Two Simple Forms of Phase Density and Models of Star Clusters

Extract

Two versions of the restrictions of the phase density are found and studied: when the integral equation for the phase density is reduced to the Abel equation. r₁, λ and α or p are parameters of models. r₁ is the radius of the model; -X is the energy integral; - a half of the angular momentum integral squared; φ(r) is the gravitational potential. The functions ψ(ξ) or f(u) are determined as solutions of the Abel equation, the given functions being the space density, ρ(r), or the potential, φ(r), known from observational data. The observational data have been approximated by two types of models: generalized Schuster models, or two-parametric generalized isochronous models, ρ_o or φ_o where r_o or r_h are scale parameters, β or q and c are structure parameters. Details of the report will be published in Publ. Tartu Astrophys. Obs.48, 1980 and in Astron. Zh. (Moscow)58, 1981.