We present a parameter estimate for continua, and He-like triplets of the high resolution X-ray spectra with a Bayesian inference and a Markov Chain Monte Carlo (MCMC) tool. The method is applied for Vela X-1 with three different orbital phases ($\unicode[STIX]{x1D719}$), Eclipse, $\unicode[STIX]{x1D719}=0.25$, and $\unicode[STIX]{x1D719}=0.5$, which are adopted from the Chandra High-Energy Transmission Grating Spectrometer (HETGS). A parameterized two-component power-law model [Sako et al., Astrophys. J. 525, 921 (1999)] and a multi-Gaussian model are applied to model these continua and He-like triplets, respectively. A uniform distribution over each parameter is used as the prior belief. Posterior probability distribution functions of parameters and the covariances among them are explored by using the MCMC method. The main advantages are (i) all model-based parameters are set to be free instead of artificially fixing some of the parameters during the data-model fitting; (ii) the contributions from satellite lines are considered; (iii) backgrounds are treated as a correction to the observation errors; and (iv) the confidence interval of each parameter is given. The fitted results show that the column density of scatter component ($N_{\text{H}}^{\text{scat}}$) varies from phase to phase, which imply a non-spherical structure of the stellar wind in Vela X-1. Moreover, the wind velocities derived from main lines of each set of He-like triplets show better self-consistency than those in previous publications, which could provide a reliable approach for the diagnostics of photoionized plasma in astrophysical objects and the laboratory.

中文翻译：

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通过对 Vela X-1 的观测使用 MCMC 进行物理参数估计

我们使用贝叶斯推理和马尔可夫链蒙特卡罗 (MCMC) 工具提出了高分辨率 X 射线光谱的连续波和类 He 三元组的参数估计。该方法适用于具有三个不同轨道相位的 Vela X-1 ($\unicode[STIX]{x1D719}$), 日食,$\unicode[STIX]{x1D719}=0.25$， 和$\unicode[STIX]{x1D719}=0.5$, 这是从钱德拉高能透射光栅光谱仪（HETGS）。参数化的二分量幂律模型 [Sako等。，天体物理学。J。525, 921 (1999)] 和多高斯模型分别用于模拟这些连续体和类似 He 的三元组。每个参数的均匀分布被用作先验信念。采用MCMC方法探索参数的后验概率分布函数及其间的协方差。主要优点是（i）所有基于模型的参数都设置为自由的，而不是在数据模型拟合期间人为地固定一些参数；(ii) 考虑来自卫星线路的贡献；(iii) 背景被视为对观察错误的修正；(iv) 给出每个参数的置信区间。拟合结果表明，散射分量的列密度（$N_{\text{H}}^{\text{scat}}$) 因相位而异，这意味着 Vela X-1 中恒星风的非球形结构。此外，每组He样三联体的主线风速显示出比先前出版物更好的自洽性，这可以为天体物理物体和实验室中光电离等离子体的诊断提供可靠的方法。