The nature of the dark matter that binds galaxies remains an open question. The favored candidate has been so far the neutralino. This massive species with evanescent interactions is now in difficulty. It would actually collapse in dense clumps and would therefore play havoc with the matter it is supposed to shepherd. We focus here on a massive and non-interacting charged scalar field as an alternate option to the astronomical missing mass. We investigate the classical solutions that describe the Bose condensate of such a field in gravitational interaction with matter. This simplistic model accounts quite well for the dark matter inside low-luminosity spirals whereas the agreement lessens for the brightest objects where baryons dominate. A scalar mass m=0.4 to 1.6 10^{-23} eV is derived when both high and low-luminosity spirals are fitted at the same time. Comparison with astronomical observations is made quantitative through a chi-squared analysis. We conclude that scalar fields offer a promising direction worth being explored.

16 pages, 5 figures