Models of Bars with Exponential Density Profiles
  We present a new model for galactic bars with exponentially falling major
axis luminosity profiles and Gaussian cross-sections. This is based on the
linear superposition of Gaussian potential-density pairs with an exponential
weight function, using an extension of the method originally introduced by Long
& Murali (1992). We compute the density, potential and forces, using Gaussian
quadrature. These quantities are given as explicit functions of position. There
are three independent scaled bar parameters that can be varied continuously to
produce bespoke bars of a given mass and shape. We categorise the effective
potential by splitting a reduced parameter space into six regions. Unusually,
we find bars with three stable Lagrange points on the major axis are possible.
Our model reveals a variety of unexpected orbital structure, including a
bifurcating $x_1$ orbit coexisting with a stable $x_4$ orbit. Propeller orbits
are found to play a dominant role in the orbital structure, and we find
striking similarities between our bar configuration and the model of Kaufmann &
Contopoulos (1996). We find a candidate orbital family, sired from the
propeller orbits, that may be responsible for the observed high velocity peaks
in the Milky Way's bar. As a cross-check, we inspect, for the first time, the
proper motions of stars in the high velocity peaks, which also match our
suggested orbital family well. This work adds to the increasing body of
evidence that real galactic bars may be supported at least partly by propeller
orbits rather than solely the $x_1$ family.
