All Figures

$\begin{figure} \par\includegraphics[angle=-90,width=6cm,clip]{5216f01.eps} \end{figure}$ Figure 1: Oxygen abundance of the galaxies in sample A, derived by Izotov et al. (2006b), as a function of redshift.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=6cm,clip]{5216f02.eps} \end{figure}$ Figure 2: Emission-line flux ratios of [S II] $\lambda$ 6717/[S II] $\lambda$ 6731 for the compiled low-metallicity galaxies, as a function of the oxygen abundance derived by us (see Sect. 2.1.2). The upper horizontal dotted line denotes the theoretical low-density limit of this flux ratio and the lower dotted line denotes the high-density limit.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=6cm,clip]{5216f03.eps} \end{figure}$ Figure 3: Oxygen abundances of the compiled low-metallicity galaxies re-calculated by us (see Sect. 2.1.2) are plotted as a function of the oxygen abundances given in the original references. Dotted line is not the best-fit line but a reference line for the case when the two quantities are the same.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=6cm,clip]{5216f04.eps} \end{figure}$ Figure 4: Frequency distribution of the redshift of the SDSS DR4 galaxies after our sample selection (sample C) described in Sect. 2.2. Galaxies at z<0.028 are not included (see text).
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=6cm,clip]{5216f05.eps} \end{figure}$ Figure 5: Frequency distribution of the oxygen abundance of galaxies in sample C.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=6.5cm,clip]{5216f06.eps} \end{figure}$ Figure 6: Emission-line flux ratios of R₂₃ (=[F([O II] $\lambda$ 3727 $) + 1.327\times F$ ([O III] $\lambda$ 5007)]/F(H $\beta$ )), F([N II] $\lambda$ 6584)/ F(H $\alpha$ ), and F([O III] $\lambda$ 5007)/F([N II] $\lambda$ 6584) for galaxies in sample A (red triangles), in sample B (green circles) and in sample C (black dots), as a function of the oxygen abundance. The compiled low-metallicity galaxies with an error of the oxygen abundance larger than 0.05 dex are not plotted. Dotted lines denote the solar metallicity [ $12+\log($ O/H) = 8.69].
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=6cm,clip]{5216f07.eps} \end{figure}$ Figure 7: Same as Fig. 6 but for the emission-line flux ratios of F([N II] $\lambda$ 6584)/F([O II] $\lambda$ 3727), F([N II] $\lambda$ 6584)/F([S II] $\lambda$ 6720), and F([O III] $\lambda$ 5007)/F([O II] $\lambda$ 3727).
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=6.5cm,clip]{5216f08.eps} \end{figure}$ Figure 8: Same as Fig. 6 but means and the RMS values are shown in each bin of oxygen abundance, instead of individual data. Filled squares and filled stars denote the mean flux ratios for galaxies in sample C and those for galaxies in sample A+B, respectively. The errorbar denotes the RMS. The dashed line denotes the best-fit polynomial function, as described in the text. Dashed lines denote the solar metallicity [ $12+\log($ O/H) = 8.69].
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=6.5cm,clip]{5216f09.eps} \end{figure}$ Figure 9: Same as Fig. 8 but for the emission-line flux ratios of F([N II] $\lambda$ 6584)/F([O II] $\lambda$ 3727), F([N II] $\lambda$ 6584)/F([S II] $\lambda$ 6720), and F([O III] $\lambda$ 5007)/F([O II] $\lambda$ 3727).
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8cm,clip]{5216f10.eps} \end{figure}$ Figure 10: Comparison of our results with the previous empirical metallicity calibrations for the R₂₃ parameter. Solid red line denotes our calibration. Blue, green, and magenta lines denote the calibration given by Tremonti et al. (2004), Edmunds & Pagel (1984), and Zaritsky et al. (1994), respectively. Symbols and errorbars are the same as those in Fig. 8. Vertical dotted line denotes the solar metallicity [ $12+\log($ O/H) = 8.69].
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8cm,clip]{5216f11.eps} \end{figure}$ Figure 11: Comparison of our results with the previous empirical metallicity calibrations for F([N II] $\lambda$ 6584)/F(H $\alpha$ ). Solid red line denotes our calibration. Blue and magenta lines denote the calibration given by Pettini & Pagel (2004) and Denicoló et al. (2002), respectively. Symbols and errorbars are the same as those in Fig. 8. Vertical dotted line denotes the solar metallicity [ $12+\log($ O/H) = 8.69].
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8cm,clip]{5216f12.eps} \end{figure}$ Figure 12: Comparison of our results with the previous empirical metallicity calibrations for F([O III] $\lambda$ 5007)/F([N II] $\lambda$ 6584). Solid red line denotes our calibration, and blue line denotes the calibration given by Pettini & Pagel (2004). Symbols and errorbars are the same as those in Fig. 8. Vertical dotted line denotes the solar metallicity [ $12+\log($ O/H) = 8.69].
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=6.5cm,clip]{5216f13.eps} \end{figure}$ Figure 13: The averaged flux ratios and the best-fit polynomial functions of the metallicity dependence of R₂₃, F([N II] $\lambda$ 6584)/F(H $\alpha$ ) and F([O III] $\lambda$ 5007)/F([N II] $\lambda$ 6584) (dashed line) are compared with the predictions of photoionization models (solid lines: Kewley & Dopita 2002; Kobulnicky & Kewley 2004). The lines with a digit 1, 2, 3, 4, 5, 6, and 7 denote the model predictions with the ionization parameter of log U = -3.8, -3.5, -3.2, -2.9, -2.6, -2.3, and -2.0, respectively. Dotted line denotes the solar metallicity [ $12+\log($ O/H) = 8.69].
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=6.5cm,clip]{5216f14.eps} \end{figure}$ Figure 14: Same as Fig. 13 but for the emission-line flux ratios of F([N II] $\lambda$ 6584)/F([O II] $\lambda$ 3727), F([N II] $\lambda$ 6584)/F([S II] $\lambda$ 6720), and F([O III] $\lambda$ 5007)/F([O II] $\lambda$ 3727).
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=6.5cm,clip]{5216f15.eps} \end{figure}$ Figure 15: ( Upper) Emission-line flux ratios of F([Ne III] $\lambda$ 3869)/ F([O II] $\lambda$ 3727) of the galaxies in sample A (red triangles), those in sample B (green circles), and those in sample C (black dots), as a function of the oxygen abundance. As for sample C, only the objects with S/N([Ne III]) > 10 and S/N([O II]) > 10 (cataloged values) are plotted. ( Lower) Same as the upper panel but the mean and the RMS values are shown for each bin of the oxygen abundance, instead of the individual data. Filled stars and filled squares denote the mean flux ratios for galaxies in sample A+B and those for galaxies in sample C, respectively. The errorbar denotes the RMS for each metallicity bin. The dashed line denotes the best-fit polynomial (second-order) function.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=6.5cm,clip]{5216f16.eps} \end{figure}$ Figure 16: Same as Fig. 15 but for the emission-line flux ratio of F(H $\alpha$ +[N II] $\lambda \lambda$ 6548,6584)/F([S II] $\lambda$ 6720).
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=6.5cm,clip]{5216f17.eps} \end{figure}$ Figure 17: Same as Fig. 15 but for the emission-line flux ratio of F([O III] $\lambda$ 5007)/F(H $\beta$ ).
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=6.5cm,clip]{5216f18.eps} \end{figure}$ Figure 18: Same as Fig. 15 but for the emission-line flux ratio of F([O II] $\lambda$ 3727)/F(H $\beta$ ).
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{5216f19.eps} \end{figure}$ Figure 19: Schematic view of the availability of various metallicity diagnostics for each redshift. The black solid curves indicate the effect of redshift for some of the diagnostic lines discussed in this paper. The colored boxes indicate the wavelength coverages of optical spectrometers (blue), of ground-based near-IR spectrometers (magenta), and of NIRSpec/MIRI on board of JWST (red). The marks on the right of the diagram indicate the maximum redshift at which some of the metallicity diagnostics can be used with the various facilities.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=6cm,clip]{5216f01.eps} \end{figure}$	Figure 1: Oxygen abundance of the galaxies in sample A, derived by Izotov et al. (2006b), as a function of redshift.
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$\begin{figure} \par\includegraphics[angle=-90,width=6cm,clip]{5216f02.eps} \end{figure}$	Figure 2: Emission-line flux ratios of [S II] $\lambda$ 6717/[S II] $\lambda$ 6731 for the compiled low-metallicity galaxies, as a function of the oxygen abundance derived by us (see Sect. 2.1.2). The upper horizontal dotted line denotes the theoretical low-density limit of this flux ratio and the lower dotted line denotes the high-density limit.
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$\begin{figure} \par\includegraphics[angle=-90,width=6cm,clip]{5216f03.eps} \end{figure}$	Figure 3: Oxygen abundances of the compiled low-metallicity galaxies re-calculated by us (see Sect. 2.1.2) are plotted as a function of the oxygen abundances given in the original references. Dotted line is not the best-fit line but a reference line for the case when the two quantities are the same.
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$\begin{figure} \par\includegraphics[angle=-90,width=6cm,clip]{5216f04.eps} \end{figure}$	Figure 4: Frequency distribution of the redshift of the SDSS DR4 galaxies after our sample selection (sample C) described in Sect. 2.2. Galaxies at z<0.028 are not included (see text).
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$\begin{figure} \par\includegraphics[angle=-90,width=6cm,clip]{5216f05.eps} \end{figure}$	Figure 5: Frequency distribution of the oxygen abundance of galaxies in sample C.
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$\begin{figure} \par\includegraphics[angle=-90,width=6cm,clip]{5216f07.eps} \end{figure}$	Figure 7: Same as Fig. 6 but for the emission-line flux ratios of F([N II] $\lambda$ 6584)/F([O II] $\lambda$ 3727), F([N II] $\lambda$ 6584)/F([S II] $\lambda$ 6720), and F([O III] $\lambda$ 5007)/F([O II] $\lambda$ 3727).
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$\begin{figure} \par\includegraphics[angle=-90,width=6.5cm,clip]{5216f09.eps} \end{figure}$	Figure 9: Same as Fig. 8 but for the emission-line flux ratios of F([N II] $\lambda$ 6584)/F([O II] $\lambda$ 3727), F([N II] $\lambda$ 6584)/F([S II] $\lambda$ 6720), and F([O III] $\lambda$ 5007)/F([O II] $\lambda$ 3727).
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$\begin{figure} \par\includegraphics[angle=-90,width=8cm,clip]{5216f12.eps} \end{figure}$	Figure 12: Comparison of our results with the previous empirical metallicity calibrations for F([O III] $\lambda$ 5007)/F([N II] $\lambda$ 6584). Solid red line denotes our calibration, and blue line denotes the calibration given by Pettini & Pagel (2004). Symbols and errorbars are the same as those in Fig. 8. Vertical dotted line denotes the solar metallicity [ $12+\log($ O/H) = 8.69].
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$\begin{figure} \par\includegraphics[angle=-90,width=6.5cm,clip]{5216f14.eps} \end{figure}$	Figure 14: Same as Fig. 13 but for the emission-line flux ratios of F([N II] $\lambda$ 6584)/F([O II] $\lambda$ 3727), F([N II] $\lambda$ 6584)/F([S II] $\lambda$ 6720), and F([O III] $\lambda$ 5007)/F([O II] $\lambda$ 3727).
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$\begin{figure} \par\includegraphics[angle=-90,width=6.5cm,clip]{5216f16.eps} \end{figure}$	Figure 16: Same as Fig. 15 but for the emission-line flux ratio of F(H $\alpha$ +[N II] $\lambda \lambda$ 6548,6584)/F([S II] $\lambda$ 6720).
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$\begin{figure} \par\includegraphics[angle=-90,width=6.5cm,clip]{5216f17.eps} \end{figure}$	Figure 17: Same as Fig. 15 but for the emission-line flux ratio of F([O III] $\lambda$ 5007)/F(H $\beta$ ).
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$\begin{figure} \par\includegraphics[angle=-90,width=6.5cm,clip]{5216f18.eps} \end{figure}$	Figure 18: Same as Fig. 15 but for the emission-line flux ratio of F([O II] $\lambda$ 3727)/F(H $\beta$ ).
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