The mass of a self-gravitating system like a galaxy can be estimated by measuring the “typical” velocity and assuming that the system is in equilibrium. In the case of a rotating disk, such as the Milky Way, the centrifugal force due to rotation must be balanced by the centripetal force due to gravity. The centrifugal force depends on the rotation velocity (which is measured from the new data from the GAIA mission), and the centripetal force depends on the mass. In this way, by measuring the rotation velocity, one can estimate the mass.
In the solar system, there is a particular simplification: the mass is essentially that of the Sun and is therefore concentrated at the center. In this case, the rotation velocity decreases as the inverse square root of the radius. For example, the Earth rotates at about 30 km/s, while Jupiter rotates at 13 km/s, and Uranus at 7 km/s, etc.
However, in the case of our galaxy (and other galaxies), the situation is less simple because the mass is not concentrated at the center. In this case, the rotation velocity is measured as a function of the distance from the center of the galaxy, and it is observed that it does not decrease with distance as in the case of the solar system. It is necessary to hypothesize a certain distribution of matter and see which one best matches the data. The standard hypothesis is that the galaxy (which, we should remember, is a flat disk that rotates) is immersed in a spherical distribution of non-rotating matter. This is the famous cosmological dark matter, and estimates suggest that, in the case of our galaxy, about ten times more dark matter is required compared to the visible matter.
We have made a different assumption. We assumed that a portion of the matter contributing to the gravitational field is distributed similar to the luminous matter, the hydrogen clouds where stars form and emit radio waves. This matter is thus in a disk. We have calculated whether this model agrees with the data and how much additional matter is needed. As seen in the figure below, the agreement is excellent. The figure shows the data of the rotation curve of the Milky Way, while the solid curve is the DMD model described by a single free parameter, the amount of dark matter. This is only twice that of the visible matter, in contrast to standard models that require at least ten times more. The idea now is to find independent evidence of this dark matter in the disk from other observations, which is not easy but, we hope, not impossible.
Francesco Sylos Labini 