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

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 MWR ≳ 6M⊙ 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 MBH ≃ (0.39 ± 0.09)MWR1.13 ± 0.09. Using the relation between masses of WR star and its CO-core, we obtain the empirical relation between the BH mass and CO-core of the collapsing WR star MBH ∼ 0.9MCO, which can be used in population synthesis calculations.