Is normal matter always accompanied by dark matter and dark matter by normal matter?
Was ever observed effect of gravity lensing without normal matter?
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We lack the precision to say that there aren't regions where there is matter without dark matter or vice-versa. But what is clear is that the ratio of dark matter to normal matter, which is (or needs to be) around 5 on average to explain the flatness of the universe, varies by orders of magnitude from place to place.
The reason for this is that matter interacts with matter in a completely different way to that in which dark matter interacts (weakly) with normal matter or itself by any other means than gravity. Gravitational interactions between normal/dark matter are not dissipative.
By that I mean that the sum of gravitational and kinetic energy is preserved. When normal matter interacts with itself there are normally dissipative consequences. For example, interacting matter may become hot and radiate away energy.
That is why the normal matter in our Milky Way galaxy is concentrated into a plane. Dissipative interactions during the gravitational collapse of our Galaxy, combined with the requirement for conservation of angular momentum result in disc formation. The same is not true for the dark matter associated with the Milky Way, which is expected to have a much more spherical distribution.
Likewise, when we look at the required density profiles of normal and dark matter in order to explain the kinematics of stars and gas in our Milky Way, we see that the normal matter is much more centrally concentrated than is the dark matter - hence we talk about a "dark halo". Again, dissipative interactions in normal matter are the reason.
Another famous example of the separation between dark and normal matter is the bullet cluster. The image below shows where the hot gas is (normal matter, observed by an X-ray telescope) compared to where it is inferred that the dark matter is (shown by contours) on the basis of gravitational lensing. This pair of galaxy clusters have recently interacted, passing through each other. The hot, intracluster gas has been stripped out of the pair and shock-heated, so that it appears concentrated between the two galaxy clusters. The dark matter content of each cluster has sailed on oblivious and remains concentrated around the visible cluster galaxies.
Yet another example would be dwarf spheroidal galaxies, these are relatively small galaxies that are nevertheless almost totally dominated by dark matter - they have mass-to-light ratios of $\sim$1000, compared with a "normal" galaxy, where this ratio might be $\sim$ 10.
There are also examples of dark galaxies. These may not be galaxies made of non-baryonic dark matter, but dark matter in the sense that for whatever reason, these galaxies do not contain many bright stars. Thus although they may be massive, they do not emit much light and contain a lot of "inert", non-starforming gas.
Mass attracts mass, and so dark matter will attract normal matter and vice versa. However, people have looked for "dark lenses", so far without success.
On the other side of the question, normal matter has a chance to cool and thus clump together more densely than is possible for dark matter. Hence, small-scale dense environments are dominated by normal matter.