Semi-analytical dark matter halos and the Jeans equation

Although high-resolution N-body simulations make robust empirical predictions for the density distribution within cold dark matter halos, these studies have yielded little physical insight into the origins of the distribution. We investigate the problem using analytic and semi-analytic approaches. Simple analytic considerations suggest that the inner slope of dark matter halos cannot be steeper than alpha=2 (rho ~ r^-alpha), with alpha=1.5-1.7 being a more realistic upper lim...

Cosmological N-body simulations indicate that the spherically-averaged density profiles of cold dark matter halos are accurately described by Einasto profiles, where the logarithmic slope is a power-law of adjustable exponent, \gamma =dln\rho /dlnr ~ r^\alpha $. The pseudo-phase-space density (PPSD) profiles of CDM halos also show remarkable regularity, and are well approximated by simple power laws, Q(r)=\rho /\sigma ^3 ~ r^-\chi . We show that this is expected from dynamica...

The radial mass distribution of dark matter haloes is investigated within the framework of the spherical infall model. We present a new formulation of spherical collapse including non-radial motions, and compare the analytical profiles with a set of high-resolution N-body simulations ranging from galactic to cluster scales. We argue that the dark matter density profile is entirely determined by the initial conditions, which are described by only two parameters: the height of ...

We present density profiles, that are solutions of the spherical Jeans equation, derived under the following two assumptions: (i) the coarse grained phase-density follows a power-law of radius, rho/(sigma^3) proportional to r^{-alpha}, and (ii) the velocity anisotropy parameter is given by the relation beta_a(r) = beta_1 + 2 beta_2 {(r/r_*)/(1+(r/r_*)^2)} where beta_1, beta_2 are parameters and r_* equals twice the virial radius, r_{vir}, of the system. These assumptions are ...

$N$-body simulations have unveiled several apparently universal properties of dark matter halos, including a cusped density profile, a power-law pseudo phase-space density $\rho/\sigma_r^3$, and a linear $\beta-\gamma$ relation between the density slope and the velocity anisotropy. We present a family of self-consistent phase-space distribution functions $F(E,L)$, based on the Dehnen-McLaughlin Jeans models, that incorporate these universal properties very accurately. These d...

We discuss the universal relation between density and size of observed Dark Matter halos that was recently shown to hold on a wide range of scales, from dwarf galaxies to galaxy clusters. Predictions of LambdaCDM N-body simulations are consistent with this relation. We demonstrate that this property of LambdaCDM can be understood analytically in the secondary infall model. Qualitative understanding given by this model provides a new way to predict which deviations from Lambda...

Various analytic expressions have been proposed for the density profile of dark matter halos. We consider six of these expressions for which the density profile has a power-law fall-off rho proportional to r^{-3} at large radii and a power-law cusp rho proportional to r^{-gamma} (gamma=0, 1/2, 1, 3/2) at small radii. The phase-space distribution function for these models is calculated assuming spherical symmetry and either an isotropic velocity dispersion tensor or an anisotr...

(Abridged) We study the outer density profiles of dark matter haloes predicted by a generalized secondary infall model and observed in a N-body cosmological simulation of a \Lambda CDM model. We find substantial systematic variations in shapes and concentrations of the halo profiles as well as a strong correlation of the profiles with the environment. In the N-body simulation, the average outer slope of the density profiles, \beta (\rho\propto r^{-\beta}), of isolated haloes ...

We examine the coarse-grained phase-space density profiles of a set of recent, high-resolution simulations of galaxy-sized Cold Dark Matter (CDM) halos. Over two and a half decades in radius the phase-space density closely follows a power-law, $\rho/\sigma^3 \propto r^{-\alpha}$, with $\alpha = 1.875$. This behaviour matches the self-similar solution obtained by Bertschinger for secondary infall in a uniformly expanding universe. On the other hand, the density profile corresp...

We investigate a hypothesis regarding the origin of the scalelength in halos formed in cosmological N-body simulations. This hypothesis can be viewed as an extension of an earlier idea put forth by Merritt and Aguilar. Our findings suggest that a phenomenon related to the radial orbit instability is present in such halos and is responsible for density profile shapes. This instability sets a scalelength at which the velocity dispersion distribution changes rapidly from isotrop...