# The SAMI Galaxy Survey: the drivers of gas and stellar metallicity
differences in galaxies.

A. Fraser-McKelvie1,2, L. Cortese1,2, B. Groves1,2, S. Brough3,2, J.
Bryant4,5,2, B. Catinella1,2<EMAIL_ADDRESS>S. Croom4,2, F.
D’Eugenio6,7, Á. R. López-Sánchez8,9,2, J. van de Sande4,2, S. Sweet10,2, S.
Vaughan4 J. Bland-Hawthorn4, J. Lawrence8, N. Lorente11, and M. Owers9,12,2.
1 International Centre for Radio Astronomy Research, The University of Western
Australia, 35 Stirling Hwy, 6009 Crawley, WA, Australia
2 ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D)
3 School of Physics, University of New South Wales, NSW 2052, Australia
4 Sydney Institute for Astronomy (SIfA), School of Physics, The University of
Sydney, NSW 2006, Australia
5 Australian Astronomical Optics, AAO-USydney, School of Physics, University
of Sydney, NSW 2006, Australia
6 Cavendish Laboratory and Kavli Institute for Cosmology, University of
Cambridge, Madingley Rise, Cambridge, CB3 0HA, United Kingdom
7 Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281 S9, B-9000
Gent, Belgium
8 Australian Astronomical Optics, Macquarie University, 105 Delhi Rd, North
Ryde, NSW 2113, Australia
9 Department of Physics and Astronomy, Macquarie University, NSW 2109,
Australia
10 School of Mathematics and Physics, University of Queensland, Brisbane, QLD
4072, Australia
11 AAO-MQ, Faculty of Science & Engineering, Macquarie University. 105 Delhi
Rd, North Ryde, NSW 2113, Australia
12 Astronomy, Astrophysics and Astrophotonics Research Centre, Macquarie
University, Sydney, NSW 2109, Australia

###### Abstract

The combination of gas-phase oxygen abundances and stellar metallicities can
provide us with unique insights into the metal enrichment histories of
galaxies. In this work, we compare the stellar and gas-phase metallicities
measured within a 1$R_{e}$ aperture for a representative sample of 472 star-
forming galaxies extracted from the SAMI Galaxy Survey. We confirm that the
stellar and interstellar medium (ISM) metallicities are strongly correlated,
with scatter $\sim$3 times smaller than that found in previous works, and that
integrated stellar populations are generally more metal-poor than the ISM,
especially in low-mass galaxies. The ratio between the two metallicities
strongly correlates with several integrated galaxy properties including
stellar mass, specific star formation rate, and a gravitational potential
proxy. However, we show that these trends are primarily a consequence of: (a)
the different star formation and metal enrichment histories of the galaxies,
and (b) the fact that while stellar metallicities trace primarily iron
enrichment, gas-phase metallicity indicators are calibrated to the enrichment
of oxygen in the ISM. Indeed, once both metallicities are converted to the
same ‘element base’ all of our trends become significantly weaker.
Interestingly, the ratio of gas to stellar metallicity is always below the
value expected for a simple closed-box model, which requires that outflows and
inflows play an important role in the enrichment history across our entire
stellar mass range. This work highlights the complex interplay between stellar
and gas-phase metallicities and shows how care must be taken in comparing them
to constrain models of galaxy formation and evolution.

###### keywords:

galaxies: evolution – galaxies: general – galaxies: ISM – galaxies: abundances

##  1 Introduction

The evolution of metal content in galaxies follows a broadly predictable
route: every generation of stars is created from the interstellar medium
(ISM), produces metals, and then expels these metals back into the ISM through
supernovae or stellar winds. The next generation of stars is created from the
enriched ISM, and they themselves will be more enriched than the previous
stellar generation. Gas inflows and outflows complicate this otherwise ‘closed
box’ scenario by providing supplies of pristine gas and ejecting metal-
enriched gas into the inter-galactic medium.

For a closed-box model of galactic chemical evolution we can assume that a
galaxy increases its metal content over time. The gas-phase and stellar
metallicities can then be calculated from a cumulative metallicity
distribution: the gas-phase metallicity will be the maximum value of the
distribution, and the stellar metallicity the (light- or mass-weighted) mean.
The maximum will always be greater than the mean value, and hence the average
stellar metallicity for a given galaxy is lower than that of the gas-phase
metallicity when a closed-box model is assumed. One might imagine that the
shape of the cumulative metallicity distribution will dictate the difference
between the maximum and mean, and hence the difference between stellar and
gas-phase metallicity values for a given galaxy.

Observationally, measuring the metal content of a galaxy’s constituents is not
trivial, however it is a worthwhile exercise. Galaxy spectra are the weighted
summation of the light from all generations of stars within a region sampled,
and so the stellar metallicity is something of an average of the metal content
of all of the stars within a galaxy. The ionised gas emission lines we observe
from star-forming regions are generally powered by young, hot stars, and as
such reflect the properties of the galaxy at $z=0$. Combining gas and stellar
metallicity measurements is therefore a powerful tool to constrain the
evolutionary pathways of galaxies throughout all of cosmic time.

The metallicity of stars and gas are measured in a different manner to one
another for several reasons. While oxygen is the most abundant element in the
Universe (after hydrogen and helium), the abundance of this element in stars
is difficult to measure. First, oxygen does not give rise to strong observable
features in the optical stellar continuum spectra, and the absorption lines we
do observe are either blended with other elemental lines (even at high
spectral resolution, Asplund, 2005), or arise outside of local thermodynamical
equilibrium (which is difficult to model, Asplund et al., 2009). Moreover,
oxygen in cool stellar atmospheres depletes onto molecules (e.g. OH, CO, TiO,
Asplund, 2005), which further complicates inferring the total abundance. For
these reasons, estimating oxygen abundances in stars is problematic. Despite
recent developments in stellar astrophysics (e.g. Ting et al., 2018),
estimating the metallicity of whole stellar populations requires the further
step of averaging over a distribution of stellar spectra which may have
different abundances. For this reason, measuring galaxy stellar metallicities
relies on the much more common and stronger iron absorption lines (Worthey,
1994). While iron is a reliable abundance indicator for stars, it cannot be
used to determine the metal content of the ISM as it depletes readily onto
dust (e.g. Jenkins, 2009; Nicholls et al., 2017). Instead, we define the gas
metallicity as the oxygen abundance, which can be estimated from strong
emission lines (e.g. Searle, 1971; Lequeux et al., 1979; Pagel et al., 1979).
Employing different tracer elements means that stellar and gas metallicities
are measured using different abundance scales, making comparisons difficult
(e.g. Peng & Maiolino, 2014).

When seeking to understand the chemical evolutionary history of galaxies, many
previous works have studied the link between either the gas-phase oxygen
abundance or stellar metallicity with other galaxy observables. For example,
there are a plethora of previous literature on the origin of the stellar
mass–gas-phase oxygen abundance relation ($M_{\star}-12+\log(\rm{O}/\rm{H})$
relation, often referred to as the $M_{\star}-Z_{gas}$ relation in the
literature; e.g. Lequeux et al., 1979; Skillman et al., 1989; Tremonti et al.,
2004; Kewley & Ellison, 2008; Maiolino & Mannucci, 2019, and references
within) and the stellar mass–stellar metallicity relation
($M_{\star}-Z_{\star}$ relation; e.g. Faber, 1973; Brodie & Huchra, 1991;
Trager et al., 2000; Gallazzi et al., 2005; Zahid et al., 2017; Lian et al.,
2018a). A positive correlation is observed in both gas and stars such that
more massive (or luminous) galaxies possess a greater fraction of metals than
their lower-mass counterparts. The $M_{\star}-Z_{gas}$ relation bends at high
stellar masses (e.g. Tremonti et al., 2004). Rather than a saturation of the
chosen gas-phase metallicity indicator, this flattening is thought to be due
to a characteristic mass (corresponding to a characteristic gravitational
potential well depth), above which galaxies are able to retain a large
fraction of their metals within their halo. At lower stellar masses, feedback
becomes effective at ejecting metals from the ISM via outflows (e.g. Blanc et
al., 2019). The source of these outflows is thought to be supernova explosions
(e.g. Larson, 1974; Kobayashi et al., 2007; Scannapieco et al., 2008). In
support of this hypothesis, observationally we see that in addition to the
stellar mass dependence, both gas-phase oxygen abundances and the stellar
metallicities of a galaxy are strongly correlated with gravitational potential
and local stellar surface mass density proxies (e.g. Scott et al., 2017;
Barone et al., 2018; D’Eugenio et al., 2018; Gao et al., 2018; Barone et al.,
2020).

Given the difference in timescales that stellar and gas metallicity probe, it
is essential to include both in studies to understand the complete metallicity
evolution of a galaxy. In addition, only through the inclusion of both
metallicities can theoretical models of galaxy evolution be constrained. Some
early Sloan Digital Sky Survey (Abazajian et al., 2004) work investigated the
differences between stellar metallicities and gas-phase oxygen abundances
within the same galaxies (Gallazzi et al., 2005). This work found that the
stellar metallicity and gas-phase oxygen abundance of a galaxy are correlated.
The substantial scatter in stellar metallicity at fixed oxygen abundance was
explained by gas inflows/outflows within an individual galaxy. Indeed,
analytic models require inflows and outflows to reliably model the cosmic
metallicity evolution in galaxies (e.g. Finlator & Davé, 2008; Lilly et al.,
2013; Peng & Maiolino, 2014).

In general, the average stellar metallicity for a given galaxy is found to be
lower than its gas-phase oxygen abundance, with the largest differences seen
at low stellar masses (e.g. González Delgado et al., 2014; Lian et al.,
2018a). Indeed, the metallicity of the youngest stars most closely matches
that of the gas-phase. Lian et al. (2018a) explain the large differences
between stellar metallicity and gas-phase oxygen abundances at low stellar
masses by expecting significant metallicity evolution throughout the life of a
galaxy. To correctly model the observed differences between the metal content
of stars and gas they invoke models with either strong metal-rich outflows, or
steep initial mass functions (IMF), both of which are quite extreme scenarios.

The large difference between stellar and gas-phase metallicities at low
stellar masses and the reason why the gap between the two closes at higher
stellar masses are both open questions. One further possible explanation could
be a variety of star formation histories (and therefore chemical enrichment
histories) in individual galaxies. Previous work has explored the fossil
record of the $M_{\star}-Z_{\star}$ relation via full spectral fitting (e.g.
Cid Fernandes et al., 2007; Panter et al., 2008; Vale Asari et al., 2009).
These works found the $M_{\star}-Z_{\star}$ relation to be steeper in older
stellar populations, and that more massive galaxies show very little evolution
since distant epochs (however this is not the case when observing star-forming
vs. passive galaxies in the current epoch e.g. Peng et al., 2015). The rapid
early growth of high-mass galaxies (referred to as a ‘chemical downsizing’
scenario) can be used to explain the differences in the stellar metallicity of
old and young stellar populations today. That said, these works rely on full
spectral fitting providing reliable metallicity estimates for young stellar
populations and provide no constraints on the gas itself.

Another key point generally overlooked by previous works is that gas and
stellar metallicity estimates are biased towards elements that form over
different timescales. As mentioned already, ionised gas abundances are usually
calibrated to oxygen, which is an $\alpha$ element, while iron, a non-$\alpha$
element, is often used to infer stellar metallicities. $\alpha$ elements are
heavy elements mostly produced in massive stars and ejected by core-collapse
supernovae on short timescales of $\sim$10 Myr (e.g. Timmes et al., 1995).
Non-$\alpha$ elements such as iron-peak elements are formed by Type Ia
supernovae over longer timescales (e.g. Kobayashi & Nomoto, 2009). Hence, the
ratio of $\alpha$ to non-$\alpha$ elements will vary as a function of time for
a galaxy depending on its star formation history (SFH). This discrepancy needs
to be taken into account when comparing gas and stellar metallicities and as
such, blindly equating stellar metallicity to an oxygen abundance does not
really provide a fair comparison between the enrichment of gas and stars.

We aim to build on previous work and combine stellar and gas-phase metallicity
information with the intention of determining the driving mechanism behind any
differences seen. In addition, we wish to gain a feel for the effects of a
galaxy’s SFH on the trends we observe by converting oxygen abundances (which
we term $Z_{gas}$ in line with previous literature) to a total gas metallicity
(which we term $Z_{gas,tot}$) to compare to the stellar metallicity. For this
work we require a large sample of galaxies with both reliable stellar
population and gas-phase oxygen abundance indicators. Such measurements are
only available for star-forming galaxies with excellent continuum signal-to-
noise. In addition, to build on early fibre spectroscopy work, it would be
advantageous to examine integrated quantities of galaxies, to understand the
evolution of metal content across entire galaxies and not just their nuclear
regions. The Sydney-AAO Multi-object Integral field spectrograph (SAMI; Croom
et al., 2012) Galaxy Survey fits this brief perfectly.

In this paper we describe the SAMI Galaxy Survey and the gas and stellar
metallicity indicators used in this work in Section 2, compare the two and
seek to understand the drivers behind the correlations seen in Section 3,
before discussing the observables driving the differences in the metal content
of gas and stars in Section 4. We summarise and conclude our results in
Section 5. Throughout, we use a Chabrier (2003) IMF and $\Lambda$CDM
cosmology, with $\Omega_{m}=0.3$, $\Omega_{\lambda}=0.7$,
$H_{0}=70~{}\rm{km}~{}\rm{s}^{-1}~{}\rm{Mpc}^{-1}$.

##  2 Data and methods

###  2.1 The SAMI Galaxy Survey

The SAMI Galaxy Survey is an integral field spectroscopy survey on the Anglo-
Australian Telescope that observed 3068 galaxies from 2013–2018 (Croom et al.,
2012). SAMI used 13 fused fibre hexabundles (Bland-Hawthorn et al., 2011;
Bryant et al., 2014) with a high (75%) fill factor. Each bundle contained 61
fibres of $1.6^{\prime\prime}$ diameter resulting in each integral field unit
(IFU) having a diameter of $15^{\prime\prime}$. The IFUs, as well as 26 sky
fibres, were plugged into pre-drilled plates using magnetic connectors. SAMI
fibres were fed to the double-beam AAOmega spectrograph (Sharp et al., 2015),
which allowed a range of different resolutions and wavelength ranges. The SAMI
Galaxy survey employed the 580V grating between 3750–5750 Å giving a
resolution of R=1810 ($\sigma=70.4~{}\rm{km}~{}\rm{s}^{-1}$) at 4800 Å and the
1000R grating from 6300–7400 Å giving a resolution of R=4260
($\sigma=29.6~{}\rm{km}~{}\rm{s}^{-1}$) at 6850 Å (Scott et al., 2018). 83% of
galaxies in the SAMI target catalogue had coverage out to 1 effective radius
(1$R_{e}$, Bryant et al., 2015).

The SAMI Galaxy Survey was comprised of a sample drawn from the Galaxy and
Mass Assembly (GAMA; Driver et al., 2011) survey equatorial regions (Bryant et
al., 2015), and an additional sample of eight clusters (Owers et al., 2017).
SAMI Data Release 3 (DR3; Croom et al., 2021) contains observations of 3068
galaxies and is the final data release of the SAMI survey. SAMI DR3 includes
observations spanning $0.04<z<0.128$ and $7.42<\log
M_{\star}[\rm{M}_{\odot}]<11.89$ (corresponding to an $r$-band magnitude range
of $18.4<m_{r}<12.1$), with environments ranging from underdense field regions
to extremely overdense clusters.

The data products used in this analysis are the spectral cubes for full
spectral fitting and aperture emission line maps for gas-phase oxygen
abundance estimates.

Figure 1: The SAMI galaxies used in this work in the SFR-stellar mass plane.
Histograms in mass and SFR for each population are shown to the top and right
side of the plot, respectively. Purple points are 472 galaxies with $Z_{gas}$
and $Z_{\star}$ information, satisfy the S/N cuts discussed in the text and
are the sample used in the following analysis. Orange points have only
$Z_{gas}$, green points have only $Z_{\star}$, and grey points have neither
indicator. The curved and linear star-forming main sequence lines of Fraser-
McKelvie et al. (2021) are shown in black for reference.

###  2.2 Star formation rates and stellar masses

Star formation rates (SFRs) and stellar masses were taken from the
$GALEX$-Sloan-$WISE$ Legacy Catalogue-2 (GSWLC-2; Salim et al., 2016; Salim et
al., 2018) using a sky match with maximum allowed separation of 2′′. In that
catalogue, Stellar masses and SFRs were determined via SED fitting using the
Code Investigating GALaxy Emission (CIGALE; Noll et al., 2009; Boquien et al.,
2019). The photometry included in the fits was sourced from the Wide-Field
Survey Explorer ($WISE$) in the mid-infrared, Sloan Digital Sky Survey in the
optical, and the Galaxy Evolution Explorer ($GALEX$) in the UV. For this work
we employ the GSWLC-X2 catalogue which uses the deepest $GALEX$ photometry
available for a given source (selected from the shallow ‘all-sky’, medium-
deep, and deep catalogues). As SDSS coverage is limited to declinations
$\gtrsim-10$°, we do not have SFRs and stellar masses from the GSWLC-2 for the
four Southern SAMI clusters. Despite this limitation, 1832 SAMI galaxies have
SFRs and stellar masses from GSWLC-2.

Figure 1 shows the distribution of all SAMI galaxies with GSWLC-2 data in the
SFR–$M{\star}$ plane (grey points). Galaxies with available stellar
metallicity estimates (and satisfy the quality cuts detailed in Section 2.3)
are shown in green, and those with gas-phase oxygen abundances (and satisfy
the quality cuts detailed in Section 2.4) are shown in orange. Galaxies with
both stellar and gas-phase abundance estimates are shown in purple.
Unsurprisingly due to their need for both good continuum and emission line
S/N, the majority of these galaxies are located on or around the star-forming
main sequence lines shown in black. The purple points in Figure 1 constitute
the sample used for the analysis in this work.

###  2.3 Stellar metallicity estimates

Full spectral fitting was employed to determine light-weighted average ages
and metallicities of the SAMI galaxies from the 1$R_{e}$ aperture spectra (for
mass-weighted results, see Appendix A). The integrated spectra were obtained
by co-adding all spectra of spaxels within an elliptical aperture of 1$R_{e}$
semi-major axis, where the aperture was defined by the axial ratio determined
from the multi-Gaussian expansion fits of D’Eugenio et al. (2021) as in Scott
et al. (2018) and using the method of Emsellem et al. (1994) and Cappellari
(2002). We employ the penalised pixel-fitting (pPXF) method of Cappellari &
Emsellem (2004) and Cappellari (2017). We follow one of the examples included
in the pPXF package closely (ppxf_example_population.py) after modifying it
for use with SAMI data.

We adopted the method of van de Sande et al. (2017) to prepare the SAMI
1$R_{e}$ aperture spectra for use with full spectral fitting codes. The
spectra from the blue and red arms of the SAMI spectrograph were initially
spliced after first convolving the red (higher resolution,
$\sigma=29.6~{}\rm{km}~{}\rm{s}^{-1}$) spectrum to the instrumental resolution
of the blue arm ($\sigma=70.4~{}\rm{km}~{}\rm{s}^{-1}$). The resultant
combined spectrum was then log rebinned.

Emission lines and stellar continuum were fit simultaneously by creating a set
of Gaussian emission line templates to fit at the same time as the stellar
templates. In this manner, only the spectral gap between the SAMI red and blue
arm wavelength coverage regions (5760–6400 Å) was masked. Barring the masked
middle region, the spectrum was fit in the rest wavelength range 3900–6800 Å.
Regularisation was employed for the pPXF fit and the template normalisation
for light-weighted properties performed over the range 5000–5500 Å. The
‘clean’ keyword was set so that an iterative sigma clipping method was used to
remove unmasked bad pixels from the spectra.

We employed the MILES SSP model templates (Vazdekis et al., 2010) with ages
0.08, 0.10, 0.13, 0.16, 0.20, 0.25, 0.32, 0.40, 0.50, 0.63, 0.79, 1.0, 1.26,
1.58, 2.0, 2.51, 3.16, 3.98, 5.01, 6.31, 7.94, 10.0, 12.59, 15.85 Gyr ,
metallicities -1.71, -1.31, -0.71, -0.4, 0.0, 0.22 , and ‘baseFe’ (Milky Way
value) $\alpha$ enhancement.

Figure 2: Stellar mass-stellar metallicity relation ($M_{\star}-Z_{\star}$
relation) derived via light-weighted stellar population analysis using the
full spectral fitting code pPXF. The mass-metallicity relation is apparent,
with the median of the relation shown as a dashed red line and the shaded
region is the 1$\sigma$ scatter. The average scatter in the
$M_{\star}-Z_{\star}$ relation is 0.15 dex. For comparison, the median
$M_{\star}-Z_{\star}$ relation for the same SAMI galaxies using the Lick
index-derived stellar metallicities presented in Scott et al. (2018) is shown
in gold.

Previous work has shown that full spectrum fitting often struggles to fit an
excess of blue light within a galaxy (e.g. Cid Fernandes & González Delgado,
2010) normally attributed to horizontal branch stars in the planetary nebula
phase (e.g. Yi, 2008). As noted in Peterken et al. (2020), this light is not
accounted for in old SSP template spectra, and so full spectral fitting
software often attributes it to young, metal-poor populations. For our stellar
population age and metallicity estimates, we therefore follow the method of
Peterken et al. (2020) and whilst we use the entire template range in our
fits, we remove the contribution of the youngest SSP templates (in our case
0.08 Gyr) weights when calculating average ages and metallicities. Peterken et
al. (2020) show that older stellar populations are unaffected by the method by
which the younger populations are modelled, and so are robust.

Given that the SSP templates are approximately evenly spaced in log age and
metallicity space, and coupled with the large dynamic range between the oldest
and youngest, and most metal-rich and metal-poor templates, we chose to
compute the average metallicity via a logarithmic mean. Logarithmically-
derived means are the default option within pPXF, and regularly utilised in
previous literature (e.g. González-Delgado et al., 2015). We are most
interested in metallicity measures for this work, and note that there will be
an offset between the logarithmically- and linearly-derived mean metallicity
measures for a given galaxy such that the mean logarithmically-derived
metallicity value will be more metal-poor than that derived linearly.

The logarithmic mean of the age and metallicity per spectrum were computed
from the output template weights following equations (1) and (2) of McDermid
et al. (2015) but excluding the youngest SSP models. The resultant [M/H]
metallicity estimate we obtain is termed $Z_{\star}$, such that

$Z_{\star}\equiv[\rm{M/H}]=\log_{10}[(\rm{M/H})/(\rm{M/H})_{\odot}].$

A $\chi^{2}$ cut was employed such that galaxies with pPXF fits with reduced
$\chi^{2}>1.5$ are not included in our results. This cut reduced the number of
galaxies with stellar metallicity measures from 2861 to 2745, and the majority
of those cut were either low-mass or low continuum signal to noise. We present
the results of the light-weighted fits here as they are more directly
comparable to observations and Lick index-derived results.

We show the $M_{\star}-Z_{\star}$ relation for all galaxies in the SAMI sample
with both $Z_{\star}$ and $Z_{gas}$ estimates in Figure 2. Here the hexbins
are coloured by the number of galaxies per bin. The median $Z_{\star}$ in bins
of $M_{\star}$ is shown as the red dashed line with the 1$\sigma$ uncertainty
shaded in red. A tight mass-metallicity relation is apparent, with a median
$1\sigma$ scatter of 0.15 dex. As a comparison, we also extracted the 1$R_{e}$
aperture stellar population parameters from Scott et al. (2017), which were
derived via Lick indices. The median $Z_{\star}$ obtained per mass bin from
the Lick index measurements is shown as a gold line in Figure 2. The mass-
metallicity relation derived via Lick indices is steeper than the light-
weighted pPXF relation, probably the result of both a larger range of
metallicity SSP templates used in the Scott et al. (2017) work, and the fact
that Lick indices assume a single-burst star formation history. Non-parametric
full spectral fitting tools such as pPXF can provide much more complicated
SFHs, and hence the difference between the Lick index and light-weighted pPXF
average metallicities is not surprising.

###  2.4 Gas-phase oxygen abundances

We use the empirical R-calibration of Pilyugin & Grebel (2016) to derive gas-
phase oxygen abundances. We note that this empirical calibration considers the
absolute oxygen abundance scale given by the direct method (i.e. that based in
the measurement of the electron temperature, $T_{e}$, of the ionized gas). It
is well known that $T_{e}$-based empirical calibrations provide results that
are systematically 1.5 - 5 times lower than those derived using calibrations
based on photoionization models (e.g. see López-Sánchez et al., 2012, and
references within), and so care should be taken when comparing the results of
this analysis to metallicities derived using photoionization models.

Emission line fluxes for this calibration were obtained from the same 1$R_{e}$
aperture spectra as for the stellar population analysis using the SAMI data
reduction pipeline and the method described in Scott et al. (2018). Briefly,
the LZIFU code of Ho et al. (2016) was employed, where the underlying stellar
continuum was subtracted first before each emission line was fit with a
Gaussian profile. All emission lines were fit simultaneously and emission line
fluxes, velocities, and velocity dispersions were obtained from the Gaussian
fits.

We correct the emission lines for dust as in Poetrodjojo et al. (2021), by
determining $E(B-V)$, and then using $A(\lambda)$ at the emission line
wavelengths to de-redden each line. We adopt the reddening function of
Fitzpatrick & Massa (2007), and assume a typical $R(V)=3.1$, along with Case B
recombination.

The 156 galaxies whose $1R_{e}$ aperture spectra were dominated by AGN
emission according to the line diagnostic ratios of Kewley et al. (2001) were
removed from the sample. A S/N cut was employed such that only galaxies with
S/N $>5$ in [O ii] $\lambda\lambda$3727,29 , H$\beta$, [O iii] $\lambda$5007,
[N ii] $\lambda\lambda$6548,84 and H$\alpha$ remained. We tested a S/N $>10$
cut and found it did not reduce the scatter in the resulting
$M_{\star}-Z_{gas}$ relation. 1660 galaxies were removed from the full SAMI
sample following this S/N cut, the majority of which were passive galaxies, as
can be seen from Figure 1.

The R-calibration of Pilyugin & Grebel (2016) was employed to determine oxygen
abundances, as replicated below:

$\begin{split}(\rm{O/H})^{*}_{R,U}&=8.589+0.022~{}\log(R_{3}/R_{2})+0.399~{}\log
N_{2}\\\ &+(-0.137+0.164\log(R_{3}/R_{2})+0.589\log N_{2})\\\ &\times\log
R_{2},\end{split}$ (1)

when $\log N_{2}\geqslant-0.6$

$\begin{split}(\rm{O/H)}^{*}_{R,L}&=7.932+0.944~{}\log(R_{3}/R_{2})+0.695\log
N_{2}\\\ &+(0.970-0.291\log(R_{3}/R_{2})-0.019\log N_{2})\\\ &\times\log
R_{2},\end{split}$ (2)

when $\log N_{2}<-0.6$, and where:
$R_{2}=I_{[\rm{OII}]\lambda 3727+\lambda 3729}/I_{\rm{H\beta}}$,
$R_{3}=I_{[\rm{OIII}]\lambda 4959+\lambda 5007}/I_{\rm{H}\beta}$,
$N_{2}=I_{[\rm{NII}]\lambda 6548+\lambda 6584}/I_{\rm{H}\beta}$,
and $(\rm{O/H})^{*}_{R,U}$ and $(\rm{O/H})^{*}_{R,L}$ refer to the upper and
lower tracks of the relation respectively, and $(\rm{O/H})^{*}_{R}\equiv
12+\log(O/H)_{R}$.

We define $Z_{gas}\equiv 12+\log(\rm{O/H})_{R}-8.76$, or
$Z_{gas}\equiv\log(\rm{O/H})+3.24$, where the solar value oxygen abundance of
8.76 (Nieva & Przybilla, 2012) has been subtracted. The $M_{\star}-Z_{gas}$
relation derived from the Pilyugin & Grebel (2016) calibration is shown in
Figure 3 for SAMI galaxies that have both $Z_{gas}$ and $Z_{\star}$ estimates,
along with a comparison relation derived from the empirical O3N2 calibration
of Pettini & Pagel (2004) for the same galaxies in gold. The flattening in the
$M_{\star}-Z_{gas}$ relation at high $Z_{gas}$ is apparent in Figure 3 as
observed in previous works (e.g. Tremonti et al., 2004; Gallazzi et al., 2005;
Foster et al., 2012; Lara-López et al., 2013).

To summarise the final sample, from the 3068 unique galaxies in the SAMI
galaxy survey, 2745 have available stellar metallicities from full spectral
fitting methods, 1251 have available gas-phase oxygen abundances, and 472 have
both indicators and available SFRs from GSWLC. These 472 galaxies are the
sample used for the rest of this work. From Figure 1 it can be seen that the
galaxies with both stellar metallicity and gas-phase oxygen abundance
measurements are representative of galaxies on the star-forming main sequence.

Figure 3: The $M_{\star}-Z_{gas}$ relation for SAMI galaxies in this work
derived using the empirical calibration of Pilyugin & Grebel (2016). Hexbins
are coloured by the number of galaxies in each bin. The red dashed line
denotes the median of this relation, and the red shaded region the 1$\sigma$
scatter, the average of which is 0.08 dex. For comparison, the median derived
from the empirical O3N2-based calibration of Pettini & Pagel (2004) is shown
in gold. The flattening of the $M_{\star}-Z_{gas}$ relation at high $Z_{gas}$
as seen in previous works is apparent.

##  3 Results

###  3.1 Comparing stellar and gas-phase metallicities

Figure 4: Comparison of $Z_{gas}$ using the Pilyugin & Grebel (2016)
calibration to the pPXF-derived light-weighted $Z_{\star}$ for SAMI galaxies.
Hexbins are coloured by the number of galaxies in each bin. The red dashed
line denotes the running median and the shaded region is the 1$\sigma$
scatter. For all but the most stellar metal-rich galaxies, $Z_{\star}$ is
always lower than $Z_{gas}$.

In Figure 4 we plot the pPXF-derived light-weighted stellar metallicity as a
function of the gas-phase oxygen abundance estimates from the Pilyugin &
Grebel (2016) calibration for the SAMI galaxies with both measures available.
The median of the distribution is shown as a red dashed line and the shaded
red region denotes the 1$\sigma$ scatter. The grey dotted line is the 1:1
line, denoting the region where the stellar and gas-phase metallicities are
equal. The relationship between $Z_{gas}$ and $Z_{\star}$ is non-linear, and
there is a ‘knee’ region above which the correlation flattens off. We expect
this flattening to be due to the curvature of the $M_{\star}-Z_{gas}$
relation, and it is for the most metal-rich galaxies that the stellar
metallicity approaches that of the gas-phase oxygen abundance. The scatter in
the $Z_{gas}-Z_{\star}$ relation is 0.1 dex, which is a considerable
improvement on the early SDSS results of Gallazzi et al. (2005), whose 1
$\sigma$ scatter in this relation was $\sim 0.3$ dex. We expect this
improvement is chiefly due to the gas-phase and stellar metallicity
calibrators employed.

We define the gas-phase oxygen abundance-to-stellar metallicity ratio, $\Delta
Z_{g,\star}$, as the ratio (or logarithmic difference) of the two metallicity
indicators, where

$\Delta Z_{g,\star}\equiv
Z_{gas}-Z_{\star}=\log(\rm{O}/\rm{H})+3.24-[\rm{M/H}].$ (3)

The metallicity ratio is on a logarithmic scale, such that $\Delta
Z_{g,\star}=0.5$ implies that the gas is $\sim 3\times$ as metal-rich as the
stars, and $\Delta Z_{g,\star}=0$ implies that the two indicators are equal to
one another.

###  3.2 Correlations with $\Delta Z_{g,\star}$

Figure 5: The correlation between $\Delta Z_{g,\star}$ and four galaxy
properties that correlate with $Z_{gas}$ and $Z_{\star}$ individually. For
each panel, the Spearman correlation coefficient (r), p-value, and the
vertical scatter in the correlation ($\sigma$) are shown. The red dashed line
denotes the running median of the SAMI galaxies. While strong correlations and
anti-correlations are seen between $\Delta Z_{g,\star}$ and $\log\Phi$,
$\log\rm{M}_{\star}$, and $\log\rm{sSFR}$, only a weak anti-correlation is
seen with $\log\Sigma_{\star}$.

With the aim of identifying why there is such a large variation in $\Delta
Z_{g,\star}$ in the SAMI sample, in Figure 5 we explore $\Delta Z_{g,\star}$
as a function of some properties that are known to scale with $Z_{gas}$ and
$Z_{\star}$ individually. In panels (a) to (d), the properties chosen are: (a)
$\Phi=\log(M_{\star}/R_{e})$ a proxy for gravitational potential, (b)
$\Sigma_{\star}\sim\log(M_{\star}/R_{e}^{2})$ a proxy for stellar surface mass
density, (c) stellar mass $M_{\star}$, and (d) specific star formation rate
($\rm{sSFR}=\rm{SFR}/M_{\star}$).

For each panel of Figure 5, the Spearman correlation coefficient (r), p-value,
and $1\sigma$ vertical scatter are displayed for each fit. Correlations are
seen between $\Delta Z_{g,\star}$ and $\Phi$ (r=-0.49), $\rm{M}_{\star}$
(r=-0.54), and sSFR (r=0.54). There is only a very weak correlation between
$\Delta Z_{g,\star}$ and $\Sigma_{\star}$ (r=-0.19). Interestingly, although
there are different degrees of correlation, stellar mass features in all four
of these quantities, and one of the strongest trends in $\Delta Z_{g,\star}$
is with stellar mass. When the additional parameter of optical size is added
to obtain $\Phi$, this correlation weakens. If we increase the contribution of
optical size to obtain $\Sigma_{\star}$ (which contains an $R_{e}^{2}$ term),
the correlation weakens further. On the other hand, when SFR is incorporated
with stellar mass to obtain sSFR, the correlation remains as tight as for with
stellar mass.

We investigate links between $\Delta Z_{g,\star}$ and stellar mass, SFR, and
optical effective radius further in Figure 6. In panel (a) we plot star
formation rate as a function of stellar mass with points coloured by $\Delta
Z_{g,\star}$. To bring out any residual trends, we have smoothed the data
using the locally weighted regression algorithm LOESS (as implemented by
Cappellari et al., 2013). The iso-contours of the smoothed $\Delta
Z_{g,\star}$ distribution in the $M_{\star}$–SFR plane are not vertical: for a
given $\rm{M}_{\star}$ there is a residual trend in $\Delta Z_{g,\star}$ with
SFR. This implies that both SFR and stellar mass are responsible for the
trends seen in $\Delta Z_{g,\star}$. Figure 6 is consistent with Figure 5 (d)
in that galaxies with higher SFRs at fixed stellar mass also have the greatest
difference between $Z_{gas}$ and $Z_{\star}$.

Panel (b) of Figure 6 shows the mass-size relation. Again, we see residual
trends in $\Delta Z_{g,\star}$ with both mass and optical effective radius
($R_{e}$). The inter-relation between stellar mass, SFR, and optical size is
not surprising. We know that galaxies with smaller radii on the star-forming
main sequence possess higher SFRs for a given stellar mass than for galaxies
with larger sizes (e.g. Wuyts et al., 2011). In addition, our estimates of
galaxy size are optical, so given the well-known relation between galaxy size
and colour (e.g. Vulcani et al., 2014), any estimate of $\Phi$ or
$\Sigma_{\star}$ will also encapsulate age differences. Finally, two galaxies
of similar stellar mass with different gravitational potentials must by
construction have different assembly histories and likely SFHs (as inferred
from their sSFR in this case), a result of the differing inflow and outflow
history. It is therefore nearly impossible to disentangle the one galaxy
property that is responsible for the observed correlations in $\Delta
Z_{g,\star}$. For now, we can say that the strongest correlations seen are
with stellar mass, followed by SFR and galaxy size.

Figure 6: Understanding the relative importance of $M_{\star}$, sSFR, and
$\rm{\Phi}$ on the galaxy metallicity ratio $\Delta Z_{g,\star}$. In panel (a)
we plot the star-forming main sequence, and in panel (b) the mass-size
relation. The points of both plots are coloured by $\Delta Z_{g,\star}$. Both
plots are LOESS smoothed to bring out trends in each parameter. In both the
star-forming main sequence and the mass-size relation, the main trend is with
stellar mass, although residual trends exist in both SFR and effective radius.

###  3.3 A step further: the correlation between $\Delta Z_{g,\star}$ and sSFR

Given the trends in $\Delta Z_{g,\star}$ with sSFR coupled with the fact that
previous literature ties steeper slopes of the $M_{\star}-Z_{\star}$ relation
to the older stellar populations in galaxies (e.g. Vale Asari et al., 2009),
we expect that the trends observed in $\Delta Z_{g,\star}$ are related to the
SFH of a galaxy. In order to understand the observed correlations between
$\Delta Z_{g,\star}$ and sSFR (which can be considered a proxy for the shape
of the SFH of a galaxy), we explore the metallicity history of the galaxies in
the SAMI sample via full spectral fitting. We split the integrated stellar
population output weights from pPXF into two bins, templates with ages $<1$
Gyr (though excluding the youngest template SSPs in the metallicity
determination), and templates with ages $>7$ Gyr, and determine the average
metallicity of both bins in the same manner as the values for the entire
population. Galaxies with very little light in either the old or young
template age ranges could bias metallicity results. For this reason, we
perform this analysis only on galaxies that have $>10\%$ of their light in
both the young and old age ranges.

In Figure 7 we show the light-weighted average stellar metallicity of the $<1$
Gyr and $>7$ Gyr stellar populations, with points coloured by $\Delta
Z_{g,\star}$. For clarity, we split the galaxy population into three bins of
metallicity ratio:

$\displaystyle\Delta Z_{g,\star}<0.4,$ $\displaystyle 0.4<$
$\displaystyle\Delta Z_{g,\star}<0.8,\rm{and}$ $\displaystyle\Delta
Z_{g,\star}>0.8,$

and determine the median values for the metallicity of $<1$ Gyr and $>7$ Gyr
stellar populations for each bin, indicated by large star-shaped markers.

A strong vertical trend is seen whereby the $<1$ Gyr stellar populations are
uniformly metal-rich, except for the greatest $\Delta Z_{g,\star}$ values
where $Z_{gas}$ and $Z_{\star}$ are most different. A slight ‘J’ shape is
observed in the distribution of galaxies in Figure 7 such that the young
stellar populations of the galaxies where $\Delta Z_{g,\star}\gtrsim 0.6$ are
more metal-poor than the rest of the galaxy population. From Figure 5 (c) we
expect these galaxies (where the stellar and gas metallicities are most
different) to be low-mass dwarfs, where the galaxy hasn’t had enough star
formation yet to increase its overall stellar metallicity.

For the overall galaxy population, the average metallicity of the $>7$ Gyr
stellar populations varies according to $\Delta Z_{g,\star}$; galaxies whose
average stellar metallicity is similar to their gas metallicity ($\Delta
Z_{g,\star}\sim 0$) possess metal-rich old stellar populations. Conversely,
galaxies whose overall average stellar metallicity is much lower than their
gas-phase oxygen abundance possess metal-poor old and young stellar
populations.

The goal of Figure 7 is primarily to show that the difference between
$Z_{gas}$ and $Z_{\star}$ is linked to the rapidness of the metallicity
enrichment history of galaxies. Such that, galaxies with a rapid early
enrichment (i.e. $Z_{\star}$ of the young stars is very similar to $Z_{\star}$
of the old stars) have $\Delta Z_{g,\star}$ closer to 0 than objects with
flatter enrichment histories. The strong correlation between the metallicity
of the older stellar populations in a galaxy and $\Delta Z_{g,\star}$ points
to the fact that it is the older stellar populations (and hence a galaxy’s
past star formation activity) that dictate trends seen in the metallicity
ratio today. We investigate scenarios in which both high and low $\Delta
Z_{g,\star}$ galaxies can occur in Section 4.2.2.

Figure 7: Splitting the full spectral fit results into young ($<1$ Gyr) and
old ($>7$ Gyr) stellar populations. The stellar metallicity $Z_{\star}$ of the
$<1$ Gyr vs. $>7$ Gyr stars within the same galaxy are plotted. Points are
coloured by their metallicity ratio $\Delta Z_{g,\star}$, with the large star-
shaped markers representing median values in three bins of $\Delta
Z_{g,\star}$. Only galaxies with $>10\%$ of light in both young and old
templates are plotted. The majority of $<1$ Gyr stars are metal rich, but the
metallicity of the $>7$ Gyr stars is correlated with the metallicity ratio.

##  4 Discussion

###  4.1 Comparing the metal content of stars and gas

Gallazzi et al. (2005) derived both stellar metallicities and gas-phase oxygen
abundance estimates for 7462 fibre spectra from SDSS DR2. In almost all cases,
the authors found that the stellar metallicity was lower than the gas-phase
oxygen abundance, and that a large range (1$\sigma$ scatter of at least 0.3
dex) of stellar metallicities exist at fixed gas-phase oxygen abundance. In
addition, the authors found trends in the stellar metallicity-to-oxygen
abundance ratio with several other galaxy observables, including stellar mass,
4000 $\rm{\AA}$ break strength, sSFR, and gas mass fraction. Gallazzi et al.
(2005) postulated that the spread of stellar metallicities at fixed gas-phase
oxygen abundance was caused by the presence of gas inflows and/or gas
outflows. That said, pristine gas inflows and enriched gas outflows should
make the ISM more metal-poor, rendering it more similar to the stellar
metallicity. In reality, both this current work and Gallazzi et al. (2005) see
the opposite behaviour - galaxies that are more likely to lose their gas via
outflows (i.e. low $M_{\star}$ and low $\Phi$ galaxies) possess stellar and
gas-phase oxygen abundances that are more different from each other.

Lian et al. (2018a) built on this previous work by aiming to create a model
that explained the observed large differences in stellar metallicity and gas-
phase oxygen abundances of SDSS galaxies. The authors found that either strong
metal outflows or a steep IMF (both quite extreme scenarios) explained the
systematically lower (mass-weighted) stellar metallicities observed when
compared to gas-phase oxygen abundances. Our results mirror those of both
Gallazzi et al. (2005) and Lian et al. (2018a): we also report stellar
metallicities at the low-mass end that are considerably lower than the gas-
phase oxygen abundances in the same galaxy.

###  4.2 The difference between oxygen abundances and the overall ISM metal
content

An important point rarely taken into account in previous works is that oxygen,
while the most abundant heavy element of the ISM, is not its only constituent.
Many other elements exist in appreciable quantities such that we cannot assume
that the oxygen abundance is equivalent to the overall metallicity of the ISM
(which we term here $Z_{gas,tot}$).

Traditionally, (and indeed in this paper up until now), gas-phase
metallicities are inferred via oxygen abundances. Stellar metallicities are
usually inferred from iron abundances, however. Directly comparing the two can
be dangerous, as while oxygen is an $\alpha$ element, iron is not. $\alpha$
elements are produced in Type II supernovae on the timescale of order $\sim
10$ Myr. In contrast, iron-peak elements are mostly produced in Type Ia
supernovae, which occur on longer timescales.

Wyse & Gilmore (1993) show that the evolution of [O/Fe] with respect to [Fe/H]
is driven by the SFH of a galaxy. In particular, the ‘knee’ of the
[$\alpha$/Fe] vs. [Fe/H] relation depends on the amount of star formation
early in a galaxy’s life. For example, galaxies with a large initial burst of
star formation will form many stars in a short amount of time, boosting
$\alpha$-elements before the Type Ia supernovae can create any substantial
amount of iron. Conversely, galaxies with lower sustained star formation
histories will produce little oxygen before iron begins production. These two
scenarios will result in different behavior on the [$\alpha$/Fe] vs. [Fe/H]
plane, and hence the comparison of iron abundances (in our case $Z_{\star}$,
which can be approximated as [Fe/H]) and oxygen abundances ($Z_{gas}$) will
not provide a reliable comparison of gas and stellar metal content between
galaxies of differing SFHs.

Figure 8: The variation of the metallicity ratio $\Delta Z_{g,\star}$ as a
function of stellar metallicity indicator $Z_{\star}$. Points are coloured by
the sSFR of the galaxy. The medians of two bins in sSFR are shown and diverge
at low $Z_{\star}$. For a given $Z{\star}$, $\Delta Z_{g,\star}$ depends on
the sSFR of the galaxy.

Figure 8 illustrates the perils of directly comparing stellar and gas
metallicities inferred from $\alpha$ and non-$\alpha$ elements to one another.
At $Z_{\star}\gtrsim-0.6$, there is a tight sequence between $Z_{\star}$ and
$\Delta Z_{g,\star}$. Below this value however, the scatter increases
considerably, and it is difficult to tell whether a second, almost parallel
sequence exists, or the relation flattens. Indeed, when the galaxy population
is split into two bins of sSFR:

$\begin{split}&\log\rm{sSFR}>-10.5~{}\rm{yr}^{-1},\rm{and}\\\
&\log\rm{sSFR}<-10.5~{}\rm{yr}^{-1}.\end{split}$

The medians of these bins diverge at low $Z_{\star}$. Clearly, at all
$Z_{\star}$, the value of $\Delta Z_{g,\star}$ appears to depend on the sSFR
of a galaxy. Indeed, studies such as Sánchez et al. (2021) take advantage of
variations in [O/Fe] as a function of [Fe/H] to describe chemical enrichment
processes within galaxies.

It is clear that to directly compare the metal content of the stars and gas
within galaxies, we must remove the effects shown in Figure 8 and compare
metallicities based on the same element. While this is not possible without
detailed reconstruction of the star formation and enrichment histories of
every single galaxy in the sample, we can still get a feel for whether the
trends shown in Figure 5 are just a by-product of the different elements
traced by gas and stellar metallicity measurements.

The challenge in converting oxygen abundances into a total $Z_{gas,tot}$ is
that we do not know the abundance of every other element in a galaxy. We do
however have nebular photoionisation models for the Milky Way, based on the
stellar abundances of 29 nearby B stars. Nicholls et al. (2017) provide these
scaling abundance patterns for H ii regions for the Milky Way, Large
Magellanic Cloud (LMC), and Small Magellanic Cloud (SMC) which we extrapolate
for use on all SAMI galaxies. Nicholls et al. (2017) derived scaling relations
from the stellar spectra to describe the way in which elemental abundances
scale in ionised nebulae. A result of their scaling relations are simple
conversions for the base of a scaling measurement - in our case, oxygen to
iron.

The Nicholls et al. (2017) work introduces a parametric enrichment factor,
$\zeta$, to describe how atomic abundances scale with total abundance. This
allows for conversion between scales based on different reference elements,
which in our case are oxygen and iron. We use the online
calculator111https://mappings.anu.edu.au/abund/ provided by Nicholls et al.
(2017) and the $\zeta$ scaling tab to convert $\log(\rm{O/H})$ to
$Z_{gas,tot}$. The online tool uses the equations described in Sections 5.3
and 5.4 of Nicholls et al. (2017).

The conversion of Nicholls et al. (2017) is superior to simple flat scaling
relations in the literature as it takes into account how individual elements
scale relative to the total nebular metallicity along with the variation of
photoionisation models with nebular metal content. That said, these scaling
relations rely on the chemical enrichment history of the Milky Way, LMC, and
SMC only, and do not allow for other variations in abundances that could arise
from different SFHs. However, the key point is that this is an improvement
over a simple linear scaling which assumes a constant oxygen to metals ratio
for all Z.

Figure 9: Comparison of the stellar and total gas metallicity indicators for
SAMI galaxies. Hexbins are coloured by the number of galaxies in each bin. The
red dashed line denotes the running median. The gold line denotes the median
for $Z_{gas}$ from Figure 4. While $Z_{gas,tot}$ and $Z_{\star}$ are more
similar to one another than $Z_{gas}$ and $Z_{\star}$ (especially at low
metallicities), the stars are still almost always more metal-poor than the gas
in the SAMI galaxies. Figure 10: Trends in $\Delta Z_{gtot,\star}$ as a
function of four galaxy properties. The red dashed line is the median of the
SAMI galaxies and the gold line shows the median from Figure 5. The trends all
flatten when using $Z_{gas,tot}$ instead of $Z_{gas}$, a reminder that gas and
stellar abundances derived from different element bases cannot be compared
between galaxies of different SFHs.

####  4.2.1 Comparing $Z_{gas}$ and $Z_{gas,tot}$

The results of converting from $Z_{gas}$ to $Z_{gas,tot}$ are shown in Figure
9 with the comparison between stellar and total gas metallicities. The median
trend line is shown in red, while the median line for the $Z_{gas}$ relation
of Figure 4 is shown for comparison in gold. The relation between
$Z_{gas,tot}$ and $Z_{\star}$ is closer to 1:1 than $Z_{gas}$ vs. $Z_{\star}$,
and the dynamic range between $Z_{\star}$ and $Z_{gas,tot}$ is less than that
of $Z_{\star}$ and $Z_{gas}$. The stars are still almost always more metal-
poor than the ISM as expected. A ‘knee’ in the $Z_{\star}-Z_{gas,tot}$
relation is still apparent and indeed enhanced with respect to the
$Z_{\star}-Z_{gas}$ relation. Given the correction we are applying is just a
multiplicative factor which increases with decreasing metallicity, this is not
surprising. What is clear is that even with the correction, it is still true
that the difference between the two metallicities is still smaller for higher
metallicities.

We define $\Delta Z_{gtot,\star}=Z_{gas,tot}-Z_{\star}$, and in Figure 10 we
plot $\Delta Z_{gtot,\star}$ as a function of $\Phi$, $\Sigma_{\star}$,
$M_{\star}$, and sSFR. The median line for $\Delta Z_{gtot,\star}$ is shown as
a red dashed line, and for direct comparison to Figure 5, the median for
$\Delta Z_{g,\star}$ is shown in gold. The closed box model prediction of
Tinsley (1980) is marked by the grey dot-dashed line. All $\Delta
Z_{gtot,\star}$ trends are flatter than $\Delta Z_{g,\star}$ trends, and this
flattening primarily occurs at the lower-mass (and lower $\Phi$ and
$\Sigma_{\star}$, greater sSFR) ends of the relations. Whilst the trends are
flatter, a mild trend remains between $\Delta Z_{gtot,\star}$ and $M_{\star}$
and sSFR. Figures 9 and 10 show that the average $\Delta Z_{gtot,\star}$ value
is 0.35 (or the gas is $\sim 2.2\times$ more metal-rich than the stars) is
below the $\Delta Z_{gtot,\star}\sim 0.5$ expected for a closed box model
(shown as a grey dot-dashed line in Figure 10). In effect, this means that the
stars are always more metal-rich (or the gas is more metal-poor) than for a
model where there is no material either being deposited onto, or leaving a
galaxy. Both of these options are consistent with a model in which metal-rich
gas is ejected from galaxies via supernova winds, leaving enriched stars, but
less enriched gas.

Alternatively, pristine gas inflows onto a galaxy will dilute the ISM such
that it is more metal-poor than expected. If the residual trend in $\Delta
Z_{gtot,\star}$ at low stellar masses is to be believed, then it is low-mass
galaxies that approach the expected value of $\Delta Z_{gtot,\star}\sim 0.5$
predicted from closed box models of galaxy evolution (Tinsley, 1980). In
reality, we do not expect the low-mass galaxies to be better at holding onto
their gas than their high-mass counterparts, and so it is clear that the
interpretation of this ratio is more complicated than it may seem and exact
values should not be blindly used to support or discard the existence of
outflows/inflows.

Perhaps most importantly, the trend with mass (or potential) seems to be going
in the opposite direction than expected for a simple inflow-outflow scenario,
as the largest deviation from the closed box model is for high mass/high
potential galaxies. At high stellar masses it is clear that $\Delta
Z_{gtot,\star}$ is lower than what is expected for a simple closed box. Thus,
there must be either an infall of pristine gas or an ejection of metals into
the ISM. At these masses, an infall of pristine gas would seem unlikely (and
unlikely anyway at z=0) and so an outflow of metals is potentially more
possible. Observational results of quenching galaxies are best modelled with
contribution from a strong metal outflow at z=0 (e.g. Lian et al., 2018a, b;
Trussler et al., 2020) We therefore infer that inflows and especially outflows
are an important part of a galaxy’s life cycle.

Additionally, simple analytical models such as the gas regulator (or
‘bathtub’) model (e.g. Lilly et al., 2013; Peng & Maiolino, 2014) predict that
stellar metallicities should be $\sim 0.2$ dex lower than gas metallicities at
all stellar masses. It is interesting to note that this value seems most in
line with what we find for galaxies of low stellar mass. Given these models
generally include inflows and outflows but the Peng & Maiolino (2014) solution
excluded variation in SFH and $Z_{gas}$, we can imply that it is not just the
inflow and outflow history of a galaxy that is important in determining
$\Delta Z_{g,\star}$ today, but the overall star formation and chemical
evolution histories of a galaxy.

It is clear in that converting from $Z_{gas}$ to $Z_{gas,tot}$, all trends in
$\Delta Z_{gtot,\star}$ flatten. Given that Wyse & Gilmore (1993) show that
the [O/Fe] abundance of a galaxy is driven by its SFH, in converting from
$Z_{gas}$ to $Z_{gas,tot}$ we are removing the dependence of the gas-phase
metallicity indicator on [O/Fe]. While the effects of SFH are not fully
removed through this method, we can still get a feel for the effects of SFH on
the trends that we observe. The resultant flattening of the trends in $\Delta
Z_{gtot,\star}$ provides independent evidence that it is indeed the SFH of a
galaxy that is driving the observed trends seen in Figures 5 and 10.

####  4.2.2 The link between stellar populations and SFH

Cid Fernandes et al. (2007) studied the evolution of stellar metallicity in
galaxies via the derivation of SFHs from full spectral fitting. The authors
found that the star formation history of a galaxy is closely linked to its
current stellar chemical abundances (and therefore the ISM metallicity).
Galaxies whose ISM is metal-poor have relatively sustained star formation
histories: they form stars slowly over a long period of time. In contrast,
galaxies that are metal-rich assembled most of their mass at early epochs in a
large burst (e.g. Thomas et al., 2005; McDermid et al., 2015).

Our results support the Cid Fernandes et al. (2007) result while adding the
additional constraint of the current-day oxygen abundances. Figure 7 shows
that the star formation history must indeed impact $\Delta Z_{g,\star}$
measured at $z=0$: we see a large difference between $Z_{gas}$ and $Z_{\star}$
at low $Z_{\star}$ for the older stellar populations and a small difference at
higher $Z_{\star}$ within the older stellar population.

In Figure 11 we provide a cartoon illustration of possible evolutionary
scenarios for two galaxies at $z=0$. The red line represents a galaxy which
has $\Delta Z_{g,\star}\sim 0$, while the blue line represents a galaxy whose
stars are much more metal-poor than its ISM ($\Delta Z_{g,\star}>0$). Panel
(a) of Figure 11 shows the metallicity evolution of the two galaxies as a
function of time and panel (b) shows the star formation histories required to
produce the observed metallicity evolution. In panel (a), the red line
represents a galaxy that enriched early. Given the link between star formation
and chemical enrichment, we can assume that this galaxy underwent a burst of
star formation early (as shown in Figure 11 (b). Assuming the burst is long
enough for a number of generations of stars to form and re-enrich the ISM such
that the stars at the end of the burst are formed metal-rich, the average
stellar metallicity of the old stellar populations will be metal-rich, similar
to both its young stellar populations and gas-phase abundance at current
times. A short burst of early star formation is expected for high-mass
galaxies, and we note in Figure 5 (c) that it is high-mass galaxies that on
average have $\Delta Z_{g,\star}\sim 0$.

The blue line of Figure 11 (a) represents a galaxy that has undergone a much
more sustained chemical enrichment. We expect the star formation history of
this galaxy to be much more prolonged, without the initial burst of star
formation. As a result, the old stellar populations are on average metal-poor,
and while the average $<1$ Gyr stellar populations are more metal-rich, they
are not as enriched as the gas at current times. For this reason, $\Delta
Z_{g,\star}>0$. Low-mass galaxies are known to have sustained bouts of star
formation throughout their lifetimes, and we note in Figure 5 (c) that it is
low-mass galaxies that on average have $\Delta Z_{g,\star}>0$. A galaxy’s
instantaneous SFR is strongly linked to the gas availability at a given time.
It therefore follows that while the galaxy represented by the red line must
have had substantial amounts of gas available to it at early times, it is the
galaxy represented by the blue line that must have a greater amount of gas
available now.

It is the shape of the SFH, which in turn is linked to the stellar mass of a
galaxy, that determines the chemical evolution history of a galaxy, and hence
the differences seen between stellar metallicity and gas-phase oxygen
abundance.

(a)

(b)

Figure 11: A cartoon representation of possible chemical evolution and star
formation histories for two galaxies. The red line represents a galaxy with
$\Delta Z_{g,\star}\sim 1$ that enriched early with an early burst of star
formation. The blue line represents a galaxy where $\Delta Z_{g,\star}<<1$ at
$z=0$ and had a more sustained metal enrichment with low-level star formation.
Panel (a) shows two possible metal enrichment pathways, and (b) the
corresponding SFHs.

##  5 Summary & Conclusions

We compare two commonly derived metallicity indicators, the stellar
metallicity ($Z_{\star}$) and the gas-phase oxygen abundance ($Z_{gas}$) to
one another for 472 galaxies in the SAMI galaxy survey. We define the ratio of
gas-phase to stellar abundances, $\Delta Z_{g,\star}$, and find that $\Delta
Z_{g,\star}$ correlates with $M_{\star}$, sSFR (a proxy for galaxy SFH), and
$\Phi$. We see a weak correlation with $\Sigma_{\star}$.

We split full spectral fitting results into young ($<1$ Gyr) and old ($>7$
Gyr) stellar ages and determine the metallicity of these populations. While
younger stars are uniformly metal-rich, it is the metallicity of the older
stars that dictates $\Delta Z_{g,\star}$. We infer a scenario whereby $\Delta
Z_{g,\star}$ is strongly influenced by a galaxy’s star formation history: a
galaxy with an early burst of star formation will build up its metals early,
enriching its older stellar populations. As a result of the early enrichment,
$Z_{\star}~{}\sim~{}Z_{gas}$. Conversely, galaxies with a delayed star
formation history that reach their peak SFR at later times will take longer to
build up their metals. Older stellar populations will be less metal-enriched,
and $Z_{\star}~{}<<~{}Z_{gas}$.

Metallicities derived via different elemental abundance indicators should not
be blindly compared when the elements are produced by processes occurring on
different timescales. In particular, the ratio of stellar metallicities
derived via iron abundances and gas-phase metallicities derived via oxygen
abundances will differ depending on the SFH of a galaxy. Indeed, we show that
the $\Delta Z_{g,\star}$ of galaxies at fixed $Z_{\star}$ depends on the sSFR
of a galaxy.

We attempt to convert oxygen abundances to $Z_{gas,tot}$ using the relation of
Nicholls et al. (2017). The resulting ratio of $\Delta Z_{gtot,\star}$ is
flatter than that with $\Delta Z_{g,\star}$, and greater than that expected
for a closed box model. We conclude that this is direct evidence for the
importance on inflows and outflows within galaxies.

Our results imply that the ratio of $\Delta Z_{g,\star}$ depends on the
chemical enrichment history of a galaxy, of which sSFR and stellar mass are
the best observational proxies. While inflows and outflows at current times
may help regulate the fraction of metals in the ISM, it is a galaxy’s star
formation history that determines the ratio of stellar metallicity and gas-
phase oxygen abundances observed today. Our work confirms that $Z_{gas}$ and
$Z_{\star}$ provide us with very different information on galaxy evolution and
that they cannot be blindly compared to one another, nor can one be used to
make assumptions about the other.

##  Appendix A Mass-weighted stellar metallicity measures

Light (or luminosity)-weighted stellar metallicity measures derived via full
spectral fitting methods are biased towards the younger (and brighter) stellar
populations in a galaxy, enabling comparison to observational quantities such
as Lick indices and emission line diagnostics. Mass-weighted measures instead
trace the distribution of stellar mass within a galaxy and therefore better
trace the metal content of old stars within a galaxy. While useful for
comparison with theoretical models, there are more assumptions involved in
their derivation. For comparative purposes, we present Figures 12 and 13,
which may be directly compared to the light-weighted metallicity measures as
shown in Figures 2 and 5.

Importantly, from Figure 12 we see that there is little difference in the
median MZR between mass-weighted and light-weighted measures: mass-weighted
metallicities are $\sim 0.1$ dex higher than light-weighted for galaxies of
$\log M_{\star}[\rm{M}_{\odot}]>10.5$ and the reverse is true for $\log
M_{\star}[\rm{M}_{\odot}]<9.5$ , meaning that the main results of this paper
are not affected by choice of metallicity determination. The behaviour of the
median mass-weighted and light-weighted metallicity values is interesting, but
a full analysis of which is reserved for future work.

If mass-weighted metallicities are used to calculate $\Delta Z_{g,\star}$ as
in Figure 13, we see that all trends with $\Phi$, $\Sigma_{\star}$,
$M_{\star}$, and sSFR steepen, though scatter increases by between 0.03-0.07
dex. When light-weighted metallicities were considered, we determined that
mass has the strongest correlation with $\Delta Z_{g,\star}$. This is still
the case when mass-weighted metallicities are used, though $\Phi$ now exhibits
a stronger trend than sSFR. While both properties are doubtless important in
determining the ratio of stellar to gas-phase metallicity within a galaxy,
there may be a residual trend between mass- and light-weighted metallicity
measures as a function of the galaxy’s current SFR which may be affecting
trends seen in panel (d).

Figure 12: Same as Figure 2, but showing the comparison between pPXF
metallicity measures derived via light-weighting (red median line, as in
Figure 2), mass-weighting (hexbins and purple median line), and those derived
via Lick indices from Scott et al. (2018).  Figure 13: Same as Figure 5, but
with $\Delta Z_{g,\star}$ derived from mass-weighted metallicity measurements.
The purple dashed line denotes the median mass-weighted values for a given
property, and the red line the light-weighted values as in Fig 5. Blue hexbins
are coloured by the number of galaxies per bin and are for the mass-weighted
measurements.

## Acknowledgements

The authors wish to thank the anonymous referee for their insightful comments
that have improved the impact of this work. The authors also wish to thank
Jianhui Lian for helpful conversations about his previous work.

The SAMI Galaxy Survey is based on observations made at the Anglo-Australian
Telescope. The Sydney-AAO Multi-object Integral field spectrograph (SAMI) was
developed jointly by the University of Sydney and the Australian Astronomical
Observatory. The SAMI input catalogue is based on data taken from the Sloan
Digital Sky Survey, the GAMA Survey and the VST ATLAS Survey. The SAMI Galaxy
Survey is supported by the Australian Research Council Centre of Excellence
for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number
CE170100013, the Australian Research Council Centre of Excellence for All-sky
Astrophysics (CAASTRO), through project number CE110001020, and other
participating institutions. The SAMI Galaxy Survey website is http://sami-
survey.org/. LC is the recipient of an Australian Research Council Future
Fellowship (FT180100066) funded by the Australian Government. SB acknowledges
funding support from the Australian Research Council through a Future
Fellowship (FT140101166). JJB acknowledges support of an Australian Research
Council Future Fellowship (FT180100231). FDE acknowledges funding through the
ERC Advanced grant 695671 “QUENCH”, the H2020 ERC Consolidator Grant 683184
and support by the Science and Technology Facilities Council (STFC). JvdS
acknowledges support of an Australian Research Council Discovery Early Career
Research Award (project number DE200100461) funded by the Australian
Government. JBH is supported by an ARC Laureate Fellowship FL140100278. The
SAMI instrument was funded by Bland-Hawthorn’s former Federation Fellowship
FF0776384, an ARC LIEF grant LE130100198 (PI Bland-Hawthorn) and funding from
the Anglo-Australian Observatory. M.S.O. acknowledges the funding support from
the Australian Research Council through a Future Fellowship (FT140100255).

## Data Availability

The SAMI Galaxy Survey data release 3 (DR3) is available online at
https://datacentral.org.au/. The additional data products derived for this
work including stellar and gas-phase metallicity estimates can be provided on
request.

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