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 (BHs) in spectroscopic binaries. Both WR and BH mass probability distributions can be well approximated by unbiased lognormal 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: $M_{\mathrm{BH}} \simeq (0.39\pm 0.09) {M_{\mathrm{WR}}}^{1.13\pm 0.09}$. 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 $M_\mathrm{BH}\sim 0.9 M_\mathrm{CO}$, which can be used in population synthesis calculations.