The central densities of Milky Way-mass galaxies in cold and self-interacting dark matter models

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 $\sim 10^{12}\, \text{M}_\odot$ at $z=0$, and we study velocity-independent self-interaction cross sections of 1 and 10 ${\rm cm^2 \, g^{-1}}$. 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 $z\leq1$, 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.