http://arxiv.org/abs/1904.03772
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 a dynamical attractor that represents an emergent property of self-gravitating collisionless systems, or it could be a mere coincidence. To address the question we work with the second derivative of the Jean’s equation, which, under the assumptions of (i) Einasto density profile, (ii) linear velocity anisotropy – density slope relation, and (iii) $\rho/\sigma^3\propto r^{-\alpha}$, can be transformed from a differential equation to a cubic algebraic equation. Relations (i)-(iii) are all observed in numerical simulations, and are well parametrized by a total of 4 or 6 model parameters. Taking advantage of the fact that the algebraic Jean’s equation puts relations (i)-(iii) on the same footing, we study the (approximate) solutions of this equation in the 4 and 6 dimensional spaces. We argue that the distribution of best solutions in these parameter spaces is inconsistent with $\rho/\sigma^3\propto r^{-\alpha}$ being an attractor, and conclude that the scale-free nature of this quantity is likely to be a fluke.
A. Arora and L. Williams
Tue, 9 Apr 19
13/105
Comments: 16 pages, 6 figures and 1 table
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