模拟16 Cyg A和B的不确定性和偏差
Uncertainties and biases in modelling 16 Cyg A and B
摘要：
在这项研究中，我评估如何现有的数据，太阳类似物16天鹅座A和B，特别是从\emph{Kepler}获得的asteroseismic测量，约束理论恒星模型。目标是双重的：第一，使用这些恒星作为基准，以讨论哪些精度可以切实预期的推断恒星数量;第二，以确定如何以及'非标准'的处方，如微观扩散和过冲，受到约束。我使用贝叶斯统计模型来推断天鹅座16 A和B的恒星参数值。我通过马尔可夫链蒙特卡罗（MCMC）算法对恒星参数的后验密度进行采样，测试不同的物理处方，并检查使用不同地震诊断的影响。一般良好的协议，发现与最近的几个建模研究这些恒星，即使存在一些差异的精确估计的参数上的不确定性。估计了该双星系统的年龄为$6.88\pm0.12$ Gyr。推断的群众，$1.07\pm0.02$ M $_{\odot}$的Cyg A和$1.05\pm0.02$ M $_{\odot}$的Cyg B，被证明是稳定的相对于考虑建模的物理处方的变化。对于这两颗恒星，微观扩散对初始金属丰度的估计有显着影响。过冲仅限于对流区以下的非常小的区域。我表明，一个适当的处理地震约束是必要的，以避免偏见的估计质量。
英文摘要：
In this study I assess how existing data for the solar analogues 16 Cyg A and B, in particular the asteroseismic measurements obtained from \emph{Kepler}, constrain theoretical stellar models. The goal is two-fold: first to use these stars as benchmarks to discuss which precisions can realistically be expected on the inferred stellar quantities; and second to determine how well 'non-standard' prescriptions, such as microscopic diffusion and overshoot, are constrained. I used a Bayesian statistical model to infer the values of the stellar parameters of 16 Cyg A and B. I sampled the posterior density of the stellar parameters via a Markov chain Monte Carlo (MCMC) algorithm, tested different physical prescription, and examined the impact of using different seismic diagnostics. General good agreement is found with several recent modelling studies on these stars, even though some discrepancies subsist regarding the precise estimates of the uncertainties on the parameters. An age of $6.88\pm0.12$ Gyr is estimated for the binary system. The inferred masses, $1.07\pm0.02$ M$_{\odot}$ for Cyg A and $1.05\pm0.02$ M$_{\odot}$ for Cyg B, are shown to be stable with respect to changes in the physical prescriptions considered for the modelling. For both stars, microscopic diffusion has a significant effect on the estimates of the initial metallicity. Overshoot is confined to very small regions below the convective zone. I show that a proper treatment of the seismic constraints is necessary to avoid biases in the estimate of the mass.
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