The Size-Luminosity Relationship of Quasar Narrow-Line Regions
  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 ($10^5 - 10^7 M_\odot$)
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 $\sim 10$ kpc which is observed at high AGN luminosities
($L_\text{ion} \simeq 10^{46}$ 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.
