Dynamical friction of massive objects in galactic centres

TL;DR

This paper improves the modeling of dynamical friction in galactic centers by refining the Coulomb logarithm and incorporating self-consistent velocity distributions, leading to more accurate orbital decay predictions.

Contribution

The authors introduce an improved Coulomb logarithm formula and account for self-consistent velocity distributions, enhancing the accuracy of dynamical friction models in galactic nuclei.

Findings

The improved formula fits N-body simulation results well for various orbits.

Correction factors vary from 0.5 to 3 depending on the orbit and distribution.

The new model can change decay timescales by up to an order of magnitude.

Abstract

Dynamical friction leads to an orbital decay of massive objects like young compact star clusters or Massive Black Holes in central regions of galaxies. The dynamical friction force can be well approximated by Chandrasekhar's standard formula, but recent investigations show, that corrections to the Coulomb logarithm are necessary. With a large set of N-body simulations we show that the improved formula for the Coulomb logarithm fits the orbital decay very well for circular and eccentric orbits. The local scale-length of the background density distribution serves as the maximum impact parameter for a wide range of power-law indices of -1 ... -5. For each type of code the numerical resolution must be compared to the effective minimum impact parameter in order to determine the Coulomb logarithm. We also quantify the correction factors by using self-consistent velocity distribution functions instead of the standard Maxwellian often used. These factors enter directly the decay timescale and cover a range of 0.5 ... 3 for typical orbits. The new Coulomb logarithm combined with self-consistent velocity distribution functions in the Chandrasekhar formula provides a significant improvement of orbital decay times with correction up to one order of magnitude compared to the standard case. We suggest the general use of the improved formula in parameter studies as well as in special applications.