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.