How dark matter halos get their cusps

This seminar derives how dark-matter halo density profiles emerge from hierarchical assembly using the Boltzmann–Poisson equations for a coarse-grained distribution of subhalos in an expanding universe. An exact self-similar solution relates density slope γ to mass growth M proportional to tˢ through γ = 6/(s + 2). Initial collapse gives a prompt γ = 3/2 cusp; hierarchical accretion recovers the Syer–White relation and an attractive n = −2 fixed point with γ = 1; stalled accretion approaches γ = 3. These stages provide a dynamical account of the inner and outer Navarro–Frenk–White profile.