EMPRESS. XIII. Chemical Enrichment of Young Galaxies Near and Far at z ∼ 0 and 4–10: Fe/O, Ar/O, S/O, and N/O Measurements with a Comparison of Chemical Evolution Models

We present gas-phase elemental abundance ratios of thirteen local extremely metal-poor galaxies (EMPGs), including our new Keck/LRIS spectroscopy determinations together with 33 James Webb Space Telescope z ∼ 4–10 star-forming galaxies in the literature, and compare chemical evolution models. We develop chemical evolution models with the yields of core-collapse supernovae (CCSNe), Type Ia SNe, hypernovae (HNe), and pair-instability supernovae (PISNe), and compare the EMPGs and high-z galaxies in conjunction with dust depletion contributions. We find that high Fe/O values of EMPGs can (cannot) be explained by PISN metal enrichments (CCSN/HN enrichments even with the mixing-and-fallback mechanism enhancing iron abundance), while the observed Ar/O and S/O values are much smaller than the predictions of the PISN models. The abundance ratios of EMPGs can be explained by the combination of Type Ia SNe and CCSNe/HNe whose inner layers of argon and sulfur mostly fallback, which are comparable to the Sculptor stellar chemical abundance distribution, suggesting that early chemical enrichment has taken place in the EMPGs. Comparing our chemical evolution models with the star-forming galaxies at z ∼ 4–10, we find that the Ar/O and S/O ratios of the high-z galaxies are comparable to those of the CCSN/HN models, while the majority of high-z galaxies do not have constraints good enough to rule out contributions from PISNe. The high N/O ratio recently reported in GN-z11 cannot be explained even by rotating PISNe, but could be reproduced by the winds of rotating Wolf–Rayet stars that end up as a direct collapse.


Introduction
Chemical properties of young galaxies are important to understand the chemical evolution in galaxy formation.Numerical simulations are conducted to reproduce galaxies at the early formation phase (Wise et al. 2012;Yajima et al. 2022).Wise et al. (2012) find that early galaxies with a stellar age of 300 Myr have low metallicities of 0.1%-1% solar abundance and low stellar masses of 10 4 -10 9 M e at a high redshift of z 7.There are observational studies for early galaxies at z 7 (e.g., Stark 2016;Mainali et al. 2018).However, early galaxies at high-z are too faint to be detected because of their low stellar masses.There are efforts of observations on galaxies at the early formation phase in the low-redshift universe (e.g., Stark et al. 2014;Berg et al. 2019), while even with the James Webb Space Telescope (JWST) it is difficult to detect early galaxies with low masses such as M * 10 6 M e at z 2 (Kikuchihara et al. 2020).
Although early galaxies are not well observationally investigated yet, one can study the early phase of galaxy formation in the local universe with dwarf galaxies (e.g., Isobe et al. 2021;Izotov et al. 2021).It should be noted that galaxy formation in the early universe may be different from the one in the local universe, studies of galaxy formation in the local universe serve as the first step in understanding galaxy formation at high redshift.
Various studies show the presence of extremely metal-poor galaxies (EMPGs) such as SBS 0335-052 (Izotov et al. 2009), AGC198691 (Hirschauer et al. 2016), J1234+3901 (Izotov et al. 2019), and I Zw 18 (Izotov & Thuan 1998).EMPGs are defined as galaxies with less than 10% solar oxygen abundance.Recently, Kojima et al. (2020) launched the project Extremely Metal-Poor Representative Explored by the Subaru Survey (EMPRESS).The EMPRESS project searches for EMPGs by the machine learning methods with Subaru and Sloan Digital Sky Survey (SDSS) data (Kojima et al. 2021;Nishigaki et al. 2023), and studies their physical properties, for example, morphologies (Isobe et al. 2021), outflows (Xu et al. 2022), strong high-ionization lines (Hiroya Umeda et al. 2022), and He abundance (Matsumoto et al. 2022) of EMPGs.One of the notable indications from the series of the EMPRESS work is a high Fe/O ratio ([Fe/O] ∼ 0) in EMPGs despite the low metallicities (Kojima et al. 2021).Although the primary driver of iron enrichment in galaxies is generally thought to be Type Ia supernovae (SNe), EMPGs would be too young to be enriched by Type Ia SNe due to a typically long (∼ 10 9 yr) delay time to happen.Isobe et al. (2022) examine other scenarios to reproduce high Fe/O in young galaxies like EMPGs, interestingly suggesting that massive-star explosions such as hypernovae (HNe) and/or pair-instability SNe (PISNe) can explain the iron-rich and oxygen-poor properties.Isobe et al. (2022) show EMPGs' Fe/O as high as those enriched by PISNe or bright HNe with the models made in the same manner as Suzuki & Maeda (2018) with core-collapse SNe (CCSNe), HNe, and PISNe yields in Umeda & Nomoto (2008), Nomoto et al. (2013, hereafter N13), and Takahashi et al. (2018), respectively.CCSN is an explosion that occurs at the end of the evolution of a massive star with a mass greater than 8 M e , while HN has higher explosion energy than that of CCSN and ejects more iron.Very massive stars (>140 M e ) cause PISNe and have no compact remnants (Takahashi et al. 2018).However, a single piece of observational evidence, the high Fe/O, is not strong enough to conclude that EMPGs are mainly enriched by PISNe or bright HNe.Moreover, one should distinguish between the contributions from PISNe and HNe because the Fe/O values given by ejecta of PISNe and HNe are comparable (Hideyuki Umeda et al. 2002;Isobe et al. 2022).Because S/O and Ar/O values are different between ejecta of PISNe and HNe, one can distinguish the origin of the abundant Fe with S/O and Ar/O.There should also remain signatures of PISNe or bright HNe in metal-poor stars of the present-day Milky Way (MW) and local dwarf galaxies, if PISNe or bright HNe took place at the early phase of galaxy formation.One should investigate the abundance ratios of metal-poor stars in the local universe.
While metal-poor galaxies and stars in the local universe are important, studies of high-z galaxies are also key to understanding the abundance ratios of young galaxies.Therefore, a discussion of abundance ratios in galaxies both at z ∼ 0 and high redshift toward the early epoch of galaxy formation at z ∼ 10 is important.
Although it is difficult to investigate abundance ratios of high-z galaxies whose observational signatures are too weak to detect, gravitational lensing magnifications allow us to detect such weak signatures in high-z galaxies with JWST.Recent studies for early chemical enrichment of high-z galaxies proceed very rapidly with observational data obtained with JWST.Diagnostic optical emission lines such as [O III]λλ 5007,4959, [O II]λ3727, and hydrogen Balmer lines have now been identified in galaxies at high redshift up to z ∼ 4-10, suggesting rapid chemical enrichment in galaxies with measurements of (O/H; Schaerer et al. 2022;Brinchmann 2023;Curti et al. 2023;Nakajima et al. 2023;Rhoads et al. 2023;Trump et al. 2023).Arellano-Córdova et al. (2022) report the abundance ratios such as Ne/O and C/O of galaxies at z 7 that are observed with JWST/NIRSpec.Although Arellano-Córdova et al. (2022) detected [Fe III]λ2465 and [Fe II]λ4360 lines for one of these high-z galaxies, an Fe/O ratio is not determined due to the low signal-to-noise ratios (S/Ns) of these emission lines.
Elemental abundance ratios in galaxies at high redshift are also drawing attention.In particular, Bunker et al. (2023) identify emission lines of a galaxy GN-z11 at z 10 such as [Ne III], [N III], and [O II] with JWST/NIRSpec data, and claim that the galaxy at z = 10.6 has an extremely high N/O larger than the solar abundance (Cameron et al. 2023).The abundance ratios with high-z galaxies are important to understand the chemical enrichment driven by galaxies in the early universe.
This paper is the XIIIth paper of the EMPRESS series.In this paper, we present spectroscopic observations for EMPGs with the Keck Telescope, and discuss the abundance ratios of EMPGs with the chemical evolution models.Our observations and data reduction methods are described in Section 2. In Section 3, we explain our sample and data analysis.In Section 4, we develop chemical evolution models of galaxies.We present our results and discuss the abundance ratios of the EMPGs by comparison with the chemical evolution models in Section 5.In Section 6, we summarize our study.
where N A and N B are the numbers of the elements A and B, respectively.The variables of N A,e and N B,e indicate the solar abundances.

Enlarging the EMPG Sample
This study needs EMPGs with measurements of Fe/O and the other various abundance ratios, Ar/O, S/O, Ne/O, and N/O.Because in the literature we find only 11 EMPGs whose Fe/O values can be determined with [Fe III]λ4658 emission, to increase the number of EMPGs we conduct deep spectroscopy for EMPGs with the Keck/the Low-Resolution Imaging Spectrometer (LRIS) spectrograph.We select three EMPGs, SBS 0335-052E (Izotov et al. 2009), J2314+0154 (Kojima et al. 2020), and J0125+0759 (Kojima et al. 2020), that are observable in the given Keck/LRIS nights.These are bright EMPGs whose faint emission lines, especially [Fe III]λ4658, can be potentially detected.We can detect the other important auroral lines that are necessary to discuss the abundance ratios (e.g., [O III]λ4363 and [S III]λ6312; see Section 3.2).

Keck/LRIS Spectroscopy
We conducted spectroscopic observations for the EMPGs on 2021 November 7 and 8 with Keck/LRIS (PI: K.Nakajima).LRIS has blue and red channels that cover the wavelength ranges of λ ∼ 3000-5500 and 6000-9000 Å with the spectral resolutions of ∼4 and 5 Å in the FWHM, respectively.We used the 600 lines mm −1 grism blazed at 4000 Å on the blue channel and the 600 lines mm −1 grating blazed at 7500 Å on the red channel.The slit widths were 0 7 for all targets.We also observed spectrophotometric standards Feige 34 and Feige 100 for flux calibration.The sky was clear during the observations with seeing sizes of 0 8-1 0. Table 1 summarizes our observation targets.

Reduction
We reduce the LRIS data using the IRAF package in a normal manner, performing bias subtraction, flat fielding, cosmic-ray cleaning, sky subtraction, wavelength calibration, one-dimensional (1D) spectrum extraction, flux calibration, atmospheric absorption correction, and Galactic-reddening correction.A 1D spectrum is derived from an aperture centered on the compact component of our galaxies.The 1D spectra are corrected for Galactic extinction according to the spatial position of each object on the Schlafly & Finkbeiner (2011)ʼs dust map and based on the extinction curve in Cardelli et al. (1989), as commonly performed for extragalactic objects.Flux calibration is obtained from the spectrophotometric standard stars observed on the same night under a similar seeing condition with the same slit width (0 7), and reduced in the same manner as done for the science targets.The wavelengths are calibrated with a HgNeArCdZnKrXe lamp.Atmospheric absorption is corrected under the assumption of the extinction curve obtained at the Maunakea Observatories.In addition, the flux calibration using the spectrophotometric standard stars eliminates local absorption features due to the Earth's atmosphere.
Figure 1 represents the reduced spectra of our targets.In the middle panels, the spectrum of J2314+0154 exhibits unusual emission lines near Hα due to the incomplete removal of certain sky emission lines.Nevertheless, these sky emission lines do not coincide with the emission lines of the object.

Emission-line Measurements
We measure the emission-line flux by fitting a Gaussian profile plus a constant continuum using the scipy.optimizepackage (Virtanen et al. 2020).We apply the χ 2 minimization approach considering the error spectra.The error spectra are extracted by taking into account the readout noise and photon noise from both sky and object counts.In the Gaussian profile fitting, there are four free parameters: the amplitude, line width, line central wavelength, and the continuum.
To perform reddening corrections for the observed fluxes, we estimate dust extinction from the Balmer decrements under the assumptions of case B (Brocklehurst 1971) recombination and the dust attenuation curve given by Calzetti et al. (2000).We estimate intrinsic Balmer decrement values using PyNeb (Luridiana et al. 2015).We summarize the atomic data used in the Pyneb calculation in Table 2.Because the Balmer decrement values depend on electron temperature T e and electron density n e , we iteratively derive E(B − V ) values that consistently explain T e and n e (see Section 3.2 for the procedures of T e and n e calculations).We utilize six Balmer line ratios, Hβ/Hα, Hγ/Hα, Hδ/Hα, Hγ/Hβ, Hδ/Hβ, and Hγ/Hδ to estimate the emissivity of the Balmer lines.We compare the Balmer line ratios of the observational measurements with those of theoretical predictions obtained with PyNeb to determine E(B − V ).With the E(B − V ) values thus obtained, we determine the best estimate E(B − V ) by the χ 2 minimization for each Balmer decrement value.We also estimate ±68% confidence intervals of E(B − V ) based on χ 2 .With the E(B − V ) values and the attenuation curve (Calzetti et al. 2000), we correct all of the observed emission-line fluxes for dust extinction that are summarized in Table 3. Table 4 summarizes the fundamental properties of our targets such as the redshift, and E(B − V ).

Developing Our Sample
We investigate the Keck/LRIS spectra of our three EMPGs (Section 2.2).Although many lines of Ar, S, Ne, N, and O emission are identified in the spectra, only two out of three EMPGs, SBS 0335-052E, and J0125+0759, have a significant detection of [Fe III] emission.We hereafter use SBS 0335-052E and J0125+0759 in our analysis.We also use 11 EMPGs with the detections of the Fe, Ar, S, Ne, N, and O emission lines, taken from the literature (Izotov & Thuan 1999;Izotov et al. 2018;Berg et al. 2021;Kojima et al. 2021;Isobe et al. 2022).We define our sample, which consists of a total of 13 EMPGs from our observations and the literature, and summarize it sample in Table 5.

Element Abundance Ratios
We derive the oxygen abundances with the direct method.We estimate the electron temperature T e of doubly ionized oxygen T e (O III) from ratios of two collisional excitation line fluxes that depend on T e (O III).We use the PyNeb package getCrossTemDen to simultaneously derive n e and T e (O III) from the emission-line ratios of [S II]λ6731/ [S II]λ6716 and [O III]λ4363/[O III]λλ4959,5007, respectively.Table 4 summarizes our estimates of n e and T e for all of our galaxies.
We use the PyNeb package getIonAbundance to obtain ion abundance ratios.Ion abundance ratios of O 2+ /H + and O + /H + are derived from emission-line ratios of [O III] λλ4959,5007/Hβ and [O II]λλ3727,3729/Hβ with T e (OIII) and T e (OII), respectively, where T e (OII) is the electron temperature of singly ionized oxygen that is estimated with the empirical relation of 1992).By adding O 2+ /H + and O + /H + , we obtain the total oxygen abundance O/H.We represent the metallicity as 12+log(O/H) of the total oxygen abundance.We derive ion abundance ratios of Fe 2+ /H + , Ar 2+ /H + , S 2+ /H + , S + /H + , N + /H + , and Ne 2+ /H + that are estimated from the fluxes of for Ar 2+ and S 2+ .Instead, we use the electron temperature of S 2+ , T e (S III), which is estimated by the empirical relation 1992).We use the ionization correction factors (ICFs) derived by Izotov et al. (2006) to calculate total gas-phase element abundances from the ion abundances  ( The ICFs depend on the ionization degree of gas measured with O + and O 2+ :    Here we estimate the errors of element abundance ratios.Conducting Monte Carlo simulations, we generate 1000 mock flux values consisting of the observed flux and a flux randomly produced on the basis of the normal distribution whose dispersion corresponds to the 1σ flux error.We obtain 1000 mock element abundance ratios from the mock flux values, and define the 1σ error of the element abundance ratio as the 68% confidence interval in the distribution of the 1000 mock element abundance ratios. Table 5 summarizes the gas-phase element abundance ratios for all of our galaxies.We use the abundance ratios taken from the literature (Izotov & Thuan 1999;Izotov et al. 2018;Berg et al. 2021;Kojima et al. 2021;Isobe et al. 2022) that derive the abundance ratios in the same manner as our methods.The abundance ratios taken from Izotov & Thuan (1999) and Berg et al. (2021) are derived from the ICFs different from Equations (9)-( 13).We calculate the abundance ratios for the galaxies in Izotov & Thuan (1999) and Berg et al. (2021) using the fluxes reported by Izotov & Thuan (1999) and Berg et al. (2021) and the ICFs of the Equations (9)-( 13).Because these abundance ratios are consistent with the values derived by Izotov & Thuan (1999) and Berg et al. (2021) within the errors, we use the abundance ratios reported by Izotov & Thuan (1999) and Berg et al. (2021).Because there are no S/O values of the four galaxies derived in Kojima et al. (2021) and Isobe et al. (2022), we calculate the S/O values from the fluxes reported by Kojima et al. (2021) and Isobe et al. (2022).We assume that the EMPGs are not affected by dust depletion since the dust in the EMPGs is poor due to low metallicities in EMPGs.Therefore, we have not corrected dust depletion in the gas-phase element abundance ratios.We discuss the effect on the abundance ratios quantitatively later.

Yield Models
We calculate yields with the models of Tominaga et al. (2007).We use these yields in the galactic chemical evolution   models (Section 4.2).We investigate the yields for EMPGs that eject rich iron without increasing sulfur and argon.

CCSN and HN Yields
We calculate CCSN and HN yields with the explosive nucleosynthesis code (Tominaga et al. 2007) in order to study the origin of enriched Fe in the EMPGs.We obtain the yields by using calculation code and explosive nucleosynthesis from Tominaga et al. (2007).We calculate the yields with different parameters.We use progenitor initial masses (13,15,18,20,25,30, and 40 M e ) and explosion energies (CCSNe with E 51 = E 10 −51 erg = 1, and HNe with E 51 10).The explosion energies are determined by the relationship between the mainsequence mass and the explosion energy which is obtained from observations and supernova (SN) models (Tominaga et al. 2007).Since we compare with the EMPGs observations, the metallicities of yields are set to Z = 0 and 0.004 ( = 0.288 Z e ).
We apply the mixing and fallback model proposed by Umeda & Nomoto (2002, 2003).This model is introduced to reproduce the abundance ratios of metal-poor stars.In this model, we assume that inner materials in the mixing region are mixed during SNe by some mixing process (e.g., Rayleigh-Taylor instabilities or aspherical explosions).Then some fraction of the material in the mixing region is ejected into interstellar space and the rest undergoes fallback to the center remnant due to gravity.This model can modify the abundance ratios of the material released by SN explosions through the mixing and fallback processes.We investigate whether the yields with the mixing and fallback model may reproduce the characteristic abundance ratios of EMPGs.
The mixing region and the amount of ejecta and fallback are described by the following parameters: M cut , M mix , and f ej .The initial mass cut M cut represents the inner boundary of the mixing region.M mix is the outer boundary of the mixing region.All material above M mix is ejected.M cut and M mix indicate the enclosed masses from the center of a star.It is likely to be difficult to eject the iron core due to energy absorption by Fe photodisintegration. f ej is the ejection fraction.A fraction f ej of the material in the mixing region (between M mix and M cut ) is ejected into interstellar space.We adopt f ej = 0.12, following Tominaga et al. (2007).We change the f ej from 0.12 to 0.05 and 0.5 and calculate the yields to examine the impact of f ej variation on the models.We find that the variations in f ej do not change our conclusion.
M mix is expressed by where M CO is the CO core mass and x is the mixing region factor (Ishigaki et al. 2018).Here, we change the mixing region by varying x.If x = 0, the mixing region M mix equals M cut, and all material above the Fe core is released.We set x = 0, 0.1, 0.2, 0.5, and 1.0 to vary the mixing region because the target elements of this study are mainly located in the CO core.N13 extends the mixing region outside of the Si-burning layer, where an x-value simply depends on mass.In our study, we extensively investigate the mixing and fallback effects with multiple x-values for a given mass because the yields of the literature do not explain the abundance ratios of EMPGs.
Table 6 summarizes the parameters of the yields.Then, we develop the models about CCSNe and HNe using the calculated yields (see Section 4.2).

Development of the Galactic Chemical Evolution Models
To understand the origin of the high Fe/O, we compare the galactic chemical evolution models with the observations.Isobe et al. (2022) constructed Fe/O evolution models based on Suzuki & Maeda (2018).We develop models about Ar/O, S/O, N/O, and Ne/O in the same way.
These models are one-box chemical evolution models.We assume instantaneous star formation.We create stars based on the Kroupa initial mass function (Kroupa 2001), which is expressed by the broken power-law function 0.3 for 0.08, 1.3 for 0.08 0.5, 2.3 for 0.5 .

⎧ ⎨ ⎩
Table 7 presents the mass ranges for each model.We determine the mass ranges of our models, following Suzuki & Maeda (2018).
In the PISN models, we adopt the mass range from 9-300 M e .The lower limit of the mass range, M e , approximately corresponds to the lower limit mass of core-collapse supernovae (CCSNe) that is just beyond the mass of the electron-capture SNe (N13).The upper limit of the mass range, 300 M e , is chosen because the upper limit mass of PISNe is ∼ 300 M e .
We derive the lifetimes of the stars as a function of masses from Portinari et al. (1998) and Takahashi et al. (2018).The ranges of time calculated by our models are from 10 6.28 yr, which is the lifetime of a 300 M e star, to 10 7.52 yr, which is the lifetime of a 9 M e star.The stars cause SN explosions after finishing their lifetimes.Adding up the ejecta of SNe on the basis of model yields, we calculate the abundance ratios of galaxies.We assume that stars in the mass range of 9-100 M e cause CCSNe, while stars in the mass range of 140-300 M e undergo PISNe.We use the PISN (Takahashi et al. 2018) and the CCSN yields (N13) that cover 140-300 and 13-40 M e , respectively.We obtain the CCSN yields in 9-13 M e by the extrapolation of the CCSN yields (13-40 M e ).The CCSN yields in 40-100 M e are calculated by the interpolation of the CCSN and PISN yields.Stars in the mass range of 100-140 M e are assumed to collapse directly into black holes.The CCSN model in the second line of Table 7 is the same as the PISN model, but for the mass range of 9-40 M e that is free from the PISN contributions.Similarly, the HN model in the third line of Table 7 is the same as the CCSN model, but for the HN yield in Hideyuki Umeda et al. (2002) in 13-40 M e .We also develop other CCSN and HN models with the yields including the mixing and fallback parameters for comparison.We summarize the parameter sets for the yields in Table 8.N13 and Umeda & Nomoto (2008) calculate the yields of the CCSNe and HNe using the same assumption as this paper, but with different mixing regions.
In addition to the models explained above, we add the Type Ia SN yields by the mass fraction of the ejecta because Type Ia SNe can eject rich iron.We take the yields of Type Ia SNe from Nomoto et al. (1984) and Iwamoto et al. (1999).This corresponds to a scenario where progenitors of Type Ia SNe are produced during an earlier formation epoch.The effect of Type Ia SN enrichment is implemented by adding the Type Ia SN ejecta to the abundance ratios of each model's endpoint and increasing the proportion of Type Ia SNe to 10% in order to the effect of Type Ia SN enrichment.Because the ICFs can increase the abundance ratios up to 0.5 dex even for EMPGs (Izotov et al. 2006), the low abundance ratios in the EMPGs are not explained by the ICF correction alone.For this reason, our conclusions do not change because of the uncertainties of the ICF corrections.The abundances of the EMPGs are generally higher than the local dwarf galaxies (Izotov et al. 2006).

Comparing the EMPGs with the Models
The   As mentioned in Section 3.2, the abundance ratios for EMPGs are derived from gas-phase quantities, while our model predictions are based on total quantities, some of which can be depleted onto dust grains.To assess the potential impact of dust depletion on each abundance ratio diagram, we include arrows indicating the degree of depletion based on depletion factors defined by Ferland (2013), where depletion factors of 0.6 and 10 −2 are assumed for O and Fe, respectively, and no depletion is considered for Ar, S, Ne, and N.For example, the value of 0.6 for O indicates that 60 % of oxygen gas remains after dust depletion.While we understand that the assumed values for dust depletions are still an open question, particularly in the lowmetallicity regime, we simply adopt these values in this paper to evaluate the possible effect of dust depletion and compare our models with the observations.These differences between the EMPGs and PISN models in [Ar/O], [S/O], [N/O], and [Ne/O] cannot be explained by the effects of the dust depletion indicated with the arrows in Figure 2, suggesting that the chemical enrichment of the EMPGs is not dominated by PISNe.Amayo et al. (2021) argue that the dust depletion of Ar is comparable to the one of oxygen, while S experiences almost no depletion.Using the dust depletions of Amayo et al. (2021), we confirm that the dust depletions little change the distribution of the EMPGs in Figures 2 and 3. We think that the differences in dust depletion for S and Ar are not a major concern.Similarly, Figure 2 suggests none of the currently available HN models can fully explain all of the observed abundance ratios of EMPGs simultaneously.While the [Fe/O] of the HN-MF models are as high as those of the EMPGs, the Z = 0 models underpredict nitrogen and the Z = 0.004 models overpredict sulfur.
Figure 3 presents the CCSN models with two metallicities of Z = 0 and 0.004 for three mixing region factors of x = 0, 0.1, and 0.2.In Figure 3, the Z = 0.004 models with x = 0.1 and 0.2 explain the iron-poor ([Fe/O] 0) EMPGs.Similarly, these models agree with the abundance ratios of the local metal-poor galaxies (Section 5.2).The iron-rich ([Fe/O] >0) EMPGs are not reproduced by these models, but the CCSN models with Type Ia SNe.The CCSN models with Type Ia show high [Fe/O] values without increasing the [Ar/O] and [S/O] values as much as the PISN models.In Figure 3, a proportion of Type Ia SNe at ∼0.05 can reproduce the abundance ratios of the ironrich EMPGs.While the x = 0 condition, which corresponds to the mixing and fallback mechanism being turned off, results in a [Fe/O] ratio higher than the x = 0.1 and 0.2 conditions by ∼0.5 dex, it is not necessarily required for the EMPGs, if an enrichment of Type Ia SNe is included.Isobe et al. (2022) conclude that the iron-rich EMPGs are not enriched by Type Ia SNe because the N/O values of EMPGs are lower than the chemical evolution models (Vincenzo et al. 2016;Suzuki & Maeda 2018).They assume the typical delay time of Type Ia SNe such as the MW.These models show higher N/O and lower Fe/O values than the iron-rich EMPGs because the enrichment of Type Ia SNe and asymptotic giant branch (AGB) stars is effective.However, we introduce the Type Ia SNe enrichment without the time information by adding up to the CCSN models.We can see the N/O and Fe/O values before the enrichment of AGB and Type Ia SNe become dominant.We can find the possibility of a shorter Type Ia SNe delay time.
In summary, we conclude that the iron-rich EMPGs are not enriched by PISNe because the iron-rich EMPGs present lower [Ar/O] and [S/O] values than those of the PISN models.The abundance ratios of the iron-poor EMPGs are explained by the Z = 0.004 CCSN models with x = 0.1 and 0.2 in Figure 3.We find no mixing and fallback models of x = 0 give higher [Fe/O] values than those of x = 0.1, 0.2, and the previous yields.However, the HN or CCSN models alone cannot reproduce the abundance ratios of the iron-rich EMPGs.Although EMPGs are young galaxies, if Type Ia SNe occur after CCSNe, we can reproduce the abundance ratios of iron-rich EMPGs.

Comparing the EMPGs with Metal-poor Stars
In Figure 4, we compare the EMPGs with local dwarf galaxies and metal-poor stars in the MW and the Sculptor galaxy on the plots of [S/Fe] and [O/Fe] as a function of [Fe/H] that are useful to understand the chemical enrichment history.The metal-poor stars in the Sculptor galaxy show low sulfur and high iron values, similar to the EMPGs.Here, we use the abundance ratio of [O/Fe] instead of [Fe/O], following the notation typically adopted in studies of metal-poor stars.We show the MW chemical evolution model in N13, which includes CCSNe, HNe, Type Ia SNe, and AGB stars.Figure 4 indicates that the EMPGs with moderately small iron ( 2)  (Skúladóttir et al. 2015;Tang et al. 2023).Tang et al. (2023) claim that a minimum Type Ia SN delay time in the Sculptor galaxy is 10 8 yr.Because the abundance ratios of the EMPGs with [O/Fe]0 are similar to those of the Sculptor galaxy stars, the EMPGs may have a minimum Type Ia SN delay time as short as 10 8 yr.It is known that the delay time of a Type Ia SN in a galaxy including the MW is typically ∼ 10 8.5 -10 9 yr (Chen et al. 2021).Type Ia SNe can theoretically occur in a delay time less than 10 8 yr (Ruiter et al. 2009).Ruiter et al. (2009) claim that the delay time depends on different evolutionary scenarios for Type Ia SNe.Ruiter et al. (2009) introduced three scenarios: the double degenerate scenario where two white dwarfs merge (Iben & Tutukov 1984;Webbink 1984), the single degenerate scenario where a white dwarf accretes material from a hydrogen-rich companion star, and the AM Canum Venaticorum scenario where a white dwarf accretes material from a helium-rich companion star (Nomoto 1982;Nomoto & Leung 2018).Double degenerate and AM Canum Venaticirym scenarios present shorter delay time than H-rich single degenerate scenarios (Ruiter et al. 2009).The delay time of Type Ia SNe in the Sculptor galaxy and the EMPGs with [O/Fe] 0 may be shorter than the one of the MW.
In Figure 4, we also compare the gas-phase abundance ratios of the local dwarf galaxies (Izotov et al. 2006).Interestingly, the local dwarf galaxies present the [S/Fe] and [O/Fe] values larger than those of the MW stars.The abundance ratios of the local dwarf galaxies (Izotov et al. 2006) and our EMPGs are derived using the same ICFs.In the local dwarf galaxies, the [O/Fe] and [S/Fe] values are higher than EMPGs.If the influence of ICFs is responsible for the elevated [O/Fe] and [S/Fe] values, the EMPGs should exhibit a similar trend.However, EMPGs do not exhibit a trend similar to that of the local dwarf galaxies.We do not think that the abundance ratios of the local dwarf galaxies are not affected by the ICFs.Instead, we think that this difference between the abundance ratios of the local dwarf galaxies and our EMPGs is due to the dust depletion.The local dwarf galaxies have higher metallicities compared to EMPGs, resulting in a higher dust content.The impact of dust depletion is greater in the local dwarf galaxies than in EMPGs.Since our EMPG samples have lower metallicities than the local dwarf galaxies (Izotov et al. 2006), the effects of dust depletion of our EMPGs are lower.

Comparison of JWST High-z Galaxies with the EMPGs and Models
Recent observations with JWST have allowed us to directly measure abundance ratios including [S/O] and [Ar/O] for the high-z (4) universe (Isobe et al. 2023;Sanders et al. 2023).It would be advantageous to conduct the above analysis using elemental abundances at higher redshifts, where previous star formation and subsequent Type Ia SN explosions are less complicating factors.
To investigate the elemental abundances in galaxies at z ∼ 4-10 using JWST, we utilize 70 galaxies analyzed and presented in Nakajima et al. (2023).These spectra are taken from the three major public spectroscopic programs, including Early Release Observations (Pontoppidan et al. 2022), GLASS (Treu et al. 2022), and CEERS (Finkelstein et al. 2023).Isobe et al. (2023) have calculated the abundance ratios of [S/O], [Ar/O], and [Ne/O] for these 70 galaxies of Nakajima et al. (2023) in the same manner as our methods.The abundance ratios of 54 out of 70 galaxies can be determined or upper limits obtained.For the other 16 galaxies, the upper limits of abundance ratios cannot be measured.We include the abundance ratios of 54 galaxies derived by Isobe et al. (2023) in our sample.
The stellar masses of these galaxies are 10 7.5 -10 9.5 M e (Nakajima et al. 2023).We can identify similarities and differences in terms of elemental abundances between high-z galaxies and EMPGs.These comparisons, combined with our chemical evolution models, offer crucial insights into the formation mechanisms of EMPGs and young galaxies in the early universe.Specifically, there is a question of whether early young galaxies at high-z are enriched by PISNe.The PISN     Figure 5 shows the abundance ratios of [Ar/O] and [S/O] as a function of [Ne/O] for the high-z galaxies.Due to the limited signal-to-noise ratios (S/Ns), there are only two, and 10 out of 54 high-z galaxies whose abundance ratios are determined in the [Ar/O], and [S/O] versus [Ne/O] planes, respectively.The rest of the high-z galaxies are shown with upper limits in the abundance ratios.In Figure 5, we compare the high-z galaxies with the local EMPGs and metal-poor galaxies investigated in Section 5.2.We find that the two and 10 high-z galaxies with the abundance determinations have abundance ratios similar to those of the local EMPGs and metal-poor galaxies.For the rest of the high-z galaxies, the upper limits are too weak to distinguish between the CCSNe, HNe, and PISNe models.Although there are many high-z star-forming galaxies whose upper limits of the abundance ratios are consistent with the PISN models, no high-z galaxies have abundance ratios clearly support the possibility of a PISN chemical enrichment.(Chen et al. 2002;Bensby et al. 2004;Nissen et al. 2007, andCayrel et al. 2004).The metal-poor stars in the Sculptor galaxy are shown by the black circles (Skúladóttir et al. 2015 andTang et al. 2023).The blue curves indicate the chemical evolution models (N13), including CCSNe, HNe, Type Ia SNe, and AGB stars.poor W-R stars whose cores are massive at the final stage of the stellar evolution (Woosley et al. 2002;Ebinger et al. 2020).For this reason, Limongi & Chieffi (2018) assume that these W-R stars directly collapse with no CCSN events, and that the W-R stars only produce ejecta via stellar winds that are rich in nitrogen.
Figure 7 presents GN-z11 and the W-R/DC model in the plane of [N/O] versus the stellar age.In Figure 7, the nitrogen abundance of the W-R/DC model decreases rapidly at ∼ 10 6.9 yr, which corresponds to the lifetime of stars with a transition mass of 25 M e .Figure 7 indicates that the stellar age and nitrogen abundance of GN-z11 falls on the W-R/DC model.The high nitrogen abundance of GN-z11 ([N/O] ∼ 0.5) can be explained by the W-R/DC model for the given young age (3-5 Myr). Figure 7 also compares the independent yield models of Meynet et al. (2006) that are presented in Figure 6 Note that the models of DC W-R stars assume no CCSN ejecta in the initial condition.In other words, these models predict [N/O] for an onset of initial star formation from primordial gas.Although the models of DC W-R stars explain the high [N/O] value of GN-z11, it is unclear whether the moderately matured system of GN-z11 with stellar masses of 10 8 -10 9 M e and [O/H] ∼0.1 can be reached in the short timescale at least within 10 6.9 yr corresponding to the lifetime of  25 M e stars that could directly collapse.First, for the stellar mass, GN-z11 has a high star formation rate of 20 M e yr −1 (Senchyna et al. 2023), it takes only 5-50 Myr to produce 10 8 -10 9 M e stars in the constant star formation history.Because it is comparable with the short timescale of 10 6.9 yr, the moderately high stellar masses of 10 8 -10 9 M e do not contradict with the initial star formation.Second, for the oxygen abundance, the moderately high value of [O/H]∼0.1 cannot be accomplished with no CCSNe, if one assumes that the moderately high [O/H] is the average value for the large hydrogen gas reservoir of the interstellar medium in the GN-z11 galaxy.However, if W-R stars do not explode as CCSNe, metals are not well mixed in GN-z11.A small amount of metals produced by W-R star winds are confined in compact star-forming regions with a relatively small amount of hydrogen gas (the scenario similar to Bastian & Lardo 2018), and the moderately high value of [O/H] ∼0.1 could be obtained by emission-line diagnostics for ionized gas of the star-forming regions with the JWST data.

Summary
We study the elemental abundance ratios of the local metalpoor galaxies, JWST high-z galaxies, and Galactic/Sculptor stars taken from the literature with the chemical evolution models.We conduct spectroscopic observations for the EMPGs, obtain the spectra for the three EMPGs, and measure line fluxes of hydrogen, oxygen, iron, argon, sulfur, neon, and nitrogen to estimate the abundance ratios.n addition to these EMPGs, we use the abundance ratios of 11 galaxies whose Fe/O ratios are obtained in the literature.We confirm that some of the EMPGs have excessive iron abundance ratios similar to or beyond the solar abundance ratio.Developing the chemical evolution models for CCSNe, HNe, and PISNe to investigate the observed abundance ratios, we calculate the yields of CCSNe and HNe including the mixing and fallback mechanism that enhances the iron abundance.The main results of this paper are summarized below.
6583, and, [Ne III]λ3869, respectively, with the electron temperatures.Here we use T e (O II) for Fe 2+ , S + , and N + because their ionization potential energies are 10.4-16.2eV close to 13.6 eV, which is the ionization potential energy of O + (Berg et al. 2021).Similarly, we apply T e (O III) for Ne 2+ since the ionization energy of Ne 2+ is 41.0 eV comparable with the one of O ++ .Because the ionization energies of Ar 2+ and S 2+ range in 23.3-27.6 eV significantly lower than the one of O ++ , we do not use T e (O III)

Figure 1 .
Figure 1.LRIS spectrum of our targets.The top, middle, and bottom panels present SBS 0335-052E, J2314+0154, and J0125+0759, respectively.The gray-shaded region indicates the gap between the LRIS blue and red channels.The top-right, middle-right, and bottom-right panels show 20″ × 20″ cutout gri-composite images of SBS 0335-052E, J2314+0154, and J0125+0759, from Pan-STARRS1, HSC, and SDSS, respectively.The inset panels at the top-left corner of each panel represent the enlarged view of the spectrum around [Fe III] λ4658.In J2314+0154, the emission line of [Fe III] λ4658 is not detected.

Figure 2
Figure 2 compares the EMPGs (Section 3.1) with the PISN (the green curves) and HN (the blue and purple curves) models (Section 4.2) on the [Fe/O] versus [Ar/O], [S/O], [N/O], and [Ne/O] planes.Because of explosive O-burning, the [Ar/O] and [S/O] values are higher than CCSNe.While the [Fe/O] values of the EMPGs are comparable to those of the PISN models, the [Ar/O] and [S/O] values of the EMPGs are significantly lower than those of the PISN models.It is possible that the Ar and S abundances may be underestimated with the ICFs.However, the [S/O] and [Ar/O] abundance ratios in the EMPGs are lower than in the PISN models by >0.5 dex.Because the ICFs can increase the abundance ratios up to 0.5 dex even for EMPGs(Izotov et al. 2006), the low abundance ratios in the EMPGs are not explained by the ICF correction alone.For this reason, our conclusions do not change because of the uncertainties of the ICF corrections.The abundances of the EMPGs are generally higher than the local dwarf galaxies(Izotov et al. 2006).The [N/O] and [Ne/O] values of the EMPGs are much higher than those of the PISN models.The x = 0 conditions of HNe can produce higher [Fe/O] values than the HN models of N13 and lower [S/O] and [Ar/O] values than the PISN models.The [Fe/O] values of the x = 0 HN-MF models are comparable with the iron-rich([Fe/O] >0) EMPGs.However, the [S/O] and [Ar/O] values of the x = 0 HN-MF models are higher than the iron-rich EMPGs.We conclude that the x = 0 Figure 2 compares the EMPGs (Section 3.1) with the PISN (the green curves) and HN (the blue and purple curves) models (Section 4.2) on the [Fe/O] versus [Ar/O], [S/O], [N/O], and [Ne/O] planes.Because of explosive O-burning, the [Ar/O] and [S/O] values are higher than CCSNe.While the [Fe/O] values of the EMPGs are comparable to those of the PISN models, the [Ar/O] and [S/O] values of the EMPGs are significantly lower than those of the PISN models.It is possible that the Ar and S abundances may be underestimated with the ICFs.However, the [S/O] and [Ar/O] abundance ratios in the EMPGs are lower than in the PISN models by >0.5 dex.Because the ICFs can increase the abundance ratios up to 0.5 dex even for EMPGs(Izotov et al. 2006), the low abundance ratios in the EMPGs are not explained by the ICF correction alone.For this reason, our conclusions do not change because of the uncertainties of the ICF corrections.The abundances of the EMPGs are generally higher than the local dwarf galaxies(Izotov et al. 2006).The [N/O] and [Ne/O] values of the EMPGs are much higher than those of the PISN models.The x = 0 conditions of HNe can produce higher [Fe/O] values than the HN models of N13 and lower [S/O] and [Ar/O] values than the PISN models.The [Fe/O] values of the x = 0 HN-MF models are comparable with the iron-rich([Fe/O] >0) EMPGs.However, the [S/O] and [Ar/O] values of the x = 0 HN-MF models are higher than the iron-rich EMPGs.We conclude that the x = 0 ) 9 M e M < 13 M e Extrapolation L 13 M e M 40 M e CCSN N13 PISN Model CCSN + DC + PISN 40 M e < M 100 M e Interpolation L 100 M e < M 140 M e DC L 140 M e < M 300 M e PISN Takahashi et al. (2018) 9 M e M < 13 M e Extrapolation L CCSN Model CCSN 13 M e M 40 M e CCSN N13 9 M e M < 13 M e Extrapolation L HN model HN 13 M e M 40 M e HN Umeda & Nomoto (2008) Note.Column (1) Model name.Column (2) Type of SN.We assume that stars with masses between 100-140 N e cause DC).Column (3) Mass range of SN.Column (4) Yields.Column (5) References for the yields.abundance ratios of [O/Fe]> 0 (purple diamonds) show abundance ratios similar to those of the metal-poor stars in the MW.The rest of the EMPGs with [O/Fe]0 (magenta diamonds) do not have the abundance ratios of the MW stars, but those of the Sculptor dwarf galaxy stars.Oxygen is unstable due to the effects of explosions because oxygen is synthesized in a layer farther from Fe compared to sulfur.The [O/Fe] values of metal-poor stars in Figure 4 exhibit greater scatter than the [S/Fe] values.The [S/Fe] values do not scatter largely, because S and Fe are synthesized in the close layers.On the other hand, oxygen is synthesized in a layer far from Fe.These are reasons why the [O/Fe] values scatter largely than the [S/Fe] values.In Figure 4, we compare these observational data points with the chemical evolution tracks (blue curves) predicted by the N13 model, and confirm that the N13 model explains the abundance ratios of the MW stars.In the N13 model, the iron abundance increases at around [Fe/H] −1 due to the chemical enrichment driven by Type Ia SNe, which makes the knees at [Fe/H]∼ −1 in the chemical evolution tracks of [S/Fe] and [O/Fe] as a function of [Fe/H].The observational data for [S/Fe] and [O/Fe] of the Sculptor galaxy stars (circles) show knees at [Fe/H]∼ −2 smaller than the one of the knees of the MW stars.In the Sculptor galaxy, it is possible that the chemical enrichment of Type Ia SNe starts at [Fe/H]∼ −2 earlier than the MW galaxy of [Fe/H]∼ −1 Model name.(2) Type of SN. (3) Mass range of SN. (4) Yields.(5) Mixing region factor value. (6) Metallicity.

Figure 2 .
Figure 2. Comparisons of the EMPGs with the PISN and HN models in the abundance ratios.The top, second, third, and bottom panels present [Fe/O] as a function of [Ar/O], [S/O], [N/O], and [Ne/O],respectively.The black and gray circles show the EMPGs and the local dwarf galaxies(Izotov et al. 2006), respectively.The green, purple, and blue lines present the time variation of PISN, the Z = 0.004 HN-MF, and the Z = 0 HN-MF models, respectively.The yellow line shows the time variation of the HN model calculated with the yields of N13.The solid, dashed-dotted, and dotted lines indicate x = 0, x = 0.1, and x = 0.2 for the HN-MF models, respectively.The red crosses indicate the abundance ratios of Type Ia SN ejecta(Iwamoto et al. 1999).The light green and cyan curves represent the PISN and Z = 0.004 HN models with the Type Ia SN ejecta added.The numbers accompanied by the light green and light purple curves indicate the proportions of Type Ia SNe to HNe and PISNe, respectively.The effects of the dust depletion are denoted by the black arrows whose lengths present the change of the values from [0, 1.3] on the planes adapted fromFerland (2013).

Figure 3 .
Figure 3. Same as Figure 2, but for the CCSN models.The red and orange lines indicate the Z = 0.004 CCSN-MF and Z = 0 CCSN-MF models, respectively.The brown curves present Z = 0.004 CCSN-MF models with the Type Ia SN ejecta added.The magenta curves show the CCSN model with the yields of N13.

Figure 4 .
Figure 4. Comparisons of the EMPGs with metal-poor stars.The left and right panels present [S/Fe] and [O/Fe] as a function of [Fe/H], respectively.The magenta and purple diamonds show EMPGs with [Fe/O] 0 and [Fe/O] < 0, respectively.The gray circles show the local dwarf galaxies (Izotov et al. 2006).The metal-poor stars in MW are represented by open circles(Chen et al. 2002;Bensby et al. 2004;Nissen et al. 2007, andCayrel et al. 2004).The metal-poor stars in the Sculptor galaxy are shown by the black circles(Skúladóttir et al. 2015 andTang et al. 2023).The blue curves indicate the chemical evolution models (N13), including CCSNe, HNe, Type Ia SNe, and AGB stars.

Figure 5 .
Figure 5.Comparison of JWST high-z galaxies with EMPGs.The left and right panels present [Ar/O] and [S/O] as a function of [Ne/O], respectively.The magenta diamonds show EMPGs.The filled brown and black open circles show JWST galaxies with measured ratios and only upper limits, respectively.The color curves represent the chemical evolution models the same as Figure 2 and Figure 3.The gray circles show the local dwarf galaxies (Izotov et al. 2006).
. Again, the yield of the W-R (wind+SN) model shows [N/O] as low as −0.78.Here, we assume that some fractions of W-R stars directly collapse, and calculate [N/O] values for the fractions of DC W-R stars.With this yield model, We find that ∼97% of the W-R stars need to directly collapse to produce [N/O] as high as the one of GN-z11 ([N/O]∼0.52).This high fraction of the DC W-R stars is consistent with that of the W-R/DC model whose W-R stars with >25 M e fully directly collapse.
1.Although the [Fe/O] values of the PISN models are as high as those of some EMPGs as claimed by Isobe et al. (2022), [Ar/O] and [S/O] values of the PISN models are

Figure 7 .
Figure 7.Comparison of GN-z11 with the W-R/DC model.The red-filled (open) circles show the abundance ratios of GN-z11 estimated by Isobe et al. (2023) in the case of stellar (AGN) photoionization.The left panel and right panels present the W-R star models without DC and with DC, respectively.The blue curves show our W-R/DC model developed with the DC W-R stars (Limongi & Chieffi 2018).The green dashed lines represent the [N/O] values of varying the percentage of DC W-R stars (Meynet et al. 2006), where the lengths of the green dashed lines indicate the lifetimes of stars in the mass range of 30-90 M e . Z by O/H, we obtain Fe/O, Ar/O, S/O, N/O, and Ne/O.We use the Ar/O values derived with [Ar III] λ7136 emission because [Ar IV]λ4711 emission lines are contaminated by He I emission lines.Although our best estimate Ar/O values are obtained with [Ar III]λ7136, we examine these Ar/O values with those estimated from the [Ar IV]λ4711, [Ar IV]λ4740, and [Ar III]λ7136 emission lines albeit with the He I emission contamination.We confirm that the best estimate Ar/O values are consistent with the Ar/O upper limits, which are the Ar/O values derived with He I emission contamination.

Table 6
Parameters of the SN yields and [S/O], and find no statistically significant correlation between [Fe/O] and [S/O].

Table 7
Models of the Yields in the Literature