Ionized-gas Metallicity of the Strong [O iii]λ5007 Emission-line Compact Galaxies in the LAMOST Survey

This article reports a sample of 1830 strong [O iii]λ5007 emission-line compact galaxies discovered with the LAMOST spectroscopic survey and the photometric catalog of the Sloan Digital Sky Survey. We newly identify 402 spectra of 346 strong [O iii]λ5007 emission-line compact galaxies by finding compact isolated point sources. Combined with the samples in our previous work, this returns a sample of 1830 unique strong [O iii]λ5007 emission-line compact galaxies with 2033 spectra of z ≤ 0.53. For the sources with 2σ[O iii]λ4363 detections, we calculate the gas-phase metallicity with the direct-T e method, and verify that the strong-line metallicity diagnostics calibrated with the direct-T e method also applies to this sample. The strong [O iii]λ5007 emission-line compact galaxies fall below several T e -calibrated mass–metallicity relations. The N/O measurements of the strong [O iii]λ5007 emission-line compact galaxies mainly locate at a plateau at low metallicity, indicating the product of primary nucleosynthesis. The Ne3O2 and O32 relation follows a tight linear relation with no redshift evolution. The Ne3O2 anticorrelates with the stellar mass, and at fixed stellar mass the Ne3O2 increases with the redshift. Eight sources with asymmetric [O iii]λ5007 emission-line profiles have been identified, however with no [O iii]λ4363 detection, which proves the rich metal content and complex ionized-gas kinematics within the galaxies. Higher-resolution spectroscopy will be necessary to identify the ionized-gas components in detail.


INTRODUCTION Strong [
O iii]λ5007 emission-line compact galaxies are well-known for their unique color, compactness, high star formation rate (SFR), low metallicity, and being in isolated environments (Cardamone et al. 2009).According to the redshifts and correspondingly the change of color, strong [O iii]λ5007 emission-line compact galaxies are also called Blueberry galaxies (at z ≤ 0.05), Green Pea galaxies (0.112 ≤ z < 0.36) and Purple Grape galaxies (0.05 < z < 0.112 and 0.36 ≤ z ≤ 0.53).
In our previous work (Liu et al. 2022), we selected 1694 spectra with 1547 unique objects from the dedicated and non-dedicated survey in the LAMOST spectra database (Wang et al. 1996;Su & Cui 2004;Luo et al. 2012).
We further analyze the star formation rate (SFR), the mass-metallicity relation (MZR), and the environment of these samples.In this work, in joint with newly identified strong [O iii]λ5007 emission-line compact galaxies, we compile a large sample of the strong [O iii]λ5007 emission-line compact galaxies and discuss the metallicity of the ionized gas.In the following discussion, these samples are called strong [O iii]λ5007 emissionline compact galaxies, which consist of 2033 spectra of 1830 unique galaxies.
The galaxies' gas-phase metallicity and ionization parameter provides rich information about their chemical evolution, among which gas-phase oxygen abundances are the best approach to measure the current metallicity.Emission lines in the spectra of the star-forming galaxies are acquired conveniently across different redshift ranges and thus are potent indicators of chemical compositions.
The well-known scaling relation between the gas-phase metallicity and the stellar mass, quoted as the massmetallicity relation (MZR, Lequeux et al. (1979)), has been studied extensively (Tremonti et al. 2004;Lee et al. 2006;Mannucci et al. 2010;Lara-López et al. 2010;Andrews & Martini 2013;Maiolino & Mannucci 2019;Yates et al. 2020;Curti et al. 2020;Nakajima et al. 2022).The MZR brings crucial observational information on understanding the build-up of the galaxies over time.Typically there are two methods to measure the metallicity: the direct-T e method and the strong-line method (Andrews & Martini 2013).The direct-T e method employs the ionized gas's electron temperature and thus the gas's metallicity, calculated from the flux ratio of the auroral line and the strong lines.It is effective because metals are the ionized gas's primary coolants.The auroral and strong lines originate from the second and excited states separately, where the electron temperature can be calculated from the relative ratios of these two populations.The metallicity is strongly correlated with the electron temperature, where the low electron temperature corresponds to the high metallicity.It is suggested by Alloin et al. (1979); Pagel et al. (1979) to use some emission lines to calibrate the oxygen abundances, usually referred to as the "strong-line method".The strong-line method does not measure the metallicity directly.Due to their sensitivity to metallicities, the strong lines are easier to measure when the auroral lines are too weak for high-metal sources.However, there are systematic discrepancies (Kewley & Ellison 2008;López-Sánchez et al. 2012) comparing the metallicity determined from the direct-T e method and the strong-line calibrations.Systematical "strong-line" calibrations have been performed (Maiolino et al. 2008;Jones et al. 2015;Curti et al. 2017;Patrício et al. 2018;Curti et al. 2020), however, more tests at the low-metallicity regimes are needed.
An alternative chemical abundance diagnostic is nitrogen, probed by N/O, which compared with oxygen produced from Helium fusion, the formation is more complex.N/O is sensitive to the chemical evolution history of a galaxy because nitrogen is the product of a primary nucleosynthetic product (independent of metallicity) and a secondary nucleosynthetic product (dependent on the metallicity of the gas cloud) (Hayden-Pawson et al. 2022).Studies have shown at low metallicities, the N/O ratios stay at a plateau and do not vary with O/H; while towards higher metallicity as the galaxies evolve, the N/O begins to increase with O/H (Shi et al. 2005;Pilyugin et al. 2012;Andrews & Martini 2013;Hayden-Pawson et al. 2022).The samples in this work will provide valuable information about the N/O vs O/H relation at the low metallicity regime.
The [Ne iii]λ3869 lines serve as an additional crucial probe of the ionized gas.Ne3O2 ([Ne iii]λ3869/[O ii]λλ3727, 3729) was first initiated as the metallicity diagnostic (Nagao et al. 2006;Shi et al. 2007).However, Pérez-Montero et al. (2007); Levesque & Richardson (2014) addressed the reason why Ne3O2 anti-correlates with the metallicity is the change of the ionization parameter.Compared with the commonly used O32 ([O iii]λ5007/[O ii]λλ3727, 3729), Ne3O2 is less prone to dust extinction due to the proximity of the wavelength coverage and can be applied to sources of higher redshifts.The strong emission-line samples in this work provide ample samples to re-examine the correlation of these two ionization parameters.
We also look into the kinematics of the ionized gas which reflects the star formation history.There are detailed optical (Amorín et al. 2010(Amorín et al. , 2012a,b;,b;Bosch et al. 2019;Hogarth et al. 2020) and UV (Jaskot & Oey 2014;Henry et al. 2015;Yang et al. 2016;Izotov et al. 2018) spectroscopic studies of Green Pea galaxies, where the authors have identified double-peak or asymmetric profiles of the emission lines.Amorín et al. (2012b) has identified the spatially offset Hα emission line profiles in their 2D spectra.Bosch et al. (2019) analyzed the kinematics of a single Green Pea galaxy with the Gemini Multi-Object Spectrograph and confirmed the existence of three components: a rotating disk, a turbulent mixing layer, and gas outflow.Hogarth et al. (2020) concluded the triple component might come from two starbursts by fitting three components from all the optical emissions lines from deep high-resolution spectra.This has revealed the presence of complex ionized gas structures within these galaxies.
The structure of the paper is summarized below.In Section 2, we introduce the newly spectroscopicallyconfirmed strong [O iii]λ5007 emission-line compact galaxies from LAMOST.In Section 3, we explain how to measure the stellar mass from multi-wavelength photometry, obtain the emission line flux and the corresponding error, and measure the velocity dispersion from the [O iii]λ5007 emission line.In Section 4, we demonstrate the result of the metallicity from the direct-T e method and compare it with the strong-line calibrations.In Section 5, we discuss the mass-metallicity relation, the N/O vs O/H relation, the Ne3O2 vs O32 relation, the Ne3O2 vs stellar mass relation, and the asymmetric [O iii]λ5007 profiles of eight sources.Finally, we present a summary of the measurements, results, and discussions in Section 6.

Sample selection
Instead of the traditional color selection criteria as in Cardamone et al. (2009), we select the strong [O iii]λ5007 emission line galaxies, which are compact and isolated.The reasons for removing the strict color selection are two-fold: to include the emission line galaxies with a broader redshift range and to select the galaxies with less severe emission lines.
This returns 594863 sources.
Using the massive amount of spectra available in the LAMOST database (Wang et al. 1996;Su & Cui 2004;Luo et al. 2012), we cross-match the photometry sources with LAMOST DR101 with a searching radius of 3" and have obtained 2847 spectra that match these positions.The goal of this work is to investigate the metallicity of the ionized gas in these low-z galaxies, the AGN components will bias the predictions from the photoionization models.Therefore, we remove the sources that show broad Balmer emission lines and display the [Mg ii]λ2800 line if located within the wavelength coverage to eliminate AGNs from our sample.Furthermore, based on the emission line ratios, we calculate the BPT diagram as in Figure 1 and keep the sources classified as 'SF' or 'comp' for further analysis in this work.We select the ones that have significant [O iii]λ5007 emission lines with ≥ 2σ detection.Thus, we have obtained 402 new spectra with 346 new sources in this work.

Flux calibration
Following the procedures in Wang et al. (2018); Liu et al. (2022), we re-calibrate the LAMOST spectra according to the SDSS gri photometry.LAMOST spectra are convolved with the SDSS gri filters (Fukugita et al. 1996) in the observed frame to obtain the synthetic magnitudes for these three bands and we calculate the difference of the synthetic magnitudes with the observed SDSS photometric magnitudes.A zeroth-order or firstorder polynomial is used to fit the magnitude difference array and apply this correction to the LAMOST spectra.

Comparison sample
To check whether there is redshift evolution of the relations discussed in Section 5, there are also measurements at different redshift ranges included in this work for comparison.At z ∼ 0, we use the measurements from the composite spectra of SDSS emission line galaxies in Andrews & Martini (2013).
At higher redshifts, we make use of two stacked measurements.Zeimann et al. (2015) used stacked lowresolution near-IR grism spectra from the Hubble Space Telescope (HST) and obtained composite measurements of z ∼ 2 low-mass (median 10 9 M ) galaxies.We include the measurements of five stellar mass bins in the composite spectra.Jeong et al. (2020) measure the doubly ionized Neon ([Ne iii]λ3869) for z ∼ 2 galaxies in the MOSFIRE DEEP Evolution Field (MOSDEF) survey (Kriek et al. 2015).We use the measurements from the stacked spectra in four stellar mass bins, which have no requirements of the [Ne iii]λ3869 detection.
The revolutionary James Webb Space Telescope (JWST) and its near-IR spectrograph NIRSpec (Ferruit et al. 2022;Jakobsen et al. 2022) has opened the new possibility of investigating the chemical abundances at higher-z.Among the 35 objects detected in the field of the lensed galaxies of cluster SMACS J0723.3-7327(Ebeling et al. 2001(Ebeling et al. , 2007(Ebeling et al. , 2010;;Mann & Ebeling 2012) from the Early Release Observations (ERO) of JWST, there are three sources at z ∼ 7.7 − 8.5.These three sources show similar rest-frame optical spectra as the strong [O iii]λ5007 emission-line compact galaxies in this sample, which is worth to be compared with.We use the measurements in Curti et al. (2023) in this work.
3. PHYSICAL PARAMETERS 3.1.Multi-wavelength spectral energy distribution fitting We cross-match the sources with the Galaxy Evolution Explorer (GALEX) (Bianchi et al. 2017) to obtain the NUV photometry and cross-match the sources with the AllWISE Multiepoch Photometry Table (Wright et al. 2010;Wright, Edward L. and Eisenhardt, Peter R. M. and Mainzer, Amy K. et al. 2019) to obtain the W 1 to W 4 photometry.For the stellar mass measurement, we fit the sources with multiwavelength photometry with CIGALE (Burgarella et al. 2005;Boquien et al. 2019) combining the GALEX NUV, SDSS ugriz, and AllWISE W 1 to W 4 photometry.For the configuration of the fitting, we use the delayed−τ star formation history, BC03 stellar population models (Bruzual & Charlot 2003), Chabrier IMF (Chabrier 2003), nebular emission lines, the dust attenuated modified starburst model, the dust emission model from Casey (2012) We measure the color excess of the galaxies from the flux ratio of the Hα to Hβ assuming the case B recombination with the intrinsic line ratio of 2.86.The color excess from the flux ratio is calculated with where k(Hα) = 3.33 and k(Hβ) = 4.6 as in Jiang et al. (2019).If the flux ratio is less than 2.86, the color excess is considered to be set to 0. The distribution of the flux ratios and E(B-V) are displayed in Figure 3.All of the emission line flux measurements are corrected with the extinction correction using the Calzetti et al. (2000) extinction law, with the color excess measured from the Balmer decrement.
We demonstrate an example of the spectrum with the emission lines marked in Figure 4. Specifically, we also calculate the velocity dispersion of the [O iii]λ5007 emission line.To calculate the intrinsic velocity dispersion of the sources, we subtract the instrumental and thermal broadening of the sources as in Bosch et al. (2019); Hogarth et al. (2020).Assuming an electron temperature T e = 1.2 × 10 4 K (Amorín et al. 2010(Amorín et al. , 2012b)), the typical thermal broadening for these galaxies are σ ther = cλem λ obs kBTe mionc 2 .The thermal broadening of a galaxy at z = 0.26 is about 2.50 km s −1 .We refer to the values given in Shi et al. (2014) for the instrumental FWHM as an average value of 3.5 Å for LAMOST spectrographs.
The rest-frame equivalent widths (EWs) of the [O iii]λ5007 emission lines are measured to be compared with other work.Figure 5 demonstrates the distribution for the measured EWs. 2ll the above measurements are compiled into a catalog https://nadc.china-vo.org/res/r101238,and the descriptions of the catalog are listed in Table 1.

Direct-T e method gas-phase metallicity
With the auroral [O iii]λ4363 line, the gas-phase metallicity could be estimated in a direct-T e method (Aller 1984;Izotov et al. 2006).This approach assumes the electron temperatures for O + and O ++ in a two-zone photoionization model: the high-ionization zone traced by the O ++ and the low-ionization one traced by the O + .We calculate the O ++ electron temperature with the following equation (as in Izotov et al. (2006) Eqs ( 1) and ( 2)): where t = 10 −4 T e ([O iii]), and where x = 10 −4 n e t −0.5 .As addressed in Andrews & Martini (2013); Curti et al. (2017), at low-metallicity environments, the O ++ abundance is dominant over that of O + .Besides, there is no direct temperature diagnostic for the low-ionization zone, the electron temperature of [O ii] for the low-metallicity situation is estimated with Izotov et al. (2006) as: This is also the method that Jiang et al. ( 2019 (3) and (5) in Izotov et al. (2006), we calculate the ionic abundances as follows:

H
to determine the oxygen abundance, neglecting the contribution from higher ionization states.
Among the total sample of the strong [O iii]λ5007 emission-line compact galaxies, there are 450 sources with 2σ [O iii]λ4363 detection.Only the sources where the t 3 range from 5 000 to 20 000 K, as noted in Izotov et al. (2006), are selected for metallicity discussion, which counts to 372.For this sub-sample, we estimate the gas-phase metallicity and use them for the following metallicity measurements and discussions.

Strong-line calibration
We use different strong-line calibrations and verify whether these strong [O iii]λ5007 emission-line compact galaxies follow the derived scaling relations of the strong-line calibrations.The definitions of the strong-line calibration are listed in Table 2. Comparing with the strong-line calibrated polynomial forms from Maiolino et al. (2008); Jones et al. (2015); Curti et al. (2020) 4 as in Figure 7, we find that the strong [O iii]λ5007 emission-line compact galaxies agree with these strong-line diagnostics.This set of calibration is valid in 7.6 ≤ 12 + log(O/H) ≤ 8.9.
For the low-metallicity regime, we also include the strong-line calibration from Nakajima et al. (2022). 5 The optical-line gas metallicity diagnostics are established by the combination of local SDSS galaxies (Curti et al. 2017) and the largest compilation of extremely metal-poor galaxies (EMPGs) identified by the Subaru EMPRESS survey (Kojima et al. 2020).This set of calibrations reaches the lower metallicity roughly down to 12 + log(O/H) ∼ 6.9.for SDSS galaxies on the T e abundance employing the strong-line metallicity calibrations, which better captures the turnover mass.The mass range is from

N/O vs O/H relation
The total N/O ratio is not easy to measure since the [N iii] lines are not readily observable, therefore, N + /O + are often used as a proxy of N/O abundance.We determine the ratios following Pagel et al. (1992); Shi et al. (2005) as : where the T e ([N ii]) = T e ([O ii]), and the definition of x is the same as in Equation 3. The relation of the N/O vs O/H is displayed in Figure 9.Most of the samples are located in the horizontal range of the distribution with an approximately constant value, where the majority of the nitrogen is produced from the primary nucleosynthesis process.The colors of the scatter mark the flux ratio of Hα to Hβ.It is wellknown that there is a plateau in the N/O ratio at low metallicity (Pagel 1997;Vincenzo et al. 2016;Hayden-Pawson et al. 2022).At 12 + log O/H = 8.5 there is a transition that N/O increases with the metallicity, which is strongly influenced by the star formation efficiency (Mollá et al. 2006).With the evolution of the galaxies, low-to intermediate-mass stars produce secondary and primary nitrogen that increases the N/O ratio with the increase of metallicity at the same time.These strong [O iii]λ5007 emission-line compact galaxies are mainly young galaxies with low metallicity.The N/O values of the strong [O iii]λ5007 emission-line compact galaxies almost have a constant value, indicated by the horizontal lines (Andrews & Martini 2013;Hayden-Pawson et al. 2022) in Figure 9.
As demonstrated in Figure 9, a considerable number of samples show N/O value above the plateau at low metallicity.However, the reason for this offset is not clear.No systematic trend of the flux ratio of Hα to Hβ, as shown with the color of the scatter points, with this offset is observed.Amorín et al. (2010)   SDSS star-forming galaxies.The inflow of gas might explain this offset as well as the high SFR, compactness, and disturbed morphology.Amorín et al. (2010) also add another explanation that this process is coupled with the selective metal-rich gas loss, driven by supernova winds.However, based on IFU observations, Komarova et al. (2021) argue that the broad wings from local Green Pea analogs do not originate from stellar winds or supernovae, but are more likely driven by radiation.It would be worth further investigation regarding the origin of this N/O offset at the low metallicity regime.Vincenzo et al. (2016) have modeled that the impact of changing IMF mainly is to shift the chemical evolution tracks along the metallicity axis, and the data from SDSS is best-fit with the Kroupa IMF (Kroupa 2001).As demonstrated in Fig. 8 in Vincenzo et al. (2016), if assuming the model with the Geneva stellar yields by taking the mass loss and rotation into consideration, the chemical evolution model predicted a dip in the N/O ratios.Based on the observations of the metal-poor stars in Spite et al. (2005), Fig. 2 in Chiappini et al. (2005) demonstrates the N/O vs O/H plane, where there is also a significant scatter at low metallicity.In Figure 9, the scatter in N/O of the strong [O iii]λ5007 emission-line compact galaxies in this work is comparable to that of the Andrews & Martini (2013) (Pérez-Montero et al. 2007;Shi et al. 2007) as well as ion-ization parameter indicators (Levesque & Richardson 2014).The tight correlation between these two ratios is verified by different star-forming galaxies, which indicate similar evolution.This is also checked for different metallicity as demonstrated in the Ne3O3 vs metallicity relation in Figure 7, where Ne3O3 is almost flat for different metallicity ranges.The strong [O iii]λ5007 emission-line compact galaxies provide rich sources to verify the relations of the two ratios in the local Universe, especially at the high ionization regime.
In Figure 10, we demonstrate the relation of these two line ratios of the strong [O iii]λ5007 emission-line compact galaxies in this work, the SDSS local star-forming galaxies from Andrews & Martini (2013), the measurements of the stacked spectra in Jeong et al. (2020), and three z ∼ 7.7 − 8.5 sources from JWST.The two ratios follow tight linear relations, although the scatter is significant at the low ratio regime as predicted by the photoionization models (Levesque & Richardson 2014).There is no significant redshift evolution of the linear relationship between these two parameters as seen from the measurements in Jeong et al. (2020); Curti et al. (2023).At the low ionization regime, there are offsets between the Jeong et al. ( 2020) measurement and the local measurements from Andrews & Martini (2013).Due to the compactness of the strong [O iii]λ5007 emissionline compact galaxies, they are less prone to the effects of the diffuse ionized gas (DIG) at the low ionization regime as seen in Jeong et al. (2020).The strong [O iii]λ5007 emission-line compact galaxies in addition to the local H ii regions are more appropriate local comparison samples for high-z star-forming galaxies on investigating the ionization parameters (Sanders et al. 2017).The offset might be explained by harder ionizing sources at higher redshifts (Strom et al. 2017;Shapley et al. 2019) or the evolution of the fundamental metallicity relation (Sanders et al. 2016).
In Figure 11, we demonstrate the anti-correlation of the Ne3O2 with the stellar mass at the mass range log M/M < 9.5.This anti-correlation is also consistent with the mass-metallicity relation, based on the anticorrelation between the ionization parameter and metallicity.This trend is also demonstrated in Pharo et al. (2023) for SDSS galaxies at z ∼ 0(Andrews & Martini 2013), and HALO7D galaxies at z ∼ 0.8 (Cunningham et al. 2019a,b).At fixed stellar mass, with the increase of redshift, the Ne3O2 is higher for the strong [O iii]λ5007 emission-line compact galaxies in this work as demonstrated by the color of the scatter points.The Ne3O2 offset is also obvious with measurements from the stacked spectra at z ∼ 2 (Zeimann et al. 2015;Jeong et al. 2020).The small offset between Zeimann et al. (2015) and Jeong et al. (2020) is due to the blended He i and H ζ lines in the low-resolution HST grism spectra.5.4.Ionized gas kinematics from the asymmetric [O iii]λ5007 profile Visually inspecting the [O iii]λ5007 emission-line lines, we notice that some sources show significant asymmetric profiles.By comparing the fitting result of the double-Gaussian model with the single-Gaussian model, we select the model where the χ 2 ν is closer to 1.The degree of freedom is the number of spectral points within the wavelength range of 4985-5029 Å minus 6 for a double-Gaussian model, or minus 3 for a single-Gaussian model.We have identified eight sources that show asymmetric [O iii]λ5007 emission-line profiles as demonstrated in Figure 12, where the χ 2 ν,double is less than 90% of the χ 2 ν,single .The properties for these sources are listed in Table 3.
To ensure the validness of the asymmetric emission line profiles, we visually check the positions of the bad pixels to avoid contaminating the spectra.In the original LAMOST spectra, the primary data arrays store the andmask and the ormask6 .The andmask is a decimal integer.If one of the six situations (bad pixel on CCD, bad profile in extraction, no sky information at this wavelength, sky level too high, fiber trace out of the CCD, or no good data) always appears in each exposure, the andmask will be set to 1. Similarly, the ormask is set to 1 if one of the above six situations happens in any of the exposures.We have checked carefully for the masks in these sources, and none of the Hβ, [O iii]λ5007 and [O iii]λ5007 spectral regions is marked with 1 with either allmask or ormask.
We also check the single-exposure spectra to validate the accuracy of the asymmetry profiles.The measured velocity dispersion, the number of exposures, the number of exposures used, and the measurement error are in Table 4. Specifically for source 811511143, we demonstrate double-Gaussian fitting result for both the  2023) have discussed the phenomenon of the double-peak or asymmetric profile in their spectra of the Green Pea galaxies.Amorín et al. (2012b) have identified multiple components with spatially-resolved offsets in their two-dimensional spectra.By analyzing the chemical abundances of each component, Hogarth et al. (2020) conclude that the outflows and turbulence are the driving force for the escape of ionizing photons and chemical enrichment.These studies show that the multiple gas component is not unique in Green Pea galaxies but also exists in z ∼ 1 − 2 extreme emission-line galaxies (Maseda et al. 2014;Masters et al. 2014;Terlevich et al. 2015) with high-velocity dispersions up to about 240 km s −1 , as well as detected in the integral field spectroscopy of other compact star-forming galaxies (Law et al. 2009;Yang et al. 2017;Turner et al. 2017) and giant H ii regions (Castaneda et al. 1990).
Due to the limits of the instrumentation resolution (R ≈ 1800), it is impossible for us to identify narrower components.It is worthwhile to conduct follow-up highresolution spectroscopy with a longer exposure time to confirm the existence of the multi-components.2020) are marked with dark orchid squares (Zeimann et al. 2015).The crimson stars mark the three galaxies from JWST.
work (Liu et al. 2022), this returns a sample of strong [O iii]λ5007 emission-line compact galaxies with 1830 unique strong [O iii]λ5007 emission-line compact galaxies with 2033 spectra up to redshift of 0.53.Using the emission lines, we check the metallicity of these sources.
Our conclusions are as follows: • The strong-line metallicity diagnostics calibrated from the direct-T e method also apply to the strong [O iii]λ5007 emission-line compact galaxies.
• The N/O vs O/H relation of the strong [O iii]λ5007 emission-line compact galaxies mainly follows the relation at low metallicity when the nitrogen is primarily produced from primary nucleosynthesis.
• The ionization parameter mapped from Ne3O2 and O32 follows a tight linear relation.No significant redshift evolution is observed.
• The Ne3O2 anti-correlates with the stellar mass for these strong [O iii]λ5007 emission-line compact galaxies at log(M /M ) < 9.5.At fixed stellar mass, the Ne3O2 is higher at higher redshifts.

Figure 1 .
Figure 1.BPT diagram for the selected sources.Only 'SF' and 'comp' sources are kept for further analysis.
, and the Fritz et al. (2006) AGN model.3.2.Emission line flux, equivalent width, and velocity dispersion We fit the emission lines with LMFIT (Newville et al. 2016).For emission line error estimation, we use the Monte Carlo method.For each instance, we perturb the flux at each wavelength sampling point 200 times by running a Gaussian distribution centered on the flux measurement with a width set by the flux error.The mean value of the resulting emission line flux is the resulting flux measurement, and the standard deviation marks the flux error.An example demonstrating the measurement of [O iii]λ4363 line is in Figure 2.

Figure 2 .Figure 3 .
Figure2.The Hγ and [O iii]λ4363 emission lines fitted with the Gaussian profiles (left panel) and histogram of the measurement of each realization (right panel).In the left panel, the flux of each realization is marked with a black line, and the fitted Gaussian profile is marked with an orange curve.In the right panel, the mean value of the distribution is marked with the black solid line, and the 1σ region is marked with the dashed lines.

Figure 4 .Figure 5 .
Figure 4.An example spectrum of the strong [O iii]λ5007 emission-line compact galaxy.The emission lines used for following metallicity and kinematics measurements and discussions are marked at different wavelengths.The grey-shaded regions mark the flux error.
) use for calculation, and they state that their measurement of the oxygen abundance depends little on the relation between t 2 and t 3 .Similarly, we use the term t 2 = 10 −4 T e ([O ii]) and t 3 = 10 −4 T e ([O iii]) for clarity.We follow the treatment as inJiang et al. (2019) using the [S ii]λ, λ6716,6731 lines to estimate the electron density n e .For 1052 sources with both 2σ detections for the [S ii]λ6716 and [S ii]λ6731 emission lines, the flux ratio is defined as R(n e ) = λ6716 λ6731 , and the electron density is estimated 3 :n e (R) = ab−Rc R−a , R ≥ 0.51 100, otherwise(5)in units of cm −3 , where a = 0.4441, b = 2514, c = 779.3.The derived distribution of n e is in Figure6.As addressed inJiang et al. (2019), under n e = 10, 100 or 10 3 cm −3 , the results do not vary much.With Eqs.

Figure 6 .
Figure 6.The distribution of the derived ne.
Mass-metallicity relationWith the gas-phase metallicity determined from the direct-T e method, we demonstrate in Figure8that the metallicity increases with the stellar mass and falls below several T e -calibrated MZRs.Tremonti et al. (2004) and later works(Mannucci et al. 2010) adopt the calibration from different grids of photoionization models.The MZR from Yates et al. (2020) is based on the samples with auroral detections from the revised version of the classical T e -based method.Furthermore, Curti et al. (2020) provide the MZR by fully anchoring the metallicity determinations 4 The Ne3O2 calibration is from Maiolino et al. (2008), and the Ne3O3 calibration is from Jones et al. (2015). 5We adopt Ne3O2 relation for large EW samples in Nakajima et al. (2022).
7.95 < log(M/M ) < 11.85, which can be extrapolated to the low-mass regime.The MZR of Yates et al. (2020) is characterized by a lower normalization, which might be caused by the requirement of the [O iii]λ4363 detection in the mass range of 5.67 < log(M/M ) < 9.87.As shown in Fig.4 in Curti et al. (2020), the galaxies in SDSS-DR7 with auroral detections locate below the MZR at low stellar masses.The majority of these strong [O iii]λ4363 emission-line compact galaxies (the strong [O iii]λ5007 emission-line compact galaxies) in this work are below the direct-T e method calibrated Tremonti et al. (2004); Curti et al. (2020) mass-metallicity relation, and overlap the Yates et al. (2020) relation.This is reasonable because at fixed stellar mass, requiring the [O iii]λ4363 detection preferentially selects the metalpoor galaxies.

Figure 7 .
Figure 7.The set of strong-line calibrations from Maiolino et al. (2008); Jones et al. (2015); Curti et al. (2020) (black curve) and Nakajima et al. (2022) (sienna curve).The x-axis marks the metallicity obtained from the direct-Te method.The distribution of the strong [O iii]λ5007 emission-line compact galaxies is displayed with blue scatter points.The crimson stars mark the three galaxies from JWST at z ∼ 7.7 − 8.5 with the measurements fromCurti et al. (2023).

Figure 8 .
Figure 8.The mass metallicity relation of the strong [O iii]λ5007 emission-line compact galaxies.Different massmetallicity relations from Tremonti et al. (2004); Yates et al. (2020); Curti et al. (2020) are marked with curves with the corresponding colors as noted in the legend.The crimson stars mark the three galaxies from JWST at z ∼ 7.7 − 8.5 with the measurements fromCurti et al. (2023).

Figure 9 .
Figure 9.The N/O vs O/H relation of the strong [O iii]λ5007 emission-line compact galaxies.The colors of the scatter points mark the flux ratio of Hα to Hβ.The measurements of the stacked spectra in bins of stellar mass and SFR from Andrews & Martini (2013) at z ∼ 0 are marked with gray stars.The blue curve is the predictions from Andrews & Martini (2013).The green curve is the fitting result from the KLEVER survey at z ∼ 2 (Hayden-Pawson et al. 2022).

Figure 10 .
Figure 10.Ne3O2 vs O32 relation.The pea samples strong [O iii]λ5007 emission-line compact galaxies are demonstrated with sienna error bars.The samples at z ∼ 0 from Andrews & Martini (2013) are marked with gray stars.The stacked samples with the dust corrected from Jeong et al. (2020) are marked with dark cyan diamonds.The crimson stars mark the three galaxies from JWST.[O iii]λ4959 and [O iii]λ5007 emission lines for each of the selected single exposures in Figure 13.Amorín et al. (2012a,b); Bosch et al. (2019); Hogarth et al. (2020); Lin et al. (2023) have discussed the phenomenon of the double-peak or asymmetric profile in their spectra of the Green Pea galaxies.Amorín et al. (2012b) have identified multiple components with spatially-resolved offsets in their two-dimensional spectra.By analyzing the chemical abundances of each component,Hogarth et al. (2020) conclude that the outflows and turbulence are the driving force for the escape of ionizing photons and chemical enrichment.These studies show that the multiple gas component is not unique in Green Pea galaxies but also exists in z ∼ 1 − 2 extreme emission-line galaxies(Maseda et al. 2014;Masters et al. 2014;Terlevich et al. 2015) with high-velocity dispersions up to about 240 km s −1 , as well as detected in the integral field spectroscopy of other compact star-forming

Figure 11 .
Figure 11.The relation of the Ne3O2 vs stellar mass of the strong [O iii]λ5007 emission-line compact galaxies, where the colors of the scatter points mark the redshift of the source.The samples at z ∼ 0 from Andrews & Martini (2013) are marked with gray stars, the stacked measurement results with the dust corrected from Jeong et al. (2020) are marked with dark cyan diamonds, the stacked measurement results from the Jeong et al. (2020) are marked with dark orchid squares(Zeimann et al. 2015).The crimson stars mark the three galaxies from JWST.

Figure 12 .
Figure12.Asymmetric [O iii]λ5007 emission-line profiles of the first four sources.The black step plot is the re-calibrated LAMOST spectra with the continuum subtracted.The error region from the inverse variance is marked with the gray-shaded regions.The central wavelengths from the spectral fit and the velocity dispersions of the profiles are marked above the emission lines.The velocity separation of the [O iii]λ5007 emission line is marked on the right part of the plot.

Figure 13 .
Figure 13.Asymmetric [O iii]λ4959 and [O iii]λ5007 emission-line profiles for each single exposure of 811511143.The black step plot is the original 1D spectra with the sky emission subtracted.The error region from the inverse variance is marked with the gray-shaded regions.The central wavelengths from the spectral fit and the velocity dispersions of the profiles are marked above the emission lines.The velocity separations of the [O iii]λ4959 and [O iii]λ5007 emission lines are marked on the right part of the plot.

Table 2 .
Strong-line calibration claim similar trends of the Green Pea samples compared with the

Table 4 .
Single exposure measurement of the asymmetric [O iii]λ5007 emission-line profiles The velocity dispersions in this table have been corrected from instrumental and thermal broadening.2Weonly use selected single exposures to calculate the velocity dispersion of the asymmetric [O iii]λ5007 emission line, for the rest of the single exposures, the emission line is not detected.3Only one measurement is valid for the σ[λ5007](km s −1 ) measurement after subtracting the thermal broadening.