引力矩作用下Angular Momentum输运的解析模型：从Galvanian到大质量黑洞
An Analytic Model of Angular Momentum Transport by Gravitational Torques: From Galaxies to Massive Black Holes
摘要：
本文给出了从~kpc尺度到中心黑洞（BH）势深处星系角动量输运和气体流入的解析计算。我们比较这些解析计算数值模拟，并使用它们来开发一个子网格模型BH的增长，可以纳入半解析模型或宇宙学模拟。分析计算和模拟都认为，当恒星引力势的非轴对称扰动在气体中产生轨道交叉和冲击时，气体上的扭矩最大。这在大半径~0.01-1 kpc和小半径<10 pc时都是正确的，在大半径时，棒状模主导非轴对称势，在小半径时，不平衡/偏心盘主导非轴对称势。传统的轨道交叉准则并不总是足以预测的位置，和流入由于，在气体+恒星盘有限声速的冲击。我们得到一个修改后的标准，预测在恒星为主的系统，即使没有正式的轨道交叉的冲击的存在。然后，我们推导出角动量的损失和由此产生的气体流入率在这种冲击的存在下的解析表达式。我们测试我们的分析预测使用流体动力学模拟在银河系尺度的范围内，并表明，他们成功地预测质量流入率和准稳态气体表面密度与小的散射（0.3 dex）。我们使用我们的分析结果，以构建一个新的估计BH吸积率在较大半径的星系属性。这捕获了数值模拟中的关键缩放。替代估计，如当地的粘性吸积率或球形邦迪率系统地再现模拟失败。
英文摘要：
We present analytic calculations of angular momentum transport and gas inflow in galaxies, from scales of ~kpc to deep in the potential of a central black hole (BH). We compare these analytic calculations to numerical simulations and use them to develop a sub-grid model of BH growth that can be incorporated into semi-analytic models or cosmological simulations. Both analytic calculations and simulations argue that the strongest torque on gas arises when non-axisymmetric perturbations to the stellar gravitational potential produces orbit crossings and shocks in the gas. This is true both at large radii ~0.01-1 kpc, where bar-like modes dominate the non-axisymmetric potential, and at smaller radii <10 pc, where a lopsided/eccentric disk dominates. The traditional orbit crossing criterion is not always adequate to predict the locations of, and inflow due to, shocks in gas+stellar disks with finite sound speeds. We derive a modified criterion that predicts the presence of shocks in stellar dominated systems even absent formal orbit crossing. We then derive analytic expressions for the loss of angular momentum and the resulting gas inflow rates in the presence of such shocks. We test our analytic predictions using hydrodynamic simulations at a range of galactic scales, and show that they successfully predict the mass inflow rates and quasi-steady gas surface densities with small scatter (0.3 dex). We use our analytic results to construct a new estimate of the BH accretion rate given galaxy properties at larger radii. This captures the key scalings in the numerical simulations. Alternate estimates such as the local viscous accretion rate or the spherical Bondi rate fail systematically to reproduce the simulations.
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