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 $M_{\mathrm{W}\mathrm{R}}\gtrsim 6M_{\odot }$ 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 $M_{\mathrm{B}\mathrm{H}}\simeq (0.39\pm 0.09){M_{\mathrm{W}\mathrm{R}}}^{1.13\pm 0.09}$. 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 $M_{\mathrm{B}\mathrm{H}}\sim 0.9M_{\mathrm{C}\mathrm{O}}$, which can be used in the population synthesis calculations.