论文标题
随心所欲：（缺乏A）用Ligo-Virgo-Kagra二进制黑洞测量自旋倾斜分布
Spin it as you like: the (lack of a) measurement of the spin tilt distribution with LIGO-Virgo-KAGRA binary black holes
论文作者
论文摘要
尽管通过分析最新的LVK目录GWTC-3来了解黑洞，但对黑洞旋转方向的天体物理分布的测量仍然难以捉摸。通常，通过测量每个黑洞旋转和轨道角动量之间的倾斜角（$ \cosτ$）的余弦来探测这一点，$ \cosτ=+1 $是完美的对齐。 Abbott等。已将$ \cosτ$分布建模为各向同性组件和高斯组件的混合物，平均固定为+1和从数据中测量的宽度。我们要验证数据是否需要$ \cosτ=+1 $的峰值存在。我们使用各种替代模型进行天体物理倾斜分布，并使用LVK GWTC-3目录测量其参数。我们发现a）增强LVK模型，以使高斯的平均$μ$在+1回报结果上不固定在很大程度上取决于先验的结果。如果我们允许$μ> +1 $ $，则由此产生的天体物理$ \cosτ$分布在+1处峰值，而不是线性而不是高斯。如果我们约束$ -1 \leqμ\ leq+1 $ $ ussian组件以$μ= 0.48^{+0.46} _ { - 0.99} $（中位数和90％对称可信间隔）。另外两种2组分混合模型产生的$ \cosτ$分布，其宽峰为$ 0.19^{ +0.22} _ { - 0.18} $，或一个跨越范围[-0.5，+1]的高原，而无需明确的峰值+1。 b）我们考虑的所有模型都同意以下事实：在-1左右，黑洞倾斜不超过。 c）尽管产生了完全不同的后代，但在这项工作中考虑的模型的贝叶斯证据在误差条中是相同的。我们得出的结论是，当前的数据集没有足够的信息丰富的信息，无法就旋转倾斜的天体物理分布得出任何独立的结论，只是没有过量的旋转过量的倾斜度负相位。
While much has been learned about black holes by analyzing the latest LVK catalog, GWTC-3, a measurement of the astrophysical distribution of the black hole spin orientations remains elusive. This is usually probed by measuring the cosine of the tilt angle ($\cosτ$) between each black hole spin and the orbital angular momentum, $\cosτ=+1$ being perfect alignment. Abbott et al. has modeled the $\cosτ$ distribution as a mixture of an isotropic component and a Gaussian component with mean fixed at +1 and width measured from the data. We want to verify if the data require the existence of such a peak at $\cosτ=+1$. We use various alternative models for the astrophysical tilt distribution and measure their parameters using the LVK GWTC-3 catalog. We find that a) Augmenting the LVK model such that the mean $μ$ of the Gaussian is not fixed at +1 returns results that strongly depend on priors. If we allow $μ>+1$ then the resulting astrophysical $\cosτ$ distribution peaks at +1 and looks linear, rather than Gaussian. If we constrain $-1\leq μ\leq+1$ the Gaussian component peaks at $μ=0.48^{+0.46}_{-0.99}$ (median and 90% symmetric credible interval). Two other 2-component mixture models yield $\cosτ$ distributions that either have a broad peak centered at $0.19^{+0.22}_{-0.18}$ or a plateau that spans the range [-0.5, +1], without a clear peak at +1. b) All of the models we considered agree on the fact that there is no excess of black hole tilts at around -1. c) While yielding quite different posteriors, the models considered in this work have Bayesian evidences that are the same within error bars. We conclude that the current dataset is not sufficiently informative to draw any model-independent conclusions on the astrophysical distribution of spin tilts, except that there is no excess of spins with negatively aligned tilts.
