论文标题
不等的质量二进制黑洞系统是否具有较大的$χ_\ text {eff} $？在重力波天文学中与Copulas的探测相关性
Do unequal-mass binary black hole systems have larger $χ_\text{eff}$? Probing correlations with copulas in gravitational-wave astronomy
论文作者
论文摘要
二进制黑洞系统的形成历史印在其质量，旋转和偏心率的分布上。尽管已经学习了很多研究这些参数，但最近的研究探索了两个或多个维度中二进制黑洞参数的联合分布。最值得注意的是，最近有人认为，二进制黑洞质量比和有效的Inspiral Spin $χ_\ text {eff} $是反相关的。我们指出，在这样的二维人群研究中，先前被忽视的微妙之处：为了进行相关性的对照测试，应该固定两个边际分布 - 以免仅在一个维度中提高所谓的相关性。我们使用来自Applied Statistics的工具来解决这个微妙之处：Copula密度函数。我们使用以前的工作相关的质量比和$χ_\ text {eff} $作为案例研究，以证明在重力波天文学中的Copulas的力量，同时仔细检查其天体物理学的推断。但是，我们的发现确认了他们的结论，即具有不等成分质量的二进制黑洞表现出较大的$χ_\ text {eff} $（98.7％的信誉）。我们通过讨论这些发现的潜在天体物理意义以及使用Copulas的未来研究的前景来得出结论。
The formation history of binary black hole systems is imprinted on the distribution of their masses, spins, and eccentricity. While much has been learned studying these parameters in turn, recent studies have explored the joint distribution of binary black hole parameters in two or more dimensions. Most notably, it has recently been argued that binary black hole mass ratio and effective inspiral spin $χ_\text{eff}$ are anti-correlated. We point out a previously overlooked subtlety in such two-dimensional population studies: in order to conduct a controlled test for correlation, one ought to fix the two marginal distributions -- lest the purported correlation be driven by improved fit in just one dimension. We address this subtlety using a tool from applied statistics: the copula density function. We use the previous work correlating mass ratio and $χ_\text{eff}$ as a case study to demonstrate the power of copulas in gravitational-wave astronomy while scrutinising their astrophysical inferences. Our findings, however, affirm their conclusions that binary black holes with unequal component masses exhibit larger $χ_\text{eff}$ (98.7% credibility). We conclude by discussing potential astrophysical implications of these findings as well as prospects for future studies using copulas.
