Bypassed Core Formation in Milky Way-Mass SIDM Halos: Implications for the Local Group Past-Pericenter Scenario

We consider a scenario in which the Milky Way (MW) and M31 have had a previous pericentric passage, and investigate its compatibility with self-interacting dark matter (SIDM). Using initial conditions sampled from Local Group (LG) analogues in the IllustrisTNG simulation, we perform controlled re-simulations of the MW-M31 orbit, evolving the system under both standard cold dark matter (CDM) and various SIDM cross-sections. We find that the deep baryonic potential of the MW preconditions the halo's thermal structure, establishing an initial negative temperature gradient. This drives SIDM halos to bypass the standard core-formation phase and enter immediate core-collapse, resulting in monotonically increasing central densities. In full orbital simulations, the compact stellar component (disk/bulge) of the MW analog remains robust against tidal disruption for pericenter distances as close as $r_{\rm peri}\lesssim20$ kpc during an encounter at cosmic time $\sim8$ Gyr. The diffuse stellar halo is comparatively more susceptible, facing disruption for $r_{\rm peri}\lesssim100$ kpc. Our results demonstrate a dichotomy in structural evolution: the compact disk/bulge is sensitive to intrinsic SIDM thermodynamics but dynamically robust against the pericenter encounter, whereas the diffuse stellar halo is largely independent of the specific SIDM model but more vulnerable to orbital tidal disruptions.