Related papers: Statistical mechanics of collisionless orbits. II.…
We present an equilibrium statistical mechanical theory of collisionless self-gravitational systems with isotropic velocity distributions. Compared to existing standard theories, we introduce two changes: (1) the number of possible…
We compare the DARKexp differential energy distribution, N(E) \propto \exp(\phi_0-E)-1, obtained from statistical mechanical considerations, to the results of N-body simulations of dark matter halos. We first demonstrate that if DARKexp…
It has been shown in previous work that DARKexp, which is a theoretically derived, maximum entropy, one shape parameter model for isotropic collisionless systems, provides very good fits to simulated and observed dark-matter halos.…
Self-gravitating Newtonian systems consisting of a very large number of particles have generally defied attempts to describe them using statistical mechanics. This is paradoxical since many astronomical systems, or simulations thereof,…
We investigate the connection between collisionless equilibria and the phase-space relation between density $\rho$ and velocity dispersion $\sigma$ found in simulations of dark matter halo formation, $F=\psd \propto r^{-\alpha}$.…
We test the DARKexp model for relaxed, self-gravitating, collisionless systems against equilibrium dark matter halos from the Millennium-II simulation. While limited tests of DARKexp against simulations and observations have been carried…
High resolution N-body simulations have all but converged on a common empirical form for the shape of the density profiles of halos, but the full understanding of the underlying physics of halo formation has eluded them so far. We…
Dark matter (DM) halos simulated via N-body techniques are known to exhibit nearly universal profiles at equilibrium; however, their origin remains uncertain despite thorough investigation. This work aims to probe the origin of simulated DM…
In the DARKexp framework for collisionless isotropic relaxation of self--gravitating matter, the central object is the differential energy distribution $n(E)$, which takes a maximum--entropy form proportional to $\exp[-\beta(E - \Phi(0))] -…
In the framework of nonextensive statistical mechanics, the equilibrium structures of astrophysical self-gravitating systems are stellar polytropes, parameterized by the polytropic index n. By careful comparison to the structures of…
For a spherical dark matter halo with isotropic velocity distribution, the phase space distribution function (DF), the energy distribution, and the density profile form a set of self-consistent description of its equilibrium state, and…
We study, using both theory and simulations, a system of self-gravitating sheets. A new statistical mechanics theory - free of any adjustable parameters - is derived to quantitatively predict the final stationary state achieved by this…
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 $\Lambda$CDM paradigm. The origin of…
Cosmological N-body simulations have revealed many empirical relationships of dark matter halos, yet the physical origin of these halo properties still remains unclear. On the other hand, the attempts to establish the statistical mechanics…
Dark-matter halos grown in cosmological simulations appear to have central NFW-like density cusps with mean values of $d\log\rho/d\log r \approx -1$, and some dispersion, which is generally parametrized by the varying index $\alpha$ in the…
The shapes of individual self-gravitating structures of an ensemble of identical, collisionless particles have remained elusive for decades. In particular, a reason why mass density profiles like the Navarro-Frenk-White or the Einasto…
In the present paper, we improve the "Extended Secondary Infall Model" (ESIM) of Williams et al. (2004) to obtain further insights on the cusp/core problem. The model takes into account the effect of ordered and random angular momentum,…
We study analytically the coarse and fine-grained distribution function established by the self-similar infall of collisionless matter. We find this function explicitly for isotropic and spherically symmetric systems in terms of…
We test the Secondary Infall Model (SIM) by direct comparison with the results of N-body simulations. Eight cluster-size and six galactic-size dark matter haloes have been selected at $z=0$ and re-simulated with high resolution. Based on…
We present an analytical and numerical study of the velocity distribution function of self gravitating collisionless particles, which include dark matter and star clusters. We show that the velocity distribution derived through the…