We present a novel analytic density profile for halos in self-interacting dark matter 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 self-interacting dark matter scenarios. It also holds practical utility in reducing simulation needs and in generating initial conditions for simulations targeting the deep core-collapse regime.

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• Dark matter
• Evolution of the Universe
• Large scale structure of the Universe