A convergent kinetic theory of collisional star clusters (i) a self-consistent 'truncated' mean-field acceleration of stars

Abstract

Fundamental relaxation processes in the secular evolution of a collisional star cluster of $N$-'point' stars have been conventionally discussed based on either of collision kinetic theory (for strong two-body encounters) and wave one (for statistical acceleration and gravitational polarization). If combining the both theories together, one must introduce a self-consistent 'truncated' Newtonian mean-field (m.f.) acceleration of star at position $r$ and time $t$ due to a phase-space distribution function $f\left(r^{\prime },p^{\prime },t\right)$ for stars $A^{△}(r,t)=-Gm\left(1-\frac{1}{N}\right){\int }_{\mid r-r^{\prime }\mid >△}\frac{r-r^{\prime }}{\mid r-r^{\prime }{\mid }^3}f\left(r^{\prime },p^{\prime },t\right){\text{d}}^3{r}^{\prime }{\text{d}}^3{p}^{\prime },$ where $G$ is the gravitational constant and $m$ the mass of stars. The lower limit $△$ of the distance between two stars is order of the Landau distance. The truncated m.f. acceleration is a necessary consequence due to the strong encounters and m.f. acceleration being not able to 'coexist' at specific distance between stars. The present paper aims at initiating a star-cluster convergent kinetic theory to self-consistently derive kinetic equations of star clusters, mathematically non-divergent in distance- and wavenumber- spaces based on the truncated m.f. acceleration, correct at time scales of the secular evolution. This will be achieved by focusing on mathematical formulations of the Kandrup's generalised-Landau equation including the effect of the strong encounters and by extending the Grad's truncated distribution function and Klimontovich's theory of non-ideal systems.

References in corpus (1)

• Three-dimensional Fourier transforms, integrals of spherical Bessel functions, and novel delta function identities

Cited by in corpus (1)

• Self-similar orbit-averaged Fokker-Planck equation for isotropic spherical dense clusters (i) accurate pre-collapse solution