The M-Sigma Relation Derived from Sphere of Influence Arguments

TL;DR

This paper investigates how the observed correlation between supermassive black hole mass and galaxy velocity dispersion might be influenced by observational resolution limits, suggesting the relation could be an upper limit rather than a fundamental law.

Contribution

It demonstrates that the M-Sigma relation can arise from spatial resolution effects and proposes it may serve as an upper limit, offering new insights into galaxy and SMBH formation.

Findings

The M-Sigma relation can result from spatial resolution constraints.

Random SMBH masses can produce a similar M-Sigma relation.

The observed relation may be an upper limit rather than a fundamental correlation.

Abstract

The observed relation between supermassive black hole (SMBH) mass (M) and bulge stellar velocity dispersion (Sigma) is described by log(M) = alpha + beta*log(Sigma/200 km/s). As this relation has important implications for models of galaxy and SMBH formation and evolution, there continues to be great interest in adding to the M catalog. The "sphere of influence" (r) argument uses spatial resolution to exclude some M estimates and pre-select additional galaxies for further SMBH studies. This Letter quantifies the effects of applying the r argument to a population of galaxies and SMBHs that do not follow the M-Sigma relation. All galaxies with known values of Sigma, closer than 100 Mpc, are given a random M and selected when r is spatially resolved. These random SMBHs produce an M-Sigma relation of alpha=8.3, beta=4.0, consistent with observed values. Consequently, future proposed M estimates should not be justified solely on the basis of resolving r. This Letter shows the observed M-Sigma relation may simply be a result of available spatial resolution. However, it also implies the observed M-Sigma relation defines an upper limit. This potentially provides valuable new insight into the processes of galaxy and SMBH formation and evolution.