Topic: self-similar solution

Uddipan Banik derives a dynamical account of dark-matter halo density profiles using the Boltzmann–Poisson equations for an expanding Universe populated by subhalos of many masses. A self-similar solution links density slope to halo mass growth; including gravitational scattering and subhalo capture gives gamma = 6/(s + 2). Initial collapse with s = 2 produces a prompt cusp of slope 3/2. Hierarchical growth connects the slope to the primordial power spectrum and recovers the Syer–White relation during matter domination. Stable clustering selects an inner Navarro–Frenk–White cusp of slope one,

This talk derives dark-matter halo profiles from their assembly using a coarse-grained Boltzmann–Poisson treatment with a continuous subhalo population. A self-similar solution connects mass-growth rate to density slope, including gravitational scattering and capture. Initial collapse produces a three-halves cusp; hierarchical accretion and stable clustering favour the inner NFW slope; stalled growth approaches its outer slope. The framework ties these familiar profiles to successive dynamical stages rather than imposing them phenomenologically.