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We describe how a simple class of out of equilibrium, rotating andasymmetrical mass distributions evolve under their self-gravity to produce aquasi-planar spiral structure surrounding a virialized core, qualitativelyresembling a spiral galaxy. The spiral structure is transient, but can survivetens of dynamical times, and further reproduces qualitatively noted features ofspiral galaxies as the predominance of trailing two-armed spirals and largepitch angles. As our models are highly idealized, a detailed comparison withobservations is not appropriate, but generic features of the velocitydistributions can be identified to be potential observational signatures ofsuch a mechanism. Indeed, the mechanism leads generically to a characteristictransition from predominantly rotational motion, in a region outside the core,to radial ballistic motion in the outermost parts. Such radial motions areexcluded in our Galaxy up to 15 kpc, but could be detected at larger scales inthe future by GAIA. We explore the apparent motions seen by external observersof the velocity distributions of our toy galaxies, and find that it isdifficult to distinguish them from those of a rotating disc with sub-dominantradial motions at levels typically inferred from observations. These simplemodels illustrate the possibility that the observed apparent motions of spiralgalaxies might be explained by non-trivial non-stationary mass and velocitydistributions without invoking a dark matter halo or modification of Newtoniangravity. In this scenario the observed phenomenological relation between thecentripetal and gravitational acceleration of the visible baryonic mass couldhave a simple explanation.

Transient spiral arms from far out of equilibrium gravitational evolution