Abstract
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.
Highlights
IntroductionThe fitting of X-ray spectra is based on reduced χ 2 method (e.g., Sako et al 1999[6], Goldenstein et al 2004[7], hereafter S99 and G04) or maximum likelihood (e.g., W06)
High-resolution X-ray spectra from stellar objects are an important tool to infer their plasma structures[1], physical conditions[2, 3], wind speed in X-ray binary systems[4], coronal abundances (e.g., Blondin et al 1990[5]) and other important physical information about astrophysical objects.Conventionally, the fitting of X-ray spectra is based on reduced χ 2 method (e.g., Sako et al 1999[6], Goldenstein et al 2004[7], hereafter S99 and G04) or maximum likelihood (e.g., W06)
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
Summary
The fitting of X-ray spectra is based on reduced χ 2 method (e.g., Sako et al 1999[6], Goldenstein et al 2004[7], hereafter S99 and G04) or maximum likelihood (e.g., W06). Among those studies, most continuum models (e.g., power-law and black body) of X-ray spectra are nonlinear with a large number of free parameters (>3). Modern Bayesian inference, a method of statistical inference in which Bayes’ theorem is used to update our knowledge of a physical parameter, was introduced in astrophysical studies to fit complex models and to interpret observations (e.g., Reichart et al 1999[10], Benıtez 2000[11], Buchner et al 2014[12], Walker et al 2015[13]).
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