CROCODILE-SIDM: Tidal Formation of Dark Matter-Deficient Galaxies as a Test Case

Abstract: We introduce CROCODILE-SIDM, a framework for treating self-interacting dark matter (SIDM) with the $N$-body part of GADGET4-Osaka code, as part of CROCODILE simulation family. As a test case, we investigate the impact of SIDM on the tidal formation of dark matter-deficient galaxies (DMDGs) with velocity-dependent cross-section models. We demonstrate that our implementation reproduces the analytic scattering rate in isolated halos. Including dynamical friction self-consistently, we evolve a dwarf satellite with $M_*=2\times10<sup>8\,\mathrm{M}_\odot$ in a $\sim10<sup>{11}\,\mathrm{M}_\odot$ halo on a decaying orbit around a massive host, comparing CDM with four SIDM cross sections for two initial satellite density profiles: a cuspy Navarro--Frenk--White (NFW) profile and a cored Burkert profile. We find that self-interactions primarily regulate the amount of DM retained between pericentric passages, and that the sign of this effect depends on the initial profile: a larger cross section retains more DM for the Burkert initial condition but less DM for the NFW initial condition. We show that this opposing behavior reflects the direction of SIDM heat conduction, which is set by the halo's evolutionary state at infall. Core formation in the cuspy profile assists DM stripping, whereas tidally accelerated gravothermal contraction in the cored profile suppresses tidal mass loss. Consequently, SIDM can either assist or hinder DMDG formation, depending on the satellite's inner structure, making DMDGs a potential probe of SIDM cross section.