用引力波模拟核坍缩超新星的贝叶斯参数估计
Bayesian parameter estimation of core collapse supernovae using gravitational wave simulations
摘要：
利用最新的旋转恒星核坍缩的数值模拟，我们提出了一个贝叶斯框架来提取编码在噪声引力波信号中的物理信息。我们拟合贝叶斯主成分回归模型与已知和未知的信号到达时间重建引力波信号，并随后拟合已知的天体物理参数的主成分系数的后验均值使用线性模型。通过从后验预测分布中采样，我们预测了内核在反弹时的旋转动能与引力能的比值，发现这些预测一般都非常接近真实的参数值，对于已知和未知的到达时间模型，$90\%$可信区间分别为$\sim 0.04$和$\sim 0.06$.两种监督机器学习方法实现了对塌陷前差分旋转进行分类，我们发现这些方法可以很好地区分快速旋转的祖细胞。我们还引入了一个约束优化方法来选择模型，以找到一个最佳数量的主成分在信号重建步骤。使用这种方法，我们选择了14个主成分作为最简约的模型。
英文摘要：
Using the latest numerical simulations of rotating stellar core collapse, we present a Bayesian framework to extract the physical information encoded in noisy gravitational wave signals. We fit Bayesian principal component regression models with known and unknown signal arrival times to reconstruct gravitational wave signals, and subsequently fit known astrophysical parameters on the posterior means of the principal component coefficients using a linear model. We predict the ratio of rotational kinetic energy to gravitational energy of the inner core at bounce by sampling from the posterior predictive distribution, and find that these predictions are generally very close to the true parameter values, with $90\%$ credible intervals $\sim 0.04$ and $\sim 0.06$ wide for the known and unknown arrival time models respectively. Two supervised machine learning methods are implemented to classify precollapse differential rotation, and we find that these methods discriminate rapidly rotating progenitors particularly well. We also introduce a constrained optimization approach to model selection to find an optimal number of principal components in the signal reconstruction step. Using this approach, we select 14 principal components as the most parsimonious model.
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