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Analytic gas orbits in an arbitrary rotating galactic potential using the linear epicyclic approximation

A code, Epic5, has been developed which computes, in the two-dimensional case, the initially circular orbits of guiding centra in an arbitrary axisymmetric potential with an arbitrary, weak perturbing potential in solid body rotation. This perturbing potential is given by its Fourier expansion. The analytic solution solves the linear epicyclic approximation of the equations of motion. To simulate the motion of interstellar matter and to damp the Lindblad resonances, we have in these equations introduced a friction which is proportional to the deviation from circular velocity. The corotation resonance is also damped by a special parameter. The program produces, in just a few seconds, orbital and density maps, as well as line of sight velocity maps for a chosen orientation of the galaxy. We test Epic5 by comparing its results with previous simulations and observations from the literature, which gives satisfactory agreement. The aim is that this program should be a useful complement to elaborate numerical simulations. Particularly so are its abilities to quickly explore the parameter space, to construct artificial galaxies, and to isolate various single agents important for developing structure of interstellar matter in disc galaxies.