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The symmetries and scaling of tidal tails in galaxies

(Abriged) We present analytic models for the formation and evolution of tidal tails and related structures following impulsive disturbances in galaxy collisions. Since the epicyclic approximation is not valid for large radial excursions, we use orbital equations of the form we call p-ellipses. These have been shown to provide accurate representations of orbits in power-law halo potentials. In the case of a purely tidal disturbance the resulting tidal tails have simple structure. Scalings for their maximum lengths and other characteristics as functions of the tidal amplitude and the exponent of the power-law potentials are described. The analytic model shows that azimuthal caustics (orbit crossing zones) are produced generically in these tails at a fixed azimuth relative to the point of closest approach. Long tails, with high order caustics at their base are also produced at larger amplitudes. The analysis is extended to nonlinear disturbances and multiple encounters, which break the symmetries of tidal perturbations. As the strength of the nonlinear terms is varied the structure of the resulting forms varies from symmetric tails to one-armed plumes. Cases with two or more impulse disturbances are also considered as the simplest analytic models distinguishing between prograde and retrograde encounters. A specific mechanism for the formation of tidal dwarf galaxies at the end of tails is suggested as a consequence of resonance effects in prolonged encounters. Qualitative comparisons to Arp Atlas systems suggest that the limiting analytic cases are realized in real systems. We identify a few Arp systems which may have swallowtail caustics, where dissipative gas streams converge and trigger star formation. UV and optical images reveal luminous knots of young stars at these 'hinge clump' locations.