Dark-Matter Halo Profiles of a General Cusp/Core with Analytic Velocity and Potential

TL;DR

This paper introduces flexible, analytic models for dark-matter halo profiles with varying inner slopes, enabling accurate fits to simulations and observations, and facilitating studies of halo evolution and dynamics.

Contribution

The authors develop a family of analytic functions for dark-matter halo profiles with adjustable inner slopes, providing simple expressions for density, potential, and velocity dispersion, and demonstrating their effectiveness in fitting simulation data.

Findings

Excellent fits to cosmological simulation haloes with 3 free parameters.

Analytic potential models match simulation profiles with fewer parameters.

The models enable efficient analysis of rotation curves and halo evolution.

Abstract

We present useful functions for the profiles of dark-matter (DM) haloes with a free inner slope, from cusps to cores, where the profiles of density, mass-velocity and potential are simple analytic expressions. Analytic velocity is obtained by expressing the mean density as a simple functional form, and deriving the local density by differentiation. The function involves four shape parameters, with only two or three free: a concentration parameter $c$, inner and outer asymptotic slopes $\alpha$ and $\bar{\gamma}$, and a middle shape parameter $\beta$. Analytic expressions for the potential and velocity dispersion exist for $\bar{\gamma}=3$ and for $\beta$ a natural number. We match the models to the DM haloes in cosmological simulations, with and without baryons, ranging from steep cusps to flat cores. Excellent fits are obtained with three free parameters ($c$, $\alpha$, $\bar{\gamma}$) and $\beta=2$. For an analytic potential, similar fits are obtained for $\bar{\gamma}=3$ and $\beta=2$ with only two free parameters ($c$, $\alpha$); this is our favorite model. A linear combination of two such profiles, with an additional free concentration parameter, provides excellent fits also for $\beta=1$, where the expressions are simpler. The fit quality is comparable to non-analytic popular models. An analytic potential is useful for modeling the inner-halo evolution due to gas inflows and outflows, studying environmental effects on the outer halo, and generating halo potentials or initial conditions for simulations. The analytic velocity can quantify simulated and observed rotation curves without numerical integrations.