Exploring Self-Interacting Dark Matter Halos with Diverse Baryonic Distributions: A Parametric Approach

Galaxies residing in dark matter halos exert significant gravitational effects that alter halo structure and dynamics. The complexity of these interactions escalates with the diversity of galactic structures and the variability in dark matter halo profiles under self-interacting dark matter (SIDM) models. This work extends the parametric model for dark matter-only halos presented in arXiv:2305.16176 to incorporate baryons. We adapt this model to consistently represent the SIDM halo density profile over time, highlighting the role of a gravothermal phase in characterizing the state of an SIDM halo. Given this phase, the density profile in SIDM is determined by a fictitious progenitor -- consisting of an NFW halo influenced by a baryonic potential -- that has evolved to its present state. In the temporal dimension, the model incorporates a form factor that rescales the evolution time in the dark matter-only case, thereby enabling the introduction of a universal phase. In the radial dimension, the halo density profile is parametrized to reflect the influences of baryons. We calibrate the model through N-body simulations with baryon potentials to fit various stellar-to-halo mass ratios and size-mass relationships. Our parametric approach is numerically efficient, enabling the exploration of SIDM effects across a diverse set of halos, as exemplified by a case study using an illustrative sample that spans five orders of magnitude in the mass range. We also demonstrate that the effects of evolution history and the specific SIDM model can be separated from the current states of galaxies and halos, leaving the task of identifying consistent SIDM models to dedicated post-processing analyses.