11institutetext:  Département de Physique, de Génie Physique et d’Optique,
Université Laval, and Centre de Recherche en Astrophysique du Québec (CRAQ),
Québec, QC, G1V 0A6, Canada
11email<EMAIL_ADDRESS>22institutetext: Instituto
de Astrofísica de Andalucía - CSIC, Glorieta de la Astronomía s.n., 18008
Granada, Spain 33institutetext: CIEMAT, Avda. Complutense 40, 28040 Madrid,
Spain 44institutetext: Main Astronomical Observatory, National Academy of
Sciences of Ukraine, 27 Akademika Zabolotnoho St., 03680, Kyiv,
Ukraine55institutetext: Institute of Theoretical Physics and Astronomy,
Vilnius University, Sauletekio av. 3, 10257, Vilnius, Lithuania
66institutetext: Faculty of Physics, Ludwig-Maximilians-Universität,
Scheinerstr. 1, 81679 Munich, Germany

# Mass-Metallicity and Star Formation Rate in Galaxies:
a complex relation tuned to stellar age††thanks: Table 1 with the values of
oxygen and nitrogen-to-oxygen abundance ratios for $\sim$195000 SDSS star-
forming galaxies and related relevant data is only available in electronic
form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/.

S. Duarte Puertas 1122 J. M. Vilchez 22 J. Iglesias-Páramo 22 M. Mollá 33 E.
Pérez-Montero 22 C. Kehrig 22 L. S. Pilyugin 4455 I. A. Zinchenko 6644

(Received ; accepted )

###### Abstract

Context. In this work we study the stellar mass – metallicity relation (MZR)
of an extended sample of star-forming galaxies in the local Universe and its
possible dependence with the star formation rate (SFR).

Aims. A sample of $\sim$195000 Sloan Digital Sky Survey (SDSS) star-forming
galaxies has been selected up to z=0.22 with the aim of analysing the
behaviour of the relation of MZR with respect to SFR and taking into account
the age of their stellar populations.

Methods. For this sample we have obtained, for the first time, aperture
corrected oxygen and nitrogen-to-oxygen abundances (O/H and N/O, respectively)
and SFR using the empirical prescriptions from the Calar Alto Legacy Integral
Field Area (CALIFA) survey. To perform this study we make use also of the
stellar mass of the galaxies and the parameter $\rm D_{n}(4000)$ as a proxy of
the age of the stellar population.

Results. We derive a robust MZR locus, which is found to be fully consistent
with the “anchoring” points of a selected set of well studied nearby galaxies
with a direct derivation of the chemical abundance. A complex relation between
MZR and SFR across the whole range of galaxy mass and metallicity has been
observed, where the slope changes seen in the O/H – SFR plane present a
pattern which seems to be tuned to the galaxies’ stellar age, and therefore,
stellar age has to be taken into account in the stellar mass – metallicity –
SFR relation.

Conclusions. In order to provide an answer to the question of whether or not
the MZR depends on the SFR it is essential to take into account the age of the
stellar populations of galaxies. A strong dependence between the MZR and SFR
is observed mainly for star-forming galaxies with strong SFR values and low
$\rm D_{n}(4000)$. The youngest galaxies of our SDSS sample show the highest
SFR measured for their stellar mass.

###### Key Words.:

galaxies: general – galaxies: star forming – galaxies: formation – galaxies:
evolution – galaxies: star formation rate – galaxies: aperture corrections –
galaxies: metallicity

##  1 Introduction

Since the pioneering work of Lequeux et al. (1979), a plethora of papers have
studied the relation between metallicity and galaxy stellar mass, as well as
with other fundamental parameters of galaxies (e.g. Vila-Costas & Edmunds
1992; Garnett 2002; Pilyugin et al. 2004; Tremonti et al. 2004; Lee et al.
2006; Zahid et al. 2014; Sánchez et al. 2017; Maiolino & Mannucci 2019;
Sánchez 2020). In all of these works a clear correlation between total stellar
mass $\rm(M_{\star})$ and metallicity of galaxies was highlighted. The mass-
metallicity relation (MZR) thus remains a key ingredient for our understanding
of the formation and evolution of galaxies. Theoretical models predict a tight
relation (e.g. Mouhcine et al. 2008; Sakstein et al. 2011; Davé et al. 2011;
Romeo Velonà et al. 2013; Okamoto et al. 2017; De Rossi et al. 2017; Torrey et
al. 2018) illustrating how galaxy evolution is driven by galaxy mass,
modulated by gas accretion and outflows.

The MZR reaches a maximum near saturation at the high mass end
($\rm\log(M_{\star}/M_{\odot})\geq 10.5$), maintaining in a metallicity
asymptotically close to the oxygen yield (e.g. Pilyugin et al. 2007). The
study of this relation for galaxies of different masses can be used to better
ascertain if the MZR could be emerging from a local relationship within
galaxies or rather represents a truly global scale relation, e.g. linked to
galaxy mass. The overall shape of the MZR is believed to respond mainly to the
action of galactic winds and enriched outflows in addition to metal astration
driven by star formation and galaxy stellar mass, but other processes related
to e.g. galaxy downsizing or massive gas accretion and star formation can be
also involved (e.g. Finlator & Davé 2008).

Star formation rate (SFR) was originally introduced as a secondary parameter
of the MZR aiming at reducing the observed scatter, and in this way the so-
called fundamental mass – metallicity – SFR relation was defined (MZSFR; e.g.
Ellison et al. 2008; Mannucci et al. 2010; Lara-López et al. 2010b). In this
fundamental relation, at a fixed galaxy stellar mass, SFR anti-correlates with
metallicity, similarly to the predictions of some models about this possible
secondary dependence of MZR with SFR (e.g. Dayal et al. 2013). An intense
debate (e.g. Sánchez et al. 2013, 2017, 2019; Salim et al. 2014; Barrera-
Ballesteros et al. 2017; Cresci et al. 2019) has developed since then about
the existence or not of this second dependence on SFR. The observations of a
large number of galaxies obtained with integral field spectroscopy (IFS) in
CALIFA (Sánchez et al. 2012; García-Benito et al. 2015), and MANGA (Bundy et
al. 2015) surveys, or with integrated spectra by Hughes et al. (2013), reach
to different conclusions which prevent to understand the exact role played by
the SFR, and the possible evolution of MZSFR with redshift.

One of the key differences among the above cited studies, which we face in the
present work, is that the integrated galaxies analysis have been usually
performed using bright emission lines measured on single aperture spectroscopy
of galaxies (e.g. spectra SDSS, VVDS, zCOSMOS, DEIMOS) to derive the oxygen
abundance (O/H) of the ionised gas, as a proxy of galaxy metallicity; and the
SFR estimates for these galaxies were also derived from the same aperture
spectral information, with present-day SFRs often computed from the luminosity
of H$\rm\alpha$ emission. The aperture corrections are produced by incomplete
or partial coverage of the observed galaxies (e.g. SDSS 3 arcsec fibre
spectroscopy), and may produce critical effects, which must be corrected. IFS
of a large sample of galaxies of CALIFA has provided the method to correct the
emission lines by aperture and spatial sampling effects (Mast et al. 2014;
Gomes et al. 2016; Iglesias-Páramo et al. 2016). It has been shown that
aperture effects translate in clear flux deficits which, in the case of e.g.
SFR, imply corrections of up to $\sim$0.6 dex (Iglesias-Páramo et al. 2013;
Duarte Puertas et al. 2017); whereas model-based aperture corrections do not
solve this problem. In the case of the emission-line fluxes the situation is
not trivial, as they, and their corresponding extinction must be aperture
corrected before deriving SFR or the different abundance ratios. In
particular, differential extinction correction across the disks of galaxies
can not be overlooked. In Iglesias-Páramo et al. (2016) empirically CALIFA
based aperture corrections are provided for the relevant lines.

The SFR of galaxies can be also derived using multiparametric fitting of their
spectral energy distribution, using evolutionary population synthesis models
and inverting population synthesis equations (with their own uncertainties).
Recent spatially resolved studies using this last technique found a clear
correlation between O/H and SFR using the IFS CALIFA and MANGA data (e.g.
Cresci et al. 2019). However, according to Sánchez (2020), whether or not a
fundamental metallicity relation exists depends on the analysis of the data,
i.e., with the same CALIFA data set, Salim et al. (2014) found a dependence
between the sSFR and the metallicity not found by Sánchez et al. (2013), who
suggested that the MZSFR relation is an artifact of spectroscopy aperture
bias. On the other hand, Cresci et al. (2019) concluded that the method used
to calculate the stellar mass of galaxies, the other key ingredient in the
MZR, also affects the obtained results. To these considerations we need to add
that other research using IFS studied the relationship between O/H and other
parameters (e.g. Barrera-Ballesteros et al. 2018, 2020; Sánchez-Menguiano et
al. 2020) propose that there might be some dependence, even indirectly,
between gas-phase metallicity and stellar age at local and global scales. Both
questions are actually related, thus the study of a possible evolution of the
zero point and slope of the MZR with cosmic time and its dependence on SFR,
can shed light on how galaxies formed, were assembled and evolve, an also on
the infall and galactic wind phases of their chemical evolution. The MZR has
been extensively studied as a general scaling relation of star-forming
galaxies in the local Universe (e.g. Mannucci et al. 2010; Lara-López et al.
2010b; Kashino et al. 2016; Curti et al. 2020), as a function of galaxy
environment (e.g. Ellison et al. 2009; Petropoulou et al. 2011, 2012; Peng &
Maiolino 2014; Pilyugin et al. 2017), and in medium and high redshift surveys
(e.g. Brown et al. 2016; Hunt et al. 2016; Kojima et al. 2017). Some evolution
is expected for the shape or for the zero point of the MZR (e.g. Lara-López et
al. 2010a; Møller et al. 2013; Pilyugin et al. 2013); though, other works find
no significant evolution for the MZSFR (e.g. Mannucci et al. 2010; Cresci et
al. 2012).

Besides the above uncertainties, we have the well known issue of metallicity
derivation from spectroscopy in large samples, which has been discussed
elsewhere (e.g. Curti et al. 2017, and references therein). Since temperature
sensitive lines fluxes are not available for the huge majority of these
objects (e.g. in SDSS), abundance calibrations are applied to derive their
metallicity. Not all abundance calibrations appear equally reliable when they
are compared with oxygen abundances derived from the direct method. In fact,
recent abundance calibrations empirically calibrated provide an abundance
which, statistically, is typically within 0.2 dex uncertainty of the direct
value. In this respect, some support can be gained using complementary
versions of the MZR relation, e.g. using stellar metallicity derived either
from integrated young stellar populations (e.g. Gallazzi et al. 2005) or for
individual massive stars (e.g. Bresolin et al. 2016); or deriving O/H directly
from stacked spectra of mass-grouped star-forming galaxies (e.g. Andrews &
Martini 2013); also, replacing O/H by nitrogen-to-oxygen abundance (N/O), an
abundance ratio less dependent on electron temperature and a well known
“chemical clock” (e.g. Edmunds & Pagel 1978; Pilyugin et al. 2003; Mollá et
al. 2006) adding useful chemical evolution information. N/O also presents a
well-known relation with stellar mass (Pérez-Montero & Contini 2009), as for
high metallicity nitrogen has mainly a secondary origin, and as its derivation
does not depend on the excitation of the gas, the study of the mass vs N/O
relation (MNOR) can thus be very useful to better understand the zero-point
and the slope of the MZR. In addition the combined study of mass, SFR, and N/O
can also be used to better discriminate the dependence of metallicity with
SFR. In this work, the caveats mentioned above have been taken into account
for the metallicity derivation and analysis, and the corresponding sanity
checks have been performed when appropriate.

In summary, in order to carry out an in depth study of the relation between
MZR and SFR, we must address the systematic effects involved, as discussed in
Telford et al. (2016) and Cresci et al. (2019), as those associated to e.g.
signal-to-noise ratio (S/N), aperture effects, or the metallicity indicators
used, among others, which can affect the derivation of the MZR and any
possible dependence of MZR with SFR. This is the main objective of this work.
To do it, we benefit from the methodology and knowledge gained with the CALIFA
survey and apply it here to minimise systematic effects. Hence we examine in
detail the behaviour of the relation between MZR and SFR for a large and
complete sample of SDSS star-forming galaxies (see Duarte Puertas et al. 2017,
for details) using the total fluxes of their emission lines empirically
corrected by extinction and aperture effects in a consistent manner. We will
analyse the MZR and SFR relationships, studying in particular the role of the
age, using the parameter $\rm D_{n}(4000)$ as a proxy, of the stellar
populations of galaxies.

The structure of this paper is organised as follows: in Sect. 2 we describe
the data providing a description of the methodology used to select the
sample(Sect. 2.1). The methodology followed to derive all the parameters used
in this work is presented in Sect. 2.2. Main results and discussion are given
in Sect. 3. Conclusions are given in Sect. 4. Finally, supplementary material
has been added in Appendix A. Throughout the paper, we assume a Friedman-
Robertson-Walker cosmology with $\Omega_{\Lambda 0}=0.7$, $\Omega_{\rm
m0}=0.3$, and $\rm H_{0}=70\,km\,s^{-1}\,Mpc^{-1}$. We use the Kroupa (2001)
universal initial mass function (IMF).

##  2 Data and sample

###  2.1 The sample of galaxies

Our study is based on the catalogue of 209276 star-forming galaxies extracted
from SDSS-DR12 (Alam et al. 2015) and presented in Duarte Puertas et al.
(2017). The galaxies span a redshift (z) and stellar mass ranges of $\rm
0.005\leq z\leq 0.22$ and $\rm 8.5\leq\log{(M_{\star}/M_{\odot})}\leq 11.5$,
respectively. All the emission line fluxes (i.e.
$\rm[OII]{\lambda\lambda\,3727,\,3729}$, $\rm[OIII]{\lambda\,5007}$, $\rm
H\beta$, $\rm[NII]{\lambda\,6584}$, and $\rm H\alpha$),
$\rm\log{(M_{\star}/M_{\odot})}$, z, and $\rm D_{n}(4000)$111$\rm D_{n}(4000)$
corresponds to the narrow definition of the 4000 $\rm\AA$ break strength from
Balogh et al. 1999 that can be considered a proxy of stellar population age.
used in this work have been taken from Max-Planck-Institut für Astrophysik and
Johns Hopkins University (MPA-JHU) public catalogue222Available at
http://www.mpa-garching.mpg.de/SDSS/. (Kauffmann et al. 2003; Brinchmann et
al. 2004; Tremonti et al. 2004; Salim et al. 2007). From this catalogue we
have selected a subset of 194353 SDSS star-forming galaxies according to the
following criteria:

  * •

i) $\rm z\geq 0.02$. Due to the SDSS spectral range (3800-9200 $\rm\AA$), this
is the minimum redshift required to include and measure
$\rm[OII]{\lambda\lambda\,3727,\,3729}$; this emission lines are necessary to
derive the metallicity (see Sect. 2.2) from our spectra (Pilyugin et al. 2012;
Pérez-Montero et al. 2013).

  * •

ii) A S/N $\geq$ 3 is imposed for all the line fluxes used to derive O/H and
N/O.

For these objects, we will determine the oxygen and nitrogen-to-oxygen
abundances, following the prescriptions explained in Sect. 2.2. For the SFR,
we use aperture corrected measurements from the database of Duarte Puertas et
al. (2017).

###  2.2 Empirical aperture correction and chemical abundances

It is well known that the 3 arcsec diameter fibres in SDSS only cover a
limited region of galaxies in the low-z Universe (z $<$ 0.22). In order to
obtain the total SFR for all the galaxies in our sample we have used the
aperture corrected SFR values from Duarte Puertas et al. (2017), where a
detailed description of the aperture correction for the $\rm H\alpha$ flux
measurements in SDSS is presented.

The aperture corrections for the $\rm H\alpha$ flux and
$\rm\log([OIII]{\lambda\,5007}/H\beta)$,
$\rm\log([NII]{\lambda\,6584}/H\alpha)$, and $\rm H\alpha/H_{\beta}$ flux
ratios in our sample were performed using the prescriptions by Iglesias-Páramo
et al. (2016). These corrections were derived for a sample of disk galaxies in
the CALIFA survey, representative of different types and masses (Iglesias-
Páramo et al. 2016). The aperture correction recipe for
$\rm[OII]{\lambda\lambda\,3727,\,3729}$ has been also provided to us by
Iglesias-Páramo et al., private communication. Conversely, as shown in
Belfiore et al. (2016), the $\rm D_{n}(4000)$ break strength index remains
substantially constant across star-forming galaxies, given that their young
stellar component appears well distributed through out all the galactic disk;
hence no aperture correction was applied for it. In summary, for each galaxy
in our sample, the line fluxes measured in the SDSS fibres (i.e.
$\rm[OII]{\lambda\lambda\,3727,\,3729}$, $\rm[OIII]{\lambda\,5007}$, $\rm
H\beta$, $\rm[NII]{\lambda\,6584}$, and $\rm H\alpha$) were corrected for
extinction following Duarte Puertas et al. (2017), and then they were
aperture-corrected applying the equations in Table 20 of Iglesias-Páramo et
al. (2016). These emission line fluxes are necessary for the derivation of
oxygen and nitrogen abundances, as explained.

In order to derive the metallicity of our sample galaxies, given that the
faint temperature sensitive lines are not available, we must rely on bright
lines abundance calibrations (including from [OII], [OIII] to [NII]). It is
well known that some calibrations produce different absolute values of O/H;
especial care has been exercised in this work in the selection of the
abundance calibrations applied. We have used three different methods:

  1. 1.

We first follow the study updated by Curti et al. (2017) for O/H derivation
and have selected their calibration of O3N2 which presents the wider O/H
prediction range with the smallest dispersion.

  2. 2.

In addition, we have also adopted the empirical calibrations by Pilyugin &
Grebel (2016) for nitrogen (their eq. 13) and oxygen (their eqs. 4, 5)
abundances.

Table 1: Compiled data for our sample of star-forming galaxies. The whole table is available in electronic format. (1) | (2) | (3) | (4) | (5) | (6)
---|---|---|---|---|---
specObjID | 12+log(O/H) | log(N/O) | $\rm\log({M_{\star}})$ | log(SFR) | $\rm D_{n}(4000)$
|  |  | [$\rm M_{\odot}$] | [$\rm M_{\odot}\,yr^{-1}$] |
1399656635961468928 | 8.44$\pm$0.07 | -1.23$\pm$0.11 | 9.98${}^{+0.15}_{-0.12}$ | 0.86$\pm$0.02 | 1.45$\pm$0.17
1302792405518411776 | 8.16$\pm$0.07 | -1.38$\pm$0.06 | 9.95${}^{+0.32}_{-0.47}$ | -0.28$\pm$0.01 | 1.21$\pm$0.03
1302813296239339520 | 8.38$\pm$0.02 | -1.17$\pm$0.02 | 10.23${}^{+0.33}_{-0.48}$ | 0.32$\pm$0.01 | 1.19$\pm$0.03
1398489229004138496 | 8.53$\pm$0.02 | -0.79$\pm$0.05 | 10.64${}^{+0.11}_{-0.08}$ | 1.45$\pm$0.01 | 1.20$\pm$0.03
1399648389624260608 | 8.40$\pm$0.01 | -1.10$\pm$0.02 | 9.51${}^{+0.13}_{-0.08}$ | 0.34$\pm$0.01 | 1.12$\pm$0.05
… | … | … | … | … | …

Figure 1: a) Aperture corrected MZR. Star-forming galaxies of our sample (grey
dots), as well as the Milky Way (green mark) and other nearby galaxies
(labelled; coloured points) with direct (from electron temperature) oxygen
abundances are shown. Blue or red colour indicate galaxies with a flat or non-
zero radial oxygen gradient, respectively. _References as follows: galaxy
name, O/H reference, stellar mass reference; SMC, LMC, and M81, Bresolin et
al. (2016), Kudritzki et al. (2012); NGC 55, Magrini et al. (2017), Lee et al.
(2006); MW, Fernández-Martín et al. (2017); Arellano-Córdova et al. (2021),
Licquia & Newman (2015); M83, Bresolin et al. (2016); Hernandez et al. (2019),
Kang et al. (2016); M33 and NGC 300, Bresolin et al. (2016); Kang et al.
(2016); M 31, Zurita & Bresolin (2012), Fisher & Drory (2011); M 101, Croxall
et al. (2016), Skibba et al. (2011); NGC 628, Berg et al. (2015), Cook et al.
(2014) (see also Vílchez et al. 2019)_. b) Relation between 12+log(O/H) and
$\rm M_{\star}$ for SDSS star-forming galaxies, grey points. Overplotted blue,
green, red, cyan, magenta, lime, and yellow solid lines represent the fits to
the running median of the SFR of the galaxies, calculated in bins of 1000
galaxy points, corresponding to seven SFR intervals as indicated.

All these calibrations are empirical, i.e. they are calibrated against direct
abundances calculated with electron temperature measurements. Finally, we have
used the ones given by the code HII-CHI-mistry (Pérez-Montero 2014), based on
photoionization models, and which reproduce chemical abundances consistent
with their corresponding direct derivations333A known feature is that most
photoionisation model abundances are typically overestimated; while HII-CHI-
mistry abundances appear consistent with direct derivations. For the sake of
consistency to compare with previous and other works performed including
spectroscopy of distant galaxies, oxygen and nitrogen-to-oxygen abundances for
our sample galaxies have been derived with the three methods mentioned above
once they are free from aperture effects (given that the emission line fluxes
used were all aperture corrected), corresponding to the entire galaxy. We have
also derived the value of oxygen and nitrogen-to-oxygen abundances in fibre
and we have obtained that the values derived in the fibre, for O/H and N/O,
are systematically higher than those aperture corrected. The mean oxygen
abundance difference between the fibre and the value corrected for aperture,
$\Delta$(12+log(O/H)), is 0.04 dex (the standard deviation is 0.01 dex) for
our sample of star-forming galaxies. In the case of the mean nitrogen-to-
oxygen abundance difference, $\rm\Delta$(log(N/O)), we have found a value of
0.06 dex (the standard deviation is 0.01 dex). All the abundances obtained for
each object resulted consistent within the errors, and overall, the three
abundance outputs from the calibrations selected (and values in the fibre) are
statistically consistent to within $\sim$0.15 dex; with the higher consistency
and lowest errors being achieved especially for the nitrogen to oxygen
abundance ratio. Taking this fact into account, in this work we adopt for each
galaxy as representative the O/H and N/O abundances obtained applying Pilyugin
& Grebel (2016). As a result, we have compiled Table 1 where we show a sample
of the online table of 194353 star-forming galaxies, where their fluxes have
been aperture-corrected, for which we have the spectroscopic identifier from
SDSS (specObjID), oxygen, as 12+log(O/H), and nitrogen-to-oxygen abundance
ratio, as log(N/O), abundances, stellar mass, as
$\rm\log{(M_{\star}/M_{\odot})}$, the SFR (in $\rm M_{\odot}\,yr^{-1}$ units),
and the parameter $\rm D_{n}(4000)$ that we use as the stellar population age
indicator. Table 1 also shows the uncertainties for each property
considered.444The uncertainties of $\rm\log{(M_{\star}/M_{\odot})}$ and $\rm
D_{n}(4000)$ have been taken from MPA-JHU.

##  3 Discussion

In Fig. 1, panel a, we show the oxygen abundance, $\rm 12+log(O/H)$, versus
total stellar mass for the 194353 galaxies in our sample, which clearly
reproduce the MZR relation. A further quality check of our MZR derivation can
be done comparing it with the oxygen abundance and total stellar mass555NGC
55, NGC 300, and M 33 stellar masses transformed from Chabrier (2003) to
Kroupa (2001) IMF dividing by 0.943 (Mannucci et al. 2010). for the Milky
Way666An effective radius face value of 5.9 kpc was assumed for the Milky Way
(Sackett 1997; Yin et al. 2009). and ten well known nearby galaxies for which
precise abundance values of their Hii regions have been derived using the
direct method from available electron temperature measurements. These nearby
galaxies show well defined spatially resolved radial abundance gradients, thus
their representative abundance, corresponding to the integrated galaxy flux
can be easily derived using the IFS measurements in the CALIFA survey. To do
so we use the O/H measured in the characteristic radius (0.4$\times$ R25,
basically similar to the effective radius of the galaxy, e.g. Sánchez et al.
2013), the most suitable representative value of the whole galaxy abundance.
According to Sánchez et al. (2013), for galaxies presenting $\rm 12+log(O/H)$
abundance at the effective radius, $\rm 12+log(O/H)_{Reff}$ $\leq$ 8.6 dex,
the mean difference between $\rm 12+log(O/H)$ of the integrated galaxy flux
and $\rm 12+log(O/H)_{Reff}$ is $\rm\sim$-0.03 dex; whereas for galaxies with
$\rm 12+log(O/H)_{Reff}$ above 8.6 dex, this difference amounts to
$\rm\sim$0.06 dex. We have applied this conversion to calculate the
representative $\rm 12+log(O/H)$ abundances of our selected nearby galaxies;
these objects are also shown in Fig. 1 panel a. It can be seen that the
selected sample of nearby galaxies and our sample of SDSS star-forming
galaxies show an excellent agreement delineating the local universe MZR, free
from aperture effects, derived in this work. As mentioned in Section 2.2, we
have derived (and compared) the O/H values using the empirical calibrations
from Pilyugin & Grebel (2016); Pérez-Montero & Contini (2009), the direct
method by using the electron temperature for objects with auroral line
measurements, and the theoretical photoionisation models (HII-CHI-mistry) from
Pérez-Montero (2014). All these methods lead to overall consistent abundances
-within the errors- and the differences between them have already been
discussed. In Fig. 9 it can be seen that all galaxies where the electron
temperature has been calculated show a high consistency between the O/H from
the direct method and the corresponding values obtained in this work using
empirical calibrators. Therefore we consider that the oxygen abundances used
are precisely estimated and better than others in the literature.

As we also want to see the role of the SFR in the MZR relation, we show in
panel b) of Fig. 1 the diagram for the same MZR as in panel a), but
overplotting the lines representing the fits to the running medians of seven
different SFR intervals. The strong correlation between oxygen abundance and
galaxy stellar mass, shown in the MZR plot, is also evident in all the shown
SFR lines separately. We can see also how these iso-SFR loci tend to saturate
at higher abundances and level off near solar metallicity777Solar metallicity:
$\rm 12+\log(O/H)_{\odot}=8.69$ (Asplund et al. 2009).. We may also see that
for a fixed $\rm\log(M_{\star}/M_{\odot})$, galaxies with a higher metallicity
present lower SFR than lower metallicity galaxies, in line with previous
findings (e.g. Mannucci et al. 2010).

We now analyse the relationship between the abundances and the SFR. In panel
a) of Fig. 2, we show our aperture corrected oxygen abundances, as $\rm
12+log(O/H)$, versus the SFR for the galaxy sample (grey points) following the
same statistical procedure as in the previous figure. We computed the running
medians for six intervals of $\rm\log{(M_{\star}/M_{\odot})}$ with
$\rm\Delta\log{(M_{\star}/M_{\odot})}=0.5$ dex each (see also Figure 10).
Their corresponding fits are plotted by black-dotted lines. The total covered
range in galaxy stellar mass is $\rm 8.5\leq\log{(M_{\star}/M_{\odot})}\leq
11.5$ in both panels. The overlaid colour dashed lines show the fits to the
running median of the $\rm D_{n}(4000)$ index of the sample galaxies,
calculated for six intervals from $\rm D_{n}(4000)<1.1$ to $\rm
D_{n}(4000)\sim 1.5$, with $\rm\Delta D_{n}(4000)=0.1$ dex each, as indicated
in the plot; in parenthesis the total number of points per interval is quoted.
We can see a clear overall trend between 12 + log(O/H) against SFR in our
sample (grey points). In panel b) of the same Fig. 2 we similarly show the
aperture corrected $\rm log(N/O)$ versus SFR. There, we have again the $\rm
log(N/O)$ versus SFR considering the same galaxy mass and $\rm D_{n}(4000)$
bins, and fits to the running median. A similar strong correlation is also
present between these two properties. A wide range in $\rm log(N/O)$ is
covered by our SDSS galaxy sample, going from over-solar888Solar
log(N/O)${}_{\odot}=-0.86$ (Asplund et al. 2009; Tsamis et al. 2011). values
to the level typical of low metallicity dwarf galaxies ($\rm log(N/O)\sim$
-1.5). All the lines shown in Fig. 2 (i.e. black for stellar mass and coloured
for $\rm D_{n}(4000)$) are representing the real statistical (median) loci of
the galaxy points and they are the result of the fit to the statistical
distribution of the properties considered (i.e. $\rm D_{n}(4000)$, stellar
mass, and O/H) for the SDSS star-forming galaxies sample used in this work.

Figure 2: a) Relation between the 12+log(O/H) and SFR corrected for aperture
for star-forming galaxies. Blue, green, red, cyan, magenta, and yellow solid
lines represent the fits to the running median for bins of 1000 objects in six
$\rm D_{n}(4000)$ bins. The number of star-forming galaxies in each $\rm
D_{n}(4000)$ bin appear on the legend. Black dash doted lines show the
12+log(O/H) vs. SFR values of the running median fits for bins of 1000 objects
in six $\rm\log{(M_{\star}/M_{\odot})}$ bins (each box shows the considered
$\rm\log{(M_{\star}/M_{\odot})}$ range). b) Relation between the log(N/O) and
SFR for star-forming galaxies (colours and numbers of star-forming galaxies in
each $\rm D_{n}(4000)$ bins as in a).

It is important to bear in mind that $\rm D_{n}(4000)$ depends on stellar
population age, presenting lowest values for the youngest stellar populations,
while the older ones show higher values (Balogh et al. 1999). In panels a) and
b) of Fig. 2 we can see how for a fixed $\rm\log{(M_{\star}/M_{\odot})}$,
galaxies with lower SFR present systematically higher values of $\rm
D_{n}(4000)$, suggesting that they host older stellar populations. For $\rm
D_{n}(4000)>1.2$, we can see that the lines corresponding to the most massive
galaxies ($\rm\log{(M_{\star}/M_{\odot})}>10.5$) tend to saturate, and seem to
flatten above $\rm 12+\log{(O/H)}\geq$ 8.55 and $\rm\log{(N/O)}\geq$ -0.9,
irrespective of their SFR. For nearly the entire mass range of the sample
($\rm\log{(M_{\star}/M_{\odot})}\leq 11$), oxygen abundance, $\rm
12+\log{(O/H)}$, shows a nearly flat or very mild decrease with respect to SFR
along the black-dotted lines. Although the usual assumption is that SFR
depends on age, showing an anticorrelation between stellar age and SFR when
the stellar mass is taken into account, actually we show in this plot that
both effects are disentangled. In Fig. 3 we have plotted the SFR as a function
of $\rm D_{n}(4000)$ to see more clearly this SFR-age effect. In this figure,
we see that at face value there is a correlation between high SFR and high
$\rm D_{n}(4000)$ values. Then, we overplotted the mass isolines and O/H
isolines for six stellar mass bins and six O/H ranges, respectively, for our
sample of SDSS star-forming galaxies. We can see how: i) at a fixed SFR the
corresponding entire range of $\rm D_{n}(4000)$ is covered; ii) at fixed
stellar mass, the lower the SFR, the higher the $\rm D_{n}(4000)$; and iii) at
fixed O/H we see that the relationship is more complex: from $\rm
D_{n}(4000)\sim 1.2$ towards the right, for O/H $<$ 8.5 the SFR stops
decreasing with $\rm D_{n}(4000)$. For the left region, however, the
anticorrelation between SFR and $\rm D_{n}(4000)$ is very strong. We consider
this relationship to be relevant and deserving of further exploration with our
sample of star-forming galaxies.

Figure 3: Relation between the SFR and $\rm D_{n}(4000)$ for our sample of
star-forming galaxies. Blue, green, red, cyan, magenta, and yellow solid lines
represent the running median for bins of 2000 objects in six O/H bins. Black
dash doted lines show the fit to the running median for bins of 1000 objects
in six $\rm\log{(M_{\star}/M_{\odot})}$, bins, from low stellar mass (8.5,
lower part of the figure) to high stellar mass (11.5, higher part of the
figure).

Depending on the stellar mass range, there is a value of SFR for which a
change in O/H is observed. This SFR value varies depending on the stellar mass
range considered. The iso-$\rm D_{n}(4000)$ line between [1.1-1.2) accompanies
the change in the O/H – SFR relation depending on the stellar mass, which
suggests that this line determines a statistical value for stellar mass, SFR,
and age.999This iso-$\rm D_{n}(4000)$ line around 1.1-1.2, as the others, is
derived as the statistical median of galaxies with $\rm D_{n}(4000)$ values
between 1.1 and 1.2. It is therefore the geometric locus of SDSS star-forming
galaxies within these $\rm D_{n}(4000)$ values. The data do not allow us to
say the exactly age where the slope of these iso-mass lines change in the
O/H-SFR diagram, but our results allow us to say that it must occur around
that $\rm D_{n}(4000)$ value (i.e. in the green line). Therefore, in order to
address this point, we have proceeded as follows:

  * •

We derived $\rm\frac{dO/H}{dSFR}\Bigr{\rvert}_{M_{\star}}$, i.e. the
derivative of O/H versus SFR at constant stellar mass, along all iso-mass
lines below the range 10 $\leq$ log(M⋆/M⊙) $<$ 10.5; (that means for four iso-
mass lines).

  * •

We obtain the value of log(SFR) for which the derivative presents the net
measurable change, $\rm log(SFR_{deri})$, with a minimum value of $-0.002$,
the half of the value obtained for the iso-mass line of the range 8.5 $\leq$
log(M⋆/M⊙) $<$ 9.0; That is the point where the slope starts to be steeper
(and negative) than this value.

  * •

The iso-mass line corresponding to this lowest mass range plotted shows a
nearly constant derivative, approximately a straight line in the plot without
any apparent change in its slope; therefore, any change in the derivative of
this iso-mass line should have occurred for $\rm\log{(SFR)}<-1.5$
(alternatively, there exists no such change in the derivative of the sub-
sample of SDSS galaxies in these stellar mass and SFR range or it is small and
we cannot statistically “see” it)

  * •

We determine $\rm\log(SFR_{cut})$ as the SFR value at which each iso-$\rm
D_{n}(4000)$ line cut each iso-mass line in the O/H vs. SFR diagram in Fig. 2.

  * •

Then we compute the difference between $\rm\log{(SFR_{cut})}$ and
$\rm\log{(SFR_{deri})}$, as
$\rm\Delta\log{(SFR)}=\log{(SFR_{cut})}-\log{(SFR_{deri})}$, for each iso-mass
line. Since the iso-$\rm D_{n}(4000)$ line between 1.2 and 1.3 does not
intersect the $\rm 8.5\leq log(M_{\star}/M_{\odot})<9.0$ iso-mass line in the
O/H vs SFR diagram, we assume the position in this diagram at which it would
intersect by extrapolating slightly the iso-$\rm D_{n}(4000)$ line for the
sake of this test.

Figure 4: Relation between $\rm\Delta\log{(SFR)}$ and the iso-$\rm
D_{n}(4000)$ ranges. The symbols are colour-coded depending on the $\rm
D_{n}(4000)$ range and according to Fig. 2, being $\rm D_{n}(4000)<1.1$
(blue), $\rm 1.1\leq D_{n}(4000)<1.2$ (green), $\rm 1.2\leq D_{n}(4000)<1.3$
(red), $\rm 1.3\leq D_{n}(4000)<1.4$ (cyan), and $\rm 1.4\leq D_{n}(4000)<1.5$
(magenta). The symbol type is related to $\rm\rm\log{(M_{\star}/M_{\odot})}$
range considered, as labelled. For the stellar mass range 8.5-9.0 (circles)
only a lower limit, if any, for $\rm\Delta\log{(SFR)}$ could be assumed from
the present SDSS sample, leading to $\rm\log{(SFR)}<-1.5$. In the case of the
iso-$\rm D_{n}(4000)$ line $\rm 1.2\leq D_{n}(4000)<1.3$, the value of the
intersect position has been derived extrapolating slightly this iso-$\rm
D_{n}(4000)$. The mean value of $\rm\Delta\log{(SFR)}$ for each iso-$\rm
D_{n}(4000)$, considering all the iso-masses, is shown in the coloured numbers
(only lower limits of $\rm\Delta\log{(SFR)}$ for the $\rm 8.5\leq
log(M_{\star}/M_{\odot})<9.0$ mass range are not considered). The black dotted
line indicates $\rm\Delta\log{(SFR)}=0$.

We show in Fig. 4 the resulting $\rm\Delta\log{(SFR)}$ for the different
stellar mass ranges we have considered, as a function of the iso-$\rm
D_{n}(4000)$ ages. The symbols are coloured-code according to the colour of
the iso-$\rm D_{n}(4000)$ lines of Fig. 2. We see as the green points show the
closest values to $\rm\Delta\log{(SFR)}=0$. The mean value of
$\rm\Delta\log{(SFR)}$= 0.72, 0.14, -0.35, -0.75, and -1.02 for galaxies in
the $\rm D_{n}(4000)$ ranges $<1.1$, [1.1-1.2), [1.2-1.3), [1.3-1.4) and
[1.4-1.5), respectively. The difference is proportionally larger as we move
away from the iso-$\rm D_{n}(4000)$ with values between 1.1 and 1.2 (green
line), i.e., this iso-$\rm D_{n}(4000)$ line is the one with values of
$\rm\Delta\log{(SFR)}$ closest to zero in all iso-masses considered in this
figure. From this, we may consider that the iso-$\rm D_{n}(4000)$ line for
$\rm 1.1\leq D_{n}(4000)<1.2$ (green line in Fig. 2) represents the best
approximation to the locus where the change of the relation between oxygen
abundance and SFR is observed, for each stellar mass range and given SFR.
Before this line, for $\rm D_{n}(4000)$ larger than 1.2, the slope of each
O/H-SFR iso-mass line may be considered flat as its absolute value is smaller
than 0.002.

This way, for all galaxies with stellar mass
$\rm\log{(M_{\star}/M_{\odot})}\leq 10.5$, the green iso-$\rm D_{n}(4000)$
line defines, de facto, an effective isochrone, which marks the locus of the
sudden change in the derivative of oxygen abundance against SFR in the sample
galaxies. This plot may illustrate why the case for a universal negative
relation between oxygen abundance and SFR is still controversial for some
samples of galaxies. The exact region in which the negative slope of the
metallicity – SFR relation may hold varies for each stellar mass range; a
negative dependence of metallicity on SFR could be seen for a given galaxy
mass range but only for those galaxies hosting the youngest stellar population
(i.e. $\rm D_{n}(4000)\leq 1.1$). A similar behaviour can be observed in panel
b) for $\rm\log{(N/O)}$. Again for galaxies with
$\rm\log{(M_{\star}/M_{\odot})}\lesssim 11$ there is a mild, if any,
dependence of $\rm\log{(N/O)}$ on SFR, except when the green iso-$\rm
D_{n}(4000)$ line is reached. Beyond this point, moving towards larger SFR for
a fixed stellar mass (i.e. along dash-dotted lines), a strong negative
dependence of $\rm\Delta\log{(N/O)}/\Delta\log{SFR}$ is evident. The value of
$\rm\log{(N/O)}$ at which these changes in the slope can be seen from the
typical values in dwarf galaxies up to the solar $\rm\log{(N/O)}_{\sun}$. The
similar behaviour exhibited by the oxygen abundance and the nitrogen-to-oxygen
abundance ratio against SFR, shown in both panels of Fig. 2, respectively, can
give us some hints to understand the chemical evolution of our sample galaxies
and the origin underlying of the MZRSFR relationship.

We have found respective loci in the planes $\rm 12+\log{(O/H)}$ – SFR and
$\rm\log{(N/O)}$ – SFR delimiting two broad regions domains in these diagrams
for the sample galaxies, in one of them the sample galaxies show a clear
dependence of metallicity on the SFR, whereas in the corresponding
complementary region no dependence is seen, along each galaxy stellar mass
sequence. These loci appear well represented on each plot by the line
corresponding to galaxies with $\rm D_{n}(4000)<1.2$, for which a mean stellar
age younger than 150 Myr is expected (Mateus et al. 2006). Along these two
loci lines, it seems that the precise oxygen abundance (N/O ratio) and SFR,
for each galaxy stellar mass (i.e. specific SFR) appear to be tuned101010By
tuned, we refer that the stellar age accompanies and it has to be taken into
account in the mass-metallicity-SFR relation., defining, de facto, the
effective isochrone corresponding to the average stellar population for each
galaxy. This applies only to galaxies with
$\rm\log{(M_{\star}/M_{\odot})}\lesssim 10.5$; for more massive galaxies we do
not observe this behaviour in our sample, since the lines of the $\rm
D_{n}(4000)$ index converge at high metallicity (near solar to oversolar), and
O/H and N/O do not show here observable decrease, suggesting an evolution
without metallicity loss and mainly driven by galaxy mass.

In Fig. 5 we show the MZSFR relation for the star-forming galaxies with $\rm
D_{n}(4000)<1.2$ (panel a) and $\rm D_{n}(4000)\geq 1.2$ (panel b). From this
figure, it can be seen that galaxies with young and old stellar populations
are located in different domains in the MZSFR three dimensional diagram. As
expected, galaxies with younger stellar populations ($\rm D_{n}(4000)<1.2$,
represented as blue dots in the figure) are located in the zone where SFR is
higher, at a fixed 12+log(O/H). In contrast, galaxies with older stellar
populations ($\rm D_{n}(4000)\geq 1.2$, represented as red dots in the figure)
fall in the area where SFR is lower, at fixed 12+log(O/H). This plot has,
however, a large dispersion, and therefore, we have analysed this possible
dependence of the OH on SFR and on the stellar age from other point of view by
using the classical method of representing residuals of a correlation as a
function of other parameters. Thus, we plot three panels in Fig. 6. In the
first one at the left, the MZR relation is drawn with a polynomial fit
overplotted and, at the bottom, the residuals of this relation. In the middle
panel, these same residuals are plotted as a function of the SFR, with a
least-square straight line overplotted and the corresponding residuals at the
bottom. These residuals, within $\pm 0.2$ dex, are represented as a function
of the $\rm D_{n}(4000)$ parameter in the right panel, where again a
correlation appears. This way, a third parameter, the age, besides the stellar
mass and the SFR, arises clearly as something to take into account in the
analysis of the MZR-SFR. In fact, in this last panel, a fit with two straight
lines may be also acceptable since, as we claim before, for $\rm
D_{n}(4000)>1.2$ the correlation is almost flat, while a strong slope would
appear in the younger objects with $\rm D_{n}(4000)<$ 1.2.

Figure 5: MZSFR for star-forming galaxies corrected for aperture. Colour-coded
star-forming galaxies with $\rm D_{n}(4000)<1.2$ (blue in panel a, represented
as grey in panel b) and $\rm D_{n}(4000)\geq 1.2$ (red in panel b, represented
as grey in panel a). Note the scale of the SFR axis decreases towards the
right in the figures. Figure 6: a) MZSFR for our sample of galaxies,
overplotted a line with a polynomial fit to these results. In the bottom the
residuals data-fit, $\rm OH-OH_{fit,M}$ are represented as a function of the
stellar mass; b) These residuals of $\rm OH-OH_{fit,M}$ as a function of the
SFR with a minimum straight line fitting the points. The residual of this fit
are represented at the bottom as a function of SFR: c) The residual of the
later fit, $\rm OH-OH_{fit,M}-Res_{fit,SFR}$ as a function of the parameter
$\rm D_{n}(4000)$. In the upper panels, the correlation coefficients for each
fit are shown in the top right.

Interestingly, a direct consequence of the above findings has been the
selection of a sub-sample of galaxies which populate the youngest part of the
two diagrams of Fig. 2. This group of (8598) galaxies are “outliers” of the
sample, and cluster around the iso-line $\rm D_{n}(4000)<1.1$, on average in
both panels of Fig. 2. It is for this group of very young galaxies for which
the largest changes in the slopes of the O/H vs. SFR relation are observed
(similar for N/O vs. SFR). The galaxies in this group are mainly but not only
dwarf galaxies, they sample a range in galaxy stellar masses, as shown; but
always showing the largest SFR measured for its stellar mass. This is easily
appreciated in Fig. 7 where the relation between SFR and M⋆ for our sample of
SDSS star-forming galaxies is presented; galaxies are colour coded according
to the Dn(4000) parameter. In this figure it can be seen that, for a fixed SFR
nearly the entire range of Dn(4000) is covered, where the parameter Dn(4000)
increases as the stellar mass increases, i.e. more massive galaxies have
higher Dn(4000) values than less massive ones. Similarly, for each fixed
stellar mass, a range in SFR is observed where the largest SFR corresponds to
the youngest objects.

In order to explore the nature of these 8598 galaxies we have performed a
sanity check in Appendix A to confirm their metallicity and SFR, (see Figures
11, 12, and 13) and to gain more insight into the nature of this sub-sample of
galaxies. We have checked that the abundances and SFR derived for these
galaxies were not affected by aperture corrections, performing a particular
study of this subsample.

Figure 7: Relation between SFR and M⋆ for star-forming galaxies colour coded
according to the Dn(4000) parameter (left panel) and its corresponding
confidence limits from 1$\sigma$ to 3$\sigma$ (right panel). All the points
and contours of Dn(4000) parameter in the figures have the same colours as
Fig. 2.

In Fig. 8 we summarise all the results concerning to O/H, SFR and age of the
stellar populations, making use of the “population box” Dn(4000) – SFR –
12+log(O/H) three dimensional diagram, where values found for the star-forming
galaxies are colour-coded according to the M⋆ of each galaxy as shown. A clear
correlation between Dn(4000), SFR and 12+log(O/H) has been found. Galaxies
with Dn(4000) values $<$ 1.2 span the range of stellar masses
$\rm\log{(M_{\star}/M_{\odot}})$ = 8.5 to 11.5, where the majority of the
sample galaxies have stellar masses less than $\sim$ 10.5. The less massive
galaxies ($\rm\log{(M_{\star}/M_{\odot})}\lesssim 9$) mostly have values of
Dn(4000) less than 1.2, and, as expected, have the lowest 12+log(O/H). On the
other hand, the most massive galaxies ($\rm\log{(M_{\star}/M_{\odot})}\gtrsim$
11) are those with the highest 12+log(O/H) values (solar metallicity) and have
Dn(4000) values higher than 1.1, although most galaxies have values above 1.2.
According to the SFR–M⋆ relation, the higher the stellar mass, the higher the
SFR.

Figure 8: Population box (Dn(4000) – SFR – 12+log(O/H) diagram) for our sample
of star-forming galaxies colour coded by M⋆.

The apparent metallicity – SFR anticorrelation appears to be controversial in
the literature; this relation has been interpreted as the consequence of a
possible selection effect, and/or possibly resulting from the existence of
massive infall of mainly metal poor gas on these galaxies, which would produce
a strong enhancement of the SFR and, as a consequence, should dilute the
metallicity of the interstellar medium (ISM) (Ellison et al. 2008; Mannucci et
al. 2010; Yates et al. 2012) giving rise to an anticorrelation between $\rm
12+log(O/H)$ and SFR. This picture seems to be supported by some theoretical
work (e.g. Sakstein et al. 2011; Dayal et al. 2013). Though recent
observational work has questioned this scenario. We have shown in this work a
deep and complex relation between the MZR and SFR which appears to be tuned to
the mean age of the galaxy stellar population. The anticorrelation found
between oxygen abundance and SFR appears to be significant only for those
galaxies hosting the youngest stellar populations. The massive infall
scenario, could be invoked to explain these high SFR objects; however for
these galaxies we can see that $\rm log(N/O)$ – SFR also anticorrelate,
suggesting a framework more complex than the standard infall scenario where
$\rm N/O$ should not be much affected. Further deep spectroscopic observations
of the extreme SFR sub-sample could provide valuable information to in order
to understand the evolution of this very active star-forming galaxies.

##  4 Summary and conclusions

In this work we have derived O/H and N/O corrected for aperture effects. These
empirical aperture corrections are based on the sample of 165 spiral galaxies
from the CALIFA project Iglesias-Páramo et al. (2016). We studied the O/H –
SFR and N/O – SFR relations, as well as their relation with the parameter
Dn(4000), a proxy of the age of the stellar populations of the galaxies. We
compared the location in the SFR – M⋆ and MZSFR diagrams of the star-forming
galaxies according to its value of the Dn(4000) for each galaxy.

Our main conclusions are the following:

  1. i)

A robust stellar mass – metallicity relation (MZR) locus has been derived
consistent with the “anchoring” points of a selected set of well studied
nearby galaxies with a direct derivation of abundance. A complex relation
between MZR and SFR across the whole range of galaxy mass and metallicity has
been observed, showing a pattern of slope changes of the MZR – SFR relation in
the O/H versus SFR plane, which appears tuned to the age of the stellar
population of the galaxies.

  2. ii)

From the study of the relation between the MZR and SFR, a new dependence
between O/H – SFR has been found with the age of the galaxies’ stellar
populations. The dependence between the MZR and SFR is strong mainly for star-
forming galaxies with high SFR and low $\rm D_{n}(4000)$. Galaxies with older
stellar populations ($\rm D_{n}(4000)\geq 1.2$) and massive (log(M⋆/M⊙)
$\gtrsim$ 10.5) tend to saturate, and seem to flatten in the O/H – SFR
relation when 12+log(O/H) $\geq$ 8.55, irrespective of their SFR; which
indicates that the metallicity remains constant only depending on the stellar
mass of these massive galaxies. We also observe a dependence between N/O – SFR
with the age of the galaxies’ stellar populations, where those galaxies with
oldest stellar populations and massive seem to flatten when log(N/O) $\geq$
-0.9.

  3. iii)

On the contrary, for galaxies with younger stellar populations ($\rm
D_{n}(4000)<1.2$), a negative dependence has been found between O/H and SFR
(also for N/O and SFR) for less massive galaxies (log(M⋆/M⊙) $\lesssim$ 10.5).
This anticorrelation has been interpreted as the existence of massive infall
of mainly metal poor gas on the galaxies, which would produce a strong
enhancement of the SFR and, as a consequence, should dilute the metallicity of
the interstellar medium (ISM).

  4. iv)

This negative dependence found between O/H and SFR for galaxies with younger
stellar populations holds in a metallicity range from typical dwarf values to
solar values, covering a wide range of stellar masses, suggesting that
galaxies with young stellar populations are not only composed of dwarf
galaxies. These young galaxies of our SDSS sample always show the highest SFR
measured for their stellar mass.

  5. v)

Galaxies with young and old stellar populations are located in different
domains in the three dimensional MZSFR diagram: i) galaxies with younger
stellar populations ($\rm D_{n}(4000)<1.2$) are located in the zone where SFR
is higher, at fixed 12+log(O/H); and ii) galaxies with older stellar
populations ($\rm D_{n}(4000)\geq 1.2$) fall in the area where SFR is lower,
at fixed 12+log(O/H).

We have found a population of outliers galaxies in the O/H – SFR relation (and
also in the N/O – SFR relation), with young stellar population ages. Further
characterisation of the physical and chemical properties of these galaxies is
necessary to understand how they evolve chemically and to unravel the O/H and
N/O relation for these galaxies.

###### Acknowledgements.

We thank the anonymous referee for very constructive suggestions that have
helped us to improve this manuscript. SDP is grateful to the Fonds de
Recherche du Québec - Nature et Technologies. SDP, JVM, JIP, CK, and EPM
acknowledge financial support from the Spanish Ministerio de Economía y
Competitividad under grants AYA2016-79724-C4-4-P and PID2019-107408GB-C44,
from Junta de Andalucía Excellence Project P18-FR-2664, and also acknowledge
support from the State Agency for Research of the Spanish MCIU through the
‘Center of Excellence Severo Ochoa’ award for the Instituto de Astrofísica de
Andalucía (SEV-2017-0709). L.S.P acknowledges support within the framework of
the program of the NAS of Ukraine Support for the development of priority
fields of scientific research (CPCEL 6541230). I.A.Z acknowledges support by
the National Academy of Sciences of Ukraine under the Research Laboratory
Grant for young scientists No. 0120U100148.
Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the
Participating Institutions, the National Science Foundation, and the U.S.
Department of Energy Office of Science. The SDSS-III web site is
http://www.sdss3.org. This study makes use of the results based on the Calar
Alto Legacy Integral Field Area (CALIFA) survey (http://califa.caha.es/). This
research made use of Python (http://www.python.org) and IPython (Pérez &
Granger 2007); APLpy (Robitaille & Bressert 2012); Numpy (Van Der Walt et al.
2011); Pandas (McKinney 2010); of Matplotlib (Hunter 2007), a suite of open-
source Python modules that provides a framework for creating scientific plots.
This research made use of Astropy, a community-developed core Python package
for Astronomy (Astropy Collaboration et al. 2013). The Astropy web site is
http://www.astropy.org.

## References

  * Alam et al. (2015) Alam, S., Albareti, F. D., Allende Prieto, C., et al. 2015, ApJS, 219, 12
  * Andrews & Martini (2013) Andrews, B. H. & Martini, P. 2013, ApJ, 765, 140
  * Arellano-Córdova et al. (2021) Arellano-Córdova, K. Z., Esteban, C., García-Rojas, J., & Méndez-Delgado, J. E. 2021, MNRAS, 502, 225
  * Asplund et al. (2009) Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481
  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33
  * Balogh et al. (1999) Balogh, M. L., Morris, S. L., Yee, H. K. C., Carlberg, R. G., & Ellingson, E. 1999, ApJ, 527, 54
  * Barrera-Ballesteros et al. (2018) Barrera-Ballesteros, J. K., Heckman, T., Sánchez, S. F., et al. 2018, ApJ, 852, 74
  * Barrera-Ballesteros et al. (2017) Barrera-Ballesteros, J. K., Sánchez, S. F., Heckman, T., Blanc, G. A., & The MaNGA Team. 2017, ApJ, 844, 80
  * Barrera-Ballesteros et al. (2020) Barrera-Ballesteros, J. K., Utomo, D., Bolatto, A. D., et al. 2020, MNRAS, 492, 2651
  * Belfiore et al. (2016) Belfiore, F., Maiolino, R., Maraston, C., et al. 2016, MNRAS, 461, 3111
  * Berg et al. (2015) Berg, D. A., Skillman, E. D., Croxall, K. V., et al. 2015, ApJ, 806, 16
  * Bresolin et al. (2016) Bresolin, F., Kudritzki, R.-P., Urbaneja, M. A., et al. 2016, ApJ, 830, 64
  * Brinchmann et al. (2004) Brinchmann, J., Charlot, S., White, S. D. M., et al. 2004, MNRAS, 351, 1151
  * Brown et al. (2016) Brown, J. S., Martini, P., & Andrews, B. H. 2016, MNRAS, 458, 1529
  * Bundy et al. (2015) Bundy, K., Bershady, M. A., Law, D. R., et al. 2015, ApJ, 798, 7
  * Chabrier (2003) Chabrier, G. 2003, ApJ, 586, L133
  * Cook et al. (2014) Cook, D. O., Dale, D. A., Johnson, B. D., et al. 2014, MNRAS, 445, 899
  * Cresci et al. (2019) Cresci, G., Mannucci, F., & Curti, M. 2019, A&A, 627, A42
  * Cresci et al. (2012) Cresci, G., Mannucci, F., Sommariva, V., et al. 2012, MNRAS, 421, 262
  * Croxall et al. (2016) Croxall, K. V., Pogge, R. W., Berg, D. A., Skillman, E. D., & Moustakas, J. 2016, ApJ, 830, 4
  * Curti et al. (2017) Curti, M., Cresci, G., Mannucci, F., et al. 2017, MNRAS, 465, 1384
  * Curti et al. (2020) Curti, M., Mannucci, F., Cresci, G., & Maiolino, R. 2020, MNRAS, 491, 944
  * Davé et al. (2011) Davé, R., Finlator, K., & Oppenheimer, B. D. 2011, MNRAS, 416, 1354
  * Dayal et al. (2013) Dayal, P., Ferrara, A., & Dunlop, J. S. 2013, MNRAS, 430, 2891
  * De Rossi et al. (2017) De Rossi, M. E., Bower, R. G., Font, A. S., Schaye, J., & Theuns, T. 2017, MNRAS, 472, 3354
  * Duarte Puertas et al. (2017) Duarte Puertas, S., Vilchez, J. M., Iglesias-Páramo, J., et al. 2017, A&A, 599, A71
  * Edmunds & Pagel (1978) Edmunds, M. G. & Pagel, B. E. J. 1978, MNRAS, 185, 77P
  * Ellison et al. (2008) Ellison, S. L., Patton, D. R., Simard, L., & McConnachie, A. W. 2008, ApJ, 672, L107
  * Ellison et al. (2009) Ellison, S. L., Simard, L., Cowan, N. B., et al. 2009, MNRAS, 396, 1257
  * Fernández-Martín et al. (2017) Fernández-Martín, A., Pérez-Montero, E., Vílchez, J. M., & Mampaso, A. 2017, A&A, 597, A84
  * Finlator & Davé (2008) Finlator, K. & Davé, R. 2008, MNRAS, 385, 2181
  * Fisher & Drory (2011) Fisher, D. B. & Drory, N. 2011, ApJ, 733, L47
  * Gallazzi et al. (2005) Gallazzi, A., Charlot, S., Brinchmann, J., White, S. D. M., & Tremonti, C. A. 2005, MNRAS, 362, 41
  * García-Benito et al. (2015) García-Benito, R., Zibetti, S., Sánchez, S. F., et al. 2015, A&A, 576, A135
  * Garnett (2002) Garnett, D. R. 2002, ApJ, 581, 1019
  * Gomes et al. (2016) Gomes, J. M., Papaderos, P., Vílchez, J. M., et al. 2016, A&A, 586, A22
  * Hernandez et al. (2019) Hernandez, S., Larsen, S., Aloisi, A., et al. 2019, ApJ, 872, 116
  * Hughes et al. (2013) Hughes, T. M., Cortese, L., Boselli, A., Gavazzi, G., & Davies, J. I. 2013, A&A, 550, A115
  * Hunt et al. (2016) Hunt, L., Dayal, P., Magrini, L., & Ferrara, A. 2016, MNRAS, 463, 2002
  * Hunter (2007) Hunter, J. D. 2007, Computing In Science & Engineering, 9, 90
  * Iglesias-Páramo et al. (2013) Iglesias-Páramo, J., Vílchez, J. M., Galbany, L., et al. 2013, A&A, 553, L7
  * Iglesias-Páramo et al. (2016) Iglesias-Páramo, J., Vílchez, J. M., Rosales-Ortega, F. F., et al. 2016, ApJ, 826, 71
  * Kang et al. (2016) Kang, X., Zhang, F., Chang, R., Wang, L., & Cheng, L. 2016, A&A, 585, A20
  * Kashino et al. (2016) Kashino, D., Renzini, A., Silverman, J. D., & Daddi, E. 2016, ApJ, 823, L24
  * Kauffmann et al. (2003) Kauffmann, G., Heckman, T. M., White, S. D. M., et al. 2003, MNRAS, 341, 33
  * Kojima et al. (2017) Kojima, T., Ouchi, M., Nakajima, K., et al. 2017, PASJ, 69, 44
  * Kroupa (2001) Kroupa, P. 2001, MNRAS, 322, 231
  * Kudritzki et al. (2012) Kudritzki, R.-P., Urbaneja, M. A., Gazak, Z., et al. 2012, ApJ, 747, 15
  * Lara-López et al. (2010a) Lara-López, M. A., Bongiovanni, A., Cepa, J., et al. 2010a, A&A, 519, A31
  * Lara-López et al. (2010b) Lara-López, M. A., Cepa, J., Bongiovanni, A., et al. 2010b, A&A, 521, L53
  * Lee et al. (2006) Lee, H., Skillman, E. D., Cannon, J. M., et al. 2006, ApJ, 647, 970
  * Lequeux et al. (1979) Lequeux, J., Peimbert, M., Rayo, J. F., Serrano, A., & Torres-Peimbert, S. 1979, A&A, 80, 155
  * Licquia & Newman (2015) Licquia, T. C. & Newman, J. A. 2015, ApJ, 806, 96
  * Magrini et al. (2017) Magrini, L., Gonçalves, D. R., & Vajgel, B. 2017, MNRAS, 464, 739
  * Maiolino & Mannucci (2019) Maiolino, R. & Mannucci, F. 2019, A&A Rev., 27, 3
  * Mannucci et al. (2010) Mannucci, F., Cresci, G., Maiolino, R., Marconi, A., & Gnerucci, A. 2010, MNRAS, 408, 2115
  * Mast et al. (2014) Mast, D., Rosales-Ortega, F. F., Sánchez, S. F., et al. 2014, A&A, 561, A129
  * Mateus et al. (2006) Mateus, A., Sodré, L., Cid Fernandes, R., et al. 2006, MNRAS, 370, 721
  * McKinney (2010) McKinney, W. 2010, in Proceedings of the 9th Python in Science Conference, ed. S. van der Walt & J. Millman, 51 – 56
  * Mollá et al. (2006) Mollá, M., Vílchez, J. M., Gavilán, M., & Díaz, A. I. 2006, MNRAS, 372, 1069
  * Møller et al. (2013) Møller, P., Fynbo, J. P. U., Ledoux, C., & Nilsson, K. K. 2013, MNRAS, 430, 2680
  * Mouhcine et al. (2008) Mouhcine, M., Gibson, B. K., Renda, A., & Kawata, D. 2008, A&A, 486, 711
  * Okamoto et al. (2017) Okamoto, T., Nagashima, M., Lacey, C. G., & Frenk, C. S. 2017, MNRAS, 464, 4866
  * Peng & Maiolino (2014) Peng, Y.-j. & Maiolino, R. 2014, MNRAS, 438, 262
  * Pérez & Granger (2007) Pérez, F. & Granger, B. E. 2007, Computing in Science and Engineering, 9, 21
  * Pérez-Montero (2014) Pérez-Montero, E. 2014, MNRAS, 441, 2663
  * Pérez-Montero & Contini (2009) Pérez-Montero, E. & Contini, T. 2009, MNRAS, 398, 949
  * Pérez-Montero et al. (2013) Pérez-Montero, E., Contini, T., Lamareille, F., et al. 2013, A&A, 549, A25
  * Petropoulou et al. (2012) Petropoulou, V., Vílchez, J., & Iglesias-Páramo, J. 2012, ApJ, 749, 133
  * Petropoulou et al. (2011) Petropoulou, V., Vílchez, J., Iglesias-Páramo, J., et al. 2011, ApJ, 734, 32
  * Pilyugin & Grebel (2016) Pilyugin, L. S. & Grebel, E. K. 2016, MNRAS, 457, 3678
  * Pilyugin et al. (2017) Pilyugin, L. S., Grebel, E. K., Zinchenko, I. A., Nefedyev, Y. A., & Mattsson, L. 2017, MNRAS, 465, 1358
  * Pilyugin et al. (2013) Pilyugin, L. S., Lara-López, M. A., Grebel, E. K., et al. 2013, MNRAS, 432, 1217
  * Pilyugin et al. (2003) Pilyugin, L. S., Thuan, T. X., & Vílchez, J. M. 2003, A&A, 397, 487
  * Pilyugin et al. (2007) Pilyugin, L. S., Thuan, T. X., & Vílchez, J. M. 2007, MNRAS, 376, 353
  * Pilyugin et al. (2004) Pilyugin, L. S., Vílchez, J. M., & Contini, T. 2004, A&A, 425, 849
  * Pilyugin et al. (2012) Pilyugin, L. S., Vílchez, J. M., Mattsson, L., & Thuan, T. X. 2012, MNRAS, 421, 1624
  * Robitaille & Bressert (2012) Robitaille, T. & Bressert, E. 2012, APLpy: Astronomical Plotting Library in Python, Astrophysics Source Code Library
  * Romeo Velonà et al. (2013) Romeo Velonà, A. D., Sommer-Larsen, J., Napolitano, N. R., et al. 2013, ApJ, 770, 155
  * Sackett (1997) Sackett, P. D. 1997, ApJ, 483, 103
  * Sakstein et al. (2011) Sakstein, J., Pipino, A., Devriendt, J. E. G., & Maiolino, R. 2011, MNRAS, 410, 2203
  * Salim et al. (2014) Salim, S., Lee, J. C., Ly, C., et al. 2014, ApJ, 797, 126
  * Salim et al. (2007) Salim, S., Rich, R. M., Charlot, S., et al. 2007, ApJS, 173, 267
  * Sánchez (2020) Sánchez, S. F. 2020, ARA&A, 58, annurev
  * Sánchez et al. (2019) Sánchez, S. F., Barrera-Ballesteros, J. K., López-Cobá, C., et al. 2019, MNRAS, 484, 3042
  * Sánchez et al. (2017) Sánchez, S. F., Barrera-Ballesteros, J. K., Sánchez-Menguiano, L., et al. 2017, MNRAS, 469, 2121
  * Sánchez et al. (2012) Sánchez, S. F., Kennicutt, R. C., Gil de Paz, A., et al. 2012, A&A, 538, A8
  * Sánchez et al. (2013) Sánchez, S. F., Rosales-Ortega, F. F., Jungwiert, B., et al. 2013, A&A, 554, A58
  * Sánchez-Menguiano et al. (2020) Sánchez-Menguiano, L., Sánchez Almeida, J., Muñoz-Tuñón, C., & Sánchez, S. F. 2020, arXiv e-prints, arXiv:2009.14211
  * Skibba et al. (2011) Skibba, R. A., Engelbracht, C. W., Dale, D., et al. 2011, ApJ, 738, 89
  * Telford et al. (2016) Telford, O. G., Dalcanton, J. J., Skillman, E. D., & Conroy, C. 2016, ApJ, 827, 35
  * Torrey et al. (2018) Torrey, P., Vogelsberger, M., Hernquist, L., et al. 2018, MNRAS, 477, L16
  * Tremonti et al. (2004) Tremonti, C. A., Heckman, T. M., Kauffmann, G., et al. 2004, ApJ, 613, 898
  * Tsamis et al. (2011) Tsamis, Y. G., Walsh, J. R., Vílchez, J. M., & Péquignot, D. 2011, MNRAS, 412, 1367
  * Van Der Walt et al. (2011) Van Der Walt, S., Colbert, S. C., & Varoquaux, G. 2011, ArXiv e-prints
  * Vila-Costas & Edmunds (1992) Vila-Costas, M. B. & Edmunds, M. G. 1992, MNRAS, 259, 121
  * Vílchez et al. (2019) Vílchez, J. M., Relaño, M., Kennicutt, R., et al. 2019, MNRAS, 483, 4968
  * Yates et al. (2012) Yates, R. M., Kauffmann, G., & Guo, Q. 2012, MNRAS, 422, 215
  * Yin et al. (2009) Yin, J., Hou, J. L., Prantzos, N., et al. 2009, A&A, 505, 497
  * Zahid et al. (2014) Zahid, H. J., Dima, G. I., Kudritzki, R.-P., et al. 2014, ApJ, 791, 130
  * Zurita & Bresolin (2012) Zurita, A. & Bresolin, F. 2012, MNRAS, 427, 1463

##  Appendix A Supplementary material

In this appendix the O/H – SFR relation as a function of the M⋆ and the
parameter Dn (4000) for the galaxies in Fig. 2 is shown in detail. From the
O/H – SFR relation, a subsample of 21 galaxies is randomly defined in selected
zones below the isochrone Dn(4000) $\leq$ 1.2. Its location on the SFR – M⋆
diagram and its spectra and SDSS three-colour images are shown. An upcoming
more detailed study on the characterisation of this subsample of galaxies will
be presented in a forthcoming work (Duarte Puertas et al. in prep.).

We have checked the SFR derived for these galaxies, confirming that these
values were not produced by aperture corrections since the correction applied
to these outliers was in fact smaller than average. We have searched and
extracted the fluxes of the measured SDSS spectra and have verified for all
these galaxies with electron temperature (i.e. with $\rm S/N([OIII]\lambda
4363)>5$) that their direct (electron temperature based) abundances agree with
our oxygen abundance values to within $\sim$-0.025 dex on average (see Fig.
9), as expected.

Figure 9: Distribution of oxygen abundance for SDSS star-forming galaxies with
S/N$\rm([OIII]\lambda 4363)>5$ using Pi16 methodology (blue dashed histogram)
and using direct (electron temperature based) methodology (orange open
histogram).

Fig. 10 shows a density plot of our aperture corrected O/H versus SFR in six
ranges of Dn(4000). In each range of Dn(4000), the density plot of the O/H –
SFR relation of the galaxies in that interval is shown and the contours
1$\sigma$, 2$\sigma$ and 3$\sigma$ in each bin are represented, highlighting
the fit to the running median.

Figure 10: Detailed analysis of the 12+log(O/H) – SFR density plot presenting
confidence limits for each Dn(4000) bin. Density plots for the relation
between the 12+log(O/H) and SFR for star-forming galaxies for six Dn(4000)
ranges. All the lines have the same colours as in Fig. 2. The dashed lines
represent the 1$\sigma$, 2$\sigma$, and 3$\sigma$ contours in each Dn(4000)
bin.

Fig. 11 shows again the aperture corrected O/H – SFR relation (left panel) and
the aperture corrected SFR – M⋆ relation (right panel). Since a population of
galaxies has been found in the zone where O/H dilution occurs, we have defined
there a subsample of 21 galaxies randomly selected, distributed below the
isochrone 1.1 $<$ Dn(4000) $\leq$ 1.2 in the O/H – SFR diagram. We have done
the selection in that way that some of them must be found in the isochrones of
Dn(4000) ¡ 1.1 and others in 1.1 $<$ Dn(4000) $\leq$ 1.2, as well as in the
iso-mass [9, 9.5]. The positions of the 21 galaxies, as well as the position
of the subsample of galaxies that have values of Dn(4000) $<$ 1.2 (blue color)
and that of Dn(4000) $\geq$ 1.2 (red color), are also shown in the SFR – M⋆
relation. Galaxies with values of Dn(4000) $<$ 1.2 (found in the lower right
of the O/H – SFR diagram) are located in the upper left of the SFR – M⋆
diagram. As expected from Fig. 2, galaxies with younger stellar populations
have higher SFR values than older ones at a given stellar mass.

Figure 11: Selection of 21 galaxies from the 12+log(O/H) vs. SFR diagram. Left
panel) Relation between 12+log(O/H) and SFR for star-forming galaxies. All the
lines have the same colours as Fig. 2. A sample of 21 galaxies has been
selected (as an example) in this diagram, the positions are represented with
grey circles and have been labelled from 1 to 21 according to their SFR. Right
panel) Relation between SFR and M⋆ for star-forming galaxies. The points have
been colour coded according to their Dn(4000), blue if Dn(4000) $<$ 1.2 and
red if Dn(4000) $\geq$ 1.2. The dashed lines represent the 1$\sigma$,
2$\sigma$, and 3$\sigma$ contours in each Dn(4000) sub-sample. Grey circles
shows the position in the SFR-M⋆ diagram of the 21 galaxies.

As said in the main text, in order to explore the nature of this subsample of
8598 galaxies, we have performed a sanity check to confirm their metallicity
and SFR, such as we show in Figures 11, 12, and 13, to gain more insight into
the nature of this sub-sample of galaxies. In Figs. 12 and 13 the spectra and
SDSS three-colour images of 21 selected galaxies are shown. By focusing on the
spectra of the galaxies found in the iso-mass [9, 9.5] (galaxies 6, 11, and
13) it can be observed how excitation decreases as the age of the galaxy’s
stellar populations, and 12+log(O/H) increases. In the isochrone Dn(4000) ¡
1.1 the spectra of these three galaxies (galaxies 4, 11, and 15) look similar,
while their morphologies are different.

Figure 12: Spectra of the 21 galaxies defined in Fig. 11. Grey dotted lines
show the location of the emission lines studied in this paper. The galaxy
label is indicated in each panel (right part). Figure 12: continued. Figure
13: SDSS three-colour images of 21 galaxies defined in Fig. 11 in the SDSS-
DR12 footprint. North is up and East is left. The galaxy label is indicated in
each panel (upper right). Figure 13: continued.