# Publications

### Liliya L.R. Williams

**Statistical Mechanics of Collisionless Orbits. II. Structure of Halos**Williams, Liliya L. R. & Hjorth, Jens,

*ApJ (2010)*
**Abstract**

In this paper, we present the density, ρ, velocity dispersion, σ, and ρ/σ3 profiles of isotropic systems which have the energy distribution, N(ɛ) vprop [exp(phi0 - ɛ) - 1], derived in Paper I. This distribution, dubbed "DARKexp", is the most probable final state of a collisionless self-gravitating system, which is relaxed in terms of particle energies, but not necessarily in terms of angular momentum. We compare the DARKexp predictions with the results obtained using the extended secondary infall model (ESIM). The ESIM numerical scheme is optimally suited for this purpose because (1) it relaxes only through energy redistribution, leaving shell/particle angular momenta unaltered and (2) being a shell code with radially increasing shell thickness, it has very good mass resolution in the inner halo, where the various theoretical treatments give different predictions. The ESIM halo properties, and especially their energy distributions, are very well fit by DARKexp, implying that the techniques of statistical mechanics can be used to explain the structure of relaxed self-gravitating systems.