We compare the structure and substructure of dark matter halos in model universes dominated by collisional , strongly self interacting dark matter ( SIDM ) and collisionless , weakly interacting dark matter ( CDM ) . While SIDM virialised halos are more nearly spherical than CDM halos , they can be rotationally flattened by as much as 20 % in their inner regions . Substructure halos suffer ram-pressure truncation and drag which are more rapid and severe than their gravitational counterparts tidal stripping and dynamical friction . Lensing constraints on the size of galactic halos in clusters are a factor of two smaller than predicted by gravitational stripping , and the recent detection of tidal streams of stars escaping from the satellite galaxy Carina suggests that its tidal radius is close to its optical radius of a few hundred parsecs — an order of magnitude smaller than predicted by CDM models but consistent with SIDM . The orbits of SIDM satellites suffer significant velocity bias \sigma _ { { } _ { SIDM } } / \sigma _ { { } _ { CDM } } = 0.85 and are more circular than CDM , \beta _ { { } _ { SIDM } } \approx 0.5 , in agreement with the inferred orbits of the Galaxy ’ s satellites . In the limit of a short mean free path , SIDM halos have singular isothermal density profiles , thus in its simplest incarnation SIDM is inconsistent with galactic rotation curves .