Physical parameter estimation with MCMC from observations of Vela X-1

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.