Models of Bars I: Flattish Profiles for Early-Type Galaxies
  We introduce a simple family of barred galaxy models with flat rotation
curves. They are built by convolving the axisymmetric logarithmic model with a
needle density. The density contours in the bar region are highly triaxial and
elongated, but become spheroidal in the outer parts. The mass distribution
differs markedly from the elliptical shape assumed in other analytical models,
like Ferrers or Freeman bars. The surface density profile along the bar major
axis is flattish, as befits models for bars in early-type galaxies (SB0, SBa).
The two-dimensional orbital structure of the models is analysed with surfaces
of section and characteristic diagrams and it reveals qualitatively new
features. For some pattern speeds, additional Lagrange points can exist along
the major axis, and give rise to off-centered, trapped orbits. When the bar is
weak, the orbital structure is very simple, comprising just prograde, aligned
$x_1$ orbits and retrograde anti-aligned $x_4$ orbits. As the bar strength
increases, the $x_1$ family becomes unstable and vanishes, with propeller
orbits dominating the characteristic diagram.
