标题： 具有参数化状态方程的中子星性质的贝叶斯分析：似然函数的作用 显示英文标题

标题： Bayesian analysis of neutron-star properties with parameterized equations of state: the role of the likelihood functions

摘要： 我们研究了在使用可变似然函数或常数似然函数时，对中子星状态方程进行贝叶斯推断分析时引入的系统性差异。前者的优势在于保留了测量分布的所有信息，从而充分使用数据；后者则具有实现简单且计算成本低的优点。在这两种方法中，状态方程都具有相同的先验，并通过声速参数化方法构建，以满足X射线和引力波观测以及从Chiral有效理论和微扰QCD得出的约束条件。在所有情况下，这两种方法得出的结果非常相似，置信水平为$90\%$的区域几乎重叠。尽管如此，还是出现了一些差异，但这些差异出现在概率密度极小的区域，主要是由于常数似然分析中用于二元潮汐变形率$\tilde \Lambda \leq 720$的尖锐截止所导致。我们的分析还产生了另外两个结果。首先，最大质量恒星的归一化中心粒子数密度$n_{\rm c, TOV}/n_s$和最大质量恒星半径$R_{\rm TOV}$之间存在明显的反相关关系。其次，也是最重要的是，它证实了啁啾质量$\mathcal{M}_{\rm chirp}$和二元潮汐变形率$\tilde{\Lambda}$之间的关系。 这一结果的重要性在于它将一个测量得非常精确的量 $\mathcal{M}_{\rm chirp}$ 与一个包含微观物理重要信息的量 $\tilde{\Lambda}$ 联系起来。因此，一旦在未来的探测中测量到 $\mathcal{M}_{\rm chirp}$，我们的关系有可能对 $\tilde{\Lambda}$ 施加严格的限制。 显示英文摘要

摘要： We have investigated the systematic differences introduced when performing a Bayesian-inference analysis of the equation of state of neutron stars employing either variable- or constant-likelihood functions. The former have the advantage that it retains the full information on the distributions of the measurements, making an exhaustive usage of the data. The latter, on the other hand, have the advantage of a much simpler implementation and reduced computational costs. In both approaches, the EOSs have identical priors and have been built using the sound-speed parameterization method so as to satisfy the constraints from X-ray and gravitational-waves observations, as well as those from Chiral Effective Theory and perturbative QCD. In all cases, the two approaches lead to very similar results and the $90\%$-confidence levels are essentially overlapping. Some differences do appear, but in regions where the probability density is extremely small and are mostly due to the sharp cutoff set on the binary tidal deformability $\tilde \Lambda \leq 720$ employed in the constant-likelihood analysis. Our analysis has also produced two additional results. First, a clear inverse correlation between the normalized central number density of a maximally massive star, $n_{\rm c, TOV}/n_s$, and the radius of a maximally massive star, $R_{\rm TOV}$. Second, and most importantly, it has confirmed the relation between the chirp mass $\mathcal{M}_{\rm chirp}$ and the binary tidal deformability $\tilde{\Lambda}$. The importance of this result is that it relates a quantity that is measured very accurately, $\mathcal{M}_{\rm chirp}$, with a quantity that contains important information on the micro-physics, $\tilde{\Lambda}$. Hence, once $\mathcal{M}_{\rm chirp}$ is measured in future detections, our relation has the potential of setting tight constraints on $\tilde{\Lambda}$.