In this paper, we present the statistical results of a search for extended optical emission-line gas in a sample of 38, predominantly "powerful," flux-density selected, radio galaxies (the "representative sample") and of an additional five radio galaxies. We have obtained optical broad-band and narrow-band and VLA radio images of these sources (Baum et al.). We establish that spatially extended emission-line gas is common in powerful radio galaxies. We detect line emission from all of the sources in the representative sample. In ~85% of these sources we have spatially resolved the line emission. The median extent of the emission-line nebulae is 10 kpc, and the median emission-line luminosity in Hα + [N II] or [O III] is 3 x 10^41^ ergs s^-1^, roughly an order of magnitude times the extent and luminosity of emission-line nebulae found in normal elliptical galaxies of similar optical magnitude. The median extent of the emission-line nebulae in sources with low radio luminosities (L_radio_ < 10^42.7^ ergs s^-1^) or edge-dimmed (Fanaroff and Riley Class I) radio morphologies is roughly one-fourth the median extent of the nebulae in the higher power sources. We estimate lower limits to the density of the emission-line gas at distances between 5 and 10 kpc from the galaxy nucleus of 0.1-1 cm^-3^, and upper limits to the total mass in emission-line gas between 5 x 10^7^ and 5 x 10^9^ M_sun_. We find that the narrow emission-line luminosity is strongly correlated with both the total radio luminosity and the radio core power in the sources from the representative sample, and that the core radio power is strongly correlated with the total radio luminosity. The number of photons required to photoionize the emission-line nebula is found to correlate strongly with the number of ionizing photons emitted by the galaxy nucleus, as estimated from measurements of the nuclear, "nonstellar" continuum from the host galaxy. These results, combined with the spectroscopic and modelling, results of Robinson et al., suggest that photoionization by the host galaxy's nuclear ultraviolet continuum is the dominant means by which both the nuclear and the extended emission-line gas in powerful radio galaxies is ionized. The strong correlation of Q_nuc_ with Q_tot_ suggests that the emission-line luminosities are limited by the flux of ionizing photons emitted by the active nucleus rather than by the availability of hydrogen atoms. We consider possible origins for the emission-line gas. Instabilities in the hot intergalactic medium of the host galaxy may be the source of the emission-line gas in sources which have small (i.e., kiloparsec scale) emission-line nebulae. However, the large spatial extent of the emission-line nebulae in some very isolated galaxies and the possible large associated masses in emission-line gas may suggest that these very extensive regions of emission-line gas did not originate in the ISM. For sources with very extended regions of emission-line gas which inhabit densely populated regions, the emission-line gas may, however, have cooled out of a hot intergalactic medium. We also consider the possibility that the emission-line gas in these galaxies originates in tidal interactions/mergers with companion galaxies which are rich in cold gas. In support of this possibility, we find that the median extent of the emission-line nebulae is larger in galaxies which show possible signs of a recent interaction than in either dumbell galaxies or galaxies which show no signs of a recent interaction. We show that there are roughly two orders of magnitude in radio luminosity separating the luminosity regime in which the sources in our sample have exclusively edge-darkened (Fanaroff and Riley [1974] Class I) radio morphologies from the regime where sources have exclusively edge-brightened or hotspot (Fanaroff and Riley, Class II) radio morphologies. We find a tendency for the radio source axis to align with the minor axis of the host radio galaxy only in galaxies which have radio sources which are greater than 200 kpc in extent. Roughly 25% of the sources in the representative sample show obvious morphological peculiarities in the distribution of their continuum optical isophotes.
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Baum et al. (1989) studied this question.
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