2025/06/02 by Uddipan Banik, A. Bhattacharjee, Amitava Bhattacharjee +2 · 1 voice
Physics and Astronomy · #astro-ph.GA #astro-ph.CO #physics.plasm-ph
paper · pdf · doi:10.48550/arxiv.2506.02104
Collisionless self-gravitating systems such as cold dark matter halos are known to harbor universal density profiles despite the intricate non-linear physics of hierarchical structure formation in the ΛCDM paradigm. The origin of such states has been a persistent mystery, particularly because the physics of collisionless relaxation has remained poorly understood. To solve this long-standing problem, we develop a self-consistent quasilinear theory in action-angle space for the collisionless relaxation of inhomogeneous, self-gravitating systems by perturbing the governing Vlasov-Poisson equations. We obtain a quasilinear diffusion equation that describes the secular evolution of the mean coarse-grained distribution function f0 of accreted matter in the fluctuating force field of a spherical isotropic halo. The diffusion coefficient not only depends on the fluctuation power spectrum but also on the evolving potential of the system, which reflects the self-consistency of the problem. Diffusive heating in the pre-assembled halo develops an r-γ inner density cusp, accretion and relaxation in which develops an r-β outer fall-off with β≈ 5 - 2γ in the quasi-steady state. Spherical collapse theory dictates that a quasi-steady outer halo must settle to β≈ 3, for which the mass enclosed within a shell barely changes with time. This implies that γ≈ 1, which is possible in the quasilinear framework only if (i) the pre-assembled halo harbors an r^-γP profile with γP \gtrsim 0.5, (ii) its fluctuations are correlated in time (red noise), and (iii) the initial value of γ is smaller than 1, implying that the r-1 cusp is a neutral equilibrium. We demonstrate for the first time how the Navarro-Frenk-White (NFW) profile emerges as a quasi-steady state of collisionless relaxation.