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The M-Sigma Relation Derived from Sphere of Influence Arguments

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.