We investigate the narrow-line region (NLR) of two radio-quiet QSOs, PG1012+008 and PG1307+085, using high signal-to-noise spatially resolved long-slit spectra obtained with FORS1 at the Very Large Telescope. Although the emission is dominated by the point-spread function of the nuclear source, we are able to detect extended NLR emission out to several kpc scales in both QSOs by subtracting the scaled central spectrum from outer spectra. In contrast to the nuclear spectrum, which shows a prominent blue wing and a broad line profile of the [O III] line, the extended emission reveals no clear signs of large scale outflows. Exploiting the wide wavelength range, we determine the radial change of the gas properties in the NLR, i.e., gas temperature, density, and ionization parameter, and compare them with those of Seyfert galaxies and type-II QSOs. The QSOs have higher nuclear temperature and lower electron density than Seyferts, but show no significant difference compared to type-II QSOs, while the ionization parameter decreases with radial distance, similar to the case of Seyfert galaxies. For PG1012+008, we determine the stellar velocity dispersion of the host galaxy. Combined with the black hole mass, we find that the luminous radio-quiet QSO follows the local M_BH-sigma* relation of active galactic nuclei.
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