Empirical correlation between masses of black holes and Wolf-Rayet stars derived from their mass distributions in spectroscopic binaries

TL;DR

The paper addresses how WR star masses map to BH masses in spectroscopic binaries by assembling observational mass distributions for WR stars and BHs and showing both follow unbiased log-normal forms. It derives an empirical WR-to-BH mass transformation from these distributions, finding $M_{ m BH} \\simeq (0.39\pm0.09) M_{ m WR}^{1.13\pm0.09}$ and, via the CO-core connection, $M_{ m BH} \\sim 0.9 M_{ m CO}$ after considering wind mass loss. The results align with theoretical CO-core relations and provide a simple prescription for BH masses in population synthesis. The study highlights the need for larger datasets to validate the relation across different environments and binary configurations, with implications for modeling BH formation in massive binaries.

Abstract

We present observationally determined mass distributions of Wolf-Rayet (WR) stars in WR+OB binaries and black holes (BH) in spectroscopic binaries. Both WR and BH mass probability distributions can be well approximated by unbiased log-normal functions. Assuming that all WR stars with $M_\mathrm{WR}\gtrsim 6 M_\odot$ after core collapse are progenitors of the BHs, the similar shape of their mass distributions before and after collapse suggests a power-law relation between them $M_{\mathrm{BH}} \simeq (0.39\pm0.09) {M_{\mathrm{WR}}}^{1.13\pm0.09}$. Using the relation between masses of a WR star and its CO-core, we obtain the empirical relation between the BH mass and CO-core of the collapsing WR star $M_\mathrm{BH}\sim 0.9 M_\mathrm{CO}$, which can be used in the population synthesis calculations.

Figures (1)

• Figure 1: Differential (upper panels) and cumulative (bottom panels) WR (to the left) and BH (to the right) mass distributions based on data from Tables \ref{['tab:WR']} and \ref{['tab:BH']}. In red shown in the best log-normal fit (mean in Table 3).