Effect of multiplicity of stellar encounters and the diffusion coefficients in the uniform stellar medium: no classical divergence ?

TL;DR

This paper demonstrates that by incorporating the Agekyan lambda-factor for multiple stellar encounters, the classical logarithmic divergence in diffusion coefficients in stellar systems is resolved, leading to finite and physically meaningful results.

Contribution

It introduces the use of the Agekyan lambda-factor to compute diffusion coefficients, eliminating the classical divergence in the velocity space of stellar systems.

Findings

The cumulative effect of distant encounters is finite.

Classical logarithmic divergence in diffusion coefficients is removed.

Formulas now contain a meaningful scale ratio without divergence.

Abstract

Agekyan lambda-factor that accounts for the effect of multiple distant encounters with large impact factors is used for the first time to compute the diffusion coefficients in the velocity space of a stellar system. It is shown that in this case the cumulative effect - the total contribution of distant encounters to the change in the velocity of the test star - is finite, and the logarithmic divergence inherent to the classical description disappears, as also was earlier noted by Kandrup (1981). At the same time, the formulas for the diffusion coefficients, as before, contain the logarithm of the ratio of two independent scale factors that fully characterize the state of the stellar system: the average interparticle distance and the impact parameter of a close encounter. However, the physical meaning of this factor is no longer associated with the classical logarithmic divergence.