NGC 1300 Dynamics: I. The gravitational potential as a tool for detailed
  stellar dynamics
  In a series of papers we study the stellar dynamics of the grand design
barred-spiral galaxy NGC~1300. In the first paper of this series we estimate
the gravitational potential and we give it in a form suitable to be used in
dynamical studies. The estimation is done directly from near-infrared
observations. Since the 3D distribution of the luminous matter is unknown, we
construct three different general models for the potential corresponding to
three different assumptions for the geometry of the system, representing
limiting cases. A pure 2D disc, a cylindrical geometry (thick disc) and a third
case, where a spherical geometry is assumed to apply for the major part of the
bar. For the potential of the disc component on the galactic plane a Fourier
decomposition method is used, that allows us to express it as a sum of
trigonometric terms. Both even and odd components are considered, so that the
estimated potential accounts also for the observed asymmetries in the
morphology. For the amplitudes of the trigonometric terms a smoothed cubic
interpolation scheme is used. The total potential in each model may include two
additional terms (Plummer spheres) representing a central mass concentration
and a dark halo component, respectively. In all examined models, the relative
force perturbation points to a strongly nonlinear gravitational field, which
ranges from 0.45 to 0.8 of the axisymmetric background with the pure 2D being
the most nonlinear one. We present the topological distributions of the stable
and unstable Lagrangian points as a function of the pattern speed $(\Omega_p)$.
In all three models there is a range of $\Omega_p$ values, where we find
multiple stationary points whose stability affects the overall dynamics of the
system.
