由影响范围论证导出的M-Sigma关系
The M-Sigma Relation Derived from Sphere of Influence Arguments
摘要：
观测到的超大质量黑洞（SMBH）质量（M）与球核恒星速度色散（Sigma）之间的关系可用log（M）= alpha + beta*log（Sigma/200 km/s）表示。由于这种关系对星系和SMBH形成和演化的模型具有重要意义，因此人们对将其添加到M目录中仍然有很大的兴趣。“影响范围”（r）的论点使用空间分辨率来排除一些M估计，并预先选择其他星系进行进一步的SMBH研究。这封信量化的影响，适用于人口的星系和SMBH不遵循M-西格玛关系的r参数。所有已知的西格玛值，接近100 Mpc的星系，被赋予一个随机的M，当r是空间分辨的选择。这些随机SMBH产生α =8.3，β =4.0的M-Sigma关系，与观察值一致。因此，未来提出的M估计值不应仅根据解决r来证明。这封信表明，观察到的M-西格玛关系可能只是一个可用的空间分辨率的结果。然而，这也意味着观察到的M-Sigma关系定义了上限。这可能为星系和SMBH的形成和演化过程提供有价值的新见解。
英文摘要：
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.
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