标题： 湍流平衡球的理论与幂律线宽-尺寸关系 显示英文标题

标题： Theory of Turbulent Equilibrium Spheres with Power-Law Linewidth-Size Relation

摘要： 致密核心从形成它们的星际介质中继承湍流运动。 作为一种与模拟和观测进行比较的工具，构建能够关联其内部密度和速度结构并预测其引力坍缩稳定性的理论核心模型是有价值的。 为此，我们在两个假设下求解角平均流体力学方程：1）系统处于准稳态平衡；2）速度场由径向整体运动加上各向同性湍流组成，湍流弥散度随半径按幂律增加。 得到的湍流平衡球（TES）解形成一个双参数族，由声学半径$r_s$和幂律指数$p$表征。 当$r_s\to \infty$时，TES 等价于 Bonnor-Ebert（BE）球。 TES 外部区域的密度分布比 BE 球稍浅，但比对数模型更陡峭。 稳定性分析表明，尺寸超过某个临界半径的 TES 对径向扰动不稳定。 临界稳定 TES 的中心-边缘密度对比、质量以及半径都随着平均速度弥散的增加而增加。 柱密度分布的 FWHM 始终小于临界半径，且在更高速度弥散时差异更大，这表明观测需要探测 FWHM 以外的区域才能捕捉湍流核心的全部范围。 当应用于典型的大尺度湍流区域时，TES 的临界质量和半径惊人地类似于观测到的星团的质量和半径。 显示英文摘要

摘要： Dense cores inherit turbulent motions from the interstellar medium in which they form. As a tool for comparison to both simulations and observations, it is valuable to construct theoretical core models that can relate their internal density and velocity structure while predicting their stability to gravitational collapse. To this end, we solve the angle-averaged equations of hydrodynamics under two assumptions: 1) the system is in a quasi-steady equilibrium; 2) the velocity field consists of radial bulk motion plus isotropic turbulence, with turbulent dispersion increasing as a power-law in the radius. The resulting turbulent equilibrium sphere (TES) solutions form a two-parameter family, characterized by the sonic radius $r_s$ and the power-law index $p$. The TES is equivalent to the Bonnor-Ebert (BE) sphere when $r_s\to \infty$. The density profile in outer regions of the TES is slightly shallower than the BE sphere, but is steeper than the logotropic model. Stability analysis shows that the TESs with size exceeding a certain critical radius are unstable to radial perturbations. The center-to-edge density contrast, mass, and radius of the marginally stable TES all increase with increasing average velocity dispersion. The FWHM of the column density profile is always smaller than the critical radius, by a larger factor at higher velocity dispersion, suggesting that observations need to probe beyond the FWHM to capture the full extent of turbulent cores. When applied to the highly turbulent regime typical of cluster-forming clumps, the critical mass and radius of the TES intriguingly resembles the typical mass and radius of observed star clusters.