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.
