Characterizing the Local Relation between Star Formation Rate and Gas-phase Metallicity in MaNGA Spiral Galaxies

Dark matter overdensities in the early universe become galaxies through a self-regulated process controlled by gas accretion and feedback from massive stars and black holes, as well as by galaxy mergers (e.g., Dekel et al. 2009; Bouché et al. 2010; Davé et al. 2011, 2012; Silk & Mamon 2012; Lilly et al. 2013; Sánchez Almeida et al. 2014). Even though this picture is thought to be reliable, the emergence of fully fledged galaxies from the underlying physical laws is not yet properly understood. The formation and evolution of galaxies has to be modeled numerically using ad hoc recipes for the key physical processes, since they cannot be computed self-consistently from first principles. This so-called subgrid physics is tuned to reproduce some of the scaling properties observed in galaxies (e.g., the distribution of luminosities or stellar masses), whereas other scaling properties are used to support the consistency of the simulated galaxies (Ceverino et al. 2014; Hopkins et al. 2014, 2018; Vogelsberger et al. 2014; Crain et al. 2015; Schaye et al. 2015; Springel et al. 2018). Thus, the observed scaling relations are fundamental to assess the realism of our understanding of galaxy formation and evolution.

Among these scaling relations, those that link star formation rates (SFRs) with the properties of the star-forming gas provide direct information on the star formation process and its regulation. It has been long known that the SFR of a galaxy scales with its stellar mass (M_⋆; e.g., Brinchmann et al. 2004; Daddi et al. 2007; Noeske et al. 2007; Renzini & Peng 2015; Cano-Díaz et al. 2016). This so-called main sequence characterizes star-forming galaxies, which also follow a scaling relation linking the metallicity of the gas involved in the ongoing star formation (Z_g) with M_⋆ (the mass–metallicity relation (MZR); e.g., Skillman et al. 1989; Tremonti et al. 2004; Berg et al. 2012; Sánchez et al. 2013). Since both SFR and Z_g increase with increasing M_⋆, one may naively think that for a fixed M_⋆, Z_g increases with increasing SFR. However, Lara-López et al. (2010) and Mannucci et al. (2010) found that galaxies with a higher SFR show lower Z_g at a given M_⋆. This relation between M_⋆, SFR, and Z_g is now called the fundamental metallicity relation (FMR), and it was already suggested in studies before the relation was coined (Ellison et al. 2008; Peeples et al. 2009; López-Sánchez 2010). This relation could be explained in terms of cosmic gas accretion predicted in cosmological numerical simulations of galaxy formation (e.g., Mannucci et al. 2010; Brisbin & Harwit 2012; Davé et al. 2012; Maiolino & Mannucci 2019, and references therein).

Most scaling relations were originally found by considering the global properties of galaxies. However, there is substantial evidence that they present a counterpart based on local variations, suggesting that the global relations could arise from the local ones (e.g., Rosales-Ortega et al. 2012; Barrera-Ballesteros et al. 2016; Cano-Díaz et al. 2016; Hsieh et al. 2017; Erroz-Ferrer et al. 2019). This may also be the case with the FMR; various observational works have hinted that, within a given galaxy, star-forming regions of particularly high surface SFR are associated with drops in metallicity. Thus, for galaxies with the same M_⋆, those holding more active star-forming regions would show larger integrated SFR and lower Z_g.

Among the observational evidence, the extremely metal-poor galaxies of the local universe studied by Sánchez Almeida et al. (2015) have a dominant starburst with a metallicity between five and 10 times lower than the underlying host galaxy (see also Sánchez Almeida et al. 2013, 2014). Cresci et al. (2010) found an anticorrelation between SFR and metallicity in three galaxies at z ∼ 3. A large H ii region at the edge of J1411–00 contains most of the SFR of the galaxy and has an oxygen abundance ∼0.2 dex lower than the rest of the galaxy (Richards et al. 2014). It is revealed that at least three H ii regions in HCG 91c harbor an oxygen abundance ∼0.15 dex lower than expected from their immediate surroundings and the abundance gradient (Vogt et al. 2015). Using a sample of 14 star-forming dwarf galaxies in the local universe, Sánchez Almeida et al. (2018) showed the existence of a spaxel-to-spaxel anticorrelation between the index N2 (i.e., the ratio between [N ii] λ6583 and Hα) and the Hα flux, which are usually employed as proxies for Z_g and SFR, respectively. Thus, the observed N2-to-Hα relation may reflect a local anticorrelation between Z_g and SFR. The galaxy sample employed by Sánchez Almeida et al. (2018) was selected without a physically motivated criterion based only on the availability of the required integral field spectroscopic (IFS) data; therefore, the relation seems to reflect a trend common to dwarf galaxies.

Also based on IFS data, Hwang et al. (2019) studied the existence of anomalously low metallicity (ALM) regions in 1222 star-forming galaxies in the Sloan Digital Sky Survey IV (SDSS-IV) Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey (Bundy et al. 2015). The ALMs are defined as star-forming regions in which the gas-phase metallicity is anomalously low compared to expectations from the empirical relation between metallicity and stellar surface mass density at a given stellar mass. Hwang et al. (2019) found ALMs in 25% of the galaxies; therefore, it is a common phenomenon. The incidence rate of ALMs increases with both global and local specific SFR (sSFR; i.e., SFR/M_⋆) and is higher in lower-mass galaxies, the outer regions of galaxies, and morphologically disturbed galaxies. Even though the presence of ALMs does not directly prove the existence of a local anticorrelation between Z_g and SFR, it is very suggestive, since ALMs are both common and associated with enhanced star formation.

In this paper, MaNGA galaxies are used for the first time to characterize the local relation between Z_g and SFR. The large statistics of the survey, described in Section 2, allows us to explore this relation in an extended range of galaxy masses not covered by previous studies. First, we explain the methodology and the procedure followed to derive the properties of the star-forming regions (Section 3). Then we show that the relation is present in most star-forming galaxies (Section 4). In the same section, we quantify the relation via the slope of a linear regression. This parameter is the basis for studying the dependence of the relation on galaxy properties, work that is carried out using tools of artificial intelligence, namely, random forests (RFs; Section 5). In order to characterize such dependences, a complementary polynomial regression analysis is also carried out (Section 6). Finally, the discussion of the results and the main conclusions are given in Section 7.

2.1. MaNGA Data

MaNGA (Bundy et al. 2015) is an ongoing survey developed as part of the SDSS-IV project (Blanton et al. 2017). The aim of MaNGA is to obtain IFS information for a sample of 10,000 galaxies up to z ∼ 0.15. The observations are conducted on the basis of an integral field unit (IFU) fiber system feeding the BOSS spectrographs (Smee et al. 2013) on the Sloan 2.5 m telescope at Apache Point Observatory, New Mexico (Gunn et al. 2006). The IFU fibers are distributed in 17 hexagonal bundles with five different configurations that comprise 19–127 fibers. The field of view (FoV) of the instrument varies from 125 to 325 in diameter (Drory et al. 2015), with uniform coverage of the targets achieved thanks to the performed three-point dither pattern (Law et al. 2015). The spectrographs provide wavelength coverage from 3600 to 10300 Å, with a nominal resolution of λ/Δλ ∼ 2100 at 6000 Å (Smee et al. 2013).

The MaNGA mother sample is split into two main subsets, named primary and secondary samples, defined by two radial coverage goals (Wake et al. 2017). The primary sample comprises ∼5000 galaxies reaching out to 1.5 effective radii (R_e), and the secondary one accounts for ∼3300 objects with coverage up to 2.5 R_e. An additional third subsample, known as the color-enhanced supplement (∼1700 galaxies), is selected to increase the number of systems that are underrepresented in the color–magnitude space (namely, high-mass blue galaxies, low-mass red galaxies, and "green valley" galaxies).

MaNGA was designed to have the same number of galaxies in each bin of i-band absolute magnitude M_i (Wake et al. 2017). Because M_i is a proxy for stellar mass, the survey contains roughly the same number of galaxies per log mass bin in the range between 10⁹ and 10¹¹ M_⊙ (see Figure 1, top panel). Since stellar mass is one of the main drivers in setting galaxy properties (e.g., Blanton & Moustakas 2009), MaNGA is a good starting point for any exploratory study such as ours.

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The data analyzed here were calibrated with version 2.4.3 of the data reduction pipeline (DRP; Law et al. 2016), which includes the standard steps for fiber-based IFS data reduction, such as bias subtraction and flat-fielding, flux and wavelength calibration, and sky subtraction. At the end, the pipeline provides a regular-grid data cube, with the first two coordinates indicating the R.A. and decl. of the target and the third one being the step in wavelength. As a result, we have individual spectra for each sampled spaxel of 05 × 05 and a final spatial resolution of FWHM ∼ 25, which corresponds to a physical resolution of ∼1.5 kpc (at an average redshift of 0.03; see Section 2.2 for details on the selected subsample).

More detailed information about the MaNGA sample, survey design, observational strategy, and data reduction can be found in Law et al. (2015, 2016), Yan et al. (2016), and Wake et al. (2017).

2.2. Analyzed Sample

3.1. Measurement of Emission Lines with Pipe3D

3.2. Selection of Star-forming Regions

3.3. Metallicity

As a proxy for Z_g, we use the oxygen abundance (O/H) of the selected star-forming spaxels. Here Z_g is the fraction of metals by mass, whereas O/H is defined as the abundance of O by number relative to H. However, there is no inconsistency in using any of them to infer the local SFR–Z_g relation, since O/H and Z_g are proportional to each other, provided that the relative abundance of the different metals is the same for all galaxies.

The oxygen abundances are derived by adopting the empirical calibration proposed by Marino et al. (2013, hereafter M13) for the O3N2 index,

$$\begin{eqnarray}&&12+\mathrm{log}\left({\rm{O}}/{\rm{H}}\right)=8.533-0.214\,\times {\rm{O}}3{\rm{N}}2,\end{eqnarray} \tag{ 1 }$$

with ${\rm{O}}3{\rm{N}}2=\mathrm{log}$ ([O iii] λ5007/Hβ × Hα/[N ii] λ6584). This relation is valid for the interval −1.1 < O3N2 < 1.7 (corresponding to $8.17\lt 12+\mathrm{log}({\rm{O}}/{\rm{H}})\lt 8.77$). Therefore, star-forming regions presenting values outside this range are excluded from the analysis (representing barely 3% of the detected H ii regions for 99.96% of the galaxies).

The M13 calibration constitutes one of the most accurate calibrations to date for the O3N2 index, since it employs T_e-based abundances of ∼600 H ii regions from the literature combined with new measurements from the CALIFA survey. The improvement of this calibration is especially significant in the high-metallicity regime, where previous calibrators based on this index lack high-quality observations (e.g., Pettini & Pagel 2004; Pérez-Montero & Contini 2009).

We also determine the oxygen abundance using version v.3.0 of HII-CHI-MISTRY (Pérez-Montero 2014) in order to show the robustness of our results that are not contingent upon the adopted method to measure the metallicity. This calibrator is based on a grid of photoionization models calculated using the CLOUDY v.13 code (Ferland et al. 2013). The grid covers a wide range of input conditions of abundances and ionization parameters, leading to the derivation of abundances consistent with the T_e method based on collisionally excited lines. This calibration can be used through a publicly available Python module.⁸ In this work, information on the [O iii] λ4363 emission line has not been fed to the code due to its faintness and consequently challenging detection. In this case, the algorithm uses a "log U limited" grid of photoionization models to derive reliable oxygen abundances (for more information, see Section 4.2 of Pérez-Montero 2014).

3.4. SFR

The SFR is derived for the star-forming spaxels of each galaxy in the sample by adopting the classical approach of Kennicutt (1998) based on the dust-corrected Hα luminosities. These luminosities are obtained by deriving the apparent magnitudes from the flux density in an Hα image recovered from the data and then transforming these quantities to luminosities knowing the galaxy distance. Finally, in order to derive the SFR from the Hα luminosities, we make use of the updated calibration presented in Hao et al. (2011) for a Salpeter initial mass function (IMF; Salpeter 1955):

$$\begin{eqnarray}&&\mathrm{SFR}\,[{M}_{\odot }\,{\mathrm{yr}}^{-1}]=8.79\,\times {10}^{-42}\,L\left({\rm{H}}\alpha \right)\,(\mathrm{erg}\,{{\rm{s}}}^{-1}).\end{eqnarray} \tag{ 2 }$$

3.5. Other Global Galaxy Properties

The aim of this study is to find and then characterize the existence of a local relation between SFR and metallicity. In order to describe local spatial variations of these properties, their characteristic radial profiles must be removed. For each individual galaxy, we derive the residuals by subtracting the azimuthally averaged radial Z_g (using the M13 calibration) and SFR distributions from the 2D maps. These averaged values are measured in elliptical annuli of 1'', taking into account the position angle and ellipticity of the galaxies in order to correct for inclination. The resulting residuals expressed in logarithmic scale (hereafter ${\rm{\Delta }}\mathrm{log}{Z}_{g}$ and ${\rm{\Delta }}\mathrm{logSFR}$, respectively) for two example galaxies in the sample are shown in the left and middle panels of Figure 2. In the first case (8312–12703; top row), we can see that the peaks (yellow areas) and dips (dark blue) of both distributions are spatially coincident, whereas in the latter (7991-12701; bottom row), the highest-metallicity residuals correspond to the lowest ${\rm{\Delta }}\mathrm{logSFRs}$.

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This behavior can be observed more clearly by representing ${\rm{\Delta }}\mathrm{log}{Z}_{g}$ of each star-forming spaxel against its ${\rm{\Delta }}\mathrm{logSFR}$. The right panels of Figure 2 show this scatter plot for the two example galaxies. As hinted by the apparent coincidences in the 2D maps, the top galaxy exhibits a positive correlation between both properties, whereas the bottom galaxy shows a clear anticorrelation.

In order to quantify the correlation, we perform a linear regression to the data points for each individual galaxy. The obtained slopes, together with their corresponding errors, are presented in Table 2 (Appendix A). Slope errors are derived via 100 Monte Carlo simulations, taking into account the errors of both parameters, ${\rm{\Delta }}\mathrm{log}{Z}_{g}$ and ${\rm{\Delta }}\mathrm{logSFR}$, that are determined from the propagation of the measurement errors of the emission line fluxes. For the metallicity, we have also propagated the calibration error associated with the scatter in the O3N2 relation (0.08 dex; see Marino et al. 2013), although it is not included in the average error bars represented in the top right corner of the right panels of Figure 2.

The PDF of the slopes of the linear fits for the entire sample is represented in Figure 3 (blue dashed line). The measured slope values range from −0.20 to 0.15, with 60% of the analyzed galaxies displaying an SFR–Z_g anticorrelation (i.e., negative slope) within the error bars. The remaining galaxies show no correlation (i.e., zero slope; 19%) or positive correlation (i.e., positive slope; 21%). We fit the PDF with a Gaussian function (green solid line) sampled using the same bins as the observed distribution. The peak of the distribution is found at −0.012, with a standard deviation of 0.054. In order to estimate the contribution of the slope errors to the resulting width of the distribution, we build 100 mock distributions of slopes in which each observed point is randomly shifted from the central value of −0.012 according to its measured error (assumed to follow a normal distribution). Gaussian fits to these mock distributions show that observational errors can only explain up to ∼35% of the slope distribution width. This result suggests a physical origin for the large range of slope values displayed by the galaxies. In the next section, we will investigate a possible dependence of the SFR–Z_g relation with different galaxy properties.

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The slopes of the local SFR–Z_g relation are also determined by applying the HII-CHI-MISTRY code to derive the gas-phase metallicities. The comparison of these values with the ones derived using the M13 calibration for the O3N2 index is represented in Figure 4. We can observe that the values corresponding to the HII-CHI-MISTRY calibration are higher than those obtained with the M13 calibration (brown solid line compared to the gray solid line representing the one-to-one relation). In this case, 35% of the galaxies exhibit an SFR–Z_g anticorrelation, 55% exhibit a positive correlation, and 10% show signs of no correlation. This is not surprising, since discrepancies in the derivation of the oxygen abundances between multiple diagnostics and calibrations are broadly known (for an extended discussion, see Kewley & Ellison 2008; López-Sánchez et al. 2012). However, the correlation between both slopes is quite tight, allowing us to conclude that, although the actual measured values for the SFR–Z_g slopes differ, the qualitative results of the analysis of the dependence with different galaxy properties are equivalent for both calibrators. For the sake of clarity, below we only show the results based on the use of the M13 calibrator. The decision is based on the tighter local SFR–Z_g relations found for the galaxies with this calibrator. This is determined using the normalized rms error (NRMSE) preferred when comparing data sets with different scales,

$$\begin{eqnarray}&&\mathrm{NRMSE}=\displaystyle \frac{\sqrt{{\displaystyle \sum }_{i=1}^{n}{\left({y}_{i}-{\hat{y}}_{i}\right)}^{2}/n}}{\left({Q}_{3}-{Q}_{1}\right)},\end{eqnarray} \tag{ 3 }$$

where Q₃ − Q₁ is the difference between the 75th and 25th percentiles, y_i is the ith observed abundance residual, and ${\hat{y}}_{i}$ is the predicted value for the linear fit. The average NRMSE for M13 is 0.76, against 0.81 for HII-CHI-MISTRY. Despite this choice, we have reproduced the analysis using the HII-CHI-MISTRY code, with no significant differences between the obtained results. The reader can find this analysis in Appendix B.

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In this section, we assess which galaxy properties may be determined in the local SFR–Z_g relation by applying the statistical technique known as RF. It is a machine-learning supervised algorithm proposed by Breiman (2001) that consists of an ensemble (combination) of decision trees. The purpose of a decision tree is to find the input features (the galaxy properties, in our case) that contain the most information regarding the target feature (the derived slope of the SFR–Z_g relation) and creating a model to predict it by defining a set of conditions on the values of the input features. When the features are categorical, we talk about classification decision trees (that lead to an RF classifier), and when they are numerical, we talk about regression decision trees (that lead to an RF regressor, as in our case). However, decision trees have the disadvantages of presenting high variance (thus leading to an overfitting of the data) and being instable against small changes, which can lead to a very different tree structure. The RF algorithm allows one to overcome these limitations by building multiple decision trees and averaging them based on the bootstrap aggregation technique (or bagging). This approach consists of (i) dividing the training sample into randomly selected subsets with replacement and fitting a decision tree to each of them and (ii) considering a randomly selected subset of features when splitting the trees. With this technique, the algorithm decreases the variance, reducing the chances of overfitting, as well as reducing the correlation between the trees.

In this study, we focus the analysis on 11 parameters that fully characterize the global properties of galaxies: total M_⋆, average Σ_⋆ at R_e, SFR, sSFR, morphological type, g − r color, σ_cen, average LW stellar age and metallicity measured at R_e, oxygen abundance at R_e, and slope of the oxygen abundance radial gradient. The goal of the RF is to assess which of these properties, if any, may be affecting the observed SFR–Z_g relation. The implementation of the algorithm was performed using the scikit-learn package for Python (Pedregosa et al. 2011). Next, we describe the basic steps followed to run the algorithm.¹⁰

We first split the sample of 708 galaxies for which all of the abovementioned properties and the slope of the SFR–Z_g relation are available into two subsets. The first subset, called the training sample, corresponds to 2/3 of the galaxies (474), and it is used to create the model. For these galaxies, the selected set of 11 properties described above is provided to the algorithm to train the model (these are the predictors). The slope of the SFR–Z_g relation is considered the target feature aimed to be predicted by the RF model (this is the solution). The algorithm requires not only the predictors but also the solutions (called labels) to train the model.

After training the model by building a set of decision trees, the RF allows one to predict the slope of the SFR–Z_g relation of a new galaxy based on the values of its galaxy properties. However, once the model is trained, it is important to evaluate its performance on a new set of data. With this purpose, we employ the second subset of data, called the test sample, corresponding to the remaining one-third of the galaxies (234). Applying the model to the test sample, we obtain a set of predictions for the slope of the SFR–Z_g relation. The comparison of these predictions with the measured values provides an estimation of the precision of the model.

Before training the model, in order to optimize the performance of the algorithm, it is recommended that one constrain the model to make it simpler and less prone to overfitting. This is called regularization. The amount of regularization can be controlled by tuning the hyperparameters (HPs), i.e., the parameters of the algorithm. In the case of an RF regressor, the main HPs include the number of trees in the forest (n), the number of randomly selected features to consider in each split (m), the maximum depth of the trees (max_depth), the minimum number of samples required in each split (min_split), and the minimum number of samples that remain at the end of the different decision tree branches (stopping the algorithm from splitting the sample if its size is below this limit, min_leaf). To select the HPs that best suit the problem, a commonly used method is called K-fold cross-validation (CV). This method consists of splitting the training sample into K subsets, called folds; training the model on a different combination of K − 1 folds; and evaluating it on the remaining one. The performance measure reported is then the average of the values computed in the loop. Most authors suggest performing K-fold CV using K = 5 or 10 (James et al. 2013). Here we use K = 5. We perform 100 iterations of the entire 5-fold CV process, each time using different values for the HPs. The selected HP values are the ones that achieve the highest average performance across the K-folds. In our case, it results in n = 100, m = 6, ${\max }_{\mathrm{depth}}\,=\,120$, ${\min }_{\mathrm{split}}\,=\,10$, and ${\min }_{\mathrm{leaf}}\,=\,4$.

Finally, using the selected HPs, we train the model on the full training sample and then evaluate on the test sample. Figure 5 represents the predicted slopes of the SFR–Z_g relation by the RF algorithm against the measured values for both the training (blue circles) and test (red triangles) samples. We can see that the dispersion of the values around the one-to-one relation (dashed line) is similar for both samples (0.018 and 0.026, respectively), showing that the algorithm is able to predict with the same accuracy the slopes of galaxies that are not used to train the model.

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As mentioned before, some interesting information provided by the RF algorithm is the relative importance or contribution of each input feature in predicting the solution. These data are very useful, since they allow us to assess which of the analyzed properties of the galaxies have a large effect on the SFR–Z_g relation and which of them are completely irrelevant for determining the relation. In rough outlines, the feature importance is a measure of how effective the feature is at reducing variance when splitting the variables along the decision trees. The higher the value, the more important the feature. In this analysis, we obtain the following importance values for the predictors (in descending order): (a) oxygen abundance at R_e (0.48), (b) g − r color (0.12), (c) M_⋆ (0.11), (d) LW stellar age at R_e (0.09), (e) average Σ_⋆ at R_e (0.07), (f) SFR (0.03), (g) slope of the oxygen abundance radial gradient (0.03), (h) LW stellar Z at R_e (0.02), (i) morphological type (0.02), (j) σ_cen (0.02), and (k) sSFR (0.02). In order to test the stability of these values, we run the RF algorithm 50 times. Figure 6 shows the trend of the values for the 50 realizations. Although the actual values change slightly, the ranking of the features is almost always the same. The values for the importance clearly show that the global Z_g of a galaxy is the primary factor determining its local SFR–Z_g relation. Secondary factors ordered by decreasing importance are g − r color, M_⋆, average LW stellar age, and, although to slightly less of an extent, average Σ_⋆ at R_e. The remaining properties have proven to be of little relevance for the relation.

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The RF approach has allowed us to identify the galaxy properties that might play a role in shaping the local SFR–Z_g relation. Among all of the analyzed properties, the characteristic Z_g of the galaxies is the more determining factor, followed by M_⋆, g − r color, LW age of the SP, and Σ_⋆. The next step is finding a parametric model for the relationship between these properties and the slope of the SFR–Z_g relation. This is the basis of the polynomial regression presented in this section.

Figure 7 shows the slope of the local SFR–Z_g relation as a function of the different galaxy properties provided as inputs to the RF algorithm. From top left to bottom right, the panels represent (a) oxygen abundance at R_e, (b) M_⋆, (c) g − r color, (d) LW stellar age at R_e, (e) average Σ_⋆ at R_e, (f) integrated SFR, (g) morphological type, (h) LW stellar Z at R_e, (i) σ_cen, (j) slope of the oxygen abundance radial gradient, and (k) sSFR. To more clearly see the general trend of the distributions, we represent (brown squares) the averaged SFR–Z_g slope values for 10 bins in which the parameter range has been divided. The error bars indicate the standard deviation of the slope values within each bin. Focusing on the first six panels ((a)–(f)), which exhibit the clearest relations from all analyzed properties, we can see that the SFR–Z_g slope presents a positive correlation with all of them. The only anticorrelation appears for the morphological type, although the dispersion is high. It is worth mentioning that in the case of the characteristic Z_g, the positive correlation seems to flatten at a slope value of around −0.1, suggesting the existence of a lower limit for the slope of the local SFR–Z_g relation for low-metallicity galaxies (with $12+\mathrm{log}({\rm{O}}/{\rm{H}})$ below ∼8.2–8.3). Finally, the observed distributions are quite narrow until panel (e), corresponding to the galaxy properties for which the RF algorithm finds significative contributions. From panel (f) on, the distributions widen until observing a near absence of any relation for the last two parameters.

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In order to characterize the relations shown in Figure 7, we fit a second-order polynomial to all of them. This fit, represented by the brown solid lines, is performed on the averaged SFR–Z_g slope values of the bins (brown squares), excluding those presenting less than 1% of the total number of galaxies (open squares). The coefficients of the polynomials are provided in Table 1. In addition, the NRMSEs of the fits are displayed in each panel and provided in Table 1. Properties are ordered by the NRMSE in the figure (in ascending order). We can see that the characteristic Z_g presents the lowest NRMSE, supporting the RF-based result that this property is the fundamental factor in shaping the local SFR–Z_g relation. The other NRMSE values also go hand in hand with the RF conclusions, with the secondary parameters presenting the intermediate values and the ones with the lowest importance levels the highest NRMSE.

Table 1.  Coefficients and NRMSE of the Second-order Polynomial Fit to the Relations between the Local SFR–Z_g Slope and the Analyzed Galaxy Properties

Galaxy Property	a0	a1	a2	NRMSE
Zga at Re	+45.15295	−11.10775	+0.68153	0.392
M⋆ (log M⊙)	−1.46183	+0.22015	−0.00781	0.526
g − r color (mag)	−0.17349	+0.38518	−0.21335	0.547
LW stellar age at Re (log yr)	−5.50915	+1.15029	−0.06002	0.557
Average Σ⋆ at Re (log (M⊙ pc−2))	−0.17756	+0.09923	−0.01201	0.584
SFR (log (M⊙ yr−1))	−0.02564	+0.03650	−0.00407	0.606
Morphological type	−0.03876	+0.02916	−0.00585	0.626
LW stellar Z at Reb	+0.02879	+0.43084	+0.56389	0.644
σcen (km s−1)	−6.5825 10−2	1.0889 10−3	−4.9851 10−6	0.658
Slope of the Zga radial gradient (dex ${R}_{e}^{-1}$)	−0.03733	−0.18969	−1.03716	0.683
sSFR (log Gyr−1)	−0.09028	−0.06067	−0.01083	0.683

Notes. The polynomial fits have the form $p(x)={a}_{0}+{a}_{1}\,x+{a}_{2}\,{x}^{2}$.

^aWith oxygen abundance as proxy, in the usual scale $12+\mathrm{log}({\rm{O}}/{\rm{H}})$. ^bIn logarithmic scale and referred to the solar metallicity.

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Finally, once we have characterized the effect of the different galaxy properties on the slope of the local SFR–Z_g relation, one important issue we need to address is whether these relations present a secondary dependence on the remaining properties. The color-coding is a useful tool to investigate this issue. As an example, in Figure 7, we color-code the individual points according to the stellar mass of the galaxies. In some cases, we can see clear trends from left to right (panels (a)–(f)). These trends are the result of a dependence between the properties exhibited in these panels and the galaxy mass. For instance, we can see in the first panel that galaxies with the lowest metallicities are less massive systems. It is just the well-known MZR. However, a secondary dependence of the SFR–Z_g slope on any galaxy property should be reflected in the plots as a trend along the vertical axis, not along the horizontal direction. This trend is indeed observed in panels (g)–(k), where we can see that the red symbols (massive galaxies) appear on the top of the distributions, and the blue ones (less massive systems) show up on the bottom. This result is not surprising, since there is no dependence of the SFR–Z_g slope on these properties (supported by insignificant importance values in the RF), whereas a clear relation of this parameter with the galaxy mass has been found (by both the polynomial regression and the RF approach).

In order to search for meaningful secondary dependences, we focus on the characteristic Z_g of the galaxies. The RF approach yielded the highest-importance value for this galaxy property, which was supported by the smallest NRMSE obtained for the second-order polynomial fit. If no secondary dependences are found in the relation between the SFR–Z_g slope and this galaxy property, we will be able to conclude that the global gas-phase metallicity of a galaxy is the fundamental factor shaping the local SFR–Z_g relation, with no additional influence of other properties. Figure 8 again represents the slope of the local SFR–Z_g relation as a function of Z_g at R_e. This time, the distribution is color-coded according to the other four galaxy properties for which the RF algorithm found significant importance values: M_⋆ (top left), g − r color (top right), average LW age of the SP (bottom left), and average Σ_⋆ at R_e (bottom right). As we can see, the vertical dispersion is not related to the color code; that is, the dependence of the slope on the average gas metallicity does not exhibit any significant secondary dependence with respect to the rest of the galaxy properties. The local SFR–Z_g relation of a galaxy seems to be unambiguously characterized by its global gas metallicity.

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In this work, we have studied a sample of 736 spiral galaxies in the local universe (z < 0.05) using IFS data from the MaNGA survey. The 2D coverage of the data has allowed us to map local spatial variations of the gas-phase metallicity (using oxygen abundances as proxy) across entire galaxy disks. These variations have been obtained by subtracting the azimuthally averaged radial profile from the observed distribution (radial profiles that show clear negative gradients in agreement with the literature; see, e.g., Sánchez et al. 2014; Ho et al. 2015; Sánchez-Menguiano et al. 2016a, 2018; Belfiore et al. 2017, among many others). The resulting residual maps show the presence of significant chemical inhomogeneities across the disks (see left panels of Figure 2), with an amplitude up to ${\rm{\Delta }}\mathrm{log}{Z}_{g}\sim 0.2$ dex. This finding supports several works that recently brought to light the nonhomogeneous nature of the chemical distribution of spiral galaxies (Sánchez-Menguiano et al. 2016b; Ho et al. 2017, 2018; Vogt et al. 2017; Hwang et al. 2019).

Connecting these gas-phase chemical inhomogeneities with local variations of SFR (${\rm{\Delta }}\mathrm{logSFR};$ derived in a similar way as for the metallicity), we find a local linear relation between both properties. The slope of this SFR–Z_g relation is negative for ∼60% of the galaxies and positive for ∼21%. The remaining 19% are compatible with a zero slope. We note that these percentages are not volume-corrected but derived specifically for the analyzed sample and therefore cannot be extrapolated as characteristic of the local universe. Determining the values for a volume-corrected sample goes beyond the scope of the paper because of the difficulties in quantifying the selection function corresponding to the galaxies used in our study.

The finding of an anticorrelation between SFR and Z_g is not novel. Previous works arrived at this relation by analyzing a sample of star-forming dwarf galaxies in the local universe (Sánchez Almeida et al. 2013, 2015, 2018). The large sample of galaxies available thanks to the MaNGA survey allows us to extend the analysis to a wider range, not only of masses but also of other galaxy properties. This way, we are able to build a sample representative of galaxies in the local universe and put a larger frame to the picture. In this new frame, we find a nonnegligible percentage of galaxies displaying a positive correlation between ${\rm{\Delta }}\mathrm{logSFR}$ and ${\rm{\Delta }}\mathrm{log}{Z}_{g}$ that was not present in previous works. The wide range of slopes obtained that cannot be explained by observational errors evidence a physical origin for the diversified behavior of the local SFR–Z_g relation.

In order to investigate its origin, we make use of a machine-learning technique known as RF. This methodology has been extensively used in astronomy in the last decade with high levels of success, mainly in its classification form (Carliles et al. 2010; Dubath et al. 2011; Richards et al. 2011; Bloom et al. 2012; Brink et al. 2013; Goldstein et al. 2015; Liu et al. 2017; Schanche et al. 2019, among many others). Analyzing a large set of galaxy properties and building a model based on decision trees, the algorithm indicates that the slope of the SFR–Z_g correlation is primarily determined by the average gas-phase metallicity of the galaxy. Galaxy mass, g − r colors, stellar age, and mass density seem to play a less significant role. We note that this conclusion might be somewhat influenced by the galaxy sample used in the analysis. MaNGA galaxies were selected so that the number of galaxies per log mass bin is the same within a large range of stellar masses (between 10⁹ and 10¹¹ M_⊙; see Wake et al. 2017). This selection is a good starting point for any exploratory study such as ours. Then we apply additional cuts in apparent size, inclination, and morphological type (Section 2.2), which modify the original distribution of masses and physical sizes, as shown in Figure 1. Such cuts should not be determining factors provided the final sample reflects the full range of physical properties, and we have no reason to think that particular types of star-forming galaxies have been excluded from the final sample (see the wide range of galaxy properties considered in Figure 7, including those that seem to have little impact on the slope of the correlation).

The result of the galaxy properties setting the value of the slope is confirmed by the NRMSE obtained with a second-order polynomial regression analysis, presenting the characteristic oxygen abundance with the lowest value. We find that the local SFR–Z_g slope varies almost linearly with the average gas-phase metallicity, being that the more metal-poor galaxies present the lowest slopes (i.e., the strongest SFR–Z_g anticorrelations). The dependence seems to flatten in the metal-poor regime, suggesting the existence of a single slope for low-metallicity galaxies (with $12+\mathrm{log}({\rm{O}}/{\rm{H}})$ below ∼8.2–8.3). However, this flattening is not observed when measuring the gas metallicities with HII-CHI-MISTRY (see Appendix B for details). Further analysis is needed in order to confirm or discard its existence. Finally, the analysis shows no secondary dependences of the relation between the SFR–Z_g slope and the average gas-phase metallicity on the rest of the galaxy properties. We can therefore conclude that the characteristic oxygen abundance of a galaxy unambiguously determines the shape of its local SFR–Z_g relation.

The performed analysis has been shown to be robust in its main results, which we prove do not depend on the used methodology to derive the gas-phase metallicity. It is true that the O3N2 calibrator and HII-CHI-MISTRY yield different values for the slopes of the local SFR–Z_g relation, which results in a different percentage of observed anticorrelations (60% and 40%, respectively) and a different metallicity and galaxy mass value for the reversion of the slope from negative to positive (∼8.5 dex and $10.5\,\mathrm{log}{M}_{\odot }$ against 8.4 dex and $10.0\,\mathrm{log}{M}_{\odot }$). However, the tight correlation between the slopes provided by both methods assures qualitatively equivalent results that lead to the global gas-phase metallicity of a galaxy as the primary factor determining the local relation between SFR and Z_g.

We also assess the effect of aperture bias in the determination of the stellar mass for the galaxies where the radial coverage of the instrument FoV only reaches out to 1.5 R_e (in contrast to galaxies where it reaches out to 2.5 R_e). We repeat the analysis using masses from the NSA catalog, derived from the SDSS and Galaxy Evolution Explorer photometric bands (Blanton et al. 2011). The differences in the resulting importance values of the RF analysis are negligible, and although the NRMSE value of the polynomial fit for the galaxy mass is reduced from 0.526 to 0.479, it is still higher than the one obtained for the characteristic oxygen abundance. All of that reinforces that oxygen abundance is the most relevant factor affecting the local SFR–Z_g relation.

Various physical scenarios have been previously invoked to explain the observed anticorrelation between SFR and gas metallicity in dwarf galaxies (Sánchez Almeida et al. 2018). One scenario is the local infall of metal-poor gas that mixes with preexisting gas and triggers star formation bursts, provided that both the accreted and preexisting gas in each star-forming region have comparable masses. Our results suggest that this could be plausible for galaxies of low-to-intermediate mass ($\lt 10\mbox{--}10.5\mathrm{log}{M}_{\odot }$). On the contrary, for more massive systems, the preexisting gas mass may exceed the external gas mass, thus reversing the SFR–Z_g relation from having a negative slope to a positive one. Alternatively, the authors also proposed that the anticorrelation could be the effect of self-enrichment due to stellar winds and supernovae. However, for this to occur, the outflows driving the metals out of the star-forming regions should be very intense, with mass-loading factors (i.e., the outflow rate in units of the SFR) larger than 10. Although large, it would still be consistent with some values found in local dwarf galaxies (e.g., Martin 1999; Veilleux et al. 2005; Olmo-García et al. 2017).

Gas accretion of pristine gas was also proposed by Hwang et al. (2019) for the ALM regions found in a sample of late-type galaxies. These authors argued that the low-metallicity regions trace sites of recent accretion of gas that stimulates ongoing star formation, in support of our findings. Furthermore, they found that the incidence rate of these regions is higher in lower-mass galaxies. These results confirm our observations of a nonhomogeneous chemical distribution of star-forming regions driven by local infall of metal-poor gas that highly affects low-mass, metal-poor galaxies.

Finally, some studies analyzing the presence of variations in the gas chemistry of disk galaxies have pointed to self-enrichment associated with the spiral arms (and/or gas flows driven by the spiral pattern) as the cause of the presence of more metal-rich gas around these structures (Sánchez-Menguiano et al. 2016b; Ho et al. 2017, 2018; Vogt et al. 2017). All analyzed galaxies correspond to quite massive systems ($\gt 10.5\mathrm{log}{M}_{\odot }$), which is in agreement with our findings of a positive SFR–Z_g correlation at this mass range as a result of localized metal recycling by preexisting gas.

All of these results are evidence that the timescales of mixing processes taking place in spiral galaxies are large enough as to allow the durability of chemical variations for long periods of time. In addition, the persistence of external inhomogeneous metal-poor gas infall could be an alternative driver of chemical differences for low-to-intermediate-mass galaxies.

In summary, this work shows the existence of a linear relation between log SFR and $\mathrm{log}\,{Z}_{g}$ at local scales (after correcting for radial trends), with the slope determined mainly by the average gas-phase metallicity of galaxies. We confirm previous studies finding an anticorrelation for dwarf galaxies, which reverses for more metal-rich (and massive) systems. As a plausible explanation, we propose a scenario in which external gas accretion fuels star formation in metal-poor galaxies, whereas the gas comes from previous star formation episodes in metal-rich systems. Numerical simulations emerge as key in confirming this framework and provide an answer to the level of contribution of gas accretion to galaxy formation and chemical evolution.

We acknowledge financial support from the Spanish Ministerio de Economía y Competitividad (MINECO) via Estallidos grant AYA2016-79724-C4-2-P. M.F. gratefully acknowledges the financial support of the "Fundação para a Ciências e Tecnologia" (FCT—Portugal) through grant SFRH/BPD/107801/2015.

We thank the anonymous referee for suggestions that allowed us to improve the paper. Thanks are also due to Dalya Baron and Marc Huertas-Company for help with the random forest tools and analysis.

This project makes use of the MaNGA-Pipe3D data products. We thank the IA-UNAM MaNGA team for creating it and the ConaCyt-180125 project for supporting them.

Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. The SDSS acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS website is www.sdss.org.

The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration, including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU)/University of Tokyo, the Korean Participation Group, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), the National Astronomical Observatories of China, New Mexico State University, New York University, the University of Notre Dame, Observatório Nacional/MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, the United Kingdom Participation Group, Universidad Nacional Autónoma de México, the University of Arizona, the University of Colorado Boulder, the University of Oxford, the University of Portsmouth, the University of Utah, the University of Virginia, the University of Washington, the University of Wisconsin, Vanderbilt University, and Yale University.

In this appendix, we present Table 2, containing information on the galaxy properties analyzed in the article, together with the determined slopes for the local SFR–Z_g relation. For information on the derivation of these parameters, we refer the reader to Sections 3 and 4.

Table 2.  Galaxy Properties and Derived Slopes for the Local SFR–Z_g Relation

Galaxy ID	[12 + log(O/H)]Re	${\rm{log}}\,{M}_{* }$	g − r	LW Age	$\mathrm{log}\,{{\rm{\Sigma }}}_{* }$	log SFR	T	LW-Z	σcen	[O/H]slope	sSFR	SFR–Zg Slope
	(dex)	(M⊙)		(log yr)	(M⊙ pc−2)	(M⊙ yr−1)		(log Z⊙)	(km s−1)	(dex ${R}_{e}^{-1}$)	(log Gyr−1)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)
9487-12701	8.50	10.43	0.67	9.00	1.66	0.08	5.9	−0.05	61.08	−0.20	−1.36	−0.021 ± 0.006
8485-12701	8.29	9.57	0.34	8.73	1.79	−0.52	6.0	−0.33	22.92	−0.06	−1.09	−0.105 ± 0.005
8134-12701	8.39	9.62	0.48	8.72	1.28	−0.75	4.2	−0.26	17.36	−0.17	−1.38	−0.112 ± 0.007
8552-12701	8.47	10.66	0.89	9.27	2.70	0.20	4.7	−0.24	114.16	−0.02	−1.46	+0.014 ± 0.008
9492-12701	8.47	10.55	0.58	8.65	1.80	0.75	5.5	−0.25	46.83	−0.19	−0.80	−0.060 ± 0.003
8985-12701	8.36	9.80	0.37	8.88	1.35	−0.38	5.1	−0.42	19.69	0.00	−1.18	−0.068 ± 0.002
8312-12701	⋯	9.52	0.35	⋯	⋯	−0.40	4.8	⋯	9.71	⋯	−0.92	−0.092 ± 0.007
9505-12701	8.56	11.07	0.83	9.47	2.61	0.63	4.3	−0.16	126.82	−0.06	−1.44	+0.007 ± 0.016
7990-12701	8.54	10.19	0.52	8.96	1.75	−0.19	5.2	−0.19	12.91	−0.05	−1.38	+0.035 ± 0.011
8243-12701	8.54	11.16	0.83	9.20	2.41	0.99	5.3	−0.23	119.16	−0.12	−1.17	+0.010 ± 0.006
8338-12701	8.31	9.96	0.24	8.65	1.70	−0.07	6.1	−0.30	15.19	−0.08	−1.03	−0.074 ± 0.003
9510-12701	8.49	10.23	0.50	8.88	1.78	0.00	5.3	−0.23	12.99	−0.13	−1.22	−0.032 ± 0.004
8323-12701	8.30	9.99	0.35	8.53	1.65	0.14	6.7	−0.33	12.99	−0.02	−0.85	−0.082 ± 0.004
8993-12701	8.57	10.60	0.84	9.02	⋯	−0.09	4.9	−0.23	90.91	0.02	−1.68	+0.046 ± 0.009
7991-12701	8.50	10.65	0.65	8.82	2.39	0.85	5.1	−0.32	63.42	−0.16	−0.80	−0.081 ± 0.004
9870-12701	8.35	9.04	0.45	8.62	0.88	−1.51	3.3	−0.24	9.81	−0.03	−1.55	−0.16 ± 0.03
8274-12701	8.51	9.72	0.58	8.92	2.40	−0.42	4.2	−0.20	9.75	0.00	−1.14	−0.016 ± 0.009
8948-12701	8.43	10.09	0.51	8.75	2.01	0.01	5.3	−0.33	21.27	−0.12	−1.09	−0.058 ± 0.005
8716-12701	8.37	8.84	0.46	8.96	0.98	−1.97	2.9	−0.09	17.72	−0.04	−1.81	−0.11 ± 0.06
8718-12701	8.52	10.64	0.70	9.17	2.13	0.26	4.1	0.01	70.28	−0.00	−1.38	+0.001 ± 0.015
8567-12701	⋯	10.00	0.50	8.83	⋯	−0.30	4.0	−0.13	13.14	⋯	−1.31	+0.051 ± 0.004
8155-12701	8.54	10.64	0.63	9.04	2.07	0.42	3.8	−0.21	41.50	−0.17	−1.22	−0.001 ± 0.005
8329-12701	8.59	10.84	0.67	9.12	2.10	0.59	4.9	−0.17	69.49	−0.09	−1.25	+0.040 ± 0.006
8080-12701	8.48	10.59	0.50	8.72	1.70	0.56	5.0	−0.13	20.43	−0.20	−1.03	−0.049 ± 0.005
7964-12701	8.29	9.51	0.37	8.57	1.07	−0.61	5.9	−0.17	16.74	−0.08	−1.12	−0.141 ± 0.008
8458-12701	8.52	10.43	0.70	8.96	2.33	0.57	3.0	−0.19	135.73	0.01	−0.86	+0.02 ± 0.03
7960-12701	8.59	11.01	0.67	9.14	2.39	0.49	4.9	−0.36	16.22	0.00	−1.52	+0.017 ± 0.004
8715-12701	8.59	10.63	0.81	9.52	2.30	−0.27	4.7	−0.26	64.48	−0.05	−1.90	+0.036 ± 0.013
9037-12701	8.29	9.70	0.38	8.73	1.79	−0.82	5.2	−0.39	158.42	−0.06	−1.52	−0.102 ± 0.006
8313-12701	8.51	10.78	0.63	8.89	2.13	0.80	5.0	−0.20	57.58	−0.08	−0.98	−0.007 ± 0.003
8241-12701	8.34	9.75	0.44	8.62	1.56	−0.86	5.1	−0.23	9.79	−0.06	−1.61	−0.071 ± 0.010
8592-12701	8.26	9.56	0.33	8.37	1.61	−0.44	5.6	−0.30	25.36	−0.04	−1.00	−0.070 ± 0.010
9872-12701	8.32	9.56	0.39	8.61	1.29	−0.70	5.6	−0.27	13.05	−0.07	−1.26	−0.076 ± 0.004
8952-12701	8.62	10.17	0.77	9.15	1.98	−0.43	4.2	−0.03	76.27	0.06	−1.59	+0.08 ± 0.06
8450-12701	8.55	10.12	0.54	9.01	1.96	−0.23	2.9	−0.24	27.34	−0.10	−1.34	+0.032 ± 0.013
8153-12701	8.40	9.85	0.46	8.65	1.28	−0.51	5.2	−0.06	24.49	−0.08	−1.36	−0.096 ± 0.014
8591-12701	8.36	9.74	0.42	8.78	1.20	−0.22	5.0	−0.21	12.77	−0.11	−0.96	−0.08 ± 0.02
8439-12701	8.32	9.32	0.45	8.62	1.29	−1.23	5.1	−0.29	13.08	−0.00	−1.55	−0.106 ± 0.011
8444-12701	8.36	9.43	0.51	8.85	1.57	−1.51	4.6	−0.29	13.08	0.02	−1.93	−0.18 ± 0.02
9048-12701	8.38	10.01	0.45	8.68	1.39	−0.41	4.6	−0.18	53.62	−0.07	−1.42	−0.120 ± 0.012
9196-12701	8.61	10.65	0.81	9.57	2.07	−0.39	2.7	−0.03	109.92	−0.11	−2.04	+0.03 ± 0.07
9871-12701	8.37	9.25	0.58	8.75	1.25	−1.28	3.1	−0.10	61.46	0.09	−1.53	−0.146 ± 0.009
9493-12701	8.49	9.55	0.55	8.96	1.80	−1.05	5.1	−0.15	13.10	−0.13	−1.60	−0.020 ± 0.010
8325-12701	8.41	10.00	0.43	8.71	1.31	−0.25	2.9	−0.19	31.07	−0.12	−1.25	−0.106 ± 0.014
8933-12701	8.54	10.49	0.78	9.27	2.59	0.23	4.1	−0.26	50.78	−0.04	−1.27	+0.02 ± 0.03
8078-12701	8.58	10.95	0.86	9.30	2.56	0.45	4.3	−0.19	105.61	−0.07	−1.50	+0.025 ± 0.006
8147-12701	8.41	9.93	0.49	8.76	1.69	−0.64	5.1	−0.18	28.40	−0.05	−1.57	−0.045 ± 0.009
8454-12701	8.38	10.19	0.34	8.53	1.67	0.34	5.8	−0.32	19.98	−0.04	−0.85	−0.046 ± 0.005
8455-12701	8.39	10.35	0.40	8.58	2.27	0.57	5.3	−0.30	51.85	−0.07	−0.78	−0.066 ± 0.004
9185-12701	⋯	10.39	0.64	8.75	1.34	−0.02	5.5	−0.14	12.88	⋯	−1.42	+0.015 ± 0.009
8149-12701	8.38	10.15	0.31	8.48	1.58	0.20	6.3	−0.13	12.76	0.11	−0.95	−0.017 ± 0.007
8257-12701	8.52	10.63	0.56	8.89	2.47	0.91	5.4	−0.26	59.22	−0.01	−0.72	−0.023 ± 0.001
8611-12701	8.40	9.89	0.46	8.79	1.64	−0.31	4.4	−0.32	13.10	−0.10	−1.20	−0.081 ± 0.005
8984-12701	8.35	9.66	0.40	8.85	1.42	−0.89	5.9	−0.25	16.30	−0.04	−1.54	−0.139 ± 0.012
8259-12701	8.29	9.51	0.39	8.61	1.60	−0.87	5.9	−0.35	13.04	−0.04	−1.38	−0.117 ± 0.007
8655-12701	8.39	9.76	0.49	8.70	1.45	−0.70	4.9	−0.25	13.01	−0.10	−1.46	−0.059 ± 0.005
8613-12701	8.58	10.52	0.76	9.11	2.49	0.41	4.3	−0.23	262.46	−0.03	−1.11	−0.009 ± 0.014
8442-12701	8.45	10.53	0.54	8.72	2.24	0.93	4.5	−0.36	113.06	−0.01	−0.60	−0.029 ± 0.007
8252-12701	8.23	9.90	0.27	8.85	−0.71	−0.87	4.3	−0.23	166.22	−0.13	−1.76	−0.12 ± 0.04
9028-12701	8.59	10.49	0.66	9.22	2.11	−0.03	3.5	−0.12	56.25	−0.08	−1.52	+0.050 ± 0.017
7962-12701	8.40	9.96	0.47	8.81	1.51	−0.51	4.7	−0.46	16.36	−0.05	−1.48	−0.081 ± 0.005
7958-12701	8.29	9.61	0.20	8.46	1.60	−0.24	5.1	−0.25	17.54	−0.04	−0.85	−0.055 ± 0.010
8727-12701	8.44	10.18	0.56	8.99	1.74	−0.33	5.0	−0.08	13.03	−0.35	−1.52	+0.002 ± 0.008
8547-12701	8.50	11.07	0.81	9.57	2.65	1.17	3.5	−0.10	150.86	0.12	−0.89	+0.040 ± 0.016
8138-12701	8.44	10.23	0.44	8.56	1.50	0.10	5.3	−0.31	13.96	−0.08	−1.13	−0.031 ± 0.008
9501-12701	8.56	10.07	0.66	9.14	1.57	−0.75	3.6	−0.42	12.92	−0.17	−1.81	−0.01 ± 0.06
7815-12701	8.33	9.43	0.42	8.70	1.59	−1.06	4.0	−0.33	13.08	0.06	−1.49	−0.067 ± 0.010
8949-12701	⋯	9.54	0.64	9.47	0.81	−1.40	1.7	−0.06	12.96	⋯	−1.93	+0.03 ± 0.03
8326-12701	8.55	10.58	0.84	9.46	2.47	0.08	4.1	−0.10	121.11	−0.03	−1.50	+0.006 ± 0.010
9881-12701	8.52	10.55	0.49	8.66	2.01	0.78	5.1	−0.17	32.36	−0.13	−0.76	−0.023 ± 0.003
8456-12701	8.30	9.88	0.45	8.61	1.29	−0.53	5.2	−0.29	20.05	−0.24	−1.41	−0.070 ± 0.008
8131-12701	8.29	9.82	0.39	8.64	1.66	−0.52	5.9	−0.40	48.77	−0.06	−1.34	−0.099 ± 0.003
10001-12701	8.39	9.99	0.40	8.63	2.13	−0.13	5.1	−0.22	69.22	−0.02	−1.12	−0.062 ± 0.013
9031-12701	8.46	10.10	0.52	8.90	1.78	−0.25	4.0	−0.15	15.15	−0.14	−1.34	−0.064 ± 0.019
8452-12701	8.38	9.96	0.44	8.58	1.34	−0.40	4.9	−0.20	11.90	−0.08	−1.36	−0.060 ± 0.017
8084-12701	8.34	10.15	0.39	8.68	1.69	−0.24	5.7	−0.35	21.89	−0.02	−1.39	−0.121 ± 0.007
8085-12701	8.32	10.43	0.42	8.59	1.92	0.65	6.4	−0.32	19.22	−0.04	−0.78	−0.059 ± 0.003
8726-12701	8.55	10.54	0.66	9.27	1.96	0.06	5.4	−0.08	16.18	−0.08	−1.47	+0.038 ± 0.008
8146-12701	8.59	10.57	0.65	9.26	2.17	−0.03	3.6	−0.11	12.94	−0.07	−1.60	+0.024 ± 0.016
8453-12701	8.58	10.37	0.63	9.27	2.07	−0.26	3.4	−0.18	12.97	−0.04	−1.63	+0.025 ± 0.018
8600-12701	8.48	10.21	0.64	9.07	1.61	−0.49	5.2	−0.15	18.44	−0.06	−1.70	−0.013 ± 0.009
8445-12701	8.59	10.85	0.78	9.20	2.30	0.49	4.8	−0.22	69.26	−0.04	−1.36	+0.050 ± 0.005
8082-12701	8.53	10.48	0.64	9.08	2.06	0.13	3.5	−0.19	47.50	−0.10	−1.35	−0.010 ± 0.005
8465-12701	8.53	10.33	0.53	8.92	2.03	0.41	5.0	−0.36	26.56	−0.11	−0.92	+0.012 ± 0.004
8602-12701	⋯	10.65	0.84	9.18	2.56	−0.02	1.3	−0.08	75.04	⋯	−1.68	+0.06 ± 0.04
8141-12701	8.51	10.61	0.66	9.15	2.38	0.47	4.4	−0.17	68.47	−0.07	−1.14	−0.003 ± 0.005
8446-12701	8.25	9.49	0.34	8.50	1.29	−0.59	6.0	−0.16	39.89	−0.01	−1.08	−0.117 ± 0.006
9486-12701	⋯	10.96	0.75	⋯	⋯	0.29	4.6	⋯	89.71	⋯	−1.67	+0.00 ± 0.03
8604-12701	8.58	10.93	0.75	9.48	2.10	−0.03	4.4	−0.07	110.94	−0.03	−1.96	−0.01 ± 0.03
9035-12701	8.38	9.92	0.26	8.40	1.50	0.27	5.4	−0.23	15.35	−0.09	−0.65	−0.061 ± 0.009
8991-12701	8.41	9.92	0.56	9.04	1.83	−0.47	3.6	−0.06	16.04	−0.08	−1.39	−0.06 ± 0.03
8931-12701	8.45	10.30	0.45	8.87	1.65	0.13	4.3	−0.31	41.19	−0.10	−1.17	−0.026 ± 0.010
8983-12701	8.55	10.35	0.68	9.18	2.10	−0.02	3.7	−0.27	73.57	−0.03	−1.37	+0.019 ± 0.009
8462-12701	8.39	9.82	0.45	8.76	1.69	−0.49	5.5	−0.25	13.01	−0.04	−1.31	−0.061 ± 0.005
8724-12701	8.56	10.56	0.68	9.24	2.05	0.14	4.3	−0.18	34.13	−0.12	−1.42	+0.002 ± 0.008
8332-12701	8.42	10.19	0.38	8.70	1.83	0.18	4.9	−0.23	16.27	−0.09	−1.01	−0.017 ± 0.005
8464-12701	8.55	10.12	0.60	9.12	1.71	−0.29	4.9	−0.46	12.99	−0.06	−1.41	+0.029 ± 0.010
8258-12701	8.44	10.05	0.52	8.84	1.68	−0.47	4.1	−0.24	14.45	−0.11	−1.52	−0.051 ± 0.008
8320-12701	8.41	9.92	0.45	8.72	1.82	−0.28	3.4	−0.15	22.67	−0.09	−1.20	−0.085 ± 0.019
9034-12701	8.29	9.24	0.44	8.58	1.14	−0.93	7.1	−0.23	67.37	−0.11	−1.18	−0.105 ± 0.005

Note. From left to right, the columns correspond to (1) galaxy ID, defined as the [plate]-[ifudesign] of the MaNGA observations; (2) gas-phase oxygen abundance value at R_e; (3) galaxy mass; (4) g − r color; (5) average LW stellar age at R_e; (6) average stellar mass density at R_e; (7) integrated SFR; (8) morphological type; (9) average LW stellar metallicity at R_e; (10) central velocity dispersion; (11) slope of the oxygen abundance gradient; (12) sSFR; and (13) slope of the local SFR–Z_g relation.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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In this appendix, we assess the effect of using the HII-CHI-MISTRY calibrator on the results presented in the paper. With this purpose, we replicate the RF analysis to study the dependence of the local SFR–Z_g relation on the different galaxy properties. For the regularization of the model, the performed 5-fold CV procedure yields the following HPs: n = 600, m = 6, ${\max }_{\mathrm{depth}}\,=\,40$, ${\min }_{\mathrm{split}}\,=\,6$, and ${\min }_{\mathrm{leaf}}\,=\,5$. With these HPs, the RF algorithm provides the predicted slopes of the SFR–Z_g relation shown in the left panel of Figure 9. Both the training (blue circles) and test (red triangles) samples are distributed around the one-to-one relation (dashed line) covering the same parameter space with a similar dispersion (0.036 and 0.045, respectively). Regarding the relative importance of the input features, we obtain the following values (in descending order): (a) oxygen abundance at R_e (0.40), (b) LW stellar age at R_e (0.24), (c) g − r color (0.10), (d) sSFR (0.06), (e) galaxy mass (0.05), (f) LW stellar metallicity at R_e (0.03), (g) slope of the oxygen abundance radial gradient (0.03), (h) average stellar mass density at R_e (0.03), (i) integrated SFR (0.02), (j) morphological type (0.02), and (k) σ_cen (0.02). The right panel of Figure 9 displays the trend of the values for 50 realizations, showing the high stability of the feature importances. In agreement with the results obtained with the O3N2 calibrator, the gas-phase metallicity remains as the primary factor determining its local SFR–Z_g relation. In this case, average LW stellar age, g − r color, sSFR, and stellar mass would be the next factors in order of importance. The remaining properties result in little relevance for the relation.

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We replicate the polynomial regression analysis for the dependence of the SFR–Z_g slope with the galaxy properties, whose outcome we present in Figure 10. The shapes of the relations are the same as those determined using the O3N2 calibrator, although the specific NRMSE values of the fits change (but still support the conclusions of the RF). We see again that the characteristic oxygen abundance presents the lowest NRMSE, significantly below the rest of the values. In this case, the flattening of the relation at the low-metallicity regime found with O3N2 is not observed. Finally, the HII-CHI-MISTRY calibrator also yields no secondary dependence of the relation between the SFR–Z_g slope and average gas metallicity with the rest of the galaxy properties (see Figure 11). We can therefore confirm the conclusion of the local SFR–Z_g relation of a galaxy being unambiguously characterized by its characteristic oxygen abundance independent of the employed calibrator to derive the gas-phase metallicity.

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