Relationship between rotation curves and matter distribution in spiral galaxy discs

Abstract: Feng & Gallo (2011) developed a numerical method of deriving rotation curves from the density distribution and, in particular, the inverse problem while considering just a self-gravitating disc and the thin disc approximation. Our first aim here is to reproduce the same analysis and expand it with various ideas and examples. The main obstacles to building this numerical implementation are certain singularities. We try to fix the instabilities using different methods. Moreover, we add a final chapter extending the problem and its method to a third dimension through the perpendicular to the galactic plane. The dark halo (whose density is usually represented by a nearby spherical distribution) is supposed to support the outer parts of the rotation curves of spiral galaxies. Here, however, we work only with a self-gravitation disc. To treat this topic we first calculate the disc density distribution from measured rotation curve data of the Milky Way. We then compare this distribution with the observed exponential stellar density, and the difference is attributed to a dark disc. This representation of Feng & Gallo of the Galaxy with a dark disc instead of a dark halo is controversial. When we analyse the effect of flares on rotation curves, the thin disc approximation fails, and we need to introduce a vertical dimension to measure and predict the effects of the flare through different heights. Just by spreading the mass perpendicularly to the plane -- without adding any further mass -- the flare provokes no severe changes on the rotation curve. The flare mainly provokes a faster velocity decrease in the outer part of the Galaxy ($r\gtrsim 14$ kpc). But we also have obtained a slight velocity increase in the first kiloparsecs after the starting point of the flare.