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This is the second paper of a series of our works on the self-similarorbit-averaged Fokker-Planck (OAFP) equation and details physical properties ofisotropic pre-collapse solution. The fundamental core collapse process at thelate stage of relaxation evolution of spherical star clusters can be describedby the self-similar OAFP equation. The accurate spectral solution was foundrecently in the first paper. The present work details the thermodynamic aspectsof the model based on the stellar DF obtained from the solution. Ourcalculation shows the following local properties (i) Equation of state is$p=1.0\rho/\chi_\text{esc}$ in the core where $p$ is the pressure, $\rho$ thedensity and $\chi_\text{esc}$ the scaled escape energy, while it is$p=0.5\rho^{1.1}/\chi_\text{esc}$ at large radii. (ii) If we consider thecenter of the core is polytropic, the polytropic index is 177. Also, as aglobal property we construct caloric curves of the model to discuss the heatcapacity together with Virial. Special focus is the cause of negative heatcapacity of the core; the well-relaxed core can be directly compared to theisothermal sphere with positive heat capacity. Comparing our results to theprevious works, we conclude, in the self-similar evolution, the negative heatcapacity in the core holds due to collisionless and high-temperature stars thatexperience a rapid change in mean field potential through stellar- and heat-flows, rather than due to the (quasi-)isolation of the core from surroundings.

Self-similar orbit-averaged Fokker-Planck equation for isotropic  spherical dense clusters (ii) physical properties and negative heat capacity  of pre-collapse core