THE REDSHIFT EVOLUTION OF OXYGEN AND NITROGEN ABUNDANCES IN EMISSION-LINE SDSS GALAXIES

Trinh X. Thuan; Leonid S. Pilyugin; Igor A. Zinchenko

doi:10.1088/0004-637X/712/2/1029

1. INTRODUCTION

The study of various correlations between the global properties of galaxies is very important for the understanding of their formation and evolution. Among these correlations, the one between galaxy mass and metallicity is one of the most important. Lequeux et al. (1979) first showed that the oxygen abundance correlates well with total mass for a sample of dwarf irregular and blue compact galaxies, in the sense that the higher the total mass, the higher the heavy element content. Since the galaxy mass is a poorly known parameter, the luminosity–metallicity relation has often been considered instead of the mass–metallicity relation. Garnett & Shields (1987) found that abundances of spiral galaxies correlate well with their luminosities. The luminosity–metallicity relation for nearby galaxies has been considered subsequently by many authors (Garnett & Shields 1987; Skillman et al. 1989; Vila-Costas & Edmunds 1992; Richer & McCall 1995; Pilyugin 2001b; Zaritsky et al. 1994; Pilyugin et al. 2004; Guseva et al. 2009, among others).

In recent years, the number of available spectra of emission-line galaxies has increased dramatically due to the completion of several large spectral surveys. Measurements of emission lines in those spectra have been carried out for abundance determinations and investigation of the luminosity–metallicity relation. Thus, Melbourne & Salzer (2002) have considered the luminosity–metallicity relation for 519 galaxies in the KPNO International Spectroscopic Survey (KISS), Lamareille et al. (2004) for 6387 galaxies in the 2dF Galaxy Survey, Tremonti et al. (2004) for about 53,000 galaxies in the Sloan Digital Sky Survey (SDSS), and Asari et al. (2007) for 82,302 SDSS galaxies.

It has been found, however, that, when mass can be determined, the mass–metallicity correlation is considerably tighter than the luminosity–metallicity correlation, suggesting that mass may be a more meaningful physical parameter than luminosity. In the last decade, the evolution of the mass–metallicity relation with redshift has been examined by many investigators (Lilly et al. 2003; Savaglio et al. 2005; Erb et al. 2006; Cowie & Barger 2008; Maiolino et al. 2008; Lamareille et al. 2009; Lara-López et al. 2009). In those investigations, oxygen abundances have been derived using various methods. The general conclusion from those studies is that the oxygen abundance change of star-forming galaxies over the last half of the age of the universe appears to be somewhat moderate, with Δ(log (O/H)) ∼ 0.3 or lower. This change is comparable to or less than the scatter in the observed oxygen abundances (see Figure 10 of Lilly et al. 2003, Figure 13 of Savaglio et al. 2005, and Figure 6 of Lara-López et al. 2009).

Until now, no attention has been paid to the redshift evolution of nitrogen abundances in galaxies, despite the fact that they present several advantages for the study of the chemical evolution of galaxies. First, since at 12 + log (O/H) ≳ 8.3, secondary nitrogen becomes dominant and the nitrogen abundance increases at a faster rate than the oxygen abundance (Henry et al. 2000), then the change in nitrogen abundances with redshift should show a larger amplitude in comparison to oxygen abundances and, as a consequence, should be easier to detect. Furthermore, there is a time delay in the nitrogen production as compared to oxygen production (Maeder 1992; van den Hoek & Groenewegen 1997; Pagel 1997). This provides an additional constraint on the chemical evolution of galaxies. These reasons have led us to consider here not only the redshift evolution of oxygen abundances but also that of nitrogen abundances. To carry out such an investigation, it is necessary to derive accurate oxygen and nitrogen abundances.

The emission line properties of photoionized H ii regions are governed by its heavy element content and by the electron temperature distribution within the photoionized nebula. In turn, the latter is controlled by the ionizing star cluster spectral energy distribution and by the chemical composition of the H ii region. The evolution of a giant extragalactic H ii region associated with a star cluster is thus caused by a gradual change in time of the integrated stellar energy distribution due to stellar evolution. This has been the subject of numerous investigations (Stasińska 1978, 1980; McCall et al. 1985; Dopita & Evans 1986; Moy et al. 2001; Stasińska & Izotov 2003; Dopita et al. 2006, among others). The general conclusion from those studies is that H ii regions ionized by star clusters form a well-defined fundamental sequence in different emission-line diagnostic diagrams. The existence of such a fundamental sequence forms the basis of various investigations of extragalactic H ii regions.

First, Baldwin et al. (1981) have suggested that the position of an object in some well-chosen emission-line diagrams can be used to separate H ii regions ionized by star clusters from other types of emission-line objects. This idea has found general acceptance and use. Thus, the [O iii]λ5007/Hβ versus [N ii]λ6584/Hα diagram has been used widely to distinguish between star-forming galaxies and active galactic nuclei (AGNs). In particular, the SDSS emission-line galaxies occupy a well-defined region shaped like the wings of a seagull (Stasińska et al. 2008). The left wing consists of star-forming galaxies while the right wing is attributed to AGNs. However, the exact location of the dividing line between H ii regions and AGNs is still controversial (Kewley et al. 2001; Kauffmann et al. 2003; Stasińska et al. 2006).

Second, Pagel et al. (1979) and Alloin et al. (1979) have suggested that the positions of H ii regions in some emission-line diagrams can be calibrated in terms of their oxygen abundances. This approach to abundance determination in H ii regions, usually referred to as the "strong line method" has been widely adopted, especially in cases where the temperature sensitive [O iii] λ4363 line is not detected. Numerous relations have been suggested to convert metallicity-sensitive emission-line ratios into metallicity or temperature estimates (Dopita & Evans 1986; Zaritsky et al. 1994; Pilyugin 2000, 2001a; Pilyugin & Thuan 2005; Pettini & Pagel 2004; Tremonti et al. 2004; Liang et al. 2006; Stasińska 2006, among many others)

It should be noted that the classic T_e method, which relies on the electron temperature T_e determined from the [O iii] λ4363 line, is also based on the existence of the fundamental sequence of H ii regions. Indeed, when only one electron temperature, t₃ or t₂, is measured (t₃ and t₂ being the electron temperatures in the [O iii] and [O ii] zones, respectively) it is standard practice to use a t₂–t₃ relation to estimate the other temperature. This relation is usually established on the basis of H ii regions models which belong to the same fundamental sequence.

Our study will be based on the SDSS database of a million spectra. To study the redshift evolution of oxygen and nitrogen abundances, accurate oxygen and nitrogen abundance determinations are mandatory. The determination of accurate abundances in H ii regions from SDSS spectra poses two problems. First, line fluxes in SDSS spectra are measured by an automatic procedure. This inevitably introduces large flux errors for some objects. We need to devise a way to recognize those objects and exclude them from consideration. Second, the SDSS galaxy spectra span a large range of redshifts. There is thus an aperture-redshift effect in SDSS spectra. Indeed, they are obtained with 3 arcsec diameter fibers. At a redshift of z = 0.05 the projected aperture diameter is ∼3 kpc, while it is ∼15 kpc at a redshift of z = 0.25. This means that, at large redshifts, SDSS spectra are closer to global spectra of whole galaxies, i.e., to that of composite nebulae including multiple star clusters, rather than to spectra of individual H ii regions. One should then expect that some SDSS objects will not follow the fundamental H ii region sequence. These need also to be identified and excluded from our sample.

We propose here a method to recognize objects that suffer from one or both of these problems. It is based on the idea that if (1) an object belongs to the fundamental H ii region sequence, and (2) its line fluxes are measured accurately, then the different relations between the line fluxes and the physical characteristic of H ii regions, based on different emission lines, should yield similar physical characteristics (such as electron temperatures and abundances) of that object.

The relations used for the determination of oxygen and nitrogen abundances and for the selection of star-forming galaxies with accurate line flux measurements are derived in Section 2. The selected subsamples of SDSS galaxies are described in Section 3. The relations between redshift, galaxy mass, and metallicity are discussed in Section 4. Section 5 presents the conclusions.

Throughout the paper, we will be using the following notations for the line fluxes:

$\begin{eqnarray} &&R_2 = [{\rm O}\,{\mathsc ii}]\lambda 3727+\lambda 3729 = I_{[{\rm O}\,\mathsc {ii}] \lambda 3727+ \lambda 3729} /I_{{\rm H}\beta },\nonumber\\ &&N_2 = [{\rm N}\,{\mathsc ii}]\lambda 6548+\lambda 6584 = I_{[{\rm N}\,\mathsc {ii}] \lambda 6548+ \lambda 6584} /I_{{\rm H}\beta },\nonumber\\ &&R_3 = [{\rm O}\,{\mathsc iii}]\lambda 4959+ \lambda 5007 = I_{{\rm [{\rm O}\,\mathsc {iii}]} \lambda 4959+ \lambda 5007} /I_{{\rm H}\beta }.\nonumber \end{eqnarray}$

The electron temperatures will be given in units of 10⁴ K, and the stellar masses of galaxies in solar units.

2. METALLICITY AND TEMPERATURE CALIBRATIONS

We noted above that many relations have been proposed to convert various metallicity-sensitive emission-line combinations into metallicity or temperature estimates. The oxygen abundances derived with these different calibrations are not in good agreement, with differences amounting up to 0.7 dex (Kewley & Ellison 2008). In fact, there appears to exist as many different oxygen abundance scales as there are calibrations. Which metallicity scale is the correct one? There is strong evidence in favor of the metallicity scale defined by the classic T_e method, considered the most reliable one (see the discussion in Pilyugin 2003; Bresolin et al. 2009a). Indeed, the oxygen abundances derived with the T_e method have been confirmed by high-precision model-independent determinations of the interstellar oxygen abundance in the solar vicinity, using high-resolution observations of the weak interstellar O iλ1356 absorption line toward stars, and by recent determinations of stellar abundances. To put our derived abundances on the T_e scale, we will use H ii regions with T_e-based abundances as the basis of our calibrations.

To establish the relations between different line fluxes and the physical characteristic of H ii regions, we will be using the data for high-metallicity H ii regions in nearby galaxies compiled by Pilyugin et al. (2009). We have added to this compilation the recent spectrophotometric measurements of Saviane et al. (2008), Bresolin et al. (2009b), Bresolin et al. (2009a), and Esteban et al. (2009). The oxygen and nitrogen abundances in those H ii regions were rederived in a uniform way within the framework of the standard H ii region model with a two-zone temperature distribution within the nebula. The equations for the electron temperatures and oxygen ionic abundances were taken from Izotov et al. (2006). The relation between the electron temperature t₂ within the O⁺ zone and t₃, that within the O⁺⁺ zone, is

$\begin{equation} t_2 = 0.672 t_3 + 0.314. \end{equation} \tag{ 1 }$

This relation derived in Pilyugin et al. (2009) is very close to the commonly used one (Campbell et al. 1986; Garnett 1992).

The abundance of the nitrogen ion N⁺ is derived from the equation

$\begin{equation} \log \frac{N^+}{O^+} = \log \frac{N_2}{R_2} + 0.273 - \frac{0.726}{t_2} - 0.02 \log t_2 + 0.007 t_2. \end{equation} \tag{ 2 }$

The total nitrogen abundance is determined from

$\begin{equation} \log \frac{N}{H} = \log \frac{O}{H} + \log \frac{N}{O} \end{equation} \tag{ 3 }$

with the assumption

$\begin{equation} \frac{N^+}{O^+} = \frac{N}{O}. \end{equation} \tag{ 4 }$

It is common practice, in constructing the calibration, to establish relations between the oxygen abundances and the strong-line fluxes. As a result, oxygen abundances are the best studied. In particular, the redshift evolution of oxygen abundances has been the subject of several recent investigations, as noted above. Here, we will adopt a different method. We will calibrate the positions of H ii regions in three different diagnostic diagrams in terms of nitrogen abundances, to which less attention has been paid. The oxygen abundance will then be estimated from the obtained nitrogen abundance and the N/O ratio using Equations (2) and (3). The independent determination of nitrogen abundances and of their redshift evolution will provide an independent check of the conclusions derived from the study of the redshift evolution of oxygen abundances.

Figure 1 shows the nitrogen abundance as a function of log (N₂) (upper panel), log (N₂/R₂) (middle panel), and log (N₂/R₃) (lower panel). The filled circles are H ii regions with measured electron temperatures t_3,O (the auroral line [O iii]λ4363 is available). The open circles are H ii regions with measured electron temperatures t_2,N (the auroral line [N ii]λ5755 is available). Those data have been fitted by the cubic expression

$\begin{equation} 12+{\rm log} (N{/}H) = a_0 + a_1X + a_2X^2 +a_3X^3, \end{equation} \tag{ 5 }$

where X is successively X = log(N₂), X = log (N₂/R₂), and X = log (N₂/R₃). The derived curves are shown in Figure 1 by solid lines. The constant coefficients in Equation (5) for all three cases are given in Table 1.

Table 1. Values of Coefficients in Equation (5) for 12 + log (N/H), and in Equation (6) for t₂

Y Value	X Value	a₀	a₁	a₂	a₃
12 + log(N/H)	log(N₂)	7.649	1.454	0.257	−0.148
12 + log(N/H)	log(N₂/R₂)	7.918	0.877	−0.058	0.038
12 + log(N/H)	log(N₂/R₃)	7.526	0.521	0.062	0.014
t₂	log(N₂)	0.778	−0.354	0.001	0.044
t₂	log(N₂/R₂)	0.702	−0.248	0.042	0.019
t₂	log(N₂/R₃)	0.802	−0.172	0.003	0.011

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Figure 2 shows the electron temperature t₂ as a function of log (N₂) (upper panel), log (N₂/R₂) (middle panel), and log (N₂/R₃) (lower panel) for the same sample of H ii regions. Those data have also been fitted by the cubic expression

$\begin{equation} t_2 = a_0 + a_1X + a_2X^2 +a_3X^3, \end{equation} \tag{ 6 }$

where X is successively X = log (N₂), X = log (N₂/R₂), and X = log (N₂/R₃). The derived curves are shown in Figure 2 by solid lines. The constant coefficients in Equation (6) for all three cases are also given in Table 1.

The relations between nitrogen abundances and the abundance-sensitive indexes N₂, N₂/R₂, and N₂/R₃ will be used for the determination of nitrogen abundances in the SDSS galaxies. They will also serve to select star-forming galaxies with accurate line fluxes measurements. As for the relations between the electron temperature t₂ and the N₂, N₂/R₂, and N₂/R₃ indexes, they will be used for estimating the N/O ratios and deriving the O/H oxygen abundances from the N/H nitrogen abundances.

3. SAMPLE SELECTION

Line flux measurements in SDSS spectra have been carried out by several groups. We use here the data in several catalogs made available publicly by the Max-Planck-Institute for Astrophysics/Johns Hopkins University (MPA/JHU) group.³ These catalogs give line flux measurements, redshifts, and various other derived physical properties such as stellar masses for a large sample of SDSS galaxies. The techniques used to construct the catalogs are described in Brinchmann et al. (2004) and Tremonti et al. (2004) and other publications of those authors. We have chosen to use these catalogs instead of the original SDSS spectral database because they contain generally more accurate line flux measurements (see a discussion of the errors in the line flux measurements by Brinchmann et al. 2004).

In a first step, we extract from the MPA/JHU catalogs all emission-line objects with measured fluxes in the Hβ, Hα, [O ii]λλ3727,3729, [O iii]λ4959, [O iii]λ5007, [N ii]λ6548, [N ii]λ6584, [S ii]λ6717, and [S ii]λ6731 emission lines. The hydrogen, oxygen, and nitrogen lines will serve to estimate oxygen and nitrogen abundances relative to hydrogen, and the ratio of the sulfur line intensities is an indicator of electron density. Since our calibrations are only valid in the low-density limit, we have included only those objects with a reasonable value of the [S ii] ratio, i.e., those with 1.25 < F_{[S ii]λ6717}/F_{[S ii]λ6731} < 1.5. This results in a sample containing 118,544 objects which will be referred to hereafter as the total sample. The wavelength range of the SDSS spectra is 3800–9300 Å so that for nearby galaxies with redshift z ≲ 0.02, the [O ii]λ3727+λ3729 emission line is out of that range. The absence of this line prevents the determination of the oxygen abundance, so all SDSS galaxies with z ≲ 0.02 were also excluded. Thus, all galaxies in our total sample have redshifts greater than ∼0.023, i.e., they are more distant than ∼100 Mpc. The redshift z and stellar mass M_S of each galaxy were also taken from the MPA/JHU catalogs.

The emission-line fluxes are then corrected for interstellar reddening using the theoretical Hα to Hβ ratio and the analytical approximation to the Whitford interstellar reddening law from Izotov et al. (1994). In several cases, the derived value of the extinction c(Hβ) is negative and has been set to zero.

For each galaxy, we have estimated three values of the nitrogen abundance and three values of the electron temperature t₂, using the calibrations discussed above and the dereddened N₂, R₂, and R₃ line intensities. Since measurements of the [N ii]λ6584 line are more reliable than those of the [N ii]λ6548 line, we have used N₂ = 1.33[N ii]λ6584 instead of the standard N₂ = [N ii]λ6548 + [N ii]λ6584. Then the mean value of N/H of the nitrogen abundance for each galaxy is determined as

$\begin{equation} {\selectfont\fontsize{8.5}{9} \log (\mbox{N}/\mbox{H})_{\rm mean} = \frac{\log (\mbox{N}/\mbox{H})_{N_2} + \log (\mbox{N}/\mbox{H})_{N_2/R_2}+ \log (\mbox{N}/\mbox{H})_{N_2/R_3}}{3}.} \end{equation} \tag{ 7 }$

The mean value of the electron temperature t₂ is determined in a similar way. Using N/H and the mean t₂, the N/O ratio and the oxygen abundance O/H are then derived using Equations (2) and (3).

We have suggested above that if (1) the object belongs to the fundamental sequence of H ii regions, and (2) its line fluxes are measured accurately, then the calibrations based on different lines should result in similar abundances. We have calculated for each galaxy the deviations of individual values of the nitrogen abundance from the mean value $\Delta{\rm log} ({\rm N}/{\rm H})_{N_2, N_2/R_2, N_2/R_3}= \log\,({\rm N}/{\rm H})_{N_2, N_2/R_2, N_2/R_3}\hbox{--}\log\,({\rm N}/{\rm H})_{\rm mean}$ . The mean deviation Δlog (N/H)_mean and the maximum deviation Δlog (N/H)_max were also computed for each object. We have then used the value of Δlog (N/H)_max as a selection criterion to extract from the total sample three subsamples of star-forming galaxies with accurate line flux measurements, going from the most stringent requirement to the least stringent one:

1.
Subsample A contains only objects with Δlog (N/H)_max ⩽ 0.05, a total of 15,548 galaxies.
2.
Subsample B contains only objects with Δlog (N/H)_max ⩽ 0.10, a total of 55,189 galaxies.
3.
Subsample C contains only objects with Δlog (N/H)_max ⩽ 0.15, a total of 84,364 galaxies.

Does selecting objects in such a way give us only (1) star-forming galaxies and (2) with accurate line flux measurements? We can test the reliability of our selection criterion concerning the first point by appealing to the [O iii]λ5007/Hβ versus [N ii]λ6584/Hα diagram which is often used to distinguish between star-forming galaxies and AGNs. Figure 3 shows such diagrams for subsamples A, B, C and for the total sample. The solid line, taken from Kauffmann et al. (2003), shows the dividing line between H ii regions ionized by star clusters and AGNs. Figure 3 clearly shows that while the total sample contains both star-forming galaxies and AGNs (lower right panel), our criterion does select out subsamples containing only star-forming galaxies.

**Figure 3.** [O iii]λ5007)/H_β vs. [N ii]λ6584)/H_α diagram for subsamples A, B, and C and the total sample. The solid line shows the dividing line between H ii regions ionized by star clusters and AGNs (Kauffmann et al. 2003).
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Concerning the second point, Figure 4 shows the classical R₃–R₂ diagram for subsamples A, B, and C and the total sample. Each galaxy is plotted as a gray (light blue in the electronic version) open circle. For comparison, H ii regions in nearby galaxies with accurate line flux measurements, from the compilation of Pilyugin et al. (2004), are shown as black filled circles. Inspection of Figure 4 shows that the selected subsamples of galaxies occupy the same area in the R₃–R₂ diagram as the H ii regions in nearby galaxies with accurate measurements, while the total sample covers a considerably larger area. Evidently, our selection criterion picks out objects which have line intensities that are in agreement with the well-measured line intensities of H ii regions in nearby galaxies.

We next investigate the O/H–N/O diagram (Figure 5). As before, the SDSS galaxies from subsamples A, B, and C are shown as gray (light-blue in the electronic version) open circles, and the H ii regions in nearby galaxies with recent precise measurements of electron temperatures (Bresolin 2007; Bresolin et al. 2009b) are shown as black filled circles. We see that the selected SDSS galaxies and the H ii regions in nearby galaxies with precise measurements lie in the same general region in the O/H–N/O diagram. However, the selected SDSS galaxies are shifted systematically toward lower N/O ratios. This slight systematic shift (of ∼ 0.2–0.3 dex in log N/O) can be understood in the following way. The selection criteria pick out galaxies with strong ongoing star formation, resulting in a higher star formation rate in the selected SDSS galaxies as compared to normal galaxies with the same mass. It has long been known that such a star formation burst would cause a temporary decrease of the N/O ratio in the galaxy (e.g., Pilyugin 1992, 1993).

We now compare the properties of the galaxies in subsamples A, B, and C. The histograms of galaxy stellar masses, redshifts, and oxygen and nitrogen abundances for the three subsamples are shown in Figure 6. The locations of the galaxies in the three subsamples in the redshift–galaxy stellar mass diagram are presented in Figure 7. Examination of the distributions of the parameters in the three subsamples reveals that while they are somewhat similar for subsamples B and C, the distribution for subsample A differs significantly. In particular, there is a shift toward higher masses (by about 0.2 dex) of the galaxy mass distribution in subsample A relative to the other two subsamples. There is also a shift toward higher nitrogen abundances (by about 0.1 dex) of galaxies in subsample A relative to subsamples B and C (see Figure 6). These shifts seem to be caused by a too restrictive selection criterion. The selection condition for subsample A, Δlog (N/H)_max ⩽ 0.05, appears to be too constraining, eliminating too many galaxies and, as a consequence, causing a selection effect. In order not to bias our results, we will consider, in the remainder of the paper, subsample B as the basic subsample, while subsample C will be used as a control subsample.

**Figure 6.** Normalized histograms of observed and derived properties for SDSS galaxies in subsamples A (short-dashed line), B (solid line), and C (long-dashed line).
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**Figure 7.** Redshift–galaxy stellar mass diagram for subsamples A, B, and C.
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4. THE REDSHIFT EVOLUTION OF OXYGEN AND NITROGEN ABUNDANCES

We investigate here the changes in oxygen and nitrogen abundances with galaxy stellar mass and redshift. Examination of Figures 6 and 7 shows that such a study is justified only in the range of stellar galaxy masses from ∼10^9.5 M_☉ to ∼10^11.5 M_☉, where the number of galaxies is large enough to give good statistics.

4.1. The z–M_S–O/H Relation

We first discuss the evolution of oxygen abundances with galaxy stellar masses. The upper panel of Figure 8 shows the oxygen abundances of galaxies in subsample B, with redshifts in the range 0.04 < z < 0.06, as a function of galaxy stellar mass. The lower panel of Figure 8 shows the same diagram, but for galaxies in a higher redshift range, 0.23 < z < 0.27. We note that our M_S–O/H diagram is very similar to that of Erb et al. (2006) (see their Figure 3). This may not be surprising since those authors also used a N₂ calibration to estimate the oxygen abundances of their SDSS galaxies. Figure 8 shows that the oxygen abundance increases with increasing galaxy stellar mass up to a value M*_S. For galaxies with M_S > M*_S, the oxygen abundance becomes constant. Comparison of the upper and lower panels of Figure 8 reveals that the value of M*_S depends on redshift, shifting to higher values at higher redshifts.

To be more quantitative, we approximate the change in oxygen abundance with redshift and galaxy stellar mass by the following "redshift–galaxy stellar mass–oxygen abundance" z–M_S–O/H relation:

${\selectfont\fontsize{9}{9.5}{\begin{eqnarray} \begin{array}{llll} 12+\log ({\rm O/H})\hspace{-7pt} & {=}\hspace{-7pt} & a_1 + a_2\,z + (a_3 + a_4\,z) \log (\frac{M_S}{M_S^*}), & M_S \le M_S^* \\ 12+\log ({\rm O/H})\hspace{-7pt} & {=}\hspace{-7pt} & a_1 + a_2\,z, & M_S \ge M_S^* \\ \log (M_S^*/M_{\odot })\hspace{-7pt} & {=}\hspace{-7pt} & a_5 + a_6\ z. & \end{array} \end{eqnarray}}} \tag{ 8 }$

Fitting the data for galaxies in subsample B gives the following:

${\selectfont\fontsize{8}{9}{\begin{eqnarray} \begin{array}{llll} 12+\log (O/H) \hspace{-7pt} & {=}\hspace{-7pt} & 8.67 - 0.027\,z + (0.41 - 0.76\,z) \log (\frac{M_S}{M_S^*}), & M_S \le M_S^* \nonumber\\ 12+\log (O/H) \hspace{-7pt} & {=}\hspace{-7pt} & 8.67 - 0.027\,z, & M_S \ge M_S^* \nonumber\\ \end{array} \end{eqnarray}}}$

${\selectfont\fontsize{8}{9}{\begin{eqnarray} &&\hspace{-130pt}\log (M_S^*/M_{\odot }) = 9.60 + 5.65\,z. \end{eqnarray}}} \tag{ 9 }$

The derived z–M_S–O/H relation for subsample B is shown in Figure 8 by the solid line for z = 0.05, and by the dashed line for z = 0.25.

To test the robustness of the derived z–M_S–O/H relation, we have also analyzed subsample C in a similar way. The data for galaxies in subsample C are shown in Figure 9. Fitting the subsample C data gives the following:

${\selectfont\fontsize{8}{9}{\begin{eqnarray} \begin{array}{llll} 12+\log (O/H) \hspace{-6pt} & {=}\hspace{-6pt} & 8.67 - 0.020\,z + (0.39 - 0.63\,z) \log (\frac{M_S}{M_S^*}), & M_S \le M_S^* \nonumber\\ 12+\log (O/H)\hspace{-6pt} & {=}\hspace{-6pt} & 8.67 - 0.020\,z, & M_S \ge M_S^* \nonumber\\ \end{array} \end{eqnarray}}}$

${\selectfont\fontsize{8}{9}{\begin{eqnarray} &&\hspace{-136pt} \log (M_S^*/M_{\odot }) = 9.54 + 5.90\,z. \end{eqnarray}}} \tag{ 10 }$

The z–M_S–O/H relation for subsample C is shown in Figure 9 by the solid line for z = 0.05, and by the dashed line for z = 0.25. Comparison between Figures 8 and 9 shows that the obtained z–M_S–O/H relations for subsamples B and C are very similar, so that our results appear to be robust. The derived relations should approximate well the redshift evolution of oxygen abundances for z ⩽ 0.25, corresponding to lookback times of up to ∼3 Gyr. Beyond z = 0.25, the number of galaxies in each subsample becomes very small (see Figure 7) and the redshift evolution of abundances cannot be studied with enough statistics. To discuss abundance evolution, we will therefore restrict ourselves to objects with z ⩽ 0.25. At the low-redshift end, to reduce errors from aperture effects and following the recommendations of Kewley et al. (2005), we will limit ourselves to objects with redshifts z > 0.04. Objects with 0.04 < z < 0.06 will be considered as a representative of the present-day epoch.

Figure 10 shows the distribution of the deviations of the oxygen abundances from the derived z–M_S–O/H relation for both subsamples B and C. It is seen that the scatter of oxygen abundances about the z–M_S–O/H relation is slightly larger for galaxies in subsample C than in subsample B. This effect can also be seen by comparing Figures 8 and 9. Nevertheless, it can be said that, for both subsamples of galaxies, the oxygen abundances follow reasonably well the derived z–M_S–O/H relation. The mean deviation is small, being ∼0.06 dex. We thus conclude that the derived relations can be used, in principle, to obtain a rough estimate of the metallicities of SDSS galaxies.

4.2. The Metallicity Plateau and the Oxygen Enrichment as a Function of Galaxy Stellar Mass

One of the most remarkable features of the M_S–O/H relation at the current epoch is the metallicity plateau at high galaxy stellar masses. For the sake of definiteness, we will discuss the results for subsample B. The oxygen abundance increases with galaxy stellar mass until M_S = 10^9.9 M_☉, but then remains approximately constant, equal to 12 + log(O/H) = 8.67, in galaxies with M_S ≳ 10^9.9 M_☉ (see the upper panel of Figure 8). What is the physical meaning of such a plateau? The observed oxygen abundance in a galaxy is defined by its astration level or gas mass fraction μ, and by the mass exchange between a galaxy and its environment (Searle & Sargent 1972; Pagel 1997). It is believed that galactic winds do not play a significant role in the chemical evolution of large spiral galaxies (Garnett 2002; Tremonti et al. 2004; Dalcanton 2007) and that the rate of gas infall onto the disk decreases exponentially with time (Matteucci & François 1989; Pilyugin & Edmunds 1996a, 1996b; Calura et al. 2009). The present-day location of a system in the μ–O/H diagram is then governed by its evolution in the recent past, and is only weakly dependent of its evolution on long time-scales (Pilyugin & Ferrini 1998). Therefore, the observed oxygen abundance in a large spiral galaxy is mainly defined by its gas mass fraction μ. The presence of a metallicity plateau in the M_S–O/H diagram at all redshifts implies then that the high-mass SDSS galaxies have very similar gas mass fractions.

The luminosity–central metallicity relation for nearby spiral galaxies also shows a plateau at high luminosities (Pilyugin et al. 2007). This plateau was interpreted as evidence that the gas in the centers of the most metal-rich galaxies has been almost completely converted into stars and that the oxygen abundance in the centers of the most luminous metal-rich galaxies has reached its maximum attainable value of 12 + log(O/H) ∼ 8.87. The plateau for oxygen abundances in the SDSS galaxies is at the level of 12 + log(O/H) = 8.67, i.e., 0.2 dex smaller. The simple model of chemical evolution of galaxies predicts that a decrease of μ by 0.1 results in an increase of oxygen abundance by ∼0.13 dex, in the range of μ from ∼0.50 to ∼0.05 (Pilyugin et al. 2007). Then, the difference between the maximum attainable value of the oxygen abundance and the mean oxygen abundance in high-mass SDSS galaxies, Δ(log (O/H)) ∼ 0.2, corresponds to a difference in gas mass fraction Δμ ∼ 0.15. Since the maximum attainable oxygen value corresponds to complete astration, i.e., μ = 0, the mean μ in high-mass SDSS galaxies at the present epoch should be ∼15%, with a probable range of μ from ∼5% to ∼25%.

Why do our SDSS subsamples not contain galaxies with abundances as high as the maximum attainable value? The reason has to do with the gas content of the SDSS galaxies in our subsamples. As said before, the maximum attainable value of the oxygen abundance corresponds to the limiting case where the gas has been completely converted into stars. The galaxies in our SDSS subsamples are all characterized by strong emission lines in their spectra, meaning that they are undergoing strong starbursts. This requires in turn that they contain an appreciable amount of gas. In other words, because our galaxies are gas-rich, they have not reached the maximum attainable value of the oxygen abundance which requires complete gas exhaustion. If galaxies were not gas-rich, they would have weak emission lines, unlikely to be measured accurately. There exists thus a lower limit on the gas mass fraction for a galaxy to have accurately measured lines and to be included in our subsamples. In that sense, the observed plateau is likely affected by the selection criteria. We note however that, even in the most evolved nearby spiral galaxies, the H ii region oxygen abundances are generally lower than the maximum attainable value. There is furthermore an aperture effect that slightly lowers the metallicities observed for SDSS galaxies. The maximum attainable value oxygen abundance observed in the central part of some nearby galaxies is usually derived by linearly fitting the variations of H ii region abundances with galactocentric distance, and extrapolating to R = 0. In the distant SDSS galaxies, because one fiber includes many H ii regions that show decreasing metallicities toward larger galactocentric distances, the oxygen abundances are slightly diluted when averaged over a large region.

In the lower panel of Figure 8, we compare the M_S–O/H relation for local (z ≈ 0.05) galaxies (solid line) with that for distant (z ≈ 0.25) ones (dashed line). Three features are to be noted. First, it can be seen that, for the galaxies of highest stellar masses, those with masses ≳10¹¹ M_☉, the plateau value of the oxygen abundance does not change in the redshift interval from 0.05 to 0.25. This implies that the galaxies of highest mass in our SDSS subsamples have reached their highest astration level some 3 Gyr ago, and have been somewhat "lazy" in their evolution afterward. Second, for lower mass galaxies with stellar masses ≲10¹¹ M_☉, it is seen that the value of the oxygen enrichment during the last 3 Gyr increases with decreasing galaxy mass, in the mass interval from 10¹¹ M_☉ to 10^9.9 M_☉, as shown by the widening gap between the solid and dashed curves toward lower masses. At M_S = 10^9.9 M_☉, there is a difference Δlog (O/H) ∼ 0.25 between a local galaxy and one at redshift 0.25. For galaxies with M_S ⩽ 10^9.9 M_☉, the oxygen enrichment during the last 3 Gyr slightly decreases with decreasing galaxy mass, the slope of the solid line being slightly steeper than that of the dashed line. Third, the value of M*_S, the mass where the oxygen abundance becomes constant with galaxy stellar mass, is redshift dependent, becoming higher at larger redshifts.

In summary, analysis of the z–M_S–O/H relation has led to the following main conclusions.

1.
The galaxies of highest masses, those with M_S ≳ 10¹¹ M_☉, have reached their highest astration level in the past and have not had an appreciable oxygen abundance enrichment during the last ∼3 Gyr.
2.
The mean value of the oxygen enrichment during the last 3 Gyr in galaxies with stellar masses in the range from 10¹⁰ M_☉ to 10¹¹ M_☉ is Δ(log (O/H)) ∼ 0.11, with Δ(log (O/H)) ∼ 0.23 at 10¹⁰ M_☉ and Δ(log (O/H)) = 0 at 10¹¹ M_☉.

The above picture will now be put to the test through the study of the redshift evolution of nitrogen abundances, which we consider next.

4.3. The z–M_S–N/H Relation

We proceed in the same way as in our analysis of the oxygen abundances. The upper panel of Figure 11 shows the nitrogen abundances of the local galaxies in subsample B, with redshifts 0.04 < z < 0.06, as a function of galaxy stellar mass. The lower panel of Figure 11 shows the same diagram, but for more distant galaxies, with redshifts 0.23 < z < 0.27. Figure 11 shows that the general behavior of nitrogen abundances with redshift and galaxy stellar mass is similar to that of oxygen abundances. The nitrogen abundance increases with increasing galaxy stellar mass up to a value M*_S of the stellar mass. Then, for galaxies with M_S > M*_S, the nitrogen abundance remains approximatively constant, reaching a plateau. The value of M*_S is redshift dependent, becoming higher at larger redshifts.

The change of nitrogen abundance with redshift and galaxy stellar mass can be approximated by a z–M_S–N/H relation, similar to the one for oxygen abundances. Fitting the data for galaxies in subsample B results in the following relation:

$\begin{eqnarray} 12+\log (N/H) & = & 7.89 - 0.110\,z + (0.99 - 1.40\,z)\nonumber\\ &&\times \log \left(\frac{M_S}{M_S^*}\right), \quad M_S \le M_S^* \nonumber\\ 12+\log (N/H) & = & 7.89 - 0.110\,z, \quad M_S \ge M_S^* \nonumber\\ \log (M_S^*/M_{\odot }) & = & 9.97 + 4.92\,z . \end{eqnarray} \tag{ 11 }$

The derived relation is shown in Figure 11 by a solid line for z = 0.05 and by a dashed line for z = 0.25.

Again, to test the robustness of the obtained z–M_S–N/H relation, we have examined subsample C in a similar way. The data for galaxies in subsample C are plotted in Figure 12. Fitting those data gives

$\begin{eqnarray} 12+\log (N/H) & = & 7.88 - 0.027\,z + (0.85 - 1.14\,z) \nonumber\\ && \times \log (\frac{M_S}{M_S^*}), \quad M_S < M_S^* \nonumber\\ 12+\log (N/H) & = & 7.88 - 0.027\,z, \quad M_S > M_S^* \nonumber\\ \log (M_S^*/M_{\odot }) & = & 10.04 + 5.03\,z. \end{eqnarray} \tag{ 12 }$

The derived z–M_S–N/H relation is shown in Figure 12 by a solid line for z = 0.05, and by a dashed line for z = 0.25. Comparison of Figures 11 and 12 shows that they are very similar and that the derived z–M_S–N/H relation is robust.

While the general behavior of nitrogen abundances with redshift and galaxy stellar mass is quite similar to that of oxygen abundances (compare Figures 8 and 11), there are significant differences, due to the different production mechanisms of these two elements. The dependence of the nitrogen abundance on galaxy stellar mass for M_S < M*_S is considerably steeper than that for oxygen abundances. This is caused by the fact that at oxygen abundances higher than about 12 + log(O/H) = 8.3, the metallicity-dependent nitrogen production by intermediate-mass stars starts to dominate. Another remarkable difference concerns M*_S, the mass which marks the transition from the linear regime to the plateau regime: at all redshifts, M*_S is shifted toward higher values in the M_S–N/H diagram as compared to in the M_S–O/H diagram. Thus, log M*_S is equal to 10.2 and 11.2 at z = 0.05 and z = 0.25, respectively, in the M_S–N/H diagram, as compared to 9.9 and 11.0 in the M_S–O/H diagram.

We now attempt to understand this M*_S shift. The time delay in nitrogen production relative to oxygen production plays an important role. Examination of Figures 8 and 11 shows that galaxies with masses ≳ 10^11.2 M_☉ are in the plateau regime in both the M_S–O/H and in M_S–N/H diagrams, at both z = 0.05 and z = 0.25. This means that those galaxies have not undergone appreciable enrichment in both oxygen and nitrogen during the last ∼3 Gyr. Evidently, there has not been appreciable star formation in those galaxies over the redshift range from z = 0.25 to z = 0.05. Significant star formation in those galaxies has occurred so long ago that stars have returned their nucleosynthesis products to the interstellar medium before the epoch corresponding to z = 0.25.

Galaxies with masses between ∼10^11.0 M_☉ and ∼10^11.2 M_☉ do not show an appreciable enrichment in oxygen abundance from z = 0.25 to z = 0.05 but do show some enrichment in nitrogen over this period. This suggests that there has not been appreciable star formation in those galaxies over the period from z = 0.25 to z = 0.05. However, they do contain stars that were formed before z = 0.25, but later in comparison to the galaxies of highest masses. The massive oxygen-producing stars die after a few million years, releasing oxygen in the interstellar medium. By contrast, the nitrogen-producing intermediate-mass stars have longer lifetimes, and so they have not returned nitrogen to the interstellar medium before z = 0.25 because they have not had enough time to evolve. This also suggests that stars that make a contribution to the nitrogen production have lifetimes of a few Gyr.

The galaxies with masses ≲10^11.0 M_☉ show enrichment in both oxygen and nitrogen abundances after the period corresponding to z = 0.25. This means that appreciable star formation has taken place in those galaxies during the last ∼3 Gyr. The nitrogen production increases with decreasing galaxy mass from 10^11.2 M_☉ to ∼10^10.2 M_☉ where it reaches a value Δlog (N/H) ∼ 0.65, then it decreases with further decrease of galaxy mass.

The lower panel of Figure 10 shows the deviations of nitrogen abundances from the derived z–M_S–N/H relation for galaxies from both subsamples B (solid line) and C (dashed line). Examination of the upper and lower panels of Figure 10 shows that the lower histogram is broader than the upper one, i.e., that the nitrogen abundances show a larger scatter around the z–M_S–N/H relation as compared to oxygen abundances around the z–M_S–O/H relation. The mean deviation for nitrogen abundances is Δ(log (N/H)) ∼ 0.15 against Δ(log (OH)) ∼ 0.06 for oxygen abundances. However, nitrogen also spans a significantly larger abundance range, from 12 + log(N/H) ∼ 6.5 to 12 + log(N/H) ∼ 8.0, as compared to oxygen which goes only from 12 + log(O/H) ∼ 8.25 to 12 + log(O/H) ∼ 8.75. Taking into account the differences in range, then the relative scatters around the z–M_S–N/H and z–M_S–O/H relations are comparable. It should be emphasized that the larger scatter of nitrogen abundances around the z–M_S–N/H relation in comparison to the scatter of oxygen abundances around the z–M_S–O/H relation cannot be attributed to larger errors in nitrogen abundance determinations. Indeed, the O/H values are derived from the N/H and N/O values, and any error in the nitrogen abundance determination is propagated into the error in the oxygen abundance determination. Then, if the large scatter of nitrogen abundances around the z–M_S–N/H is caused by large errors in the nitrogen abundance determinations, then the oxygen abundances would show a similar or larger scatter around the z–M_S–O/H relation. Just the opposite is observed.

The larger scatter of nitrogen abundances as compared to that of oxygen abundances can be understood in the following way. The oxygen abundance in a galaxy is mainly defined by its astration level. In contrast, the nitrogen abundance is defined not only by the astration level but depends also on the star formation history of the galaxy. As noted above, a star formation burst results in a temporary decrease of the N/O ratio in a galaxy (e.g., Pilyugin 1992, 1993). As a result, galaxies with a given oxygen abundance can have different N/O ratios and nitrogen abundances, depending on their star formation histories. We now check that expectation with our data. We use subsample C to have the most statistics. Figure 13 shows the oxygen and nitrogen abundances as a function of redshift for galaxies with masses in the lower range 10^10.0 M_☉–10^10.3 M_☉ (upper left panel) and in the upper range 10^11.2 M_☉–10^11.5 M_☉ (upper right panel). The N/O abundance ratios of those galaxies as a function of redshift are shown in the lower panels. It can be seen that the galaxies in the two different mass ranges show different behaviors with redshift, reflecting the difference in the level of star formation activity in them. That in the lower mass range is high (those galaxies show an appreciable increase of oxygen abundance with decreasing redshift) while that in galaxies in the upper mass range is very low (those galaxies do not show a significant oxygen enrichment with decreasing redshift). Figure 13 shows that, in spite of the different behaviors of the oxygen abundances with redshift in the two galaxy mass ranges, the scatter in oxygen abundances at a given redshift is comparable in the two cases, the dispersion of the data points in the low mass range being only slightly larger than that in the high mass range. By contrast, the scatter in the N/O ratios and in the nitrogen abundances at a given redshift is considerably higher for galaxies with high star formation activity (those in the low mass range, left upper and lower panels in Figure 13) than for galaxies with low star formation activity (those in the high mass range, right upper and lower panels in Figure 13). At z = 0.05, oxygen abundances in galaxies with masses 10^10.0 M_☉–10^10.3 M_☉ are similar to those in galaxies with masses 10^11.2 M_☉–10^11.5 M_☉. The maximum value of the N/O ratio in the two galaxy mass ranges is also similar. However, many galaxies in the low mass range possess low N/O ratios (Figure 13, lower left panel). The fact that the N/O ratios of many galaxies with high star formation activity are significantly lower than those in galaxies with low star formation activity does confirm our expectation that the larger scatter of nitrogen abundances around the z–M_S–N/H in comparison to that of oxygen abundances around the z–M_S–O/H is caused by the temporary decrease of the N/O ratio, due to star formation bursts of different amplitudes and/or ages, i.e., to different star formation histories in galaxies.

**Figure 13.** Oxygen and nitrogen abundances as a function of redshift for galaxies with masses 10^10.0 M_☉–10^10.3 M_☉ (upper left panel) and 10^11.2 M_☉–10^11.5 M_☉ (upper right panel). Oxygen abundances are shown by dark (black in the electronic version) filled circles, and nitrogen abundances by gray (light-blue in the electronic version) filled circles. The nitrogen-to-oxygen abundance ratios as a function of redshift for those galaxies are shown in the corresponding lower panels.
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Thus, the consideration of the nitrogen abundance evolution with redshift and galaxy stellar mass has confirmed the general picture obtained from the oxygen abundance evolution analysis. Examination of both the z–M_S–N/H and the z–M_S–O/H relations has led to the following conclusions.

1.
The galaxies of highest masses, those with masses ≳10^11.2 M_☉, have reached their high astration level more than 3 Gyr ago, so that stars in those galaxies have returned their nucleosynthesis products to the interstellar medium before z = 0.25.
2.
The galaxies with masses in the range from ∼10^11.0 M_☉ to ∼10^11.2 M_☉ also form their stars before z = 0.25, but later in comparison to the galaxies of highest masses. The intermediate-mass stars in those galaxies have not returned nitrogen to the interstellar medium before z = 0.25 because they have not had enough time to evolve.
3.
Significant star formation has occurred in galaxies with masses lower than ∼10¹¹ M_☉ during the last 3 Gyr. Those galaxies have converted up to 20% of their total mass into stars over this period.
4.
Stars with lifetimes of a few Gyr contribute to the nitrogen production.

4.4. Influence of the Selection Criteria on the Redshift–Galaxy Mass–Metallicity Relations

We wish to examine here how our selection criteria affect the results obtained. We compare the results obtained for our SDSS subsamples with those obtained for a sample of star-forming SDSS galaxies selected with commonly used criteria. We use the diagnostic diagram proposed by Baldwin et al. (1981) where the excitation properties of H ii regions are studied by plotting the low-excitation [N ii]λ6584/Hα line ratio against the high-excitation [O iii]λ5007/Hβ line ratio. The diagram can be used to separate different types of emission-line objects according to their main excitation mechanism. We have thus excluded from the total SDSS sample all objects above the solid line given by the equation

$\begin{equation} \log (\mbox{\rm [O\,{\sc iii}]$\lambda $5007/H$\beta $}) = \frac{0.61}{\log (\mbox{\rm [N\,{\sc ii}]$\lambda $6584/H$\alpha $})-0.05} +1.3, \end{equation} \tag{ 13 }$

which separates objects with H ii spectra from those containing an AGN (Kauffmann et al. 2003). We have extracted from the total sample a subsample of 95,046 star-forming galaxies, referred to hereafter as the "all star-forming galaxies" or SFG subsample.

We compare the z–M_S–O/H and z–M_S–N/H diagrams for the SFG and C subsamples. The upper panel of Figure 14 shows the oxygen abundances of galaxies in the SFG subsample, with redshifts in the range 0.04 < z < 0.06, as a function of galaxy stellar mass. The lower panel of Figure 14 shows the same diagram, but for galaxies in a higher redshift range, 0.23 < z < 0.27. The derived z–M_S–O/H relations for subsample C, superimposed on the data points of the SFG subsample, are shown in Figure 14 by the solid line for z = 0.05, and by the dashed line for z = 0.25. Inspection of Figure 14 shows that the galaxies from the SFG subsample follow well the z–M_S–O/H relation derived for subsample C. Comparison of Figure 14 with Figure 9 shows however that the scatter of the points about the z–M_S–O/H relation is larger for the SFG subsample than for subsample C. This is evidence that our selection criteria effectively weed out galaxies with less reliable measurements.

Figure 15 shows the z–M_S–N/H diagram. As before, the z–M_S–N/H relations derived for subsample C are superimposed on the datapoints of the SFG subsample. Again, the galaxies from the SFG subsample follow well the z–M_S–N/H relation derived for subsample C. Thus, the results obtained with the commonly used method of selecting star-forming galaxies do not differ appreciably from those obtained with our selection method. We emphasize that our approach presents however two important advantages. First, it is not necessary to know a priori the precise location of the dividing line between H ii regions and AGNs, a subject which is, as noted before, still controversial (Kewley et al. 2001; Kauffmann et al. 2003; Stasińska et al. 2006). Second, our approach allows us to reject all unreliable measurements. The counterpart of these advantages is that our approach requires a good sample of calibration datapoints—a reasonably large sample of H ii regions with precise spectrophotometric measurements, including weak auroral lines—to establish reliable relations between the strong line fluxes and the physical characteristics of H ii regions. Those relations should however be established in any case, as they are necessary for abundance determinations in star-forming galaxies, independently of the particular method used to select them.

4.5. Comparison to Previous Work on the z–M_S–O/H Relation

The evolution of the mass–metallicity relation of galaxies with redshift has been considered previously by several groups, as described in Section 1. But, as discussed before, each group uses a different calibration to derive abundances which show as a result sometimes large discrepancies. So it is difficult to directly compare, or put on the same scale, the abundances derived by other groups and our own. Thus, we will not attempt such a comparison. Rather, we will limit ourselves to comparing the evolution in oxygen abundances with redshift which seems to be less sensitive to the adopted calibration. As for the nitrogen evolution with redshift, it has not been considered before.

We first summarize the results obtained by previous investigators. Lilly et al. (2003) have estimated the oxygen abundance in a sample of 66 Canada–France Redshift Survey galaxies in the redshift range 0.47 < z < 0.92, using the flux ratios of bright oxygen emission lines. They concluded that, at half the present age of the universe, the overall oxygen abundance of the galaxies in their sample, with luminosities ranging from M_B = −20 to M_B = −22 (or log(L_B/L_B☉) ∼ 10.2–11.0), is only slightly lower than the oxygen abundance in similar luminous galaxies today. They found a variation Δ(log(O/H)) = 0.08 ± 0.06.

Savaglio et al. (2005) have investigated the mass–metallicity relation using galaxies from the Gemini Deep Survey and the Canada–France Redshift Survey in the redshift range 0.4 < z < 1.0. Their galaxies with M_S > 10¹⁰M_☉ have oxygen abundances close to those in local galaxies of comparable mass, while the oxygen abundances in galaxies with M_S < 10¹⁰ M_☉ are lower on average (with a large scatter) than those in galaxies of similar masses at the present epoch (see their Figure 13).

Cowie & Barger (2008) have studied the oxygen abundance evolution from z = 0.9 to z = 0.05 using a large sample of galaxies in the Great Observatories Origins Deep Survey-North (GOODS-N). They have found an evolution of the metallicity–mass relation corresponding to a decrease of 0.21 ± 0.03 dex between the value at z = 0.77 and the local value in the 10¹⁰–10¹¹ M_☉ range. They also found that star formation in the most massive galaxies (>10¹¹ M_☉) ceases at z < 1.5 because of gas starvation.

Lamareille et al. (2009) have derived the mass–metallicity relation of star-forming galaxies up to z ∼ 0.9 using data from the VIMOS VLT Deep Survey. They found that the galaxies of 10^10.2 solar masses show a larger oxygen enrichment (Δ(log(O/H)) ∼ 0.28 from z ∼ 0.77 to z = 0) than the galaxies of 10^9.4 solar masses (Δ(log (O/H)) ∼ 0.18).

Lara-López et al. (2009) have studied the oxygen abundance of relatively massive (log (M_S/M_☉) ⩾ 10.5) star-forming galaxies from SDSS/DR5 at different redshift intervals from 0.4 to 0.04. They found an oxygen enrichment Δ(log (O/H)) ∼ 0.1 from redshift 0.4 to 0.

Asari et al. (2009) have derived the mass–metallicity relation at different lookback times for SDSS galaxies using the stellar metallicities estimated with their spectral synthesis code. They have found that the more massive galaxies show very little evolution since a lookback time of 9 Gyr.

Examination of all these studies shows good qualitative agreement between them, but with a rather large scatter in the estimated values of the oxygen enrichment. The results of these investigations can be summarized as followed: (1) the most massive galaxies (those with masses > 10¹¹ M_☉) do not show an appreciable enrichment in oxygen from z ∼ 0.7 to z = 0; (2) in the 10¹⁰–10¹¹ M_☉ mass range, an increase of the oxygen abundance Δ(log (O/H)) ∼ 0.08–0.28 is observed in the redshift range from z ∼ 0.7 to z ∼ 0. Our results are also in good qualitative agreement with those previous results. We also see no change in oxygen abundance with redshift for galaxies with masses greater than 10¹¹ M_☉, in the redshift range from ∼0.25 to 0. We estimate the mean increase of the oxygen abundance with redshift in the 10¹⁰–10¹¹ M_☉ galaxy stellar mass range to be Δ(log (O/H)) ∼ 0.11, with Δ(log (O/H)) ∼ 0.23 at 10¹⁰ M_☉ and Δ(log (O/H)) = 0 at 10¹¹ M_☉. This is in agreement with the upper range of values found in previous works, especially when we take into account the fact that we have considered a smaller redshift interval than previous investigators.

4.6. Nitrogen Enrichment by Intermediate Mass Stars: A Discrepancy with Current Stellar Evolution Theory

Edmunds & Pagel (1978) have suggested that observations of the N/O abundance ratio in galaxies can be understood if N is manufactured in stars of 1–2.5 M_☉. The N/O ratio of a galaxy then becomes an indicator of the time that has elapsed since the bulk of star formation occurred, or in other words of the nominal "age" of the galaxy. Pilyugin et al. (2003) have found that the N/O ratios in H ii regions of galaxies of early morphological types are systematically higher than those in H ii regions with the same O/H value in galaxies of late morphological types. Moreover, it is known that the star formation histories of galaxies of different morphological types differ, in the sense that the spiral galaxies of early morphological types have a significantly larger fraction of old stars than the galaxies of late morphological type (Sandage 1986). These two facts lead to the conclusion that the contribution to the nitrogen production by low- and intermediate-mass stars, with a long time delay of a few Gyr between their moment of birth and the time of release of their nucleosynthetic products in the interstellar medium, can be significant.

One of the main conclusions of this study is that there has been a significant evolution in nitrogen abundances in star-forming galaxies over the last 2–3 Gyr. This appears not to agree with the predictions of current theoretical models of intermediate mass stars. Indeed, a time duration of 2–3 Gyr corresponds to the lifetime of stars in the 1.5–2 M_☉ mass range. While stellar evolution models of intermediate mass stars have long predicted that they contribute significantly to nitrogen enrichment, it is stars of 3–8 M_☉ that are supposed to do the job, not stars in the 1.5–2 M_☉ mass range. Intriguingly, there are other types of observations that also suggest that stars in the 1.5–2 M_☉ mass range contribute to nitrogen enrichment. Richer & McCall (2008) have found that planetary nebulae in nearby galaxies (with or without ongoing star formation) often show large nitrogen enrichments. They have argued that these planetary nebulae are the descendants of relatively low mass progenitors, of approximately 1.5M_☉ or less, i.e., that low- and intermediate-mass stars are a more important source of nitrogen than has been hitherto considered. Thus, our conclusion that stars with lifetimes of a few Gyr contribute to the nitrogen production, derived from the consideration of the nitrogen abundance evolution with redshift in galaxies, is in line with the conclusions of other types of investigations. While stellar evolution theory does not yet predict nitrogen production in stars with masses of ∼1.5–2 M_☉, several lines of observations now do so.

5. CONCLUSIONS

The redshift evolution of oxygen and nitrogen abundances in emission-line SDSS galaxies has been studied.

We have paid particular attention to the construction of our galaxy sample, using the MPA/JHU catalogs of line flux measurements and other derived physical properties for SDSS galaxies. We have devised a way to recognize and exclude from consideration not only AGNs, but also star-forming galaxies with large errors in their line flux measurements. We have found that the requirement that nitrogen abundances, derived with different calibration relations based on different emission lines, agree, can be used as a reliable criterion to select star-forming galaxies with accurate line flux measurements.

We have derived relations between nitrogen abundances and the abundance-sensitive N₂, N₂/R₂, and N₂/R₃ indexes. Those relations have been used to determine nitrogen abundances in the SDSS galaxies. The small dispersion among the various derived nitrogen abundances for a given galaxy is used as a criterion to select star-forming galaxies with accurate line fluxes measurements. The relations between the electron temperature t₂ and the N₂, N₂/R₂, and N₂/R₃ indexes have also been established. Those calibrations have been used to estimate the N/O ratio and derive the oxygen abundances O/H from the nitrogen abundances N/H.

Subsamples of star-forming SDSS galaxies have been extracted from the MPA/JHU catalogs, using the small nitrogen abundance dispersion criterion described above. The nitrogen and oxygen abundances are estimated for these galaxies. The evolution of the oxygen and nitrogen abundances with redshift and galaxy stellar mass of galaxy is investigated, that of nitrogen abundances for the first time. We have obtained the following main results.

1.
The galaxies of highest masses (those more massive than ∼10^11.2 M_☉) do not show an appreciable enrichment in both oxygen and nitrogen from z = 0.25 to z = 0.05. Those galaxies have reached their high astration level in such a distant past that their stars have returned their nucleosynthesis products to the interstellar medium before z = 0.25.
2.
The galaxies in the mass range from ∼10^11.0 M_☉ to ∼10^11.2 M_☉ do not show an oxygen enrichment, but do show some enrichment in nitrogen. Those galaxies also formed stars before z = 0.25, but at a later epoch in comparison to the galaxies of highest masses. Their stars have not returned nitrogen to the interstellar medium before z = 0.25 because they have not had enough time to evolve.
3.
The galaxies with masses lower than ∼10¹¹ M_☉ show enrichment in both oxygen and nitrogen abundances over the redshift period from z = 0.25 to z = 0.05, i.e., during the last 3 Gyr. The oxygen enrichment increases with decreasing galaxy mass, from 10¹¹ M_☉ to M_S = 10^9.9 M_☉. It reaches a value Δlog (O/H) ∼ 0.25 at M_S = 10^9.9 M_☉ and slightly decreases with further decrease of galaxy mass. The nitrogen enrichment increases with decreasing galaxy mass, from ∼10¹¹ M_☉ to ∼10^10.2 M_☉. It reaches a value Δlog (N/H) ∼ 0.65 at ∼10^10.2 M_☉ and slightly decreases with further decrease of galaxy mass. Significant star formation has occurred in those galaxies during the last 3 Gyr. They have converted up to 20% of their total mass to stars over this period.
4.
Stars with lifetimes of 2–3 Gyr, i.e., in the 1.5–2 M_☉ mass range, contribute to the nitrogen production. This is not in agreement with current stellar evolutionary models of intermediate mass stars which predict that stars in the 3–8 M_☉ mass range do the job, not stars in the 1.5–2 M_☉ mass range.
5.
The general picture of the oxygen abundance evolution with redshift and galaxy stellar mass obtained here and in the previous work is confirmed and strengthened by consideration of the nitrogen abundance evolution.

We are grateful to the referee for his/her constructive comments. L.S.P. thanks the hospitality of the Astronomy Department of the University of Virginia where part of this investigation was carried out. L.S.P. and I.A.Z. acknowledge the partial support of the Cosmomicrophysics-2 project of the National Academy of Sciences of Ukraine. The authors acknowledge the work of the SDSS team. Funding for the SDSS has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society. The SDSS Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the Korean Scientist Group, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington.

THE REDSHIFT EVOLUTION OF OXYGEN AND NITROGEN ABUNDANCES IN EMISSION-LINE SDSS GALAXIES

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ABSTRACT

1. INTRODUCTION

2. METALLICITY AND TEMPERATURE CALIBRATIONS

3. SAMPLE SELECTION

4. THE REDSHIFT EVOLUTION OF OXYGEN AND NITROGEN ABUNDANCES

4.1. The z–M_S–O/H Relation

4.2. The Metallicity Plateau and the Oxygen Enrichment as a Function of Galaxy Stellar Mass

4.3. The z–M_S–N/H Relation

4.4. Influence of the Selection Criteria on the Redshift–Galaxy Mass–Metallicity Relations

4.5. Comparison to Previous Work on the z–M_S–O/H Relation

4.6. Nitrogen Enrichment by Intermediate Mass Stars: A Discrepancy with Current Stellar Evolution Theory

5. CONCLUSIONS

Footnotes

THE REDSHIFT EVOLUTION OF OXYGEN AND NITROGEN ABUNDANCES IN EMISSION-LINE SDSS GALAXIES

Article metrics

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Share this article

Author e-mails

Author affiliations

Dates

ABSTRACT

1. INTRODUCTION

2. METALLICITY AND TEMPERATURE CALIBRATIONS

3. SAMPLE SELECTION

4. THE REDSHIFT EVOLUTION OF OXYGEN AND NITROGEN ABUNDANCES

4.1. The z–MS–O/H Relation

4.2. The Metallicity Plateau and the Oxygen Enrichment as a Function of Galaxy Stellar Mass

4.3. The z–MS–N/H Relation

4.4. Influence of the Selection Criteria on the Redshift–Galaxy Mass–Metallicity Relations

4.5. Comparison to Previous Work on the z–MS–O/H Relation

4.6. Nitrogen Enrichment by Intermediate Mass Stars: A Discrepancy with Current Stellar Evolution Theory

5. CONCLUSIONS

Footnotes

4.1. The z–M_S–O/H Relation

4.3. The z–M_S–N/H Relation

4.5. Comparison to Previous Work on the z–M_S–O/H Relation