用自旋-质量平面上的分布约束大质量黑洞的生长历史
On Constraining the Growth History of Massive Black Holes via Their Distribution on the Spin-Mass Plane
摘要：
大质量黑洞的自旋分布包含了关于大质量黑洞生长历史的丰富信息。在本文中，我们研究的自旋演化的MBH的假设，每个MBH经历两个阶段的吸积，与初始阶段的相干吸积通过标准薄盘或super-Eddington盘，其次是混沌吸积阶段组成的许多情节与不同的磁盘取向。如果混沌阶段对MBH的生长有重要意义，则由于初始的相干吸积，MBH自旋很快达到最大值，然后转变为准平衡态，并在混沌吸积阶段围绕一个主要由盘与MBH质量的平均比值（$M_{\bullet}$）决定的值波动，如果是$M_\bullet \gtrsim (1-3) \times 10^8 M_\odot$，则由于后期的混沌吸积，MBH自旋进一步下降。这种下降的转折点是由圆盘翘曲半径和圆盘尺寸的相等性决定的。通过将现有的自旋测量结果与自旋-质量平面上的两相模型模拟样品进行匹配，我们发现MBH必须经历大量的混沌吸积阶段，每一幕吸积的质量大约为M_bh的1- 2%或更少，具有$M_{\bullet}\gtrsim 10^8 M_{\odot}$的MBH似乎具有中到高的自旋（$\sim 0.5-1$），而较轻的MBH具有较高的自旋（$\gtrsim 0.8$）。最佳匹配还推断出：（1）这些活跃MBH的辐射效率（$η$）似乎随着$M_{\bullet}$略有下降;然而，$η$和$M_{\bullet}$之间的相关性（如果有的话）很弱;（2）活跃MBH的平均辐射效率为$<η> \sim 0.09-0.15$，与全局约束一致。
英文摘要：
The spin distribution of massive black holes (MBHs) contains rich information on the MBH growth history. In this paper, we investigate the spin evolution of MBHs by assuming that each MBH experiences two-phase accretion, with an initial phase of coherent-accretion via either the standard thin disc or super-Eddington disc, followed by a chaotic-accretion phase composed of many episodes with different disc orientations. If the chaotic-phase is significant to the growth of an MBH, the MBH spin quickly reaches the maximum value because of the initial coherent-accretion, then changes to a quasi-equilibrium state and fluctuates around a value mainly determined by the mean ratio of the disc to the MBH mass ($M_{\bullet}$) in the chaotic-accretion episodes, and further declines due to late chaotic-accretion if $M_\bullet \gtrsim (1-3) \times 10^8 M_\odot$. The turning point to this decline is determined by the equality of the disc warp radius and disc size. By matching the currently available spin measurements with mock samples generated from the two-phase model(s) on the spin-mass plane, we find that MBHs must experience significant chaotic-accretion phase with many episodes and the mass accreted in each episode is roughly 1-2 percent of M_bh or less. MBHs with $M_{\bullet}\gtrsim 10^8 M_{\odot}$ appear to have intermediate-to-high spins ($\sim 0.5-1$), while lighter MBHs have higher spins ($\gtrsim 0.8$). The best matches also infer that (1) the radiative efficiencies ($η$) of those active MBHs appear to slightly decrease with $M_{\bullet}$; however, the correlation between $η$ and $M_{\bullet}$, if any, is weak; (2) the mean radiative efficiency of active MBHs is $<η> \sim 0.09-0.15$, consistent with the global constraints.
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