Gas Disks and Supermassive Black Holes in Nearby Radio Galaxies

4.2.4 Dynamical models
As discussed above we assume that the gas is organized into an infinitesimally thin,
settled, rotating disk which is located in the major (equatorial) plane of the galaxy,
with a circularly symmetric flux distribution, F(R), as given in Section 4.2.2. The
inclinations of the dust and gas are again assumed to be identical and were determined
as discussed earlier; the major axis was assumed to lie along the major axis of the
galaxy, as the model requires a coplanar system.
For each galaxy we generate three models where we compute the circular velocity
Vc(R) from the combined gravitational potential of the stars with a black hole with
mass M• = 0, 1 × 10 8 M⊙, and 9 × 10 8 M⊙. The line of sight velocity profile of the
gas at position (x, y) on the sky is a Gaussian with
where
155
Mean = Vc(R) sin(ix/R), and (4.8)
Sigma = σgas(R), (4.9)
R = [x 2 + (y/ cosi) 2 ] 1/2
(4.10)
is the radius in the disk. We assume an isotropic model for the velocity dispersion,