  We present a new set of cosmological zoom-in simulations of a MW-like galaxy
which for the first time include elastic velocity-dependent self interacting
dark matter (SIDM) and IllustrisTNG physics. With these simulations we
investigate the interaction between SIDM and baryons and its effects on the
galaxy evolution process. We also introduce a novel set of modified DMO
simulations which can reasonably replicate the effects of fully realized
hydrodynamics on the DM halo while simplifying the analysis and lowering the
computational cost. We find that baryons change the thermal structure of the
central region of the halo to a greater extent than the SIDM scatterings for
MW-like galaxies. Additionally, we find that the new thermal structure of the
MW-like halo causes SIDM to create cuspier central densities rather than cores
because the SIDM scatterings remove the thermal support by transferring heat
away from the center of the galaxy. We find that this effect, caused by baryon
contraction, begins to affect galaxies with a stellar mass of $10^8$ M$_\odot$
and increases in strength to the MW-mass scale. This implies that any
simulations used to constrain the SIDM cross sections for galaxies with stellar
masses between $10^8$ and at least $10^{11}$ M$_\odot$ will require baryons to
make accurate predictions.
