Testing the isothermal Jeans model for self-interacting dark matter halos in the collapse phase

We benchmark the semi-analytical isothermal Jeans model against a high-resolution isolated N-body simulation that follows a self-interacting dark matter (SIDM) halo into deep core collapse. The model accurately reproduces the density evolution through much of the collapse phase, although it does not capture the sharp rise in central velocity dispersion during collapse. When applied to strong gravitational lensing observables, such as the projected mass and logarithmic density slope of SIDM halos, the Jeans model tracks the simulated evolution more closely than the parametric approach in the deep collapse regime. Our results demonstrate that the isothermal Jeans model provides a reliable and computationally efficient description of SIDM halo evolution.