2024/11/28 by Uddipan Banik, A. Bhattacharjee, Banik, Uddipan +1
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Astrophysics of Galaxies (astro-ph.GA) #Classical Physics (physics.class-ph) #Cosmology and Gravitation Theories #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #Plasma Physics (physics.plasm-ph) #Statistical Mechanics (cond-mat.stat-mech) #Stellar, planetary, and galactic studies
paper · pdf · doi:10.48550/arxiv.2411.18827
openalex publication_date 2024/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Collisionless self-gravitating systems, e.g., cold dark matter halos, harbor universal density profiles despite the intricate non-linear physics of hierarchical structure formation, the origin of which has been a persistent mystery. To solve this problem, we develop a self-consistent quasilinear theory (QLT) in action-angle space for the collisionless relaxation of driven, inhomogeneous, self-gravitating systems by perturbing the governing Vlasov-Poisson equations. We obtain a quasilinear diffusion equation (QLDE) for the secular evolution of the mean distribution function f0 of a halo due to linear fluctuations (induced by random perturbations in the force field) that are collectively dressed by self-gravity, a phenomenon described by the response matrix. Unlike previous studies, we treat collective dressing up to all orders. Well-known halo density profiles ρ(r) commonly observed in N-body simulations, including the r-1 NFW cusp, an Einasto central core, and the r-1.5 prompt cusp, emerge as quasi-steady state attractor solutions of the QLDE. The r-1 cusp is a constant flux steady-state solution for a constantly accreting massive halo perturbed by small-scale white noise fluctuations induced by substructure. It is an outcome of the universal nature of collisionless relaxation: lower energy particles attract more particles, gain higher effective mass and get less accelerated by the fluctuating force field. The zero-flux steady state solution for an isolated halo is an f0 that is flat in energy, and the corresponding ρ(r) can either be cored or an r-1.5 cusp depending on the inner boundary condition. The latter forms around a central dense object, e.g., a compact subhalo or a black hole. We demonstrate for the first time that these halo profiles emerge as quasi-steady state attractors of collisionless relaxation described by a self-consistent QLT.