Gas Disks and Supermassive Black Holes in Nearby Radio Galaxies

the PSF as
PSF(r) =
5�
γi
i=1 2πσ2 i
152
e −1
� �2 r
2 σi . (4.2)
The parameters γi, and σi were obtained by fitting the STIS PSF using the Tiny
Tim software (Krist & Hook, 1999) and are listed in Table 4.2. Differences between
the actual PSF and the analytical fit cause differences in the modeled kinematics
that are smaller than the errors in the data. We tested this by repeating all modeling
using a single Gaussian component to represent the PSF (see Section 4.2.6).
4.2.3 Stellar luminosity densities and mass distributions
For the purposes of the dynamical modeling we use a three-dimensional parameteri-
zation of the stellar luminosity density (j). We assume that j is oblate and axisym-
metric, i.e. there are isoluminosity spheroids with constant flattening q as a function
of radius, and that j can be parameterized as
j(R, z) = j0(m/a) α [1 + (m/a) 2 ] β , (4.3)
m 2 ≡ R 2 + (z/q) 2
(4.4)
Where R and z are cylindrical coordinates from the major plane of the galaxy. α, β,
a and j0 are free parameters. When viewed at an inclination angle i, the projected