The Astrophysical Journal Letters
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-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• catalog. The "sphere of influence" (ri) 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 ri 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 ri 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 ri. 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.
Batcheldor, Daniel P., "The M•–σ* Relation Derived From Sphere Of Influence Arguments" (2010). Aerospace, Physics, and Space Science Faculty Publications. 366.