On the orbital and physical parameters of the HDE 226868/Cygnus X-1 binary system

TL;DR

This study refines the orbital and physical parameters of the HDE 226868/Cygnus X-1 binary system using recent mass measurements, optical data, and Kepler's law, revealing constraints on the system's inclination and stellar dimensions.

Contribution

It provides updated estimates of the system's inclination, semimajor axis, and Roche lobe size based on new mass determinations and orbital analysis, addressing deviations from Kepler's law.

Findings

Inclination angle i = (48 +/- 7) degrees.

Semimajor axis a = (42 +/- 9) solar radii.

Roche lobe radius r_M = (21 +/- 6) solar radii.

Abstract

In this paper we explore the consequences of the recent determination of the mass m=(8.7 +/- 0.8)M_Sun of Cygnus X-1, obtained from the Quasi-Periodic Oscillation (QPO)-photon index correlation scaling, on the orbital and physical properties of the binary system HDE 226868/Cygnus X-1. By using such a result and the latest spectroscopic optical data of the HDE 226868 supergiant star we get M=(24 +/- 5)M_Sun for its mass. It turns out that deviations from the third Kepler law significant at more than 1-sigma level would occur if the inclination i of the system's orbital plane to the plane of the sky falls outside the range 41-56 deg: such deviations cannot be due to the first post-Newtonian (1PN) correction to the orbital period because of its smallness; interpreted in the framework of the Newtonian theory of gravitation as due to the stellar quadrupole mass moment Q, they are unphysical because Q would take unreasonably large values. By conservatively assuming that the third Kepler law is an adequate model for the orbital period we obtain i=(48 +/- 7) deg which yields for the relative semimajor axis a=(42 +/- 9)R_Sun. Our estimate for the Roche's lobe of HDE 226868 is r_M = (21 +/- 6)R_Sun.