http://arxiv.org/abs/2003.13179
This is the second paper of a series of our works on the isotropic self-similar orbit-averaged Fokker-Planck (OAFP) equation and details physical properties of pre-collapse solution. The fundamental core collapse process at the late stage of relaxation evolution of spherical star clusters can be described by the self-similar OAFP equation. The accurate spectral solution was found recently in the first paper. The present work details the thermodynamical aspects of the model based on the stellar DF obtained from the solution. Our calculation shows the following local properties (i) Equation of state in the core is local ideal gas $p=1.0\rho/\chi_\text{esc}$ where the $p$ is the pressure, $\rho$ density and $\chi_\text{esc}$ the scaled escape energy, while it is polytropic $p=0.5\rho^\Gamma/\chi_\text{esc}$ at large radii where $\Gamma$ is the adiabatic index. (ii) If we consider the center is polytropic sphere, the polytropic index is 177. Also, as global property we construct caloric curves of the model to discuss the heat capacity together with Virial. Special focus is the cause of negative heat capacity of the core; the negativity is directly related to the deep potential well or large scaled escape energy through the criterion condition $\phi=-6/\chi_\text{esc}$ where $\phi$ is the central mean field potential in a well-relaxed core. Comparing our results to the previous works, we conclude, in the self-similar evolution, the negative heat capacity in the core holds due to collisionless and high-temperature stars that experience a rapid change in mean field potential through stellar- and heat- flow, rather than the isolation from surroundings due to self-gravity.
Y. Ito
Tue, 31 Mar 20
79/94
Comments: N/A