Dark matter seems to interact with normal matter only through gravity, but, based on the way known particles interact, theorists think it’s possible that dark matter might also interact with itself.
If dark matter were to interact with itself (as regular matter does), wouldn't we expect it to clump together and form the same structures as regular matter does, especially given that there's supposed to be much more dark matter to interact together than the regular stuff? AIUI one of the defining features of dark matter is that it doesn't clump together.
Actually dark matter clumps, e.g. so called dark matter halo of a galaxy[1]. It is seen from rotational curves of galaxies and can be also checked with with strong and weak lensing effects [2].
No, dark matter will form halos even if it's interactions are solely gravitational. "Clumping" refers to much stronger concentrations from non-gravitational interactions.
Yes, it is correct that clumping can be solely gravitational effect, though so far we have pretty vague idea about the density in those clumps and halos, which are mostly derived from N-body simulation, which are obviously model dependent, e.g. NFW profile [1]. If dark matter interacts with itself one can expect deviations from purely gravitational description due to dark matter analogues of pressure, temperature, viscosity, etc.
Yes, but this just upper bounds the interaction strength rather than constrains it to be zero. Additionally, if there are multiple species of dark matter, there may be subpopulations (up to 10%, I think) that interact very strongly without conflicting with observation.
If dark matter were to interact with itself (as regular matter does), wouldn't we expect it to clump together and form the same structures as regular matter does, especially given that there's supposed to be much more dark matter to interact together than the regular stuff? AIUI one of the defining features of dark matter is that it doesn't clump together.