Black hole binary remnant mass and spin: A new phenomenological formula
Black hole binary remnant mass and spin: A new phenomenological formula
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黑洞二元残余质量和自旋：一个新的现象学公式
DOI：
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发表时间：
2013
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通讯作者：
Y. Zlochower
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作者：
C. Lousto;Y. Zlochower
我们对38个等质量黑洞双星进行了一组数值模拟，其中黑洞自旋在双星中的大小和方向相等，以研究进动效应。我们改变了总自旋S相对于轨道角动量L的初始方向，覆盖了取向角的二维空间，有38种构型，其中36种构型分布在方位角和极角上，两种构型在极点上。在所有情况下，我们将初始无量纲黑洞自旋设为0.8。我们观察到，在吸气后期，系统J的总角动量保持在其原始方向的5°范围内，当自旋与轨道角动量几乎反向排列时，方向变化最大。我们还观察到S和L之间的角度在吸气阶段几乎是守恒的。这两种动力学性质使我们能够提出一种新的现象学公式，用于描述合并黑洞的最终质量和自旋，该公式是根据远分离的前体双星的单个质量和自旋得出的。我们使用最小二乘拟合的方法来确定这个公式的系数（在等质量极限下），该方法适用于这组新的38次运行的结果，另外一组五种自旋与轨道角动量对齐/反对齐的新配置，以及最近的100多次模拟。我们发现我们的公式再现了这些模拟的残余质量和自旋，相对误差在2.5%以内。我们讨论了这种动态图象处理不等质量双星的有效区域。最后，我们进行了一项统计研究，以观察这个新的自旋星等和残余质量分布公式的结果，并将其应用于涉及几次合并的宇宙学场景中的bh -自旋分布和引力辐射。
We perform a set of 38 numerical simulations of equal-mass BH binaries in a configuration where the BH spins in the binary are equal in both magnitude and direction, to study precession effects. We vary the initial direction of the total spin S with respect to the orbital angular momentum L, covering the 2 dimensional space of orientation angles with 38 configurations consisting of 36 configurations distributed in the azimuthal angle phi and polar angle theta, and two configurations on the poles. In all cases, we set the initial dimensionless BH spins to 0.8. We observe that during the late-inspiral stage, the total angular momentum of the system J remains within 5 deg of its original direction, with the largest changes in direction occurring when the spins are nearly counter-aligned with the orbital angular momentum. We also observe that the angle between S and L is nearly conserved during the inspiral phase. These two dynamical properties allow us to propose a new phenomenological formula for the final mass and spin of merged BHs in terms of the individual masses and spins of the progenitor binary at far separations. We determine coefficients of this formula (in the equal-mass limit) using a least-squares fit to the results of this new set of 38 runs, an additional set of five new configurations with spins aligned/counteraligned with the orbital angular momentum, and over 100 recent simulations. We find that our formulas reproduce the remnant mass and spin of these simulations to within a relative error of 2.5%. We discuss the region of validity of this dynamical picture for precessing unequal-mass binaries. Finally, we perform a statistical study to see the consequence of this new formula for distributions of spin-magnitudes and remnant masses with applications to BH-spin distributions and gravitational radiation in cosmological scenarios involving several mergers.