We perform high-resolution simulations of a MW-like galaxy in a self-interacting cold dark matter model with elastic cross section over mass of 1 ~ { } cm ^ { 2 } / g ( 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 disk 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 center than the CDM host and has no discernible core , in sharp contrast to the case without the baryonic potential ( core size \sim 7 kpc ) .
The most massive subhalos ( with V _ { \mathrm { peak } } > 20 km / s ) in our SIDM simulations , expected to host the classical satellite galaxies , have density profiles that are less dense than their CDM analogs at radii less than 500 pc but the deviation diminishes for less massive subhalos .
With the baryonic potential included in the CDM and SIDM simulations , the most massive subhalos do not display the too-big-to-fail problem .
However , the least dense among the massive subhalos in both these simulations tend to have the smallest pericenter values , a trend that is not apparent among the bright MW satellite galaxies .