A statistical-mechanical explanation of dark matter halo properties

Context. Cosmological N-body simulations have revealed many empirical relationships of dark matter halos, yet the physical origin of these halo properties still remains unclear. On the other hand, the attempts to establish the statistical mechanics for self-gravitating systems have encountered many formal difficulties, and little progress has been made for about fifty years. Aims. The aim of this work is to strengthen the validity of the statistical-mechanical approach we have proposed previously to explain the dark matter halo properties. Methods. By introducing an effective pressure instead of the radial pressure to construct the specific entropy, we use the entropy principle and proceed in a similar way as previously to obtain an entropy stationary equation. Results. An equation of state for equilibrated dark halos is derived from this entropy stationary equation, by which the dark halo density profiles with finite mass can be obtained. We also derive the anisotropy parameter and pseudo-phase-space density profile. All these predictions agree well with numerical simulations in the outer regions of dark halos. Conclusions. Our work provides further support to the idea that statistical mechanics for self-gravitating systems is a viable tool for investigation.