旋转等温环的平衡序列和引力不稳定性
Equilibrium Sequences and Gravitational Instability of Rotating Isothermal Rings
摘要：
棒星系中心的核环表现出强烈的恒星形成活动。它们被认为在质量足够大时会经历引力不稳定性。我们将它们近似为刚性旋转的等温物体，并研究它们的引力不稳定性。首先用自洽场方法构造了由两个参数确定的平衡序列：α对应于相对于引力势能的热能，R_B代表椭圆度或环厚度。与不可压缩情况不同，并非所有R_B值都会产生等温平衡，并且此类平衡的R_B范围随着α的减小而缩小。对于较小的α，椭圆平面中的密度分布更陡，并且对于细长环，可以很好地近似于无限圆柱体的密度分布。我们还计算了角频率为Ω_0、中心密度为rho_max的刚性旋转细长环中非轴对称模的色散关系。环与较小的α被发现更不稳定与更大的不稳定范围内的方位角模式数。当Omega_0超过临界值时，旋转完全抑制了不稳定性。发现当α> 0.01时，临界角频率几乎恒定在~ 0.7 sqrt（G*rho_c），当α较小时，临界角频率迅速增加。我们将我们的结果应用到观察到的恒星形成环的样本中，并确认没有明显的年轻星团方位角年龄梯度的环确实是引力不稳定的。
英文摘要：
Nuclear rings at centers of barred galaxies exhibit strong star formation activities. They are thought to undergo gravitational instability when sufficiently massive. We approximate them as rigidly-rotating isothermal objects and investigate their gravitational instability. Using a self-consistent field method, we first construct their equilibrium sequences specified by two parameters: alpha corresponding to the thermal energy relative to gravitational potential energy, and R_B measuring the ellipticity or ring thickness. Unlike in the incompressible case, not all values of R_B yield an isothermal equilibrium, and the range of R_B for such equilibria shrinks with decreasing alpha. The density distributions in the meridional plane are steeper for smaller alpha, and well approximated by those of infinite cylinders for slender rings. We also calculate the dispersion relations of nonaxisymmetric modes in rigidly-rotating slender rings with angular frequency Omega_0 and central density rho_max. Rings with smaller alpha are found more unstable with a larger unstable range of the azimuthal mode number. The instability is completely suppressed by rotation when Omega_0 exceeds the critical value. The critical angular frequency is found to be almost constant at ~ 0.7 sqrt(G*rho_c) for alpha > 0.01 and increases rapidly for smaller alpha. We apply our results to a sample of observed star-forming rings and confirm that rings without a noticeable azimuthal age gradient of young star clusters are indeed gravitationally unstable.
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