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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

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