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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].

[1] https://en.wikipedia.org/wiki/Dark_matter_halo

[2] https://en.wikipedia.org/wiki/Gravitational_lens

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.

[1] https://en.wikipedia.org/wiki/Navarro%E2%80%93Frenk%E2%80%93...

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