Gas metallicity in the narrow-line regions of high-redshift active galactic nuclei

We analyze optical (UV rest-frame) spectra of X-ray selected narrow-line QSOs at redshift $1.5 \la z \la 3.7$ found in the Chandra Deep Field South and of narrow-line radio galaxies at redshift $1.2 \la z \la 3.8$ to investigate the gas metallicity of the narrow-line regions and their evolution in this redshift range. Such spectra are also compared with UV spectra of local Seyfert 2 galaxies. The observational data are inconsistent with the predictions of shock models, suggesting that the narrow-line regions are mainly photoionized. The photoionization models with dust grains predict line flux ratios which are also in disagreement with most of the observed values, suggesting that the high-ionization part of the narrow-line regions (which is sampled by the available spectra) is dust-free. The photoionization dust-free models provide two possible scenarios which are consistent with the observed data: low-density gas clouds ($n_{\rm H} \la 10^3$ cm-3) with a sub-solar metallicity ($0.2 \la Z_{\rm gas}/Z_\odot \la 1.0$), or high-density gas clouds ($n_{\rm H} \sim 10^5$ cm-3) with a wide range of gas metallicity ($0.2 \la Z_{\rm gas}/Z_\odot \la 5.0$). Regardless of the specific interpretation, the observational data do not show any evidence for a significant evolution of the gas metallicity in the narrow-line regions within the redshift range $1.2 \la z \la 3.8$. Instead, we find a trend for more luminous active galactic nuclei to have more metal-rich gas clouds (luminosity-metallicity relation), which is in agreement with the same finding in the studies of the broad-line regions. The lack of evolution for the gas metallicity of the narrow-line regions implies that the major epoch of star formation in the host galaxies of these active galactic nuclei is at $z \ga 4$