The M-$\sigma$ relation from the disruption of binaries from the galactic bulge

TL;DR

This paper proposes a new explanation for the $M_{ullet}-\sigma$ relation, suggesting that binary disruptions near the galactic center influence the velocity dispersion of the bulge, aligning with observations.

Contribution

It introduces a novel model linking binary disruptions in a triaxial potential to the $M_{ullet}-\sigma$ relation, providing a physical mechanism for this correlation.

Findings

Model agrees with observed $M_{ullet}-\sigma$ relation

Binary disruptions affect bulge velocity dispersion

Energy exchange during disruptions alters galactic core dynamics

Abstract

We present a novel explanation of the well known $M_{\bullet}-\sigma$ relation. In a triaxial potential binaries with chaotic orbits within a sphere that encompass $\sim100$ times the mass of the super-massive black-hole (SMBH) have a finite probability to be tidally disrupted by the SMBH. As a result one component loses energy and might itself break apart tidally and accreted onto the SMBH. More significantly, the other component, which gains energy, returns to the bulge and equilibrates its excess energy with the environment thereby changing the kinetic temperature, hence the velocity dispersion. We develop a mathematical model and find that its results are in agreement with the observed relation.