(Abridged) The two-dimensional distribution and kinematics of the molecular,
ionized, and highly ionized gas in the nuclear regions of Seyfert 1 galaxies
have been measured using high spatial resolution (~0''.09) near-infrared
spectroscopy from NIRSPEC with adaptive optics on the Keck telescope. Molecular
hydrogen, H2, is detected in all nine Seyfert 1 galaxies and, in the majority
of galaxies, has a spatially resolved flux distribution. In contrast, the
narrow component of the BrG emission has a distribution consistent with that of
the K-band continuum. In general, the kinematics of H2 are consistent with thin
disk rotation, with a velocity gradient of over 100 km/s measured across the
central 0''.5 in three galaxies, and across the central 1''.5 in two galaxies.
The kinematics of BrG are in agreement with the H2 rotation, except in all four
cases the central 0''.5 is either blue- or redshifted by more than 75 km/s. The
highly ionized gas, measured with the [Ca VIII] and [Si VII] coronal lines, is
spatially and kinematically consistent with BrG in the central 0''.5. Dynamical
models have been fitted to the two-dimensional H2 kinematics, taking into
account the stellar mass distribution, the emission line flux distribution, and
the point spread function. For NGC 3227 the modeling indicates a black hole
mass of Mbh = 2.0{+1.0/-0.4} x 10^7 Msun, and for NGC 4151 Mbh =
3.0{+0.75/-2.2} x 10^7 Msun. In NGC 7469 the best fit model gives Mbh < 5.0 x
10^7 Msun. In all three galaxies, modeling suggests a near face-on disk
inclination angle, which is consistent with the unification theory of active
galaxies. The direct black hole mass estimates verify that masses determined
from the technique of reverberation mapping are accurate to within a factor of
three with no additional systematic errors.Comment: 43 pages, including 47 figures; Accepted for publication in ApJ. All
2-D maps (in high resolution) are available at
http://www.astro.ucla.edu/~ehicks . Minor changes to the text and updated
reverberation mapped black hole mass estimates; the conclusions are unchange