基本面与超大质量黑洞质量的统一
Unification of the Fundamental Plane and Super-Massive Black Holes Masses
摘要：
根据维里定理，所有处于平衡状态的引力系统都位于由它们的质量、大小和速度张量的二阶矩定义的三维参数空间中的一个平面上。虽然这些量不能直接观测到，但有合适的替代指标：光度Lk，半光半径Re和色散σ_e。这些代理实际上位于非常紧密的基本面（FP）上。星系中心的黑洞与FP有什么关系？已知它们的质量与星系总质量没有很强的相关性，但它们与星系核球质量（当存在时）的相关性很弱，并且通过Mbh = sigma_e ^[5.4]关系与速度色散的相关性非常好。这些事实一起意味着，一个紧平面也必须存在由黑洞质量，星系总质量和大小定义。在这里，我表明，这确实是使用一个异构的230个黑洞的情况下。样本包括从零到100亿太阳质量的BH和宿主星系，从低表面亮度的矮星，通过无膨胀的盘，到最明亮的星系团。由此得到的BH-尺寸-光度Mbh=（Lk/Re）^[3.8]与M-西格玛关系式具有相同的散射量，并且与星系FP对齐，因此它只是西格玛的再投影。推导出的BH-尺寸-质量关系为Mbh=（M_star/Re）^[2.9]。这些关系是普遍的，并延伸到没有凸起的星系。这意味着黑洞主要与其整体速度色散相关，而不是与凸起的性质相关。我表明，经典的凸起-质量关系是一个投影的M-西格玛关系。当速度色散无法测量时（在高z或低色散时），BH-尺寸-质量关系应该被用作黑洞质量的代理，而只支持星系或凸起质量。
英文摘要：
According to the Virial Theorem, all gravitational systems in equilibrium sit on a plane in the 3D parameter space defined by their mass, size and second moment of the velocity tensor. While these quantities cannot be directly observed, there are suitable proxies: the luminosity Lk, half-light radius Re and dispersion sigma_e. These proxies indeed lie on a very tight Fundamental Plane (FP). How do the black holes in the centers of galaxies relate to the FP? Their masses are known to exhibit no strong correlation with total galaxy mass, but they do correlate weakly with bulge mass (when present), and extremely well with the velocity dispersion through the Mbh = sigma_e^5.4 relation. These facts together imply that a tight plane must also exist defined by black hole mass, total galaxy mass and size. Here I show that this is indeed the case using a heterogeneous set of 230 black holes. The sample includes BHs from zero to 10 billion solar masses and host galaxies ranging from low surface brightness dwarfs, through bulge-less disks, to brightest cluster galaxies. The resulting BH-size-luminosity Mbh=(Lk/Re)^3.8 has the same amount of scatter as the M-sigma relation and is aligned with the galaxy FP, such that it is just a re-projection of sigma. The inferred BH-size-mass relation is Mbh=(M_star/Re)^2.9. These relationships are universal and extend to galaxies without bulges. This implies that the black hole is primarily correlated with its global velocity dispersion and not with the properties of the bulge. I show that the classical bulge--mass relation is a projection of the M-sigma relation. When the velocity dispersion cannot be measured (at high-z or low dispersions), the BH-size-mass relation should be used as a proxy for black hole mass in favor of just galaxy or bulge mass.
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