Semi-analytical dark matter halos and the Jeans equation
Abstract
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 \sim 3 decades in radius. Here, we demonstrate that this property is common to halos whose collapse and formation is modeled fully with numerical or semi-analytic techniques. Using the Extended Secondary Infall Model (ESIM), we demonstrate that the nearly scale-free nature of \rho/\sigma^3 is a robust feature of virialized halos in equilibrium and one must concoct rather extreme conditions to cause significant deviations from a simple power-law. At present, there are no detailed studies that provide a physical explanation for this behavior. By examining the processes in common between numerical 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. An analytic analysis shows that while the Jeans equation of hydrostatic equilibrium does not isolate a unique value of the power-law index (\rho/\sigma^3\propto r^{-\alpha}), it does point to \alpha=1.9444 as a special solution.Keywords
All Related Versions
This publication has 0 references indexed in Scilit: