical diagnostic diagrams, and
therefore, the values of the line ratios involved on those diagrams are
tightly connected with their physical properties, and the properties of the
underlying stellar populations.

  * •

This correspondence between observed and physical properties is univocal in
most of the cases (within a certain dispersion), contrary to the predictions
of photoionization models when they cover a Cartesian grid in O/H, N/O, age
and log(U). But if additional relations between these parameters are used to
restrict the grid, models may recover the observed behavior.

  * •

Most of the explored physical properties present clear radial gradients with
patterns that depend on the mass and morphology of the host galaxies,
relations that in many cases have been reported and discussed before in the
literature. Once again those trends are tightly related to those of the
underlying stellar populations (e.g., fy).

  * •

The physical properties of the H ii regions present clear relations between
themselves and with the properties of the underlying stellar populations, that
in some cases are more evident when exploring the azimutal averaged radial
patterns discussed before.

In conclusion we confirm the results from previous explorations suggesting
that the astrophysical context in which H ii regions are generated are of a
fundamental importance in shaping their observed properties. Indeed, most of
those properties are the result from the local chemical evolution of the
stellar populations at the locations in which those regions are found. In
summary, H ii regions are a fundamental proxy of the chemical evolution of
galaxies that have left clear imprints in their observed properties.

## Acknowledgements

We are very grateful with the referee for the comments and suggestions that
have improved the quality of this paper.

CM acknowledges support from grant UNAM / PAPIIT - IN101220. We are grateful
for the support of the PAPIIT-DGAPA-IG100622 and PAPIIT-DGAPA-IN112620 (UNAM)
projects.

RGB acknowledges additional financial support from the State Agency for
Research of the Spanish MCIU through the Center of Excellence Severo Ochoa
award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709), grants
PID2019- 109067GB-I00 (MCIU) and P18-FRJ-2595 (Junta de Andalucía).

L.G. acknowledges financial support from the Spanish Ministerio de Ciencia e
Innovación (MCIN), the Agencia Estatal de Investigación (AEI)
10.13039/501100011033, and the European Social Fund (ESF) "Investing in your
future" under the 2019 Ramón y Cajal program RYC2019-027683-I and the
PID2020-115253GA-I00 HOSTFLOWS project, and from Centro Superior de
Investigaciones Científicas (CSIC) under the PIE project 20215AT016.

## Data Availability

The H ii regions catalog used in this paper are presented in Espinosa-Ponce et
al. (2020). The estimated physical properties of H ii regions are available
online at http://ifs.astroscu.unam.mx/CALIFA/HII_regions/. An example code to
read and use the data is available at
https://github.com/cespinosa/HII_regions_catalog.

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Column | Keyword | Description
---|---|---
COLUMN1 | HIIREGID | Ionized region ID
COLUMN2 | f_y | Fraction of young stars to the total luminosity
COLUMN3 | dist | Galactocentric distance normalized by $R_{e}$
COLUMN4 | Av | Dust extinction
COLUMN5 | OH_author_elines_ftype 1 | Oxygen abundance
COLUMN6 | OH_author_elines_ftype 2 | Oxygen abundance
$\vdots$ | $\vdots$ | $\vdots$
COLUMN29 | OH_author_elines_ftype 26 | Oxygen abundance
COLUMN30 | OH_IZI_value_model 1 | Oxygen abundance
$\vdots$ | $\vdots$ | $\vdots$
COLUMN44 | OH_IZI_value_model 15 | Oxygen abundance
COLUMN45 | U_author_elines_ftype 1 | Ionization Parameter (adimensional)
$\vdots$ | $\vdots$ | $\vdots$
COLUMN52 | U_author_elines_ftype 8 | Ionization Parameter (adimensional)
COLUMN53 | q_IZI_value_model 1 | Ionization Parameter
$\vdots$ | $\vdots$ | $\vdots$
COLUMN67 | q_IZI_value_model 15 | Ionization Parameter
COLUMN68 | NH_author_ftype | Nitrogen abundance
COLUMN69 | NO_HCm_ftype 1 | Nitrogen-Oxygen ratio
COLUMN70 | NO_HCm_ftype 2 | Nitrogen-Oxygen ratio
COLUMN71 | Ne_Oster_S | Electronic density ratio
COLUMN72 | eAv | Error of dust extinction
COLUMN73 | eOH_author_elines_ftype 1 | Error of oxygen abundance
$\vdots$ | $\vdots$ | $\vdots$
COLUMN172 | eNe_Oster_S | Error of electronic density ratio
Table 1: Description of the distributed files comprising the derived physical
properties for the H ii regions. Each ionized region is identified by their
HIIREGID, therefore, these new tables can be used with the previous ones
published by (Espinosa-Ponce et al., 2020), that include only the
observational properties the regions.

##  Appendix A Description of the Catalogue

The catalog of physical properties of HII regions used along this study is
publicly available. It is distributed through the same webpage as the original
catalog of H ii regions published Espinosa-Ponce et al.
(2020)333http://ifs.astroscu.unam.mx/CALIFA/HII_regions/, comprising a set of
additional files. Each file, labeled by the name of the host galaxy
(HII.GALNAME.phys_props.fits), contains the full set of parameters derived for
each region in a FITs-table format. Each row in the table corresponds to one H
ii region, labeled with the same ID used in the original HII regions catalog
(HIREGID): the galaxy name (GALNAME) plus the corresponding index of its
segmentation map, seg_Ha.GALNAME.fits.

The general structure of each file is show in Table 1. We include the HIREGID,
the fraction of young stars to the total luminosity, the galactocentric
distance, and the dust extinction for each object. The next set of properties
correspond to the oxygen abundances, ionization parameters and
nitrogen/nitrogen-to-oxygen abundances derived using several calibrators
described in the literature. The keyword of each one includes a description of
the considered physical property (e.g., OH for O/H) and a reference to the
article from which it was taken. In most keywords is included the lines ratios
used for the respective calibrations and, if it were the case, the type of
calibration (i.e. linear or polynomial fitting).

As indicated before, we include several values of oxygen abundances calculated
with different calibrators, all them listed in Table 11. We use the v5.1 of
HCm code, the v0.9.9 of NebulaBayes code, and the python version of IZI code.

For the ionization parameter, $U$, we include the results from several studies
too: Dors et al. (2011), Morisset et al. (2016, Mor16), Thomas et al. (2018,
NB) and Pérez-Montero (2014, HCm). The nitrogen abundance was calculated with
the calibration described by Pilyugin & Grebel (2016, Pil16). In the later
case N/O relative abundance was not included, however, it could be calculated
with the oxygen and nitrogen abundances described above. In addition, we
include the N/O ratio estimated by the HII-CHI-mistry code (Pérez-Montero,
2014). The electron density described in the Section 3.1 is included in this
table too. Finally, we include the complete output of IZI code (Mingozzi et
al., 2020) for both the oxygen abundance and ionization parameter, $q$. In
order to run the IZI code, we use the photionization models set presented in
Dopita et al. (2013, labeled as d13_k_20 and d13_k_inf), Levesque et al.
(2010, labeled as levesque) and Byler et al. (2017, labeled as byler and
byler_CSFR). The description of each of those photoionization grids and their
respective results derived by IZI are fully explored in Blanc et al. (2015)
and Mingozzi et al. (2020).

##  Appendix B Physical properties on other diagnostic diagrams

Figure 7: Physical properties of the H ii regions explored along this study
across the [OIII]$\lambda 5007/$H$\beta$ vs. [SII]$\lambda 6716+30/$H$\alpha$
diagnostic diagram. In each panel the color code represents one of the
physical properties described in the text: top left panel: fraction of young
stars to the total luminosity, $f_{y}$; top right panel: ionization parameter;
middle left panel: oxygen abundance; middle right panel: nitrogen-to-oxygen
abundance; bottom left panel: dust extinction; and bottom right panel electron
density. The density contours are similar to those shown Figure 1. The most
frequently used demarcation curves (Kewley et al., 2006) for this diagram are
shown. In each panel the solid-line corresponds to the demarcation line
proposed by Espinosa-Ponce et al. (2020), the dashed-dotted line to the AGN
demarcation line and the dotted-line to the LINER/Sy2 demarcation line.
Figure 8: Similar plots as those shown in Figure 7 for the [OIII]$\lambda
5007/$H$\beta$ vs. [OI]$\lambda 6300/$H$\alpha$ diagnostic diagram, using the
same representation for the parameters, similar color-codes, contours and
meaning for the plotted lines. Figure 9: Similar plots as those shown in
Figure 7 for the [OIII]$\lambda 5007/$H$\beta$ vs. [OII]$\lambda
3727/$H$\beta$ diagnostic diagram, using the same representation for the
parameters, similar color-codes, contours and meaning for the plotted lines.

As we show in § 3.2, the physical properties described in § 3.1 present
evident trends across the BPT diagram. In this appendix, we include the
distributions those properties in other most frequently used diagnostic
diagrams: Figure 7 and Figure 8 show the distribution across the
[OIII]$\lambda 5007/$H$\beta$ vs. [SII]$\lambda 6716+30/$H$\alpha$ and
[OIII]$\lambda 5007/$H$\beta$ vs. [OI]$\lambda 6300/$H$\alpha$ diagrams,
respectively. In addition, we include the [O ii]$\lambda 3726+29$/H$\beta$ vs.
[O iii]$\lambda 5007$/H$\beta$ diagnostic diagram in Figure 9. Some trends are
clearly highlighted in the observed distributions: (i) H ii regions with high
$f_{y}$ values are always found in the upper range of the three diagrams, with
a decreasing gradient along the Y-axis for the first two diagrams, and a
diagonal gradient for the third one (i.e., the larger values are at the upper-
right end of this diagram); (ii) regions with higher values of log(U) are also
located in the upper range of the diagrams, with a diagonal distribution from
the upper-left (high values) to the lower-right (low values) in the first two
diagrams, and an inverse diagonal distribution, from the upper-right (high
values) to the lower-left (low values) for the third diagram; (iii) O/H and
N/O present similar trends, as expected due to the strong correlation between
both parameters. In the first two diagrams the gradient is vertical, with both
abundances increasing from the upper to the lower values, which in the third
diagram the gradient is diagonal (or even horizontal), with abundances
declining from the lower-left to the upper-right distribution of this
diagrams; (iv) the trends for $A_{\rm V}$ and $n_{e}$ are the less evident
ones. For the dust extinction there is a clearer diagonal trend in the third
diagram, with lower values at the upper-left regime and higher values at the
lower-right locations. A similar trend, weaker, but still appreciated, is
observed for the $n_{e}$ in this diagram too. For the other two diagrams
trends are much weaker or absent. For $A_{\rm V}$ it is observed a loose trend
to lower values in the upper range of the distribution. Finally, no trend is
observed for $n_{e}$.

##  Appendix C Physical properties of edge-on galaxies

In this section, we study how the galaxy inclination affects the trends
described for the different physical properties on the diagnostic diagrams.
For doing so we select those H ii regions in edge-on galaxies, i.e., with an
inclination $>70^{\circ}$. There are $\sim$100 of these galaxies in which we
detect $3,600$ H ii regions.

As we can see in the Figure 10, we find similar trends for all physical
properties as those ones found for the non edge-on galaxies, shown in Fig. 1.
The H ii regions with high $f_{y}$ values are found in the upper-left end of
the distribution, with values decreasing towards the lower-right zone of the
diagram. The trends of log(U), O/H and N/O present the same trends along the
Y-axis. The log(U) is higher in those regions on the upper-left of the
distribution, and O/H and N/O present a diagonal trend with higher abundances
on the upper-left of the distribution and lower abundances on the lower-right
of the diagram. Finally, the previously trends for $A_{\mathrm{V}}$ and
$n_{e}$ are found in this sub-sample of the H ii regions. There is a clear
diagonal trend for the dust extinction, with higher values at the lower-right
zone of the diagram and lower values at the upper-left of the distribution. A
weaker trend is observed for the $n_{e}$, the regions with the highest density
are found on the right-hand area of the diagram. The only appreciated
difference is that the average dust attenuation is clearly higher for the H ii
regions residing in edge-on galaxies ($\sim$1.2 mag vs. $\sim$0.9 mag). This
is in any case expected just due to inclination effects. In summary the
inclusion or exclusion of edge-on galaxies does not affect the main trends
described across the diagnostic-diagrams.

Figure 10: Similar plots as those shown in Figure 1 for the [OIII]$\lambda
5007/$H$\beta$ vs. [N ii]$\lambda 6583/$H$\alpha$ diagnostic diagram for the H
ii regions hosted by edge-on galaxies.

##  Appendix D Physical Properties along the galactocentric distance: Fitting
results

Tables 2, 3, 4, 5, 6, 7 and 8 show the zero-point ($c_{0}$) and slopes
($c_{1}$), and their associated errors, derived from the linear regression to
the radial distributions shown in Fig. 2, 3 and 4 and discussed in § 3.3. In
addition we provide with the $rms$ of the residual for each radial
distribution once subtracted the best fitted linear relation.

$f_{y}$ M∗ | Parameter | ALL | $\mathrm{E/S0}$ | $\mathrm{Sa}$ | $\mathrm{Sb}$ | $\mathrm{Sbc}$ | $\mathrm{Sc}$ | $\mathrm{Sd/Sm/Irr}$
---|---|---|---|---|---|---|---|---
7.0 - 9.5 | $c_{0}$ | 0.324 | 0.284 | … | … | 0.182 | 0.218 | 0.354
| $\sigma_{c_{0}}$ | 0.009 | 0.142 | … | … | 0.037 | 0.014 | 0.011
| $c_{1}$ | 0.077 | -0.033 | … | … | 0.194 | 0.11 | 0.076
| $\sigma_{c_{1}}$ | 0.007 | 0.073 | … | … | 0.039 | 0.014 | 0.008
| $rms_{r}$ | 0.0353 |  $\sim$ 0.0 | … | … | 0.0138 | 0.0673 | 0.0306
9.5 - 10.5 | $c_{0}$ | 0.268 | 0.223 | 0.278 | 0.203 | 0.163 | 0.28 | 0.351
| $\sigma_{c_{0}}$ | 0.004 | 0.023 | 0.013 | 0.009 | 0.006 | 0.005 | 0.007
| $c_{1}$ | 0.049 | -0.022 | -0.035 | 0.038 | 0.066 | 0.068 | 0.051
| $\sigma_{c_{1}}$ | 0.003 | 0.023 | 0.008 | 0.007 | 0.004 | 0.004 | 0.004
| $rms_{r}$ | 0.003 | 0.0544 | 0.0057 | 0.0263 | 0.0203 | 0.0151 | 0.0186
10.5 - 11.0 | $c_{0}$ | 0.243 | 0.32 | 0.21 | 0.21 | 0.182 | 0.289 | 0.353
| $\sigma_{c_{0}}$ | 0.004 | 0.019 | 0.011 | 0.008 | 0.008 | 0.007 | 0.019
| $c_{1}$ | 0.023 | -0.059 | -0.01 | 0.027 | 0.068 | 0.009 | 0.0
| $\sigma_{c_{1}}$ | 0.003 | 0.011 | 0.007 | 0.005 | 0.005 | 0.005 | 0.012
| $rms_{r}$ | 0.0105 | 0.0275 | 0.0151 | 0.0197 | 0.0192 | 0.0179 | 0.0473
11.0 - 13.0 | $c_{0}$ | 0.167 | 0.056 | 0.169 | 0.136 | 0.219 | 0.081 | 0.108
| $\sigma_{c_{0}}$ | 0.006 | 0.018 | 0.014 | 0.008 | 0.011 | 0.015 | 0.023
| $c_{1}$ | 0.037 | 0.039 | -0.002 | 0.056 | 0.04 | 0.13 | 0.159
| $\sigma_{c_{1}}$ | 0.004 | 0.012 | 0.007 | 0.005 | 0.007 | 0.012 | 0.019
| $rms_{r}$ | 0.0059 | 0.0279 | 0.0218 | 0.0033 | 0.0103 | 0.0334 | 0.0386
Table 2: Coefficients of the linear fit ($c_{0}$ for the zero-point and $c_{1}$ for the slope) and their associated errors ($\sigma_{i}$) for the radial distributions of $f_{y}$ along the galactocentric distance shown in Fig. 2. The RMS of the residuals is listed for each linear regression. $\log\mathrm{EW}(\mathrm{H}\alpha)$ M∗ | Parameter | ALL | $\mathrm{E/S0}$ | $\mathrm{Sa}$ | $\mathrm{Sb}$ | $\mathrm{Sbc}$ | $\mathrm{Sc}$ | $\mathrm{Sd/Sm/Irr}$
---|---|---|---|---|---|---|---|---
7.0 - 9.5 | $c_{0}$ | 1.466 | 1.421 | … | … | 1.283 | 1.286 | 1.496
| $\sigma_{c_{0}}$ | 0.02 | 0.244 | … | … | 0.079 | 0.045 | 0.023
| $c_{1}$ | 0.086 | -0.095 | … | … | 0.269 | 0.169 | 0.084
| $\sigma_{c_{1}}$ | 0.014 | 0.121 | … | … | 0.073 | 0.032 | 0.016
| $rms_{r}$ | 0.0438 | 0.0 | … | … | 0.0282 | 0.0954 | 0.0306
9.5 - 10.5 | $c_{0}$ | 1.323 | 1.092 | 1.287 | 1.216 | 1.18 | 1.336 | 1.47
| $\sigma_{c_{0}}$ | 0.009 | 0.047 | 0.034 | 0.018 | 0.016 | 0.012 | 0.015
| $c_{1}$ | 0.111 | 0.099 | -0.055 | 0.08 | 0.128 | 0.151 | 0.081
| $\sigma_{c_{1}}$ | 0.006 | 0.048 | 0.021 | 0.013 | 0.01 | 0.009 | 0.01
| $rms_{r}$ | 0.0208 | 0.0633 | 0.0736 | 0.045 | 0.0283 | 0.0328 | 0.023
10.5 - 11.0 | $c_{0}$ | 1.269 | 1.165 | 1.211 | 1.153 | 1.169 | 1.406 | 1.51
| $\sigma_{c_{0}}$ | 0.009 | 0.033 | 0.026 | 0.015 | 0.017 | 0.015 | 0.034
| $c_{1}$ | 0.049 | -0.055 | -0.022 | 0.09 | 0.118 | 0.013 | -0.063
| $\sigma_{c_{1}}$ | 0.005 | 0.022 | 0.015 | 0.009 | 0.01 | 0.01 | 0.021
| $rms_{r}$ | 0.0117 | 0.076 | 0.0282 | 0.0105 | 0.0319 | 0.0345 | 0.0303
11.0 - 13.0 | $c_{0}$ | 1.101 | 1.014 | 0.924 | 1.051 | 1.156 | 1.127 | 1.163
| $\sigma_{c_{0}}$ | 0.013 | 0.057 | 0.033 | 0.018 | 0.023 | 0.033 | 0.073
| $c_{1}$ | 0.069 | 0.051 | 0.097 | 0.091 | 0.083 | 0.134 | 0.179
| $\sigma_{c_{1}}$ | 0.007 | 0.032 | 0.018 | 0.01 | 0.013 | 0.022 | 0.055
| $rms_{r}$ | 0.0082 | 0.1037 | 0.0475 | 0.0141 | 0.0302 | 0.0453 | 0.0537
Table 3: Coefficients of the linear fit ($c_{0}$ for the zero-point and $c_{1}$ for the slope) and their associated errors ($\sigma_{i}$) for the radial distributions of EW(H$\alpha$) along the galactocentric distance shown in Fig. 2. The RMS of the residuals is listed for each linear regression. $\log(\mathrm{U})$ M∗ | Parameter | ALL | $\mathrm{E/S0}$ | $\mathrm{Sa}$ | $\mathrm{Sb}$ | $\mathrm{Sbc}$ | $\mathrm{Sc}$ | $\mathrm{Sd/Sm/Irr}$
---|---|---|---|---|---|---|---|---
7.0 - 9.5 | $c_{0}$ | -2.36 | … | … | … | … | … | -2.402
| $\sigma_{c_{0}}$ | 0.077 | … | … | … | … | … | 0.083
| $c_{1}$ | 0.006 | … | … | … | … | … | 0.032
| $\sigma_{c_{1}}$ | 0.066 | … | … | … | … | … | 0.073
| $rms_{r}$ | 0.0863 | … | … | … | … | … | 0.1019
9.5 - 10.5 | $c_{0}$ | -2.813 | -2.767 | -3.101 | -2.902 | -2.606 | -2.877 | -2.868
| $\sigma_{c_{0}}$ | 0.018 | 0.163 | 0.07 | 0.04 | 0.051 | 0.025 | 0.02
| $c_{1}$ | 0.035 | 0.342 | 0.046 | 0.08 | -0.031 | 0.051 | 0.105
| $\sigma_{c_{1}}$ | 0.012 | 0.325 | 0.091 | 0.032 | 0.029 | 0.016 | 0.015
| $rms_{r}$ | 0.0188 | 0.0 | 0.1196 | 0.1547 | 0.0729 | 0.0291 | 0.0178
10.5 - 11.0 | $c_{0}$ | -2.805 | -3.033 | -2.843 | -2.772 | -2.782 | -2.793 | -2.813
| $\sigma_{c_{0}}$ | 0.018 | 0.069 | 0.047 | 0.034 | 0.039 | 0.033 | 0.048
| $c_{1}$ | 0.0 | 0.015 | 0.024 | 0.01 | 0.028 | -0.087 | -0.096
| $\sigma_{c_{1}}$ | 0.011 | 0.073 | 0.036 | 0.021 | 0.021 | 0.021 | 0.036
| $rms_{r}$ | 0.0473 | 0.2942 | 0.0858 | 0.0465 | 0.031 | 0.0703 | 0.098
11.0 - 13.0 | $c_{0}$ | -2.919 | -3.035 | -3.04 | -2.596 | -3.122 | -3.175 | -3.515
| $\sigma_{c_{0}}$ | 0.038 | 0.179 | 0.11 | 0.059 | 0.055 | 0.118 | 0.229
| $c_{1}$ | -0.031 | -0.095 | 0.071 | -0.147 | 0.03 | -0.053 | 0.274
| $\sigma_{c_{1}}$ | 0.022 | 0.107 | 0.058 | 0.035 | 0.035 | 0.074 | 0.166
| $rms_{r}$ | 0.0436 | 0.2406 | 0.0286 | 0.0381 | 0.0353 | 0.2389 | 0.0283
Table 4: Coefficients of the linear fit ($c_{0}$ for the zero-point and $c_{1}$ for the slope) and their associated errors ($\sigma_{i}$) for the radial distributions of $\log(\mathrm{U})$ along the galactocentric distance shown in Fig. 3. The RMS of the residuals is listed for each linear regression. $12+\log(\mathrm{O/H})$ M∗ | Parameter | ALL | $\mathrm{E/S0}$ | $\mathrm{Sa}$ | $\mathrm{Sb}$ | $\mathrm{Sbc}$ | $\mathrm{Sc}$ | $\mathrm{Sd/Sm/Irr}$
---|---|---|---|---|---|---|---|---
7.0 - 9.5 | $c_{0}$ | 8.175 | … | … | … | … | … | 8.186
| $\sigma_{c_{0}}$ | 0.028 | … | … | … | … | … | 0.035
| $c_{1}$ | -0.094 | … | … | … | … | … | -0.099
| $\sigma_{c_{1}}$ | 0.03 | … | … | … | … | … | 0.037
| $rms_{r}$ | 0.0105 | … | … | … | … | … | 0.0143
9.5 - 10.5 | $c_{0}$ | 8.671 | 8.75 | 8.707 | 8.669 | 8.85 | 8.653 | 8.559
| $\sigma_{c_{0}}$ | 0.007 | 0.066 | 0.028 | 0.013 | 0.016 | 0.01 | 0.01
| $c_{1}$ | -0.105 | -0.062 | -0.011 | -0.049 | -0.144 | -0.119 | -0.136
| $\sigma_{c_{1}}$ | 0.005 | 0.129 | 0.029 | 0.01 | 0.01 | 0.007 | 0.007
| $rms_{r}$ | 0.0062 | 0.0 | 0.0382 | 0.0361 | 0.0288 | 0.0139 | 0.0156
10.5 - 11.0 | $c_{0}$ | 8.73 | 8.658 | 8.749 | 8.778 | 8.826 | 8.631 | 8.635
| $\sigma_{c_{0}}$ | 0.007 | 0.027 | 0.017 | 0.01 | 0.013 | 0.013 | 0.028
| $c_{1}$ | -0.026 | 0.029 | 0.021 | -0.04 | -0.085 | 0.007 | -0.011
| $\sigma_{c_{1}}$ | 0.004 | 0.027 | 0.011 | 0.006 | 0.008 | 0.008 | 0.02
| $rms_{r}$ | 0.0141 | 0.0307 | 0.0216 | 0.0292 | 0.0282 | 0.0297 | 0.0324
11.0 - 13.0 | $c_{0}$ | 8.755 | 8.727 | 8.818 | 8.824 | 8.633 | 8.748 | 8.844
| $\sigma_{c_{0}}$ | 0.01 | 0.081 | 0.031 | 0.013 | 0.018 | 0.023 | 0.049
| $c_{1}$ | -0.023 | 0.029 | -0.022 | -0.047 | 0.001 | -0.068 | -0.139
| $\sigma_{c_{1}}$ | 0.006 | 0.055 | 0.015 | 0.008 | 0.011 | 0.014 | 0.037
| $rms_{r}$ | 0.0097 | 0.0434 | 0.0202 | 0.0044 | 0.0233 | 0.0354 | 0.0191
Table 5: Coefficients of the linear fit ($c_{0}$ for the zero-point and $c_{1}$ for the slope) and their associated errors ($\sigma_{i}$) for the radial distributions of 12+$\log(\mathrm{O}/\mathrm{H})$ along the galactocentric distance shown in Fig. 3. The RMS of the residuals is listed for each linear regression. $\log(\mathrm{N/O})$ M∗ | Parameter | ALL | $\mathrm{E/S0}$ | $\mathrm{Sa}$ | $\mathrm{Sb}$ | $\mathrm{Sbc}$ | $\mathrm{Sc}$ | $\mathrm{Sd/Sm/Irr}$
---|---|---|---|---|---|---|---|---
7.0 - 9.5 | $c_{0}$ | -1.102 | … | … | … | … | … | -1.105
| $\sigma_{c_{0}}$ | 0.056 | … | … | … | … | … | 0.071
| $c_{1}$ | -0.119 | … | … | … | … | … | -0.117
| $\sigma_{c_{1}}$ | 0.051 | … | … | … | … | … | 0.062
| $rms_{r}$ | 0.1606 | … | … | … | … | … | 0.1893
9.5 - 10.5 | $c_{0}$ | -0.755 | -0.85 | -0.861 | -0.764 | -0.5 | -0.776 | -0.848
| $\sigma_{c_{0}}$ | 0.009 | 0.048 | 0.034 | 0.019 | 0.021 | 0.012 | 0.012
| $c_{1}$ | -0.134 | 0.051 | -0.002 | -0.066 | -0.211 | -0.145 | -0.156
| $\sigma_{c_{1}}$ | 0.007 | 0.123 | 0.04 | 0.017 | 0.015 | 0.009 | 0.01
| $rms_{r}$ | 0.0074 | 0.0 | 0.0566 | 0.1086 | 0.0292 | 0.0301 | 0.0356
10.5 - 11.0 | $c_{0}$ | -0.725 | -0.852 | -0.797 | -0.667 | -0.527 | -0.793 | -0.858
| $\sigma_{c_{0}}$ | 0.011 | 0.027 | 0.025 | 0.016 | 0.02 | 0.017 | 0.038
| $c_{1}$ | -0.068 | -0.022 | 0.039 | -0.066 | -0.162 | -0.086 | -0.132
| $\sigma_{c_{1}}$ | 0.007 | 0.039 | 0.019 | 0.011 | 0.013 | 0.013 | 0.03
| $rms_{r}$ | 0.0558 | 0.213 | 0.0472 | 0.0637 | 0.0837 | 0.0423 | 0.022
11.0 - 13.0 | $c_{0}$ | -0.701 | -0.544 | -0.88 | -0.544 | -0.824 | -0.643 | -0.802
| $\sigma_{c_{0}}$ | 0.02 | 0.157 | 0.067 | 0.025 | 0.025 | 0.056 | 0.125
| $c_{1}$ | -0.081 | -0.308 | 0.053 | -0.113 | -0.084 | -0.181 | -0.052
| $\sigma_{c_{1}}$ | 0.012 | 0.113 | 0.031 | 0.016 | 0.019 | 0.034 | 0.084
| $rms_{r}$ | 0.0129 | 0.08 | 0.0482 | 0.0563 | 0.0375 | 0.1048 | 0.0314
Table 6: Coefficients of the linear fit ($c_{0}$ for the zero-point and $c_{1}$ for the slope) and their associated errors ($\sigma_{i}$) for the radial distributions of N/O ratio along the galactocentric distance shown in Fig. 3. The RMS of the residuals is listed for each linear regression. $\log(n_{e})$ M∗ | Parameter | ALL | $\mathrm{E/S0}$ | $\mathrm{Sa}$ | $\mathrm{Sb}$ | $\mathrm{Sbc}$ | $\mathrm{Sc}$ | $\mathrm{Sd/Sm/Irr}$
---|---|---|---|---|---|---|---|---
7.0 - 9.5 | $c_{0}$ | 2.355 | 3.12 | … | … | 2.239 | 2.405 | 2.383
| $\sigma_{c_{0}}$ | 0.021 | 0.714 | … | … | 0.128 | 0.05 | 0.024
| $c_{1}$ | 0.034 | -0.152 | … | … | 0.001 | 0.07 | 0.004
| $\sigma_{c_{1}}$ | 0.017 | 0.347 | … | … | 0.114 | 0.036 | 0.019
| $rms_{r}$ | 0.049 | 0.0 | … | … | 0.0609 | 0.0431 | 0.041
9.5 - 10.5 | $c_{0}$ | 2.483 | 2.418 | 2.438 | 2.553 | 2.393 | 2.498 | 2.406
| $\sigma_{c_{0}}$ | 0.014 | 0.064 | 0.068 | 0.043 | 0.029 | 0.02 | 0.02
| $c_{1}$ | -0.026 | 0.162 | 0.086 | -0.095 | -0.023 | -0.015 | 0.012
| $\sigma_{c_{1}}$ | 0.009 | 0.05 | 0.041 | 0.028 | 0.017 | 0.013 | 0.013
| $rms_{r}$ | 0.0349 | 0.1272 | 0.0196 | 0.1234 | 0.0301 | 0.0336 | 0.0356
10.5 - 11.0 | $c_{0}$ | 2.523 | 2.511 | 2.603 | 2.574 | 2.392 | 2.468 | 2.748
| $\sigma_{c_{0}}$ | 0.019 | 0.107 | 0.069 | 0.036 | 0.037 | 0.033 | 0.053
| $c_{1}$ | -0.01 | 0.077 | -0.044 | -0.047 | 0.016 | 0.06 | -0.092
| $\sigma_{c_{1}}$ | 0.012 | 0.079 | 0.041 | 0.022 | 0.021 | 0.021 | 0.037
| $rms_{r}$ | 0.0645 | 0.1595 | 0.0614 | 0.1008 | 0.0893 | 0.0647 | 0.0431
11.0 - 13.0 | $c_{0}$ | 2.604 | 3.163 | 2.756 | 2.572 | 2.34 | 2.906 | 2.294
| $\sigma_{c_{0}}$ | 0.034 | 0.175 | 0.082 | 0.05 | 0.064 | 0.112 | 0.221
| $c_{1}$ | -0.072 | -0.222 | -0.107 | -0.052 | -0.025 | -0.206 | 0.37
| $\sigma_{c_{1}}$ | 0.019 | 0.095 | 0.042 | 0.03 | 0.038 | 0.071 | 0.173
| $rms_{r}$ | 0.0339 | 0.1537 | 0.1078 | 0.0979 | 0.0496 | 0.1494 | 0.0503
Table 7: Coefficients of the linear fit ($c_{0}$ for the zero-point and $c_{1}$ for the slope) and their associated errors ($\sigma_{i}$) for the radial distributions of $n_{e}$ along the galactocentric distance shown in Fig. 4. The RMS of the residuals is listed for each linear regression. $\log(A_{v})$ M∗ | Parameter | ALL | $\mathrm{E/S0}$ | $\mathrm{Sa}$ | $\mathrm{Sb}$ | $\mathrm{Sbc}$ | $\mathrm{Sc}$ | $\mathrm{Sd/Sm/Irr}$
---|---|---|---|---|---|---|---|---
7.0 - 9.5 | $c_{0}$ | 0.42 | 1.478 | … | … | 0.166 | 1.032 | 0.317
| $\sigma_{c_{0}}$ | 0.041 | 1.527 | … | … | 0.192 | 0.141 | 0.035
| $c_{1}$ | 0.172 | -0.188 | … | … | 0.313 | -0.048 | 0.198
| $\sigma_{c_{1}}$ | 0.03 | 0.739 | … | … | 0.183 | 0.09 | 0.028
| $rms_{r}$ | 0.0564 | 0.0 | … | … | 0.2565 | 0.0925 | 0.0322
9.5 - 10.5 | $c_{0}$ | 1.003 | 0.892 | 1.476 | 0.864 | 1.135 | 1.058 | 0.546
| $\sigma_{c_{0}}$ | 0.022 | 0.154 | 0.094 | 0.05 | 0.05 | 0.035 | 0.022
| $c_{1}$ | -0.1 | 0.249 | -0.212 | 0.043 | -0.152 | -0.139 | 0.037
| $\sigma_{c_{1}}$ | 0.014 | 0.186 | 0.055 | 0.037 | 0.029 | 0.02 | 0.016
| $rms_{r}$ | 0.0477 | 0.5836 | 0.1325 | 0.0979 | 0.0778 | 0.0863 | 0.027
10.5 - 11.0 | $c_{0}$ | 1.476 | 1.374 | 1.616 | 1.295 | 1.27 | 1.591 | 1.059
| $\sigma_{c_{0}}$ | 0.029 | 0.152 | 0.086 | 0.044 | 0.043 | 0.051 | 0.125
| $c_{1}$ | -0.17 | -0.079 | -0.216 | -0.119 | -0.177 | -0.092 | 0.076
| $\sigma_{c_{1}}$ | 0.017 | 0.091 | 0.053 | 0.027 | 0.026 | 0.033 | 0.083
| $rms_{r}$ | 0.0635 | 0.2236 | 0.1811 | 0.0464 | 0.1685 | 0.1195 | 0.2395
11.0 - 13.0 | $c_{0}$ | 1.685 | 1.312 | 2.03 | 1.548 | 1.674 | 1.629 | 1.3
| $\sigma_{c_{0}}$ | 0.049 | 0.256 | 0.161 | 0.077 | 0.093 | 0.106 | 0.155
| $c_{1}$ | -0.129 | 0.312 | -0.291 | -0.088 | -0.165 | -0.071 | -0.146
| $\sigma_{c_{1}}$ | 0.029 | 0.151 | 0.083 | 0.045 | 0.056 | 0.065 | 0.122
| $rms_{r}$ | 0.026 | 0.1908 | 0.0941 | 0.0601 | 0.0483 | 0.237 | 0.0971
Table 8: Coefficients of the linear fit ($c_{0}$ for the zero-point and $c_{1}$ for the slope) and their associated errors ($\sigma_{i}$) for the radial distributions of $A_{v}$ along the galactocentric distance shown in Fig. 4. The RMS of the residuals is listed for each linear regression. Parameter | $f_{y}$ | EW(H$\alpha$) | $\log(U)$ | $\log(\mathrm{N}/\mathrm{O})$ | $A_{v}$ | $\log(n_{e})$
---|---|---|---|---|---|---
$c_{0}$ | 6.78 | 14.16 | 3.81 | -8.85 | -18.2 | -5.79
$\sigma_{c_{0}}$ | 1.8 | 3.49 | 2.58 | 1.46 | 5.8 | 3.71