We use high-resolution hydrodynamical simulation to test the difference of halo properties in cold dark matter ( CDM ) and a self-interacting dark matter ( SIDM ) scenario with a constant cross-section of \sigma ^ { \text { T } } / m _ { \chi } = 1 \text { cm } ^ { 2 } \text { g } ^ { -1 } .
We find that the interplay between dark matter self-interaction and baryonic physics induces a complex evolution of the halo properties , which depends on the halo mass and morphological type , as well as on the halo mass accretion history .
While high mass haloes , selected as analogues of early-type galaxies , show cored profiles in the SIDM run , systems of intermediate mass and with a significant disk component can develop a profile that is similar or cuspier than in CDM .
The final properties of SIDM haloes – measured at z = 0.2 – correlate with the halo concentration and formation time , suggesting that the differences between different systems are due to the fact that we are observing the impact of self-interaction .
We also search for signatures of self-interacting dark matter in the lensing signal of the main haloes and find hints of potential differences in the distribution of Einstein radii , which suggests that future wide-field survey might be able to distinguish between CDM and SIDM models on this basis .
Finally , we find that the subhalo abundances are not altered in the adopted SIDM model with respect to CDM .