Accuracy of the component mass estimation methods in LMXB

TL;DR

This paper evaluates the accuracy of methods used to estimate optical star masses in black hole low-mass X-ray binaries, revealing significant biases that lead to underestimating companion star masses and challenging existing evolutionary models.

Contribution

It compares two common approximations of Roche lobe filling stars, demonstrating their biases and proposing corrections to optical star mass estimates in BH LMXB.

Findings

Spherical star approximation overestimates rotational velocity and underestimates mass ratio.

Disk approximation overestimates rotational velocity by about 20%.

Corrected optical star masses are 1.5 times smaller, conflicting with standard models.

Abstract

There is a mismatch between modelled and observed distributions of optical stars masses in BH LMXB. Companion masses in BH LMXB are found in the mass range 0.1 - 1.6 $M_{\odot}$ with the peak at 0.6 $M_{\odot}$. The standard evolutionary scenarios require the donor mass distribution peaks to be at least $\sim 1\, M_{\odot}$ to eject a massive envelope of the black hole progenitor. Imperfect of the methods of optical stars masses determination may cause this difference. Two common used approximations of real Roche lobe filling star as distortion sources have been tested. On the one hand, there is the a approximation of real Roche lobe filling optical stars as sphere. We tested rotational broadening of absorption lines based on an exact calculation of CaI $\lambda 6439.075 \, \AA$ absorption profiles in the spectra of Roche lobe filling optical stars. There is overestimation of projected equatorial rotational velocity $V_{rot} \sin i$ and, accordingly, underestimation of mass ratio $q=M_x/M_v$ in the spherical star model. On the other hand, the approximation of a real Roche lobe filling star as disk with uniform local profile and linear limb darkening law is more rough. In this case overestimation of projected equatorial rotational velocity $V_{rot} \sin i$ is $ \sim 20\%$. Such overestimation of $V_{rot} \sin i$ can result in significant underestimation of mass ratio $q=M_x/M_v$ at hight value of $q=M_x/M_v$. Refined value of $q$ does not affect the mass of a black hole, but the mass of an optical star has shrunk 1.5 times. Hence, the masses of optical stars in BH LMXB must be corrected downward, despite the contradictions to the standard evolutionary scenarios.