How can the speed of dark matter be measured? The prerequisite is to find a galaxy in the universe that moves relative to the dark matter. Since everything in the universe is in motion and there is a great deal of dark matter, it is not difficult to find such galaxies.
Heavy objects, like galaxies, attract matter of all kinds, dark matter and also matter we seem to encounter every day. When dark matter moves across a galaxy, the galaxy begins to pull the dark matter particles towards it. But changing the direction of the speed of the dark matter particles takes time. Before their trajectory curves towards the galaxy, they already manage to pass it.
Therefore, the dark matter particles do not enter the galaxy, but move behind it (see video below). Behind the galaxy, therefore, the density of matter increases, and this causes the galaxy to slow down - a phenomenon called dynamical friction. The strength of the dynamical friction depends on the transit speed of the dark matter particles across the galaxy, i.e. how much time the galaxy has to change the trajectory of the dark matter particles. As the particles move slowly, the density of matter increases closer to the galaxy, causing it to slow down more.
Figure 1. Dynamic friction. The panels show sparse regions of the universe in dark color and dense regions in light color. The panels above show the density around the galaxy if the galaxy's gravity bends (left) or does not bend (right) the orbits of the dark matter particles. The panel below shows the difference between them, or how the galaxy affects the distribution of the dark matter. The arrows represent the acceleration caused by the overdensity behind the galaxy, due to which the friction at the center of the galaxy is reduced. Since pressures have different directions and strengths in different regions, tidal forces manage to change the shape of a galaxy. Credit: Rain Kipper
Let's assume that the galaxy that causes the dynamical friction is not small but large. In this case, the overdensity behind it creates friction of different strength at different points in the galaxy as shown in Figure 1. Because of the difference in friction the galaxy is more curved. We experience a similar change in the shape of the Earth as tidal cycles caused by the Moon's gravity.
The size of the dark matter particles is ultimately irrelevant - their orbit still curves behind the galaxy. If the size of the particles were comparable to the galaxies themselves, the method might not have produced accurate results. But these dark matter models are no longer included.