We derived a bi-dimensional calibration between the emission-line ratios $R_{23}= ([\mathrm{ O}\, {\small {\rm II}}]\,\lambda 3726 +\lambda 3729 +[\mathrm{ O}\mathrm{ }\, {\small {\rm III}}]\,\lambda 4959 + \lambda 5007)/\rm H\,\beta$, ${\it P}=[([\mathrm{ O}\, {\small {\rm III}}]\,\lambda 4959+\lambda 5007)/{\rm H}\,\beta ]/R_{23}$ and the oxygen abundance relative to hydrogen (O/H) in the gas phase of Seyfert 1 and 2 nuclei. In view of this, emission-line intensity ratios for a sample of objects taken from the Sloan Digital Sky Survey Data Release 7 measured by the MPA/JHU group and direct estimates of O/H based on Te-method, adapted for active galactic nuclei (AGNs), are considered. We find no variation of R23 observed along the radii of AGNs, which shows that this line ratio is a good oxygen abundance (O/H) indicator for the class of objects considered in this work. The derived O/H = f(R23, P) relation produces O/H values similar to estimations via Te-method in a wide range of metallicities [$\rm 8.0 \: \lesssim \: 12+\log \,(O/H) \: \lesssim \: 9.2$]. Conversely to star-forming regions in the high-metallicity regime, R23 shows a positive correlation trend with O/H in AGNs. This indicates that the hardness of ionizing radiation is not affected by the metallicities in these objects or narrow-line regions are not significantly modified by changes in the spectral energy distribution due to metallicity variations.

中文翻译：

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Seyfert 星系中的化学丰度 - VI。经验丰度校准

我们在发射线比率 $R_{23}= ([\mathrm{ O}\, {\small {\rm II}}]\,\lambda 3726 +\lambda 3729 +[\ mathrm{ O}\mathrm{ }\, {\small {\rm III}}]\,\lambda 4959 + \lambda 5007)/\rm H\,\beta$, ${\it P}=[([ \mathrm{ O}\, {\small {\rm III}}]\,\lambda 4959+\lambda 5007)/{\rm H}\,\beta ]/R_{23}$ 和氧丰度相对于Seyfert 1 和 2 原子核气相中的氢 (O/H)。鉴于此，由 MPA/JHU 小组测量的 Sloan 数字巡天数据第 7 版中采集的物体样本的发射线强度比以及基于 Te 方法的 O/H 直接估计，适用于活动星系核（AGN），被考虑。我们发现沿 AGN 的半径没有观察到 R23 的变化，这表明该线比是本工作中考虑的对象类别的良好氧丰度 (O/H) 指标。导出的 O/H = f(R23, P) 关系产生的 O/H 值类似于通过 Te 方法在各种金属丰度 [$\rm 8.0 \: \lesssim \: 12+\log \,(O /H) \: \lesssim \: 9.2$]。与高金属度区域的恒星形成区域相反，R23 与活动星系核中的 O/H 呈正相关趋势。这表明电离辐射的硬度不受这些物体中金属丰度的影响，或者窄线区域不会因金属丰度变化引起的光谱能量分布变化而显着改变。12+\log \,(O/H) \: \lesssim \: 9.2$]。与高金属度区域的恒星形成区域相反，R23 与活动星系核中的 O/H 呈正相关趋势。这表明电离辐射的硬度不受这些物体中金属丰度的影响，或者窄线区域不会因金属丰度变化引起的光谱能量分布变化而显着改变。12+\log \,(O/H) \: \lesssim \: 9.2$]。与高金属度区域的恒星形成区域相反，R23 与活动星系核中的 O/H 呈正相关趋势。这表明电离辐射的硬度不受这些物体中金属丰度的影响，或者窄线区域不会因金属丰度变化引起的光谱能量分布变化而显着改变。