Spectroscopic modelling of two high-mass X-ray binaries, Cyg X–3 and 4U 1538–522

Abstract

\n We report a detailed modelling of soft X-ray emission lines from two stellar wind-fed Galactic high-mass X-ray binary (HMXB) systems, Cyg X-3 and 4U 1538-522, and estimate physical parameters, e.g. hydrogen density, radiation field, chemical abundances, wind velocity, etc. The spectral synthesis code cloudy is utilized for this modelling. We model highly ionized X-ray spectral lines, such as Fe XXV (6.700\xa0keV) and Fe XXVI (6.966\xa0keV), and reproduce the observed line flux values. We find that for Cyg X–3 and 4U 1538-522, the inner radius of the ionized gas is at a distance of 1012.25 cm and 1010.43 cm, respectively, from the primary star, which is the main source of ionization. The densities of the ionized gas for Cyg X–3 and 4U 1538–522 are found to be ∼1011.35 cm−3 and 1011.99 cm−3, respectively. The corresponding wind velocities are 2000\xa0km s−1 and 1500\xa0km s−1. The respective predicted hydrogen column densities for Cyg X–3 and 4U 1538–522 are 1023.2 cm−2 and 1022.25 cm−2. In addition, we find that magnetic field affects the strength of the spectral lines through cyclotron cooling. Hence, we perform separate model comparisons including magnetic field for both the sources. Most of the parameters, except the hydrogen column density, have similar values with and without magnetic field. We estimate that the most probable strength of the magnetic field for Cyg X–3 and 4U 1538–522, where the Fe XXV and Fe XXVI lines originate, is ∼102.5 G.