Novel density profile for isothermal cores of dark matter halos

We present a novel analytic density profile for halos in self-interacting dark matter (SIDM) models, which accurately captures the isothermal-core configuration, i.e. where both the density and velocity dispersion profiles exhibit central plateaus in the halo innermost region. Importantly, the profile retains a simple and tractable functional form. We demonstrate analytically how our density profile satisfies the aforementioned conditions, with comparisons to other contemporary functional choices. We further validate the profile using idealized N-body simulations, showing that it provides excellent representations of both the density and velocity dispersion profiles across a broad range of evolutionary stages, from the early thermalization phase to the late core-collapse regime. As a result of its accuracy and simplicity, the proposed profile offers a robust framework for analyzing halo evolution in a variety of SIDM scenarios. It also holds practical utility in reducing simulation needs and in generating initial conditions for simulations targeting the deep core-collapse regime.