SASHIMI-SIDM: Semi-analytical subhalo modelling for self-interacting dark matter at sub-galactic scales

We combine the semi-analytical structure formation model, SASHIMI, which predicts subhalo populations in collisionless, cold dark matter (CDM), with a parametric model that maps CDM halos to self-interacting dark matter (SIDM) halos. The resulting model, SASHIMI-SIDM, generates SIDM subhalo populations down to sub-galactic mass scales, for an arbitrary input cross section, in minutes. We show that SASHIMI-SIDM agrees with SIDM subhalo populations from high-resolution cosmological zoom-in simulations in resolved regimes. Crucially, we predict that the fraction of core-collapsed subhalos peaks at a mass scale determined by the input SIDM cross section and decreases toward higher halo masses, consistent with the predictions of gravothermal models and cosmological simulations. For the first time, we also show that the core-collapsed fraction decreases toward lower halo masses. While the dependence of the collapse time on mass and concentration implies such behaviour, our semi-analytical approach allows us to quantify and illustrate this trend clearly across the full mass spectrum of subhalos, including for subhalo masses below the resolution limit of any current cosmological SIDM simulation. As a proof of principle, we apply SASHIMI-SIDM to predict the boost to the local dark matter density and annihilation rate from core-collapsed SIDM subhalos, which can be enhanced relative to CDM by an order of magnitude for viable SIDM models. Thus, SASHIMI-SIDM provides an efficient and reliable tool for scanning SIDM parameter space and testing it with astrophysical observations. The code is publicly available at https://github.com/shinichiroando/sashimi-si.