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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 r/s3 r , and a linear b-g relation between the density slope and the velocity anisotropy. We present a family of self-consistent phase-space distribution functions (DFs) F(E, L), based on the Dehnen-McLaughlin Jeans models, that incorporate these universal properties very accurately. These DFs, derived using a quadratic programming technique, are analytical, positive, and smooth over the entire phase space and are able to generate four-parameter velocity anisotropy profiles b(r) with arbitrary asymptotic values b0 and b[?]. We discuss the orbital structure of six radially anisotropic systems in detail and argue that, apart from its use for generating initial conditions for N-body studies, our dynamical modeling provides a valuable complementary approach to understand the processes involved in the formation of dark matter halos.

Abstract: The majority of elliptical galaxies is believed to contain interstellar dust, particularly in the innermost regions. We have investigated the effects of a diffuse dust component on the observed kinematics of spherical galaxies, and modelled dusty observables as if no dust were present. We find that the total mass and the orbital structure of the best fitting models differ considerably from the input models, primarily due to the changes in the observed light profile. We argue that dust should therefore be taken into account in the modelling procedure.

Recently, some intriguing results have led to speculations whether the central density slope-velocity dispersion anisotropy inequality (An & Evans) actually holds at all radii for spherical dynamical systems. We extend these studies by providing a complete analysis of the global slope-anisotropy inequality for all spherical systems in which the augmented density is a separable function of radius and potential. We prove that these systems indeed satisfy the global inequality if their central anisotropy is b0 [?] 1/2. Furthermore, we present several systems with b0>1/2 for which the inequality does not hold, thus demonstrating that the global density slope-anisotropy inequality is not a universal property. This analysis is a significant step toward an understanding of the relation for general spherical systems.