We present a procedure to constrain the redshifts of obscured ($N_H > 10^{22}$ cm$^{-2}$) Active Galactic Nuclei (AGN) based on low-count statistics X-ray spectra, which can be adopted when photometric and/or spectroscopic redshifts are unavailable or difficult to obtain. We selected a sample of 54 obscured AGN candidates on the basis of their X-ray hardness ratio, $HR>-0.1$, in the Chandra deep field ($\sim$479 ks, 335 arcmin$^2$) around the $z=6.3$ QSO SDSS J1030+0524. The sample has a median value of $\approx80$ net counts in the 0.5-7 keV energy band. We estimate reliable X-ray redshift solutions taking advantage of the main features in obscured AGN spectra, like the Fe 6.4 keV K$\mathrm{\alpha}$ emission line, the 7.1 keV Fe absorption edge and the photoelectric absorption cut-off. The significance of such features is investigated through spectral simulations, and the derived X-ray redshift solutions are then compared with photometric redshifts. Both photometric and X-ray redshifts are derived for 33 sources. When multiple solutions are derived by any method, we find that combining the redshift solutions of the two techniques improves the rms by a factor of two. Using our redshift estimates ($0.1\lesssim z \lesssim 4$), we derived absorbing column densities in the range $\sim 10^{22}-10^{24}$ cm$^{-2}$ and absorption-corrected, 2-10 keV rest-frame luminosities between $\sim 10^{42}$ and $10^{45}$ erg s$^{-1}$, with median values of $N_H = 1.7 \times 10^{23}$ cm$^{-2}$ and $L_{\mathrm{2-10\, keV}} = 8.3\times10^{43}$ erg s$^{-1}$, respectively. Our results suggest that the adopted procedure can be applied to current and future X-ray surveys, for sources detected only in the X-rays or that have uncertain photometric or single-line spectroscopic redshifts.

中文翻译：

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模糊 AGN 的 X 射线红移：J1030 深场案例研究

我们提出了一种基于低计数统计 X 射线光谱来约束被遮蔽的 ($N_H > 10^{22}$ cm$^{-2}$) 活动星系核 (AGN) 红移的程序，可以采用当光度和/或光谱红移不可用或难以获得时。我们在钱德拉深场（$\sim$479 ks, 335 arcmin$^2$）的基础上根据他们的 X 射线硬度比选择了 54 个被遮蔽的 AGN 候选样本，$HR>-0.1$ =6.3$ QSO SDSS J1030+0524。该样本在 0.5-7 keV 能带中的净计数中值为 $\approx80$。我们利用模糊的 AGN 光谱中的主要特征估计可靠的 X 射线红移解决方案，如 Fe 6.4 keV K$\mathrm{\alpha}$ 发射线、7.1 keV Fe 吸收边和光电吸收截止。通过光谱模拟研究这些特征的重要性，然后将导出的 X 射线红移解与光度红移进行比较。光度和 X 射线红移均来自 33 个源。当通过任何方法推导出多个解决方案时，我们发现将两种技术的红移解决方案结合起来可以将 rms 提高两倍。使用我们的红移估计值 ($0.1\lesssim z \lesssim 4$)，我们推导出了 $\sim 10^{22}-10^{24}$ cm$^{-2}$ 范围内的吸收柱密度和吸收校正, $\sim 10^{42}$ 和 $10^{45}$ erg s$^{-1}$ 之间的 2-10 keV 静止帧光度，中值为 $N_H = 1.7 \times 10^{23 }$ cm$^{-2}$ 和 $L_{\mathrm{2-10\, keV}} = 8.3\times10^{43}$ erg s$^{-1}$。