2010ApJ...711L.108B

The observed relation between supermassive black hole (SMBH) mass (M _•) and bulge stellar velocity dispersion (σ_*) is described by log M_•= α + βlog(σ_*/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_i) 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_i argument to a population of galaxies and SMBHs that do not follow the M_•-σ_*relation. All galaxies with known values of σ_*, closer than 100 Mpc, are given a random M_• and selected when r_i is spatially resolved. These random SMBHs produce a M_•-σ_* relation of α = 8.3±0.2, β = 4.0±0.3, consistent with observed values. Consequently, future proposed M_• estimates should not be justified solely on the basis of resolving r_i. This Letter shows that the observed M_•-σ_* relation may simply be a result of available spatial resolution. However, it also implies that the observed M_•-σ_* relation defines an upper limit. This potentially provides valuable new insight into the processes of galaxy and SMBH formation and evolution.