We perform high-resolution simulations of an MW-like galaxy in a self-interacting cold dark matter model with elastic cross-section over mass of 1 cm2 g−1 (SIDM) and compare to a model without self-interactions (CDM). We run our simulations with and without a time-dependent embedded potential to capture effects of the baryonic disc and bulge contributions. The CDM and SIDM simulations with the embedded baryonic potential exhibit remarkably similar host halo profiles, subhalo abundances, and radial distributions within the virial radius. The SIDM host halo is denser in the centre than the CDM host and has no discernible core, in sharp contrast to the case without the baryonic potential (core size ∼7 kpc). The most massive subhaloes (with Vpeak > 20 km s−1) in our SIDM simulations, expected to host the classical satellite galaxies, have density profiles that are less dense than their CDM analogues at radii less than 500 pc but the deviation diminishes for less massive subhaloes. With the baryonic potential included in the CDM and SIDM simulations, the most massive subhaloes do not display the too-big-to-fail problem. However, the least dense among the massive subhaloes in both these simulations tend to have the smallest pericenter values, a trend that is not apparent among the bright MW satellite galaxies.

We present a suite of baryonic cosmological zoom-in simulations of self-interacting dark matter (SIDM) haloes within the 'Feedback In Realistic Environment' (FIRE) project. The three simulated haloes have virial masses of ∼ 1012 M⊙ at z = 0, and we study velocity-independent self-interaction cross sections of 1 and 10 cm2, g-1. We study star formation rates and the shape of dark matter density profiles of the parent haloes in both cold dark matter (CDM) and SIDM models. Galaxies formed in the SIDM haloes have higher star formation rates at z ≤ 1, resulting in more massive galaxies compared to the CDM simulations. While both CDM and SIDM simulations show diverse shape of the dark matter density profiles, the SIDM haloes can reach higher and more steep central densities within few kpcs compared to the CDM haloes. We identify a correlation between the build-up of the stars within the half-mass radii of the galaxies and the growth in the central dark matter densities. The thermalization process in the SIDM haloes is enhanced in the presence of a dense stellar component. Hence, SIDM haloes with highly concentrated baryonic profiles are predicted to have higher central dark matter densities than the CDM haloes. Overall, the SIDM haloes are more responsive to the presence of a massive baryonic distribution than their CDM counterparts.