The properties of narrow-line Seyfert 1 (NLS1) galaxies, the links and correlations between them, and the physics behind them, are still not well understood. Apart from accretion rates and black hole masses, density and outflows were speculated to be among the main drivers of the NLS1 phenomenon. Here, we utilize the diagnostic power of the [SII]6716,6731 intensity ratio to measure the density of the NLR systematically and homogeneously for a large sample of NLS1 galaxies, and we perform a comparison with a sample of broad-line type 1 AGN. We report the discovery of a zone of avoidance in density in the sense that AGN with broad lines (FWHM_Hbeta > 2000 km/s) avoid low densities, while NLS1 galaxies show a wider distribution in the NLR density, including a significant number of objects with low densities. A correlation analysis further shows that the Eddington ratio L/L_Edd anti-correlates with density. We investigate a number of different models for the zone of avoidance in density. Supersolar metallicities and temperature effects, a strong starburst contribution in NLS1 galaxies, different NLR extents and selective obscuration are considered unlikely. Possible differences in the fraction of matter-bounded clouds and differences in the interstellar media of the host galaxies of NLS1 galaxies and broad-line Seyfert 1 (BLS1) galaxies can only be tested further with future observations. We tentatively favor the effects of winds/outflows, stronger in NLS1 galaxies than in BLS1 galaxies, to explain the observations.
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