  We propose a simple geometrical mechanism for the flattening of galactic rotation curves, the local compression of field lines around their planes induced either by the presence of thin string-like objects at the centers of galaxies or by elongated dark-matter halos, and elaborate on its possible role in Nature. We fit 83 rotation curves from the SPARC database with logarithmic potentials produced by a thin "wire" at the origin and then, after selecting 2 galaxies that yield the most interesting fits, analyze them with an alternative model, deformed versions of two popular models of dark-matter halos. Our conclusion is that the presence of a filament clearly improves the fit quality in a number of cases, while bulged dark matter profiles have a lesser effect. If taken at face value, these results would imply the presence of elongated mass distributions away from the galactic plane in a number of galaxies, and may also have some indirect impact on the controversy between cold dark matter (CDM), self-interacting dark matter (SiDM), and modified Newtonian dynamics (MOND). 
On Filaments, Prolate Halos and Rotation Curves