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The observed relation between supermassive black hole (SMBH) mass (M) andbulge stellar velocity dispersion (Sigma) is described by log(M) = alpha +beta*log(Sigma/200 km/s). As this relation has important implications formodels of galaxy and SMBH formation and evolution, there continues to be greatinterest in adding to the M catalog. The "sphere of influence" (r) argumentuses spatial resolution to exclude some M estimates and pre-select additionalgalaxies for further SMBH studies. This Letter quantifies the effects ofapplying the r argument to a population of galaxies and SMBHs that do notfollow the M-Sigma relation. All galaxies with known values of Sigma, closerthan 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 estimatesshould not be justified solely on the basis of resolving r. This Letter showsthe observed M-Sigma relation may simply be a result of available spatialresolution. However, it also implies the observed M-Sigma relation defines anupper limit. This potentially provides valuable new insight into the processesof galaxy and SMBH formation and evolution.

The M-Sigma Relation Derived from Sphere of Influence Arguments