June 23, 2005
Although N-body studies of dark matter halos show that the density profiles, rho(r), are not simple power-laws, the quantity rho/sigma^3, where sigma(r) is the velocity dispersion, is in fact a featureless power-law over ~3 decades in radius. In the first part of the paper we demonstrate, using the semi-analytic Extended Secondary Infall Model (ESIM), that the nearly scale-free nature of rho/sigma^3 is a robust feature of virialized halos in equilibrium. By examining the processes in common between numerical N-body and semi-analytic approaches, we argue that the scale-free nature of rho/sigma^3 cannot be the result of hierarchical merging, rather it must be an outcome of violent relaxation. The empirical results of the first part of the paper motivate the analytical work of the second part of the paper, where we use rho/sigma^3 proportional to r^{-alpha} as an additional constraint in the isotropic Jeans equation of hydrostatic equilibrium. Our analysis shows that the constrained Jeans equation has different types of solutions, and in particular, it admits a unique ``periodic'' solution with alpha=1.9444. We derive the analytic expression for this density profile, which asymptotes to inner and outer profiles of rho ~ r^{-0.78}, and rho ~ r^{-3.44}, respectively.
Similar papers 1
December 16, 2004
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 investigate the formation and structure of dark matter halos using analytical and semi-analytical techniques. Our halos are formed via an extended secondary infall model (ESIM); they contain secondary perturbations and hence random tangential and ra...
April 8, 2019
It has been known for nearly 20 years that the pseudo phase-space density profile of equilibrium simulated dark matter halos, $\rho(r)/\sigma^3(r)$, is well described by a power law over 3 decades in radius, even though both the density $\rho(r)$, and the velocity dispersion $\sigma(r)$ deviate significantly from power laws. The origin of this scale-free behavior is not understood. It could be an inherent property of self-gravitating collisionless systems, or it could be a me...
June 22, 2005
We investigate, using the spherical Jeans equation, self-gravitating dynamical equilibria satisfying a relation rho/sigma_r^3 propto r^-alpha, which holds for simulated dark-matter haloes over their whole resolved radial range. Considering first the case of velocity isotropy, we find that this problem has only one solution with realistic density profile, which occurs only for a critical value of alpha_crit = 35/18 ~= 1.94, which is consistent with the empirical value of 1.9+/...
October 7, 2008
[abridged] In the dark matter (DM) halos embedding galaxies and galaxy systems the `entropy' K = \sigma^2 / \rho^{2/3} (a quantity that combines the radial velocity dispersion \sigma with the density \rho) is found from intensive N-body simulations to follow a powerlaw run K ~ r^{\alpha} throughout the halos' bulk, with \alpha around 1.25. Taking up from phenomenology just that \alpha ~ const applies, we cut through the rich analytic contents of the Jeans equation describing ...
July 17, 2009
The latest cosmological N-body simulations find two intriguing properties for dark matter haloes: (1) their radial density profile, rho, is better fit by a form that flattens to a constant at the halo center (the Einasto profile) than the widely-used NFW form; (2) the radial profile of the pseudo-phase-space density, rho/sigma3, on the other hand, continues to be well fit by a power law, as seen in earlier lower-resolution simulations. In this paper we use the Jeans equation ...
September 28, 2006
It has long been realized that dark matter halos formed in cosmological N-body simulations are characterized by density profiles rho(r) that, when suitably scaled, have similar shapes. Additionally, combining the density and velocity dispersion profiles sigma(r), each of which have decidedly nonpower-law shapes, leads to quantity rho/(sigma^3) that is a power-law in radius over 3 orders of magnitude in radius. Halos' velocity anisotropy profiles beta(r) vary from isotropic ne...
October 11, 2005
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, $F=\psd \propto r^{-\alpha}$. Understanding this relation will shed light on the physics relevant to collisionless collapse and on the subsequent structures formed. We show that empirical density profiles that provide good fits to N-body halos also happen to have nearly scale-fre...
October 13, 2010
We investigate the dynamical basis of the classic empirical models (specifically, Sersic-Einasto and generalized NFW) that are widely used to describe the distributions of collisionless matter in galaxies. We submit that such a basis is provided by our \alpha-profiles, shown to constitute solutions of the Jeans dynamical equilibrium with physical boundary conditions. We show how to set the parameters of the empirical in terms of the dynamical models; we find the empirical mod...
November 23, 2007
Dark matter (DM) halos formed in CDM cosmologies seem to be characterized by a power law phase-space density profile. The density of the DM halos is often fitted by the NFW profile but a better fit is provided by the Sersic fitting formula. These relations are empirically derived from cosmological simulations of structure formation but have not yet been explained on a first principle basis. Here we solve the Jeans equation under the assumption of a spherical DM halo in dynami...
May 19, 2004
We make a simple analytical study of radial profiles of dark matter structures, with special attention to the question of the central radial density profile. We let our theoretical assumptions be guided by results from numerical simulations, and show that at any radius where both the radial density profile, rho, and the phase-space-like density profile, rho/sigma^epsilon, are exact power laws, the only allowed density slopes in agreement with the spherical symmetric and isotr...