THE M•-σ* RELATION DERIVED FROM SPHERE OF INFLUENCE ARGUMENTS

The observed relation between supermassive black hole (SMBH) mass (M-center dot) and bulge stellar velocity dispersion (sigma(*)) is described by log M-center dot = alpha + beta log (sigma(*)/200 km s(-1)). 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-center dot catalog. The sphere of influence (r(i)) argument uses spatial resolution to exclude some M-center dot 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-center dot-sigma(*) relation. All galaxies with known values of sigma(*), closer than 100 Mpc, are given a random M-center dot and selected when r(i) is spatially resolved. These random SMBHs produce a M-center dot-sigma(*) relation of alpha = 8.3 +/- 0.2, beta = 4.0 +/- 0.3, consistent with observed values. Consequently, future proposed M-center dot estimates should not be justified solely on the basis of resolving r(i). This Letter shows that the observed M-center dot-sigma(*) relation may simply be a result of available spatial resolution. However, it also implies that the observed M-center dot-sigma(*) relation defines an upper limit. This potentially provides valuable new insight into the processes of galaxy and SMBH formation and evolution.