(abridged) We analyze and model HST /STIS observations of a sample of 27 galaxies; 16 Fanaroff & Riley Type I radio galaxies and 11 (more) normal early-type galaxies. We focus here on what can be learned from the nuclear velocity dispersion (line width) of the gas as a complement to the many studies dealing with gas rotation velocities. We find that the dispersion in a STIS aperture of ~0.1-0.2 generally exceeds the large-scale stellar velocity dispersion of the galaxy. This is qualitatively consistent with the presence of central BHs, but raises the question whether the excess gas dispersion is of gravitational or non-gravitational origin and whether the implied BH masses are consistent with our current understanding of BH demography(as predicted by the M-sigma relation between BH mass and stellar velocity dispersion). To address this we construct dynamical models for the gas, both thin disk models and models with more general axis ratios and velocity anisotropies. For the normal galaxies the nuclear gas dispersions are adequately reproduced assuming disks around BHs with masses that follow the M-sigma relation. In contrast, the gas dispersions observed for the radio galaxies generally exceed those predicted by any of the models. We attribute this to the presence of non-gravitational motions in the gas that are similar to or larger than the gravitational motions. The non- gravitational motions are presumably driven by the active galactic nucleus (AGN), but we do not find a relation between the radiative output of the AGN and the non-gravitational dispersion. It is not possible to uniquely determine the BH mass for each galaxy from its nuclear gas dispersion. However, for the sample as a whole the observed dispersions do not provide evidence for significant deviations from the M-sigma relation.
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