The luminosity dependence of the type 1 active galactic nucleus fraction

Using a complete, magnitude-limited sample of active galaxies from the Sloan Digital Sky Survey, we show that the fraction of broad-line (type I) active galactic nuclei (AGNs) increases with luminosity of the isotropically emitted [O-III] narrow emission line. Our results are quantitatively in agreement with, and far less uncertain than, similar trends found from studies of X-ray and radio-selected active galaxies. While the correlation between broad-line fraction and luminosity is qualitatively consistent with the receding torus model, its slope is shallower and we therefore propose a modification to this model where the height of the torus increases slowly with AGN luminosity. We demonstrate that the faint-end slope of the AGN luminosity function steepens significantly when a correction for 'missing' type 2 objects is made, and that this can substantially affect the overall AGN luminosity density extrapolated from samples of more luminous objects.