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