张量维里定理在空穴+涡+球系统中的应用
An application of the tensor virial theorem to hole + vortex + bulge systems
摘要：
张量维里定理的子系统制定为三个组件的系统和进一步的努力致力于一个特殊的情况下，内部的子系统和外部的中心区域是均匀的，最后包围的等温homeoid。维里方程是在附加的限制条件下显式写出的。在内部子系统扁平的限制下，应用于空穴+涡+凸起系统。使用Faber-Jackson关系，从定性考虑推导出标准的$M_{\rm H}$ - $σ_0$形式。在几种情况下，作为分数半径y_{\rm BV}和分数质量$m_{\rm BH}$和$m_{\rm VH}$的函数，绘制了凸出速度弥散与涡速度比$η$的关系图。它示出，一个固定值的$η$低于最大值对应于两个不同的配置：一个紧凑的凸起的左边和一个扩展的凸起的右边。此外，对于固定的$m_{\rm BH}$或$m_{\rm BV}$和$y_{\rm BV}$，较大的隆起与较大的$η$相关，反之亦然。将该模型应用于NGC 4374和NGC 4486，推导了核团的质量，并与不同方法的结果进行了比较。在存在大质量涡旋$(m_{\rm VH}=5)$的情况下，相对于无质量涡旋的情况，孔质量必须减少2-3倍才能得到拟合。
英文摘要：
The tensor virial theorem for subsystems is formulated for three-component systems and further effort is devoted to a special case where the inner subsystems and the central region of the outer one are homogeneous, the last surrounded by an isothermal homeoid. The virial equations are explicitly written under additional restrictions. An application is made to hole + vortex + bulge systems, in the limit of flattened inner subsystems. Using the Faber-Jackson relation, the standard $M_{\rm H}$-$σ_0$ form is deduced from qualitative considerations. The projected bulge velocity dispersion to projected vortex velocity ratio, $η$, as a function of the fractional radius, y_{\rm BV}, and the fractional masses, $m_{\rm BH}$, and $m_{\rm VH}$, is plotted for several cases. It is shown that a fixed value of $η$ below the maximum corresponds to two different configurations: a compact bulge on the left and an extended bulge on the right. In addition, for fixed $m_{\rm BH}$ or $m_{\rm BV}$, and $y_{\rm BV}$, more massive bulges are related to larger $η$ and vice versa. The model is applied to NGC 4374 and NGC 4486, and the bulge mass is inferred and compared with results from different methods. In presence of a massive vortex $(m_{\rm VH}=5)$, the hole mass has to be reduced by a factor 2-3 with respect to the case of a massless vortex, to get the fit.
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