One of the biggest mysteries in modern astrophysics is the appearance and characteristics of the peculiar dark matter (DM) structures. Several relations for DM structures have been identified and are generally accepted as fundamental. Assuming that these relations are valid we will with this work contribute to the continuing unravel of the ’DM mystery’.
Recent numerical simulations show that the angular momentum of DM struc- tures is quite small. We suggest a generalized collisionless Jeans equation (CJE) including a new rotational term, appearing when adding a small bulk rotation to a DM system. This is done under the assumption of a reasonable parameteriza- tion of the distortion of the DM particle ensemble velocity distribution function. Conjecturing that the (new) rotational supplement to the Jeans equation is pro- portional to the (old) mass term, we find analytically a clear connection, which we compare with recent high resolution DM structure simulations. This new suggested relation is shown to be in good agreement with these simulations. We also present a new relation between the velocity anisotropy and the rotation, which is shown to be in fair agreement with numerical findings. The spin pa- rameter arising from the new rotation term in the CJE is shown to increase as a function of radius, in agreement with recent studies.
Furthermore we derive (another) form of the CJE, assuming a general phase space density to be a power law in radius. We write a Monte Carlo code which analyzes recent high resolution simulations to find the most probable values of the unknowns in this new CJE. Using the results from this we show how the form of the general phase space density is closely related to the size of the exponent in the assumed radial dependence. We quantify this via a set of linear relations which are able to reproduce the results of Dehnen & McLaughlin (2005) as a special example. Furthermore these relations are able to predict the radial dependence for various types of phase space densities and suggest that no generally preferred value of the different optimized parameters exist for DM structures. Finally we quantify the outer density slopes in DM structures using this new CJE. We are not able to quantify the inner slopes because of uncertainty in the optimization of some of the unknown parameters.