The presence of an active galactic nucleus ( AGN ) can strongly affect its host .
Due to the copious radiative power of the nucleus , the effects of radiative feedback can be detected over the entire host galaxy and sometimes well into the intergalactic space .
In this paper we model the observed size-luminosity relationship of the narrow-line regions ( NLRs ) of AGN .
We model the NLR as a collection of clouds in pressure equilibrium with the ionizing radiation , with each cloud producing line emission calculated by Cloudy .
The sizes of the NLRs of powerful quasars are reproduced without any free parameters , as long as they contain massive ( \SIrange e5e7M_ \sun ) ionization-bounded clouds .
At lower AGN luminosities the observed sizes are larger than the model sizes , likely due to additional unmodeled sources of ionization ( e.g. , star formation ) .
We find that the observed saturation of sizes at \sim \SI { 10 } { kpc } which is observed at high AGN luminosities ( L _ { \text { ion } } \simeq \SI { e 46 } { erg / s } ) is naturally explained by optically thick clouds absorbing the ionizing radiation and preventing illumination beyond a critical distance .
Using our models in combination with observations of the [ O III ] /IR ratio and the [ O III ] size – IR luminosity relationship , we calculate the covering factor of the obscuring torus ( and therefore the type 2 fraction within the quasar population ) to be f = 0.5 , though this is likely an upper bound .
Finally , because the gas behind the ionization front is invisible in ionized gas transitions , emission-based NLR mass calculations underestimate the mass of the NLR and therefore of the energetics of ionized-gas winds .