The contribution of the dark matter to the rotation of spiral galaxies and its mass distribution

The rotation of a test spiral galaxy with two contributors - the disc and the corona - is considered. The disc is exponential, whereas the corona is the dark subsystem. For the latter several variants of mass distribution are considered. It is found that the homogeneous sphere is almost unavoidable if the circular velocity has a continuous increase, at least in its observable part. On the other hand the rather often applied quasi-isothermal law offers the most satisfactory fit for the case of constant circular velocity though the classical Schuster law may also be used, especially taking into account its simplicity and the consequent possibility of generalising its potential towards the more general case of axial symmetry