Dynamical Friction around Supermassive Black Holes

TL;DR

This paper investigates dynamical friction near supermassive black holes, showing that including fast-moving stars and stellar distribution changes improves predictions of orbital decay rates, with implications for black hole populations and galactic nuclei.

Contribution

It refines Chandrasekhar's dynamical friction theory by incorporating fast stars and stellar distribution effects, providing more accurate decay rate predictions near SMBHs.

Findings

Fast-moving stars contribute significantly to dynamical friction.

Orbital decay rates are lower than traditional Chandrasekhar predictions.

Black hole densities remain low near galactic centers over billions of years.

Abstract

The density of stars in galactic bulges is often observed to be flat or slowly rising inside the influence radius of the supermassive black hole (SMBH). Attributing the dynamical friction force to stars moving more slowly than the test body, as is commonly done, is likely to be a poor approximation in such a core since there are no stars moving more slowly than the local circular velocity. We have tested this prediction using large-scale N-body experiments. The rate of orbital decay never drops precisely to zero, because stars moving faster than the test body also contribute to the frictional force. When the contribution from the fast-moving stars is included in the expression for the dynamical friction force, and the changes induced by the massive body on the stellar distribution are taken into account, Chandrasekhar's theory is found to reproduce the rate of orbital decay remarkably well. However, this rate is still substantially smaller than the rate predicted by Chandrasekhar's formula in its most widely-used forms, implying longer time scales for inspiral. Motivated by recent observations that suggest a parsec-scale core around the Galactic center SMBH, we investigate the evolution of a population of stellar-mass black holes (BHs) as they spiral in to the center of the Galaxy. After ~10Gyr, we find that the density of BHs can remain substantially less than the density in stars at all radii; we conclude that it would be unjustified to assume that the spatial distribution of BHs at the Galactic center is well described by steady-state models. One consequence is that rates of capture of BHs by the SMBH at the Galactic center (EMRIs) may be much lower than in standard models. We finally study the orbital decay of satellite galaxies into the central region of giant ellipticals and discuss the formation of multiple nuclei and multiplet of black holes in such systems.