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 _ { H } \la 10 ^ { 3 } cm ^ { -3 } ) with a sub-solar metallicity ( 0.2 \la Z _ { gas } / Z _ { \odot } \la 1.0 ) , or high-density gas clouds ( n _ { H } \sim 10 ^ { 5 } cm ^ { -3 } ) with a wide range of gas metallicity ( 0.2 \la Z _ { 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 .