We have investigated the influence of nuclear parameters such as black hole (BH) mass and photoionizing luminosity on the FRI/FRII transition in a sample of nearby (z<0.2) 3CR radio galaxies. The sample was observed with medium-resolution, optical spectroscopy and contains some galaxies with unpublished velocity dispersion measurements and emission-line fluxes. Measured velocity dispersions are 130-340 km/s with a mean of 216 km/s. Converting to BH mass, we find that the BH mass distribution is identical for FRIs and FRIIs, with a mean of approximately 2.5x10^8 Msun. We convert [OII] and [OIII] emission-line luminosities to photoionizing luminosity under the assumption that the gas is ionized by the nuclear UV continuum. Most of the galaxies with FRI morphology and/or low-excitation emission-line spectra have progressively lower BH masses at lower photoionizing (and jet) luminosities. This agrees with the Ledlow-Owen relation which states that the radio luminosity at the FRI/FRII transition depends on the optical luminosity of the host, L_radio ~ L_optical^1.8, because both L_radio and L_optical relate to AGN nuclear parameters. When recasting the Ledlow-Owen relation into BH mass versus photoionizing and jet luminosity, we find that the recasted relation describes the sample quite well. The FRI/FRII transition occurs at approximately an order of magnitude lower luminosity relative to the Eddington luminosity than the soft-to-hard transition in X-ray binaries. This difference is consistent with the Ledlow-Owen relation, which predicts a weak BH mass dependence in the transition luminosity. We conclude that the FRI/FRII dichotomy is caused by a combination of external and nuclear factors, with the latter dominating.
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