We analyze optical (UV rest-frame) spectra of X-ray selected narrow-line QSOs
at redshift 1.5 < z < 3.7 found in the Chandra Deep Field South and of
narrow-line radio galaxies at redshift 1.2 < z < 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 < 10^3 cm^-3) with a sub-solar metallicity (0.2 < Z/Z_sun < 1.0),
or high-density gas clouds (n ~ 10^5 cm^-3) with a wide range of gas
metallicity (0.2 < Z/Z_sun < 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 <
z < 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 > 4.Comment: 16 pages, 12 figures, submitted to Astronomy and Astrophysic
