What controls the [O III] λ5007 line strength in active galactic nuclei?

Active galactic nuclei (AGN) display an extreme range in the narrow emission-line equivalent widths. Specifically, in the Palomar-Green (PG) quasar sample, the equivalent width of the narrow [O-III] lambda 5007 line has a range of > 300 (< 0.5 to 157 angstrom), while the broad H beta line, for example, has a range of 10 only (23 to 230 angstrom). The strength of [O-III] lambda 5007 is modulated by the covering factor (CF) of the narrow-line region (NLR) gas, its density (n(e)) and ionization parameter (U). To explore which of these factors produces the observed large range in [O-III] lambda 5007 strength, we measure the strength of the matching narrow H beta and [O-III] lambda 4363 lines, detected in 40 out of the 87 PG quasars with z < 0.5 in the Boroson & Green sample. The photoionization code CLOUDY is then used to infer CF, n(e) and U in each object, assuming a single uniform emitting zone. We find that the range of CF (similar to 0.02-0.2) contributes about twice as much as the range in both n(e) and U towards modulating the strength of the [O-III] lambda 5007 line. The CF is inversely correlated with luminosity, but it is not correlated with L/L-Edd as previously speculated. The single-zone [O-III] lambda 5007 emitting region is rather compact, having R-NLR= 40L(44)(0.45) pc. These emission lines can also be fitted with an extreme two-zone model, where [O-III] lambda 4363 is mostly emitted by a dense (n(e)= 10(7) cm(-3)) inner zone at R-NLR(in)=L-44(0.5) pc, and [O-III] lambda 5007 by a low-density (n(e)= 10(3) cm(-3)) extended outer zone at R-NLR(out) = 750L(44)(0.34) pc. Such an extended [O-III] lambda 5007 emission should be well resolved by Hubble Space Telescope imaging of luminous AGN. Further constraints on the radial gas distribution in the NLR can be obtained from the spectral shape of the infrared continuum emitted by the associated dust.