I have read through this Wikipedia article on Dark Matter and it contains references to the methods used to demonstrate the existence of dark matter.
A galaxy rotation curve is a plot of the orbital velocities (i.e., the speeds) of visible stars or gas in that galaxy versus their radial distance from that galaxy's center. The rotational/orbital speed of galaxies/stars does not decline with distance, unlike other orbital systems such as stars/planets and planets/moons that also have most of their mass at the centre. In the latter cases, this reflects the mass distributions within those systems. The mass observations for galaxies based on the light that they emit are far too low to explain the velocity observations. The dark matter hypothesis accounts for the missing mass, explaining the anomaly.
My post is not to question anything that the article says, but rather to ask how can we judge the amount of gravitional force exerted by an arbitrary mass of dark matter, if we cannot use light or any other form of em radiation to estimate the volume or density involved?
If gravity is the only force that we can use to detect dark matter, how do we know it couples to ordinary matter with the same strength as ordinary matter does? I am not advancing any particular reason it should not, but would the density of the CDM support this assumption that dark matter attracts ordinary matter to the same degree as ordinary matter does?
Or does it depend on the nature of the particles involved with each particular model of what dark matter is composed of?