M33 X-7 located in the Triangulum Galaxy, is the only known eclipsing black hole high mass X-ray binary. The system was previously reported to contain a very massive O supergiant donor of 70 solar masses and a massive black hole of 16 solar masses in a short orbital period (Orosz et al. 2007). The total mass of the system was estimated to be around 85.7 solar masses, making it the most massive black hole binary system. These high masses and other properties of the M33 X-7 binary system were difficult to explain using conventional stellar evolutionary models.
The most reliable way to measure the mass of a star is by using Kepler’s Third Law of Motion. However, in the case of black hole X-ray binaries, which are similar to single-lined spectroscopic binaries, only the radial velocity curve of the donor star is available. This provides information about the orbital period and the radial velocity semi-amplitude of the companion star. These two values can be combined in the mass function equation to determine the masses of both the compact object and the companion star, as well as the binary mass ratio and inclination angle. However the biggest challenge is measuring the mass of the massive donor star!
In contrast to low-mass stars, estimates of the mass of massive stars based on luminosity, photometry, or spectral type calibrations can be highly inaccurate. Especially in X-ray binaries, there is already a history of interaction and mass exchange. One need to perform a detailed spectroscopic analysis to derive the mass of the donor and hence the mass of the black hole. For that we need to employ current generation of expanding stellar atmosphere codes.
We used phase-resolved simultaneous HST and XMM-Newton spectroscopic observations along with archival optical spectra to study M33 X-7. Then we carry out a detailed atmospheric analysis of multiwavelength spectra, taking into account line-driven winds, wind clumping, complex effects of millions of spectral lines, and X-ray photoionization. Our comprehensive spectroscopic investigation of the donor star (X-ray+UV+optical) yields new stellar and wind parameters for the system that differ significantly from previous estimates. In particular, the masses of the components are considerably reduced to 38 solar masses for the O-star donor and 11 solar masses for the black hole.
Taking the updated parameters of M33 X-7 from the new observations into account, we attempted to trace its evolution using binary evolution models. We modeled the system from a ZAMS binary system until its current state. We found that the initial masses of the M33 X-7 progenitors are comparable to that of typical O-star binaries. The system is transitioning toward an unstable mass transfer phase, resulting in a common envelope with a deep spiraling of the black hole to the envelope of the massive donor. Since the mass ratio is q > 3.3 and the period is short, the common envelope phase is likely to result in the merger of two companions resulting in a heavier black hole.
Paper link: https://www.aanda.org/articles/aa/abs/2022/11/aa43683-22/aa43683-22.html