Wandering of the central black hole in a galactic nucleus and correlation of the black hole mass with the bulge mass

TL;DR

This paper explores how super-massive black holes can wander within galactic nuclei due to gravitational interactions and dynamical friction, and how this wandering influences the correlation between black hole and bulge mass.

Contribution

It introduces a model for black hole wandering driven by gravitational attraction and dynamical friction, explaining the observed black hole-bulge mass correlation.

Findings

Black hole wandering distance can reach several 10 pc for smaller masses.

An upper mass limit exists beyond which black holes spiral inward.

The upper mass limit scales with the bulge mass, explaining observed correlations.

Abstract

We investigate a mechanism for a super-massive black hole at the center of a galaxy to wander in the nucleus region. A situation is supposed in which the central black hole tends to move by the gravitational attractions from the nearby molecular clouds in a nuclear bulge but is braked via the dynamical frictions by the ambient stars there. We estimate the approximate kinetic energy of the black hole in an equilibrium between the energy gain rate through the gravitational attractions and the energy loss rate through the dynamical frictions, in a nuclear bulge composed of a nuclear stellar disk and a nuclear stellar cluster as observed from our Galaxy. The wandering distance of the black hole in the gravitational potential of the nuclear bulge is evaluated to get as large as several 10 pc, when the black hole mass is relatively small. The distance, however, shrinks as the black hole mass increases and the equilibrium solution between the energy gain and loss disappears when the black hole mass exceeds an upper limit. As a result, we can expect the following scenario for the evolution of the black hole mass: When the black hole mass is smaller than the upper limit, mass accretion of the interstellar matter in the circum-nuclear region, causing the AGN activities, makes the black hole mass larger. However, when the mass gets to the upper limit, the black hole loses the balancing force against the dynamical friction and starts spiraling downward to the gravity center. From simple parameter scaling, the upper mass limit of the black hole is found to be proportional to the bulge mass and this could explain the observed correlation of the black hole mass with the bulge mass.